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Molecular Mechanics

Efficient Molecular Dynamics Simulations of Deep Eutectic Solvents with First-Principles Accuracy Using Machine Learning Interatomic Potentials
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Journal of Chemical Theory and Computation

Cite this: J. Chem. Theory Comput. 2023, 19, 23, 8732–8742
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https://doi.org/10.1021/acs.jctc.3c00944
Published November 16, 2023

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Abstract

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In recent years, deep eutectic solvents emerged as highly tunable and ecofriendly alternatives to common organic solvents and liquid electrolytes. In the present work, the ability of machine learning (ML) interatomic potentials for molecular dynamics (MD) simulations of these liquids is explored, showcasing a trained neural network potential for a 1:2 ratio mixture of choline chloride and urea (reline). Using the ML potentials trained on density functional theory data, MD simulations for large systems of thousands of atoms and nanosecond-long time scales are feasible at a fraction of the computational cost of the target first-principles simulations. The obtained structural and dynamical properties of reline from MD simulations using our machine learning models are in good agreement with the first-principles MD simulations and experimental results. Running a single MD simulation is highlighted as a general shortcoming of typical first-principles studies if the dynamic properties are investigated. Furthermore, velocity cross-correlation functions are employed to study the collective dynamics of the molecular components in reline.

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1. Introduction

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Deep eutectic solvents (DESs) are an emerging class of compounds characterized by melting points significantly lower than their individual components. (1−4) They have many desirable characteristics such as low vapor pressure, thermal stability, and tunable properties, which make them suitable candidates as room-temperature solvents (5−7) and electrolytes. (8,9) DESs are generally nontoxic, (10,11) biodegradable, (12) and easy to prepare. Furthermore, the ability to fine-tune their physicochemical properties, through the exchange or modification of their components, makes them a promising class of “designer solvents”.
Preparation of novel DESs from a large number of potential components and a wide range of compositions is still a challenging task. In this context, computer modeling and simulation are valuable complements to experiment, providing insights into the nature of interactions at the atomic scale and the connections between structure and functionality. In particular, molecular dynamics (MD) simulations are an efficient and predictive tool for exploring a large number of potential compounds and their properties for targeted applications. There are a large number of MD simulation studies of DESs, including first-principles MD (FPMD) simulations (13−15) and classical MD simulations using additive (16−20) and polarizable (21−23) interatomic potentials (or force fields). While FPMD simulations based on electronic structure methods such as density functional theory (DFT) (24) can predict the structure and dynamics of the studied systems with a higher accuracy, their computational cost generally scales as the cube of the number of electrons in the system (25) and thus are limited to short length and time scales. In classical force fields (FFs), interatomic interactions are modeled using physically inspired functional forms that can be evaluated efficiently. (26,27) Hence, they are better suited for the size and time scales required to properly reproduce the structural and dynamical correlations in extended systems, such as DESs. MD simulations using FFs based on fixed atomic charges can provide important insights into the structure of ionic systems such as DESs, but their predicted thermodynamic and transport properties are often inconsistent with experiments showing significantly reduced dynamics. (28,29) The use of polarizable FFs can greatly improve the simulated dynamics in these systems since the explicit inclusion of induced dipoles in polarizable models effectively screens the long-range electrostatic interactions. (30) However, a frequent issue of polarizable FFs is the overpolarization of small ionic species, which demand special considerations such as damping of the electrostatic interactions between the selected pair of atoms. (22,23,31) This makes the parametrization of polarizable models for ionic systems such as DESs challenging, and the resulting FFs are not generally transferable. The main drawback of classical FFs is that their accuracy is limited to the underlying functional forms and the quality of their parametrization. Furthermore, classical FFs require predefined bonding patterns and, thus, cannot describe bond breaking or bond formation.
In recent years, with the advancement of machine learning (ML) techniques, a data-driven approach to the development of interatomic potentials has emerged in the context of ML. In this approach, the parametrization of an interatomic potential is regarded as a regression problem, where a set of continuous inputs such as atomic coordinates are mapped to a set of continuous outputs such as energies and atomic forces. Thus, the focus is shifted toward a sufficiently general functional form that can be trained on a set of data from electronic-structure (e.g., DFT) calculations. ML interatomic potentials (MLIPs) hence aim to approximate a set of energy and forces for a given atomic configuration, with the target first-principles accuracy at improved computational efficiency that scales linearly with the number of atoms. A variety of different approaches for training MLIPs based on kernel methods (32−35) and deep neural networks (NNs) (36−43) have been proposed. NN-based models, in particular, gained a lot of attention due to their high flexibility and scalability to larger data sets. A common approach for the construction of MLIPs is the decomposition of the total energy of a chemical system into atomic contributions. (36) To ensure the invariance of the energy under translation, rotation, and permutation of equivalent atoms, the atomic energies depend on the local environment of atoms through atom-centered representations rather than directly on the Cartesian coordinates. This is based on the chemically intuitive assumption that an atom’s contribution to the total energy is local and depends on its environment. In recent years, many different structural representations have been proposed such as ACSFs, (44) SNAP, (45) DeepPot, (42) and ACE, (46) for which the environment of an atom is encoded in a hand-crafted descriptor and SchNet (41) and PhysNet (43) as rotationally invariant and NequIP, (47) PaiNN, (48) and NewtonNet (49) as rotationally equivariant graph-based message-passing neural networks (MPNNs), for which the suitable atomic representations are learned from the reference data. While MPNNs, especially the equivariant types, are generally more data efficient and could achieve higher prediction accuracies, they are more expensive to train and evaluate, which limits their application for larger systems. It should be noted that the more recently proposed class of equivariant networks, with a strictly local representation of the atomic environments, can readily scale to large systems. (50)
In this work, we utilized DeePMD, (51) a descriptor-based NN representation, to train an MLIP for reline DES, a mixture of choline chloride (ChCl) and urea in 1:2 ratio (Figure 1). We employ an iterative active learning scheme based on model ensemble uncertainty estimates to systematically improve our models. We show that our trained MLIP on a set of DFT data points can achieve small prediction errors for energies and atomic forces on a set of unseen atomic configurations. Using our MLIP, we are able to run nanoseconds-long MD simulations for thousands of atoms with the target DFT accuracy. Finally, we show that our MLIP can successfully recover the structural and dynamic properties of reline from MD simulations.

Figure 1

Figure 1. Schematic representation of choline chloride (left) and urea (right) with the corresponding atom labels used throughout this study.

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2. Methods

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2.1. Machine Learning Model

We utilized the DeePMD (52) framework, an end-to-end deep NN representation of a many-body potential energy surface (PES), (51) to train and evaluate our ML interatomic potentials. In the deep potential (DP) model, like many of the size-extensive MLIPs, (36,37,39) the total energy of the system is decomposed into atomic contributions using a local geometric description of the atomic environment. Initially, the local environment of atom i is represented by matrix Ri∈RNi×3, where Ni is the number of neighboring atoms within a cutoff radius rc. In Ri, each row represents one neighbor j and is given by the relative coordinate rij ≡ rj – ri = (xij, yij, zij), with ri and rj being the Cartesian coordinates of atom i and j, respectively. Next, the relative coordinates Ri are mapped onto generalized coordinates R~i∈RNi×4. In R~i, each row is given by {s(rij),x^ij,y^ij,z^ij} where x^ij=s(rij)xij/rij, y^ij=s(rij)yij/rij, and z^ij=s(rij)zij/rij, with rij being the Euclidean distance between atoms i and j and s(rij) is a continuous and differentiable weighting function applied to each component
s(rij)={1rijrij<rs1rij[x3(−6x2+15x−10)+1],rs≤rij<rc0rij≥rc
(1)
where x = (rij – rs)/(rc – rs) switches from 0 at rs to 1 at the cutoff radius rc. The function s(rij) gives greater weight to the nearest neighbors of atom i, and parameter rs defines a smooth cutoff radius that allows the components in R~i to smoothly go to zero at the boundary of the local region rc. (51) In order to include the global symmetries including translation, rotation, and atomic permutation invariance of the energy in the local atomic representations, (34,37) the first column of the generalized coordinates R~i is mapped to an embedding matrix Gi∈RNi×M1 using a local embedding NN. Finally, by taking the first M2 columns of the embedding matrix, as Gi2∈RNi×M2, an invariant feature matrix Di∈RM1×M2 is constructed
Di=(Gi)TR~i(R~i)TGi2
(2)
The parameters of the embedding network are optimized simultaneously with the fitting network, which maps the feature matrix Di to the atomic energy Ei. The total energy E is then calculated as the sum of atomic energies Ei. Atomic forces are obtained by taking the derivative of the total energy with respect to the atomic coordinates; this enables the use of the force components in addition to the total energy for the training of the NNs. We used a cutoff value of rc = 6 Å, the smoothing cutoff rs = 5 Å, and the periodic boundary condition to construct the local atomic representations. A three-layer embedding network containing 25, 50, and 100 neurons was used with M2 = 16 axis neurons. We used a three-layer fitting network containing 240 neurons in each layer for mapping the atomic representations Di to the atomic energies. The hyperbolic tangent was used as the activation function in both embedding and fitting networks.
The objective in the training of the networks is to minimize a loss function with respect to NN parameters using an Adam stochastic gradient descent optimizer. (53) For the optimization step n, the loss function is defined as an average over a batch of Nb configurations, denoted as B
L(n)=1Nb∑BNbL(B,n)
(3)
L(B,n)=pε(n)ΔE2+pf(n)3N∑iN|ΔFi|2
(4)
Here, Δ denotes the difference between the prediction and the reference training data, N is the number of atoms, E is the total potential energy of the configuration, and Fi is the force on atom i. The use of forces in the training process significantly reduces the number of reference data needed to train accurate and robust models. (51) The prefactors pϵ and pf are tunable weights that vary during the training. We progressively increased pϵ and decreased pf, so that the force term dominates at the beginning of the training, while the energy term becomes equally important toward the end. We used a batch size Nb = 1, 0.02 and 1 as starting and final values of pϵ and 1000 and 1 as starting and final values for pf, respectively. The learning rate (i.e., the step size in gradient descent optimization) is decreased during training following the formula α(n) = α(0)λ(n/τ), where λ is the decay rate and τ is the decay steps. We used decay steps of 5000 and set the starting and stopping values of the learning rate to 10–3 and 5 × 10–8, respectively.

2.2. Reference Data Generation

For generation of the training data sets, sampling the configuration space of the system using faster methods such as density functional-based tight-binding (DFTB) (54) or classical FFs is significantly more efficient than performing FPMD simulations using the target DFT method. Our primary data set is built on the basis of configurations sampled from DFTB MD trajectories for a system containing 8 ChCl and 16 urea molecules. The sampled structures are subsequently labeled with energy and atomic forces using the target DFT method. The details of the DFTB-based simulations are provided in the Supporting Information. The DFT calculations on the selected configurations are carried out using the Gaussian and plane-wave (GPW) method as implemented in the CP2K package. (55,56) The Becke–Lee–Yang–Parr (BLYP) functional (57,58) is used along with the empirical dispersion correction (D3) of Grimme. (59) We used a MOLOPT-TZVP basis set and a plane wave cutoff of 700 Ry. The core electrons were described with the Goedecker–Teter–Hutter (GTH) pseudopotential. (60,61) The periodic boundary conditions were applied in all directions. A total of 19,000 configurations were selected and labeled with DFT energies and atomic forces, from which 18,000 are used as our primary training data set and the rest as the validation set.

2.3. Active Learning

In order to reduce the computational cost of the reference data generation and to ensure that the generated data set is representative of the relevant parts of the PES, we utilized an active learning scheme to extend the primary training data set. (62,63) In active learning, which can be seen as the generation of training data on demand, an uncertainty measure is used to validate the model predictions for new configurations. (64) A set of configurations with high prediction error are then selected to be labeled with the reference DFT energies and forces to extend the data set. We used the DP-GEN package as the active learning platform to extend our primary data set. (65) In the DP-GEN workflow, a series of successive iterations are performed, with each iteration composed of three steps of exploration, labeling, and training. (19) Initially, in the training step, a set (i.e., an ensemble) of four models are trained on our primary data set. The trained models differ only in the initialization of NN parameters. Since the loss function in eq 4 is a nonconvex function of the NN parameters, such a difference in initialization leads to different local solutions to the optimization problem and therefore different PES models. Around atomic configurations where there are sufficient training data, the different models should all be reasonably accurate and give predictions that are close to each other. For configurations far from the training data, the predictions from the different models will deviate from each other with considerable variance. Accordingly, the variance of the set of predictions from the model ensemble for a particular configuration can be used as a measure of uncertainty of the prediction and a criterion for whether the configuration should be selected as a candidate to extend the data set. For a configuration Rt, the error indicator ϵt is defined as the maximal standard deviation of the atomic force predicted by the model ensemble
εt=maxi⟨∥Fi(Rt)−⟨Fi(Rt)⟩∥2⟩1/2
(5)
where Fi(Rt) denotes the predicted force on atom i and the notations ⟨···⟩ denote the ensemble average of the predictions. Being a derivative of energy, forces typically show higher variability outside the training domain and thus describe uncertainty better than the energy. Furthermore, for a given atomic configuration, the energy is a global quantity and does not provide sufficient resolution. However, force is an atomic property and is sensitive to the local accuracy of the models, especially when a failure happens. (19) Given an upper and lower bound as the trust level, σhi and σlo, those structures whose error indicator εt fall between these bounds will be considered candidates to be labeled with DFT energy and forces and be added to the training data set. In the exploration step, a series of 30 MD simulations were carried out using a trained model, starting from different initial configurations, which were randomly selected from a set of 100 configurations. MD simulations are performed in LAMMPS, (66) using the DeePMD extension, (52) at different temperatures in 360–440 K interval with an integrator time step of 0.5 fs and an increasing time length of 10–200 ps from the starting to the final iteration. The structures along MD trajectories were saved and evaluated by the model ensemble at a time interval of 0.05 ps and those with error indicator εt between 0.15 and 0.30 eV Å–1 were selected as candidates for the labeling step. The upper and lower bounds for εt were determined through experimenting and are selected in a way to minimize the number of candidate structures while maintaining a reasonable accuracy. In the labeling step, a maximum number of 900 structures were randomly selected from the set of candidates collected in the exploration step and labeled with DFT energy and forces as described before. In the next iteration, new approximations of the PES were obtained by retraining the models using the extended training data set. These steps are repeated until the number of candidate structures from the exploration step was less than 100 structures. At the end of the active learning steps, around 10,000 configurations were generated, labeled and added to the primary data set.

2.4. Molecular Dynamics Simulations

From the set of trained models, the one with the lowest root-mean-square error (RMSE) value for the predicted energies and atomic forces on a test set was chosen as our MLIP to run MD simulations. MD simulations were carried out in LAMMPS (66) using the DeePMD extension. (52) The canonical (NVT) ensemble was used with an integrator time step of 0.5 fs, and trajectories were collected at a time interval of 10 fs. A mixture of 64 ChCl and 128 urea molecules in a periodic box was simulated at six different temperatures from 323 to 373 K in 10 K steps. A Nose–Hoover chain thermostat was used with a relaxation time of 0.1 ps. (67) Initial configurations are generated using the selected structures from our DFTB trajectories, which subsequently deformed to the experimental densities. (68) The simulation box lengths are reported in Table S1 of the Supporting Information. The mixtures were equilibrated for 1 ns, followed by a production run of 2 ns for the first three temperatures and 1 ns for the rest. To estimate the liquid densities, additional simulations were performed using the isothermal–isobaric (NPT) ensemble at each temperature for 0.5 ns. The pressure was set to 1 bar using a Nose–Hoover barostat with a relaxation time of 1.0 ps. The error indicator described in the active learning step can also be used to validate the simulation runs. During the simulations, we evaluated the structures at a time interval of 0.1 ps using our set of trained models to ensure that the maximum standard deviation of the ensemble predictions on atomic forces stays below a certain trust value.

3. Results and Discussion

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3.1. Model Accuracy

The accuracy of the trained model was evaluated for a set of 100 atomic configurations that were not part of the training data set. Half of these test configurations are selected from a separate DFTB MD trajectory than the ones used for generation of the primary data set and have the same composition (8 ChCl and 16 urea molecules) as the configurations used for the training of the models. The other half are configurations randomly sampled from a FPMD trajectory by Zahn (13) for a larger system of 18 ChCl and 36 urea molecules, which were subsequently labeled with our target DFT energy and forces. Figure 2 shows a comparison of the predicted and reference values of the total energy per atom and force on each atom for all configurations. Our MLIP for reline achieves an RMSE of 0.92 meV/atom (0.02 kcal mol–1) and 5.48 meV/atom (0.13 kcal mol–1) in predicted energies for systems of size 304 and 684 atoms, respectively. Unlike energies, our trained model achieves consistent accuracy in the prediction of forces for both sets of structures, as is evident by an RMSE value of ∼ 0.05 eV Å–1 for both systems. These results indicate that our trained models on configurations from a smaller system can be successfully employed for larger systems without a noticeable loss in accuracy. It should be noted that achieving small prediction errors on a test set by an ML potential does not necessarily guarantee stable MD simulations. (69) It has been shown that sufficiently large training data sets and improved data generation schemes such as active learning are essential for obtaining robust ML potentials. (70)

Figure 2

Figure 2. Reference DFT energies and atomic forces are compared to the predicted values by the ML model for 50 test structures of a system of 304 atoms (left) and 684 atoms (right). The reference (ref) and predicted (pred) energies are standardized by subtracting their mean value from them.

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3.2. Density and Structure of the Liquid

To investigate the ability of our ML potential to predict the liquid density of reline, average densities from NPT simulations are presented in Table 1 and compared to the reported experimental densities. (68) The estimated densities from MD simulations using our ML potential are within the acceptable range and underpredict the experimental densities by 3–3.5%. It should be mentioned that training the ML potentials on stress tensor data, together with energy and forces, could further improve the accuracy of the predicted densities from NPT simulations.
Table 1. Comparison of the Liquid Density of Reline (in g cm–3) from MD Simulations Using the MLIP to Experimental Values of Ref (68) at the Range of Studied Temperatures
T [K]323333343353363373
Exp.1.1831.1781.1731.1671.1621.157
MLIP1.1431.1381.1341.1291.1241.118
% error3.433.383.293.313.253.40
The ability of the trained model to reproduce the equilibrium structure of the reline mixture was tested by comparing the pair distribution functions from MD simulations using MLIP to an FPMD reference. A mixture of 18 ChCl and 36 urea molecules was simulated at 375 K for 0.5 ns. As a reference, a short FPMD trajectory was generated for a system of the same size using our target DFT method. The computed radial distribution functions (RDFs) in Figure 3, for different interaction sites on choline and urea, are in excellent agreement with the FPMD reference. Considering that none of the structures in the training data set were generated using our reference DFT potential, reference energies and atomic forces are sufficient to train an accurate MLIP, regardless of the method used to sample or generate the training structures. Additionally, RDFs of chloride (Cl) and urea’s oxygen (OU) as hydrogen-bond acceptors around hydrogen atoms of urea separated for the cis and trans hydrogen atoms, as well as selected intramolecular bond lengths and bond angle distribution functions, are also presented and compared to the FPMD reference in the Supporting Information. In Figure S4, the RDFs of OU and Cl around the hydrogen atom(s) of choline (H4) and urea (HU) are compared to selected classical and polarizable FF simulations from the literature. The RDFs around HU atoms from FF simulations are in good agreement with the MLIP results, but the selected FFs could not accurately predict the RDFs around the hydrogen atom of choline. The polarizable FF overestimates the intensity of the Cl–H4 interaction and underestimates the intensity of the OU–H4 interactions. The classical FF underestimates the intensity of both interactions with H4 atoms, most likely as a result of scaled atomic charges, but the relative intensity of the OU and Cl RDFs around H4 is in qualitative agreement with the MLIP results.

Figure 3

Figure 3. Comparison of the redial distribution functions from the FPMD simulation (dashed lines) and simulations using the MLIP (solid lines) for interactions with H4 and N1 of choline (top) and hydrogen atoms of urea HU (bottom). Atom labels are given in Figure 1.

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3.3. Translational Dynamics

In Figure 4, as depicted by the center-of-mass velocity autocorrelation functions (VACFs)
A(t)=⟨vi(0)·vi(t)⟩⟨vi2⟩−1
(6)
the equilibrium diffusive dynamics of the three components of reline mixture are successfully reproduced compared to the reference FPMD simulations.

Figure 4

Figure 4. Center-of-mass velocity autocorrelation functions A(t) for the three components of the reline mixture from the reference FPMD simulations (dashed lines) are compared to the MLIP simulations (solid lines) for a mixture of 18 ChCl and 36 urea molecules at 375 K.

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The self-diffusion coefficients (D) were calculated from the MD trajectories of a mixture of 64 ChCl and 128 urea molecules using the mean-square displacement of the molecular center-of-mass and the Einstein relation
D=16limt→∞⁡ddt⟨∑i=1N[ri(0)−ri(t)]2⟩
(7)
where ri is the position of the center of mass of particle i at any specific time and the brackets indicate the average over all particles and over all time origins. The mean-square displacements of the center of mass for three components of reline are shown in Figure S7, and the diffusion coefficients are obtained from a linear fit to the second half of the plots. Reline is a highly viscous liquid, and its viscosity is comparable to some room-temperature ionic liquids. This makes the prediction of the diffusion coefficients from MD simulations challenging, and as it has been shown before, long simulation times are needed to converge the dynamical properties at room temperature. (71) To investigate the suitability of single trajectories for computing the dynamical properties such as diffusion coefficients, at a selected temperature of 353 K, 10 separate trajectories were generated and the results are presented in Figure S6 of the Supporting Information. As is evident from the obtained results, at least five trajectories are needed for sufficient sampling and more reliable calculation of diffusion coefficients from our MD simulations. Considering the efficiency of the MD simulations using our ML potential, as 1 ns simulation of a system of ∼ 2500 atoms on a single graphics processing unit (GPU) takes about 9 h, the additional computational cost of generating more trajectories is overall small. The self-diffusion coefficients in Figure 5, for the three components of reline mixture, are obtained from the average of five different trajectories and are corrected for the finite-size effects of the MD simulations using the correction term of Yeh and Hummer (eq S1). (72) The lines in Figure 5 are the best exponential fits to the data used to obtain the activation energies of diffusion using Arrhenius’ law
D=D0exp(−EaRT)
(8)
with pre-exponential factor D0 and activation energy of diffusion Ea. The experimental values (73) of self-diffusion coefficients for the cation and urea are also plotted in Figure 5, and the calculated activation energies of diffusion are summarized in Table 2. The self-diffusion coefficients from our MD simulations in Figure 5 underestimate the reported experimental results by a factor of 3–4, which could be attributed to the limited accuracy of the reference DFT method. The obtained self-diffusion coefficients are similar to the reported results from MD simulations using a polarizable FF (22) and are ∼10 times higher than the obtained values from nonpolarizable FFs that do not empirically scale the charge on the ions. Furthermore, the obtained activation energies of diffusion match very well with the experimental values, indicating the ability of the MLIP to accurately predict the temperature dependence of the diffusive dynamics in reline.

Figure 5

Figure 5. Calculated values of self-diffusion coefficients for the three components of reline mixture from MD simulations (filled symbols) are plotted against the inverse of the simulation temperature and compared to the experimental values (empty symbols) of ref (73). Lines are the best exponential fits to the data used to obtain the activation energies listed in Table 2.

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Table 2. Activation Energies of Diffusion (in kJ mol–1) for the Three Components of Reline Mixture Calculated from an Arrhenius Exponential Fit to the Data in Figure 5 Are Compared to the Reported Experimental Values of Ref (73)
 Exp.MLIP
cation47.8 ± 0.148.26
anion 46.83
urea45.0 ± 0.146.76
To better understand the collective motions of the different components in reline, the velocity cross-correlation functions were computed. The time cross-correlation function between the initial velocity of a particle of species i and the latter velocities of particles of species j, initially located inside a spherical shell of radius R centered at the particle of species i, are defined as
C(t)=⟨vi(0)·vj(t)⟩r(⟨vi2⟩⟨vj2⟩)−1/2
(9)
where vi(t) and vj(t) are the velocity of the particles i and j, ⟨vj2⟩ is the mean-squared velocities of all particles of species i and j, and ⟨ ⟩r is a restricted statistical average
⟨vi(0)·vj(t)⟩r=N−1⟨∑jvi(0)·vj(t)·u(R−rij(0))⟩
(10)
where u(x) is the step function, rij(0) is the initial distance between the central particle i and a particle j, and the brackets indicate the average over all particles i and over all time origins. N is the coordination number or the mean number of j particles in the spherical shell of particle i. The values of R for each cross-correlation function between species i and j is set to the position of the first minima of the corresponding center-of-mass RDFs in Figure S5 and are listed in Table 3. The functions NC(t) in Figure 6, represent the sum of the velocity cross-correlations between a central particle and all the neighboring particles within the first shell and are plotted alongside the VACFs. The values of N for different pair of species are listed in Table 3. It should be noted that due to the finite size of the system, initial values of the velocity cross-correlation functions are less than 0. (74)
Table 3. Mean Number of Particles (Nij) of Species j in a Spherical Shell of Radius R (in Å) Around a Particle of Species ia
 CCCACUAAACAUUUUCUA
Nij4.893.319.542.863.313.634.914.771.81
R8.06.57.47.06.55.36.27.45.3
a

i and j are choline cation (C), chloride anion (A), or urea molecule (U).

Figure 6

Figure 6. Velocity cross-correlation functions NC(t) for the cation as the central particle (top), anion as the central particle (middle), and urea as the central particle (bottom). The dashed lines are the velocity autocorrelation functions A(t) of the cation (gray), anion (green), and urea (red). The cross-correlation functions for longer correlation times are presented in Figures S8–S10.

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Figure 6 shows the velocity cross-correlation functions between the different components of reline DES at 363 K. The initial rise of the velocity cross-correlation functions, with the decay of the corresponding VACFs toward the minimum, indicates the transfer of the initial momentum of the central particle to the neighboring particles, which on average tend to move in the same direction. The decay of NC(t) functions after the first peak should be associated with the spread of the momentum to the particles in the outer shells. Furthermore, the cross-correlation functions show a negative region at intermediate times, which could be attributed to the rebound between the central particle and particles within the first shell. (75) With the exception of the cross-correlation function between distinct anions, which does not show a clear peak, the velocity cross-correlation functions between species with a larger mass show a slower increase and reach their first maximum later than those between lighter ones. In the case of correlation between cations and urea molecules (cation-urea and urea-cation) and between urea molecules and anions (urea-anion and anion-urea), the velocity cross-correlation functions reach their maximum at the same time that the particles with larger mass lose their initial momentum and the corresponding VACF becomes negative. These results are in agreement with the findings for dense simple liquids. (76−78) However, the cross-correlation functions between the cations and anions reach their maximum shortly before the VACF of cations becomes negative. This suggests that anions on average lose the momentum, they initially gained from the cations, to their surrounding particles faster than urea molecules. In the case of cross-correlations between distinct like species, the velocity cross-correlation between distinct urea molecules becomes maximum at the same time that the corresponding VACF becomes negative. However, the velocity cross-correlation function between distinct cations reaches its maximum shortly after the corresponding VACF becomes negative, indicating that the heavier cations on average maintain their initially gained momentum for longer times. Furthermore, a clear relationship between the oscillations of the urea-anion (also anion-urea) and urea–urea cross-correlation function with those of the urea’s VACF is visible, suggesting that a part of the initial momentum transferred to the neighboring particles is returned to a urea molecule. (79,80) In the middle panel of Figure 6, even though the anion–cation cross-correlation function does not show clear oscillations after the first maximum, a noticeable phase relationship with the oscillations of the anion-urea velocity cross-correlation function is visible. The maxima of the anion-urea cross-correlation function coincide with the minima of the anion–cation cross-correlation function and vice versa. These features could be attributed to the oscillatory motion of the anions surrounded by the heavier cations and urea molecules. (23,81)

3.4. Ionic Conductivity

The ionic conductivity (σ) of the simulated mixtures was calculated by integrating the charge current autocorrelation function using the following Green–Kubo relation
σ=13VkBT∫0∞⟨j(0)·j(t)⟩dt
(11)
where kB is the Boltzmann constant, T is the temperature, V is the volume of the simulation box, and the brackets indicate the average over all time origins. The charge current j(t) is given by
j(t)=∑i=1Nqivi(t)
(12)
where N is the number of ions and qi and vi(t) represent the charge and the center-of-mass velocity of the ith ion at time t, respectively. The ionic conductivity (σ) is obtained from the long-time limit of an exponential decay function fitted to the running integral of the charge current autocorrelation function. It is difficult to evaluate the true conductivity through this approach since conductivity is a collective dynamical property and, for this reason, suffers from a relatively high statistical uncertainty. (82) However, the ability to calculate its value from a larger number of MD simulations leads to considerably more sampling and more reliable results. The obtained ionic conductivities were corrected for the finite-size effect using the same relative correction factor as for diffusion coefficients of ionic species and are plotted alongside a set of experimental values in Figure 7. The reported experimental values for the ionic conductivity of reline cover a wider range, but the results from more recent measurements are in better agreement and are expected to be more accurate. The estimated values of ionic conductivity from our MD simulations, as is expected from the self-diffusion coefficient results, are closer to the lower end of the range of experimental values and underestimate the more recent results by a factor of 1.5–2. The temperature dependence of ionic conductivity is best described by the Vogel–Fulcher–Tammann (VFT) equation
σ=σ0exp(−BT−TVF)
(13)
with pre-exponential factor σ0, fitting parameter B, and the Vogel–Fulcher temperature Tvf. The dashed line in Figure 7 is the VFT fit to the data with pre-exponential factor (σ0) of 2585 S m–1, 1941, and 112 K for B and Tvf, respectively.

Figure 7

Figure 7. Calculated values of ionic conductivity from MD simulations using our ML potential are plotted against the inverse of the simulation temperature and compared to the experimental values from refs (1), (68), and (83). Lines are the VFT fits to the data.

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The ionic conductivity can also be estimated using the Nernst–Einstein (NE) expression from the self-diffusion coefficients of ions
σNE=NpairVkBT∑i=1Nqi2Di
(14)
where Npair is the number of ion pairs, D is the diffusion coefficient, and i denotes cations or anions. The NE expression assumes that the diffusion of individual ions contributes entirely to the ionic conductivity of the system. Consequently, the deviations of the Green–Kubo conductivity from the NE conductivity can be interpreted as cross-correlations among ions. The obtained values for ionic conductivity from the Green–Kubo and NE expressions and the corresponding ratio γ = σ/σNE are listed in Table 4. The NE conductivities are calculated using the self-diffusion coefficients obtained from the VACFs. The self-diffusion coefficients are estimated from an exponential fit to the running integral of VACFs and are listed in Table S2 of the Supporting Information. The ratio γ is the percentage of ions that contribute to the ionic conductivity and can be seen as the degree of uncorrelated motion of ions. A γ = 1 indicates that the ion motions are completely uncorrelated, and γ values of less than one point to some degree of correlated motion between oppositely charged ions. Moreover, the obtained results suggest a temperature-dependent trend for the σ/σNE ratio in reline.
Table 4. Estimated Values of Ionic Conductivity from the Green–Kubo (σ) and NE (σNE) Approach (in S m–1) and the Corresponding Ratio (γ = σ/σNE) at the Range of Studied Temperatures
T [K]323333343353363373
σ0.2830.3920.5830.8411.1621.543
σNE0.2450.3610.6100.9411.3901.962
γ1.151.080.960.890.840.79

4. Conclusions

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We trained an MLIP for reline DES, on a set of atomic configurations labeled with DFT energies and forces, using the DeePMD framework. To the best of our knowledge, this is the first time that the ability of MLIPs to represent the PES of DESs has been explored and evaluated. Our trained model achieves small prediction errors for energies and atomic forces on a set of unseen atomic configurations. Using our MLIP, we are able to run fast and scalable MD simulations with the target DFT accuracy for thousands of atoms and nanosecond time scales. The obtained structural and dynamical properties of reline from our MD simulations are in good agreement with the results from experiments and first-principles MD simulations. Furthermore, we investigated the collective motions of the three components of reline DES using velocity cross-correlation functions, showing that there are positive correlations at short time scales, mainly due to the transfer of momentum from species with a larger mass to surrounding particles. Additionally, we showed that for a reliable investigation of dynamical properties, such as self-diffusion coefficients, a larger number of simulation runs are required. Considering the size and time scale of the performed simulations, MLIPs enable these types of analyses that otherwise are not accessible by the first-principles methods.
We used an iterative active learning scheme based on uncertainty estimates from an ensemble of models to efficiently explore the underrepresented regions of the configuration space in the training data set and systematically improve our model. The use of an active learning approach is considered an important step in the construction of a robust ML potential. Additionally, the uncertainty estimates of the predicted forces by the ML model are a valuable metric to validate the fidelity of the MD simulation runs. It should be noted that the quality of the uncertainty quantification method plays an important role in active learning. It has been shown that the ensemble-based uncertainty quantification, compared to single-model quantification methods, performs consistently better across different data sets albeit at a higher computational cost. (84)
In the DeePMD model, similar to many other ML potentials, the total energy of the system is predicted as the sum of atomic energies that are a function of local atomic descriptors. Thus, it is considered a short-range potential in a sense that it does not include a separate treatment of long-range interactions. Although, the long-range contributions to the total energy are present in the reference training data and hence are implicitly accounted for in the fitting process. Nevertheless, as it has been shown before and the current results suggest, an accurate approximation of the PES of polarizable bulk liquids (85) and dense ionic systems (86) by ML potentials does not necessarily require a specific treatment of long-range interactions. This can be rationalized in terms of an efficient screening of electrostatic interactions in a bulk system. However, in systems lacking translational invariance such as extended interfaces, truncated interactions result in unbalanced forces, which are difficult to approximate with short-range ML potentials, and specific treatment of long-range interactions becomes important. (85)

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00944.

  • Details of the DFTB-based MD simulations, additional radial and angular distribution functions, simulation box sizes and viscosities, mean-square displacement plots and self-diffusion coefficients from the Green–Kubo approach with details of the correction term for the finite-size effects, and velocity cross-correlation functions for longer correlation times (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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Acknowledgments

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The authors thank the German Research Foundation (DFG) for financial support (project ZA 606/8-1). Computational time from the Center for Information Services and High Performance Computing (ZIH) of TU Dresden is gratefully acknowledged.

References

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This article references 86 other publications.

  1. 1
    Abbott, A. P.; Capper, G.; Davies, D. L.; Rasheed, R. K.; Tambyrajah, V. Novel solvent properties of choline chloride/urea mixturesElectronic supplementary information (ESI) available: spectroscopic data. See http://www.rsc.org/suppdata/cc/b2/b210714g/. Chem. Commun. 2002, 70– 71,  DOI: 10.1039/b210714g
    Google Scholar
    There is no corresponding record for this reference.
  2. 2
    Zhang, Q.; De Oliveira Vigier, K.; Royer, S.; Jérôme, F. Deep eutectic solvents: syntheses, properties and applications. Chem. Soc. Rev. 2012, 41, 7108– 7146,  DOI: 10.1039/c2cs35178a
    Google Scholar
    2
    Deep eutectic solvents: Syntheses, properties and applications
    Zhang, Qinghua; De Oliveira Vigier, Karine; Royer, Sebastien; Jerome, Francois
    Chemical Society Reviews (2012), 41 (21), 7108-7146CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. Within the framework of green chem., solvents occupy a strategic place. To be qualified as a green medium, these solvents have to meet different criteria such as availability, non-toxicity, biodegradability, recyclability, flammability, and low price among others. Up to now, the no. of available green solvents are rather limited. Here we wish to discuss a new family of ionic fluids, so-called Deep Eutectic Solvents (DES), that are now rapidly emerging in the current literature. A DES is a fluid generally composed of two or three cheap and safe components that are capable of self-assocn., often through hydrogen bond interactions, to form a eutectic mixt. with a m.p. lower than that of each individual component. DESs are generally liq. at temps. lower than 100 °C. These DESs exhibit similar physico-chem. properties to the traditionally used ionic liqs., while being much cheaper and environmentally friendlier. Owing to these remarkable advantages, DESs are now of growing interest in many fields of research. In this review, we report the major contributions of DESs in catalysis, org. synthesis, dissoln. and extn. processes, electrochem. and material chem. All works discussed in this review aim at demonstrating that DESs not only allow the design of eco-efficient processes but also open a straightforward access to new chems. and materials.
  3. 3
    Smith, E. L.; Abbott, A. P.; Ryder, K. S. Deep Eutectic Solvents (DESs) and Their Applications. Chem. Rev. 2014, 114, 11060– 11082, PMID: 25300631  DOI: 10.1021/cr300162p
    Google Scholar
    3
    Deep Eutectic Solvents (DESs) and Their Applications
    Smith, Emma L.; Abbott, Andrew P.; Ryder, Karl S.
    Chemical Reviews (Washington, DC, United States) (2014), 114 (21), 11060-11082CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    This article describes the phys. and chem. properties of deep eutectic solvents (DESs) and ionic liq. (ILs), and how their applications differ. DESs are now widely acknowledged as a new class of IL analogs because they share many characteristics and properties with ILs. The terms DES and IL have been used interchangeably in the literature, though it is necessary to point out that these are actually two different types of solvent. DESs are systems formed from a eutectic mixt. of Lewis or Bronsted acids and bases which can contain a variety of anionic and/or cationic species; in contrast, ILs are formed from systems composed primarily of one type of discrete anion and cation.
  4. 4
    Hansen, B. B.; Spittle, S.; Chen, B.; Poe, D.; Zhang, Y.; Klein, J. M.; Horton, A.; Adhikari, L.; Zelovich, T.; Doherty, B. W.; Gurkan, B.; Maginn, E. J.; Ragauskas, A.; Dadmun, M.; Zawodzinski, T. A.; Baker, G. A.; Tuckerman, M. E.; Savinell, R. F.; Sangoro, J. R. Deep Eutectic Solvents: A Review of Fundamentals and Applications. Chem. Rev. 2021, 121, 1232– 1285, PMID: 33315380  DOI: 10.1021/acs.chemrev.0c00385
    Google Scholar
    4
    Deep Eutectic Solvents: A Review of Fundamentals and Applications
    Hansen, Benworth B.; Spittle, Stephanie; Chen, Brian; Poe, Derrick; Zhang, Yong; Klein, Jeffrey M.; Horton, Alexandre; Adhikari, Laxmi; Zelovich, Tamar; Doherty, Brian W.; Gurkan, Burcu; Maginn, Edward J.; Ragauskas, Arthur; Dadmun, Mark; Zawodzinski, Thomas A.; Baker, Gary A.; Tuckerman, Mark E.; Savinell, Robert F.; Sangoro, Joshua R.
    Chemical Reviews (Washington, DC, United States) (2021), 121 (3), 1232-1285CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. Deep eutectic solvents (DESs) are an emerging class of mixts. characterized by significant depressions in m.ps. compared to those of the neat constituent components. These materials are promising for applications as inexpensive "designer" solvents exhibiting a host of tunable physicochem. properties. A detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding is postulated as the root cause of their m.p. depressions and physicochem. properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and expts. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework needed for a deeper understanding of DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies promising research thrusts aligned with the advancement of the field toward predictive models and fundamental understanding of these solvents.
  5. 5
    Abbott, A. P.; Capper, G.; Davies, D. L.; McKenzie, K. J.; Obi, S. U. Solubility of Metal Oxides in Deep Eutectic Solvents Based on Choline Chloride. J. Chem. Eng. Data 2006, 51, 1280– 1282,  DOI: 10.1021/je060038c
    Google Scholar
    5
    Solubility of Metal Oxides in Deep Eutectic Solvents Based on Choline Chloride
    Abbott, Andrew P.; Capper, Glen; Davies, David L.; McKenzie, Katy J.; Obi, Stephen U.
    Journal of Chemical & Engineering Data (2006), 51 (4), 1280-1282CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
    The soly. of 17 commonly available metal oxides in the elemental mass series Ti through Zn have been detd. in three ionic liqs. based on choline chloride. The hydrogen bond donors used were urea, malonic acid, and ethylene glycol. The results obtained are compared with aq. solns. of HCl and NaCl. Some correlation is obsd. between the soly. in the deep eutectic solvents and that in aq. solns. but some significant exceptions offer an opportunity for novel extractive metallurgical processes.
  6. 6
    Jenkin, G. R.; Al-Bassam, A. Z.; Harris, R. C.; Abbott, A. P.; Smith, D. J.; Holwell, D. A.; Chapman, R. J.; Stanley, C. J. The application of deep eutectic solvent ionic liquids for environmentally-friendly dissolution and recovery of precious metals. Miner. Eng. 2016, 87, 18– 24, Processing of Precious Metal Ores  DOI: 10.1016/j.mineng.2015.09.026
    Google Scholar
    6
    The application of deep eutectic solvent ionic liquids for environmentally-friendly dissolution and recovery of precious metals
    Jenkin, Gawen R. T.; Al-Bassam, Ahmed Z. M.; Harris, Robert C.; Abbott, Andrew P.; Smith, Daniel J.; Holwell, David A.; Chapman, Robert J.; Stanley, Christopher J.
    Minerals Engineering (2016), 87 (), 18-24CODEN: MENGEB; ISSN:0892-6875. (Elsevier Ltd.)
    The processing of ore by hydrometallurgy or pyrometallurgy typically has a high energy demand, and assocd. release of carbon dioxide. Thus there is a need to develop more energy-efficient and environmentally-compatible processes. This article demonstrates that deep eutectic solvent (DES) ionic liqs. provide one such method since they can be used to selectively dissolve and recover native gold and tellurium, sulfides and tellurides. Ionic liqs. are anhyd. salts that are liq. at low temp. They are powerful solvents and electrolytes with potential for high selectivity in both dissoln. and recovery. Deep eutectic solvents are a form of ionic liq. that are mixts. of salts such as choline chloride with hydrogen-bond donors such as urea. DESs are environmentally benign, yet chem. stable and, furthermore, the components are already produced in large quantities at comparable costs to conventional reagents. Electrum, galena and chalcopyrite, as well as tellurobismuthite (Bi2Te3), were sol. in DES through an oxidative leach at 45-50°C. Leaching rates detd. by a novel technique employing an optical profiler were very favorable in comparison to the current industrial process of cyanidation. Pyrite was notably insol. by an oxidative leach. However, pyrite, and indeed any other sulfide, could be selectively dissolved by electrolysis in a DES, thus suggesting a protocol whereby target inclusions could be liberated by electrolysis and then dissolved by subsequent oxidn. Ionometallurgy could thus offer a new set of environmentally-benign process for metallurgy.
  7. 7
    Söldner, A.; Zach, J.; König, B. Deep eutectic solvents as extraction media for metal salts and oxides exemplarily shown for phosphates from incinerated sewage sludge ash. Green Chem. 2019, 21, 321– 328,  DOI: 10.1039/C8GC02702A
    Google Scholar
    There is no corresponding record for this reference.
  8. 8
    Chakrabarti, M. H.; Mjalli, F. S.; AlNashef, I. M.; Hashim, M. A.; Hussain, M. A.; Bahadori, L.; Low, C. T. J. Prospects of applying ionic liquids and deep eutectic solvents for renewable energy storage by means of redox flow batteries. Renew. Sustain. Energy Rev. 2014, 30, 254– 270,  DOI: 10.1016/j.rser.2013.10.004
    Google Scholar
    8
    Prospects of applying ionic liquids and deep eutectic solvents for renewable energy storage by means of redox flow batteries
    Chakrabarti, Mohammed Harun; Mjalli, Farouq Sabri; Al Nashef, Inas Muen; Hashim, Mohd. Ali; Hussain, Mohd. Azlan; Bahadori, Laleh; Low, Chee Tong John
    Renewable & Sustainable Energy Reviews (2014), 30 (), 254-270CODEN: RSERFH; ISSN:1364-0321. (Elsevier Ltd.)
    A review. Ionic liqs. (ILs) and deep eutectic solvents (DESs) have been applied in various fields such as electrolytes for lithium ion batteries, electrodeposition, electropolishing and even in fuel cells. ILs and molten salts have found some applications in redox flow batteries (RFBs) in the past and recently some metal ion based ILs have been proposed and used by Sandia National Labs. In addn., only two papers have very recently reported on the application of DESs for the same. This review gives an overview on DESs and discusses the possibility of employing them in RFBs for renewable energy storage and utility-scale load leveling applications. Commencing with a discussion on energy storage technologies and the RFB, this paper goes on to provide an account on ILs and DESs as well as their applications in electrochem. and energy conversion. A succinct discussion on the results of Sandia National Labs. on using ILs as electrolytes for RFBs is provided building onto the feasibility of replacing ILs with DESs in the near future (based upon recent publications on the topic).
  9. 9
    Cong, G.; Lu, Y.-C. Organic Eutectic Electrolytes for Future Flow Batteries. Chem 2018, 4, 2732– 2734,  DOI: 10.1016/j.chempr.2018.11.018
    Google Scholar
    9
    Organic Eutectic Electrolytes for Future Flow Batteries
    Cong, Guangtao; Lu, Yi-Chun
    Chem (2018), 4 (12), 2732-2734CODEN: CHEMVE; ISSN:2451-9294. (Cell Press)
    In this issue of Chem, Yu and coworkers report phthalimide-based eutectic anolytes, which achieved a high concn. and enhanced redox reversibility. The org.-mol.-based eutectic electrolytes take advantages of both the superior tunability of the org. mol. and the high molar concn. of the redox-active mols. of the eutectic solvents. With combined computational and exptl. anal., this work demonstrates that forming eutectic electrolytes with self-contg. redox-active orgs. is a promising strategy for the future development of high-energy-d. redox-flow batteries.
  10. 10
    Radošević, K.; Cvjetko Bubalo, M.; Gaurina Srček, V.; Grgas, D.; Landeka Dragičević, T.; Radojčić Redovniković, I. Evaluation of toxicity and biodegradability of choline chloride based deep eutectic solvents. Ecotoxicol. Environ. Saf. 2015, 112, 46– 53,  DOI: 10.1016/j.ecoenv.2014.09.034
    Google Scholar
    10
    Evaluation of toxicity and biodegradability of choline chloride based deep eutectic solvents
    Radosevic, Kristina; Cvjetko Bubalo, Marina; Gaurina Srcek, Visnje; Grgas, Dijana; Landeka Dragicevic, Tibela; Radojcic Redovnikovic, Ivana
    Ecotoxicology and Environmental Safety (2015), 112 (), 46-53CODEN: EESADV; ISSN:0147-6513. (Elsevier B.V.)
    Deep eutectic solvents (DESs) have been dramatically expanding in popularity as a new generation of environmentally friendly solvents with possible applications in various industrial fields, but their ecol. footprint has not yet been thoroughly investigated. In the present study, three choline chloride-based DESs with glucose, glycerol and oxalic acid as hydrogen bond donors were evaluated for in vitro toxicity using fish and human cell line, phytotoxicity using wheat and biodegradability using wastewater microorganisms through closed bottle test. Obtained in vitro toxicity data on cell lines indicate that choline chloride: glucose and choline chloride:glycerol possess low cytotoxicity (EC50>10 mM for both cell lines) while choline chloride:oxalic acid possess moderate cytotoxicity (EC50 value 1.64 mM and 4.19 mM for fish and human cell line, resp.). Results on phytotoxicity imply that tested DESs are non-toxic with seed germination EC50 values higher than 5000 mg L-1. All tested DESs were classified as'readily biodegradable' based on their high levels of mineralization (68-96%). These findings indicate that DESs have a green profile and a good prospect for a wider use in the field of green technologies.
  11. 11
    Halder, A. K.; Cordeiro, M. N. D. S. Probing the Environmental Toxicity of Deep Eutectic Solvents and Their Components: An In Silico Modeling Approach. ACS Sustain. Chem. Eng. 2019, 7, 10649– 10660,  DOI: 10.1021/acssuschemeng.9b01306
    Google Scholar
    11
    Probing the Environmental Toxicity of Deep Eutectic Solvents and Their Components: An In Silico Modeling Approach
    Halder, Amit Kumar; Cordeiro, M. Natalia D. S.
    ACS Sustainable Chemistry & Engineering (2019), 7 (12), 10649-10660CODEN: ASCECG; ISSN:2168-0485. (American Chemical Society)
    Because of the increasing demand of greener solvents, deep eutectic solvents (DES) have just emerged as low-cost alternative solvents for a broad range of applications. However, recent toxicity assay studies showed a non-negligible toxic behavior for these solvents and their components. Alternative in silico-based approaches such as the one proposed here, multitasking-Quant. Structure Toxicity Relationships (mtk-QSTR), are increasingly used for risk assessment of chems. to speed up policy decisions. This work reports a mtk-QSTR modeling of 572 DES and their components under multiple exptl. conditions. To set up a reliable model from such data, the authors examd. here the use of 0D-2D descriptors along with classification anal., and the Box-Jenkins approach. This procedure led to a final mtk-QSTR model with high overall accuracy and predictivity (∼90%). The model highlights also the crucial role that polarizability, electronegativity, hydrogen-bond donor (HBD), and topol. properties play into the DES toxicity. Furthermore, with the help of the derived mtk-QSTR model, 30 different HBD components were ranked on the basis of their toxic contributions to DES. More importantly, the proposed in silico modeling approach is shown to be a valuable tool to mine relevant STR information, therefore guiding the rational design of potentially safe DES.
  12. 12
    Khandelwal, S.; Tailor, Y. K.; Kumar, M. Deep eutectic solvents (DESs) as eco-friendly and sustainable solvent/catalyst systems in organic transformations. J. Mol. Liq. 2016, 215, 345– 386,  DOI: 10.1016/j.molliq.2015.12.015
    Google Scholar
    12
    Deep eutectic solvents (DESs) as eco-friendly and sustainable solvent/catalyst systems in organic transformations
    Khandelwal, Sarita; Tailor, Yogesh Kumar; Kumar, Mahendra
    Journal of Molecular Liquids (2016), 215 (), 345-386CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
    A review. The use of environmentally benign and inexpensive DES as solvent and catalyst in the field of org. chem was discussed.
  13. 13
    Zahn, S. Deep eutectic solvents: similia similibus solvuntur?. Phys. Chem. Chem. Phys. 2017, 19, 4041– 4047,  DOI: 10.1039/C6CP08017K
    Google Scholar
    13
    Deep eutectic solvents: similia similibus solvuntur?
    Zahn, Stefan
    Physical Chemistry Chemical Physics (2017), 19 (5), 4041-4047CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Deep eutectic solvents, mixts. of an org. compd. and a salt with a deep eutectic m.p., are promising cheap and eco-friendly alternatives to ionic liqs. Ab initio mol. dynamics simulations of reline, a mixt. consisting of urea and choline chloride, reveal that not solely hydrogen bonds allow similar interactions between both constituents. The chloride anion and the oxygen atom of urea also show a similar spatial distribution close to the cationic core of choline due to a similar charge located on both atoms. As a result of multiple similar interactions, clusters migrating together cannot be obsd. in reline which supports the hypothesis similia similibus solvuntur. In contrast to previous suggestions, the interaction of the hydroxyl group of choline with a hydrogen bond acceptor is overall rigid. Fast hydrogen bond acceptor dynamics is facilitated by the hydrogen atoms in the trans position to the carbonyl group of urea which contributes to the low m.p. of reline.
  14. 14
    Stefanovic, R.; Ludwig, M.; Webber, G. B.; Atkin, R.; Page, A. J. Nanostructure, hydrogen bonding and rheology in choline chloride deep eutectic solvents as a function of the hydrogen bond donor. Phys. Chem. Chem. Phys. 2017, 19, 3297– 3306,  DOI: 10.1039/C6CP07932F
    Google Scholar
    14
    Nanostructure, hydrogen bonding and rheology in choline chloride deep eutectic solvents as a function of the hydrogen bond donor
    Stefanovic, Ryan; Ludwig, Michael; Webber, Grant B.; Atkin, Rob; Page, Alister J.
    Physical Chemistry Chemical Physics (2017), 19 (4), 3297-3306CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Deep eutectic solvents (DESs) are a mixt. of a salt and a mol. hydrogen bond donor, which form a eutectic liq. with a depressed m.p. Quantum mech. mol. dynamics (QM/MD) simulations were used to probe the 1 : 2 choline chloride-urea (ChCl : U), choline chloride-ethylene glycol (ChCl : EG) and choline chloride-glycerol (ChCl : Gly) DESs. DES nanostructure and interactions between the ions is used to rationalise differences in DES eutectic point temps. and viscosity. Simulations show that the structure of the bulk hydrogen bond donor is largely preserved for hydroxyl based hydrogen bond donors (ChCl:Gly and ChCl:EG), resulting in a smaller m.p. depression. By contrast, ChCl:U exhibits a well-established hydrogen bond network between the salt and hydrogen bond donor, leading to a larger m.p. depression. This extensive hydrogen bond network in ChCl:U also leads to substantially higher viscosity, compared to ChCl:EG and ChCl:Gly. Of the two hydroxyl based DESs, ChCl:Gly also exhibits a higher viscosity than ChCl:EG. This is attributed to the over-satn. of hydrogen bond donor groups in the ChCl:Gly bulk, which leads to more extensive hydrogen bond donor self-interaction and hence higher cohesive forces within the bulk liq.
  15. 15
    Fetisov, E. O.; Harwood, D. B.; Kuo, I.-F. W.; Warrag, S. E. E.; Kroon, M. C.; Peters, C. J.; Siepmann, J. I. First-Principles Molecular Dynamics Study of a Deep Eutectic Solvent: Choline Chloride/Urea and Its Mixture with Water. J. Phys. Chem. B 2018, 122, 1245– 1254, PMID: 29200290  DOI: 10.1021/acs.jpcb.7b10422
    Google Scholar
    15
    First-Principles Molecular Dynamics Study of a Deep Eutectic Solvent: Choline Chloride/Urea and Its Mixture with Water
    Fetisov, Evgenii O.; Harwood, David B.; Kuo, I-Feng William; Warrag, Samah E. E.; Kroon, Maaike C.; Peters, Cor J.; Siepmann, J. Ilja
    Journal of Physical Chemistry B (2018), 122 (3), 1245-1254CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    First principles mol. dynamics simulations in the canonical ensemble at temps. of 333 and 363 K and at the corresponding exptl. densities are carried out to investigate the behavior of the 1:2 choline chloride/urea (reline) deep eutectic solvent and its equimolar mixt. with water. Anal. of atom-atom radial and spatial distribution functions and of the H-bond network reveals the microheterogeneous structure of these complex liq. mixts. In neat reline, the structure is governed by strong H-bonds of the trans- and cis-H atoms of urea to the chloride ion. In hydrous reline, water competes for the anions, and the H atoms of urea have similar propensities to bond to the chloride ions and the O atoms of urea and water. The vibrational spectra exhibit relatively broad peaks reflecting the heterogeneity of the environment. Although the 100-ps trajectories allow only for a qual. assessment of transport properties, the simulations indicate that water is more mobile than the other species and its addn. also fosters faster motion of urea.
  16. 16
    Perkins, S. L.; Painter, P.; Colina, C. M. Molecular Dynamic Simulations and Vibrational Analysis of an Ionic Liquid Analogue. J. Phys. Chem. B 2013, 117, 10250– 10260, PMID: 23915257  DOI: 10.1021/jp404619x
    Google Scholar
    16
    Molecular Dynamic Simulations and Vibrational Analysis of an Ionic Liquid Analogue
    Perkins, Sasha L.; Painter, Paul; Colina, Coray M.
    Journal of Physical Chemistry B (2013), 117 (35), 10250-10260CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Atomistic mol. dynamics simulations have been performed over a range of temps. for the 1:2 choline chloride-urea mixt. using different force field modifications. Good agreement was achieved between simulated d., vol. expansion coeff., heat capacity, and diffusion coeffs. and exptl. values in order to validate the best performing force field. Atom-atom and center-of-mass radial distribution functions are discussed in order to understand the atomistic interactions involved in this eutectic mixt. Exptl. IR spectra are also reported for choline chloride-urea mixts., and band assignments are discussed. The distribution of hydrogen-bond interactions from mol. simulations is correlated to curve-resolved bands from the IR spectra. This work suggests that there is a strong interaction between the NH2 of urea and the chlorine anion where the system wants to maximize the no. of hydrogen bonds to the anion. Addnl., the disappearance of free carbonyl groups upon increasing concns. of urea suggests that at low urea concns., urea will preferentially interact with the anion through the NH2 groups. As this concn. increases, the complex remains but with addnl. interactions that remove the free carbonyl band from the spectra. The results from both mol. simulations and exptl. IR spectroscopy support the idea that key interactions between the moieties in the eutectic mixt. interrupt the main interactions within the parent substances and are responsible for the decrease in f.p.
  17. 17
    Doherty, B.; Acevedo, O. OPLS Force Field for Choline Chloride-Based Deep Eutectic Solvents. J. Phys. Chem. B 2018, 122, 9982– 9993, PMID: 30125108  DOI: 10.1021/acs.jpcb.8b06647
    Google Scholar
    17
    OPLS Force Field for Choline Chloride-Based Deep Eutectic Solvents
    Doherty, Brian; Acevedo, Orlando
    Journal of Physical Chemistry B (2018), 122 (43), 9982-9993CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Deep eutectic solvents (DES) are a class of solvents frequently composed of choline chloride and a neutral hydrogen bond donor (HBD) at ratios of 1:1, 1:2, or 1:3, resp. As cost-effective and eco-friendly solvents, DESs have gained considerable popularity in multiple fields, including materials, sepns., and nanotechnol. In the present work, a comprehensive set of transferable parameters have been fine-tuned to accurately reproduce bulk-phase phys. properties and local intermol. interactions for 8 different choline chloride-based DESs. This nonpolarizable force field, OPLS-DES, gave near quant. agreement at multiple temps. for exptl. densities, viscosities, heat capacities, and surface tensions yielding overall mean abs. errors (MAEs) of ca. 1.1%, 1.6%, 5.5%, and 1.5%, resp. Local interactions and solvent structuring between the ions and HBDs, including urea, glycerol, phenol, ethylene glycol, levulinic acid, oxalic acid, and malonic acid, were accurately reproduced when compared to radial distribution functions and coordination nos. derived from exptl. liq.-phase neutron diffraction data and from first-principles mol. dynamics simulations. The reprodn. of transport properties presented a considerable challenge and behaved more like a supercooled liq. near room temp.; higher-temp. simulations, e.g., 400-500 K, or an alternative polarizable force field is recommended when computing self-diffusion coeffs.
  18. 18
    Nandy, A.; Smiatek, J. Mixtures of LiTFSI and urea: ideal thermodynamic behavior as key to the formation of deep eutectic solvents?. Phys. Chem. Chem. Phys. 2019, 21, 12279– 12287,  DOI: 10.1039/C9CP01440C
    Google Scholar
    18
    Mixtures of LiTFSI and urea: ideal thermodynamic behavior as key to the formation of deep eutectic solvents?
    Nandy, Aniruddha; Smiatek, Jens
    Physical Chemistry Chemical Physics (2019), 21 (23), 12279-12287CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    At certain mixing ratios, urea and lithium bis(trifluorosulfonyl)imide (LiTFSI) form deep eutectic solvents with a pronounced lowering of the melting temp. when compared to the individual components. Using atomistic mol. dynamics (MD) simulations and d. functional theory (DFT) calcns., we study the structural and dynamic properties of these mixts. at various urea concns. Our findings show that the diffusivity of all species increases linearly with the urea mole fraction which can be explained by a successive replacement of TFSI- ions from the first coordination shell around lithium ions. A comparable linear change is also obsd. for the interaction energies between the individual components. Broad electrochem. stability windows in combination with high lithium ion transport nos. are brought into agreement with electronic reshuffling mechanisms between the interacting species. Further calcns. of chem. potential derivs. and transfer free energies highlight an ideal thermodn. behavior for certain LiTFSI/urea mixing ratios. Our findings thus provide a rationale for the unique properties of these mixts. in reasonable agreement with exptl. outcomes.
  19. 19
    Zhang, Y.; Poe, D.; Heroux, L.; Squire, H.; Doherty, B. W.; Long, Z.; Dadmun, M.; Gurkan, B.; Tuckerman, M. E.; Maginn, E. J. Liquid Structure and Transport Properties of the Deep Eutectic Solvent Ethaline. J. Phys. Chem. B 2020, 124, 5251– 5264, PMID: 32464060  DOI: 10.1021/acs.jpcb.0c04058
    Google Scholar
    19
    Liquid Structure and Transport Properties of the Deep Eutectic Solvent Ethaline
    Zhang, Yong; Poe, Derrick; Heroux, Luke; Squire, Henry; Doherty, Brian W.; Long, Zhuoran; Dadmun, Mark; Gurkan, Burcu; Tuckerman, Mark E.; Maginn, Edward J.
    Journal of Physical Chemistry B (2020), 124 (25), 5251-5264CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    A range of techniques including phys. property measurements, neutron scattering expts., ab initio mol. dynamics, and classical mol. dynamics simulations are used to probe the structural, thermodn., and transport properties of a deep eutectic solvent comprised of a 1:2 molar ratio of choline chloride and ethylene glycol. This mixt., known as Ethaline, has many desirable properties for use in a range of applications, and therefore, understanding its liq. structure and transport properties is of interest. Simulation results are able to capture exptl. densities, diffusivities, viscosities, and structure factors extremely well. The solvation environment is dynamic and dominated by different hydrogen bonding interactions. Dynamic heterogeneities resulting from hydrogen bonding interactions are quantified. Rotational dynamics of mol. dipole moments of choline and ethylene glycol are computed and found to exhibit a fast and slow mode.
  20. 20
    Shayestehpour, O.; Zahn, S. Molecular Features of Reline and Homologous Deep Eutectic Solvents Contributing to Nonideal Mixing Behavior. J. Phys. Chem. B 2020, 124, 7586– 7597, PMID: 32790398  DOI: 10.1021/acs.jpcb.0c03091
    Google Scholar
    20
    Molecular Features of Reline and Homologous Deep Eutectic Solvents Contributing to Nonideal Mixing Behavior
    Shayestehpour, Omid; Zahn, Stefan
    Journal of Physical Chemistry B (2020), 124 (35), 7586-7597CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Deep eutectic solvents based on choline chloride and a series of urea derivs. are studied by mol. dynamics simulations with the aim to identify mol. features contributing to nonideal mixing behavior of these compds. In case of reline, a mixt. of choline chloride and urea in 1:2 ratio, urea mols. provide sufficient hydrogen bond donor sites to take up the chloride anions into their polar network. Replacing any of the hydrogen atoms of urea by a Me group strongly pushes the anion to interact with these alkyl chains, resulting in a pos. deviation of the activity coeffs. of choline chloride compared to reline. Furthermore, the oxygen atom of urea can interact with the nitrogen atom of the cation. This enables the chloride anion to move off-center of the cation toward the hydrogen atom of its hydroxyl group, possessing stronger directional Coulomb interactions than the nitrogen atom of the cation. The substitution of urea's hydrogen atoms in cis position to the carbonyl group as in 1,3-dimethylurea, pushes the newly introduced nonpolar alkyl chains toward the nitrogen atom of the cation. This effect can be responsible for the exptl. obsd. increase of the activity coeff. of the urea deriv. compared to urea. Addnl., indications for formation of nonpolar domains within the liq. and, thus, nanoscale segregation is visible as soon as one hydrogen atom of urea is replaced by an alkyl group.
  21. 21
    Goloviznina, K.; Gong, Z.; Costa Gomes, M. F.; Pádua, A. A. H. Extension of the CL&Pol Polarizable Force Field to Electrolytes, Protic Ionic Liquids, and Deep Eutectic Solvents. J. Chem. Theory Comput. 2021, 17, 1606– 1617, PMID: 33555860  DOI: 10.1021/acs.jctc.0c01002
    Google Scholar
    21
    Extension of the CL&Pol Polarizable Force Field to Electrolytes, Protic Ionic Liquids, and Deep Eutectic Solvents
    Goloviznina, Kateryna; Gong, Zheng; Costa Gomes, Margarida F.; Padua, Agilio A. H.
    Journal of Chemical Theory and Computation (2021), 17 (3), 1606-1617CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The polarizable CL and Pol force field presented in our previous study, Transferable, Polarizable Force Field for Ionic Liqs. (J. Chem. Theory Comput.2019,15, 5858, DOI: http://doi.org/10.1021/acs.jctc.9b0068910.1021/acs.jctc.9b00689), is extended to electrolytes, protic ionic liqs. (PIL), deep eutectic solvents (DES), and glycols. These systems are problematic in polarizable simulations because they contain either small, highly charged ions or strong hydrogen bonds, which cause trajectory instabilities due to the pull exerted on the induced dipoles. We use a Tang-Toennies (TT) function to dampen, or smear, the interactions between charges and induced dipole at a short range involving small, highly charged atoms (such as hydrogen or lithium), thus preventing the "polarization catastrophe". The new force field gives stable trajectories and is validated through comparison with exptl. data on d., viscosity, and ion diffusion coeffs. of liq. systems of the above-mentioned classes. The results also shed light on the hydrogen-bonding pattern in ethylammonium nitrate, a PIL, for which the literature contains conflicting views. We describe the implementation of the TT damping function, of the temp.-grouped Nose-Hoover thermostat for polarizable mol. dynamics (MD) and of the periodic perturbation method for viscosity evaluation from non-equil. trajectories in the LAMMPS MD code. The main result of this work is the wider applicability of the CL and Pol polarizable force field to new, important classes of fluids, achieving robust trajectories and a good description of equil. and transport properties in challenging systems. The fragment-based approach of CL and Pol will allow ready extension to a wide variety of PILs, DES, and electrolytes.
  22. 22
    Jeong, K.-j.; McDaniel, J. G.; Yethiraj, A. Deep Eutectic Solvents: Molecular Simulations with a First-Principles Polarizable Force Field. J. Phys. Chem. B 2021, 125, 7177– 7186, PMID: 34181852  DOI: 10.1021/acs.jpcb.1c01692
    Google Scholar
    22
    Deep Eutectic Solvents: Molecular Simulations with a First-Principles Polarizable Force Field
    Jeong, Kyeong-jun; McDaniel, Jesse G.; Yethiraj, Arun
    Journal of Physical Chemistry B (2021), 125 (26), 7177-7186CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    The unique properties of deep eutectic solvents make them useful in a variety of applications. In this work we develop a first-principles force field for reline, which is composed of choline chloride and urea in the molar ratio 1:2. We start with the symmetry adapted perturbation theory (SAPT) protocol and then make adjustments to better reproduce the structure and dynamics of the liq. when compared to first-principles mol. dynamics (FPMD) simulations. The resulting force field is in good agreement with expts. in addn. to being consistent with the FPMD simulations. The simulations show that primitive mol. clusters are preferentially formed with choline-chloride ionic pairs bound with a hydrogen bond in the hydroxyl group and that urea mols. coordinate the chloride mainly via the trans-H chelating hydrogen bonds. Incorporating polarizability qual. influences the radial distributions and lifetimes of hydrogen bonds and affects long-range structural order and dynamics. The polarizable force field predicts a diffusion const. about an order of magnitude larger than the nonpolarizable force field and is therefore less computationally intensive. We hope this study paves the way for studying complex hydrogen-bonding liqs. from a first-principles approach.
  23. 23
    Shayestehpour, O.; Zahn, S. Ion Correlation in Choline Chloride–Urea Deep Eutectic Solvent (Reline) from Polarizable Molecular Dynamics Simulations. J. Phys. Chem. B 2022, 126, 3439– 3449, PMID: 35500254  DOI: 10.1021/acs.jpcb.1c10671
    Google Scholar
    23
    Ion Correlation in Choline Chloride-Urea Deep Eutectic Solvent (Reline) from Polarizable Molecular Dynamics Simulations
    Shayestehpour, Omid; Zahn, Stefan
    Journal of Physical Chemistry B (2022), 126 (18), 3439-3449CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    In recent years, deep eutectic solvents (DESs) emerged as highly tunable and environmentally friendly alternatives to common ionic liqs. and org. solvents. In this work, a polarizable model based on the CHARMM Drude polarizable force field is developed for a 1:2 ratio mixt. of choline chloride/urea (reline) DES. To successfully reproduce the structure of the liq. as compared to first-principles mol. dynamics simulations, a damping factor was introduced to correct the obsd. over-binding between the chloride and the hydrogen bonding site of choline. Investigated radial distributions reveal the formation of hydrogen bonds between all the constituents of reline and similar interactions for chloride and urea's oxygen atoms, which could contribute to the m.p. depression of the mixt. Predicted dynamic properties from our polarizable force field are in good agreement with expts., showing significant improvements over nonpolarizable models. Similar to some ionic liqs., an oscillatory behavior in the velocity autocorrelation function of the anion is visible, which can be interpreted as a rattling motion of the lighter anion surrounded by the heavier cations. The obtained results for ionic cond. of reline show some degree of correlated ion motion in this DES. However, a joint diffusion of ion pairs cannot be obsd. during the simulations.
  24. 24
    Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133– A1138,  DOI: 10.1103/PhysRev.140.A1133
    Google Scholar
    There is no corresponding record for this reference.
  25. 25
    Goedecker, S. Linear scaling electronic structure methods. Rev. Mod. Phys. 1999, 71, 1085– 1123,  DOI: 10.1103/RevModPhys.71.1085
    Google Scholar
    25
    Linear scaling electronic structure methods
    Goedecker, Stefan
    Reviews of Modern Physics (1999), 71 (4), 1085-1123CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
    A review with many refs. Methods exhibiting linear scaling with respect to the size of the system, the so-called O(N) methods, are an essential tool for the calcn. of the electronic structure of large systems contg. many atoms. They are based on algorithms that take advantage of the decay properties of the d. matrix. In this article the phys. decay properties of the d. matrix are be studied for both metals and insulators. Several strategies for constructing O(N) algorithms are presented and critically examd. Some issues that are relevant only for self-consistent O(N) methods, such as the calcn. of the Hartree potential and mixing issues, are also discussed. Some typical applications of O(N) methods are briefly described.
  26. 26
    Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225– 11236,  DOI: 10.1021/ja9621760
    Google Scholar
    26
    Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids
    Jorgensen, William L.; Maxwell, David S.; Tirado-Rives, Julian
    Journal of the American Chemical Society (1996), 118 (45), 11225-11236CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The parametrization and testing of the OPLS all-atom force field for org. mols. and peptides are described. Parameters for both torsional and nonbonded energetics have been derived, while the bond stretching and angle bending parameters have been adopted mostly from the AMBER all-atom force field. The torsional parameters were detd. by fitting to rotational energy profiles obtained from ab initio MO calcns. at the RHF/6-31G*//RHF/6-31G* level for more than 50 org. mols. and ions. The quality of the fits was high with av. errors for conformational energies of less than 0.2 kcal/mol. The force-field results for mol. structures are also demonstrated to closely match the ab initio predictions. The nonbonded parameters were developed in conjunction with Monte Carlo statistical mechanics simulations by computing thermodn. and structural properties for 34 pure org. liqs. including alkanes, alkenes, alcs., ethers, acetals, thiols, sulfides, disulfides, aldehydes, ketones, and amides. Av. errors in comparison with exptl. data are 2% for heats of vaporization and densities. The Monte Carlo simulations included sampling all internal and intermol. degrees of freedom. It is found that such non-polar and monofunctional systems do not show significant condensed-phase effects on internal energies in going from the gas phase to the pure liqs.
  27. 27
    Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J. Comput. Chem. 2010, 31, 671– 690,  DOI: 10.1002/jcc.21367
    Google Scholar
    27
    CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields
    Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D., Jr.
    Journal of Computational Chemistry (2010), 31 (4), 671-690CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The widely used CHARMM additive all-atom force field includes parameters for proteins, nucleic acids, lipids, and carbohydrates. In the present article, an extension of the CHARMM force field to drug-like mols. is presented. The resulting CHARMM General Force Field (CGenFF) covers a wide range of chem. groups present in biomols. and drug-like mols., including a large no. of heterocyclic scaffolds. The parametrization philosophy behind the force field focuses on quality at the expense of transferability, with the implementation concg. on an extensible force field. Statistics related to the quality of the parametrization with a focus on exptl. validation are presented. Addnl., the parametrization procedure, described fully in the present article in the context of the model systems, pyrrolidine, and 3-phenoxymethyl-pyrrolidine will allow users to readily extend the force field to chem. groups that are not explicitly covered in the force field as well as add functional groups to and link together mols. already available in the force field. CGenFF thus makes it possible to perform "all-CHARMM" simulations on drug-target interactions thereby extending the utility of CHARMM force fields to medicinally relevant systems. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2010.
  28. 28
    Cadena, C.; Zhao, Q.; Snurr, R. Q.; Maginn, E. J. Molecular Modeling and Experimental Studies of the Thermodynamic and Transport Properties of Pyridinium-Based Ionic Liquids. J. Phys. Chem. B 2006, 110, 2821– 2832, PMID: 16471891  DOI: 10.1021/jp056235k
    Google Scholar
    28
    Molecular Modeling and Experimental Studies of the Thermodynamic and Transport Properties of Pyridinium-Based Ionic Liquids
    Cadena, Cesar; Zhao, Qi; Snurr, Randall Q.; Maginn, Edward J.
    Journal of Physical Chemistry B (2006), 110 (6), 2821-2832CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    A combined exptl. and mol. dynamics study has been performed on the following pyridinium-based ionic liqs.: 1-n-hexyl-3-methylpyridinium bis(trifluoromethanesulfonyl)imide ([hmpy][Tf2N]), 1-n-octyl-3-methylpyridinium bis(trifluoromethanesulfonyl)imide ([ompy][Tf2N]), and 1-n-hexyl-3,5-dimethylpyridinium bis(trifluoromethanesulfonyl)imide ([hdmpy][Tf2N]). Pulsed field gradient NMR spectroscopy was used to det. the self-diffusivities of the individual cations and anions as a function of temp. Exptl. self-diffusivities range from 10-11 to 10-10 m2/s. Activation energies for diffusion are 44-49 kJ/mol. A classical force field was developed for these compds., and mol. dynamics simulations were performed to compute dynamic as well as thermodn. properties. Evidence of glassy dynamics was found, preventing accurate detn. of self-diffusivities over mol. dynamics time scales. Volumetric properties such as d., isothermal compressibility, and volumetric expansivity agree well with expt. Simulated heat capacities are within 2% of exptl. values.
  29. 29
    Rajput, N. N.; Murugesan, V.; Shin, Y.; Han, K. S.; Lau, K. C.; Chen, J.; Liu, J.; Curtiss, L. A.; Mueller, K. T.; Persson, K. A. Elucidating the Solvation Structure and Dynamics of Lithium Polysulfides Resulting from Competitive Salt and Solvent Interactions. Chem. Mater. 2017, 29, 3375– 3379,  DOI: 10.1021/acs.chemmater.7b00068
    Google Scholar
    29
    Elucidating the Solvation Structure and Dynamics of Lithium Polysulfides Resulting from Competitive Salt and Solvent Interactions
    Rajput, Nav Nidhi; Murugesan, Vijayakumar; Shin, Yongwoo; Han, Kee Sung; Lau, Kah Chun; Chen, Junzheng; Liu, Jun; Curtiss, Larry A.; Mueller, Karl T.; Persson, Kristin A.
    Chemistry of Materials (2017), 29 (8), 3375-3379CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    Fundamental mol. level understanding of functional properties of liq. solns. provides an important basis for designing optimized electrolytes for numerous applications. In particular, exhaustive knowledge of solvation structure, stability and transport properties is crit. for developing stable electrolytes for fast charging and high energy d. next-generation energy storage systems. Here we report the correlation between soly., solvation structure and translational dynamics of a lithium salt (Li-TFSI) and polysulfides species using well-benchmarked classical mol. dynamics simulations combined with NMR. It is obsd. that the polysulfide chain length has a significant effect on the ion-ion and ion-solvent interaction as well as on the diffusion coeff. of the ionic species in soln. In particular, extensive cluster formation is obsd. in lower order polysulfides (Sx2-; x≤4), whereas the longer poly-sulfides (Sx2-; x>4) show high soly. and slow dynamics in the soln. It is obsd. that optimal solvent/salt ratio is essential to control the soly. and cond. as the addn. of Li salt increases the soly. but decreases the mobility of the ionic species. This work provides a coupled theor. and exptl. study of bulk solvation structure and transport properties of multi-component electrolyte systems, yielding design metrics for developing optimal electrolytes with improved stability and soly.
  30. 30
    Yan, T.; Wang, Y.; Knox, C. On the Dynamics of Ionic Liquids: Comparisons between Electronically Polarizable and Nonpolarizable Models II. J. Phys. Chem. B 2010, 114, 6886– 6904, PMID: 20443608  DOI: 10.1021/jp908914d
    Google Scholar
    30
    On the Dynamics of Ionic Liquids: Comparisons between Electronically Polarizable and Nonpolarizable Models II
    Yan, Tianying; Wang, Yanting; Knox, Craig
    Journal of Physical Chemistry B (2010), 114 (20), 6886-6904CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    An electronically polarizable model has been developed for the ionic liq. (IL) 1-ethyl-3-methyl-imidazolium nitrate (EMIM+/NO3-). Mol. dynamics simulations were then performed with both the polarizable and nonpolarizable models. Both models exhibited certain properties that are similar to a supercooled liq. behavior even though the simulations were run at 400 K (89 K above the m.p. of EMIM+/NO3-). The ionic mean-squared displacement and transverse current correlation function of both models were well represented by a memory function with a fast Gaussian initial relaxation followed by the two-step exponential functions for β- and α- structural relaxations. Another feature shared by both models is the dynamic heterogeneity, which highlights the complex dynamic behavior of ILs. Apart from the overall slow dynamics, the relaxation of the H-atoms attached to the Me group demonstrates a "free rotor" type of motion. Also, the Et group shows the fastest overall relaxation, due to the weak electrostatic interactions on it. Such flexibility enhances the entropic effect and thus favors the liq. state at room temp. For the dynamical properties reported in this paper, the polarizable model consistently exhibited faster relaxations (including translational and reorientational motions), higher self-diffusion and ionic cond., and lower shear viscosity than the nonpolarizable model. The faster relaxations of the polarizable model result from attenuated long-range electrostatic interactions caused by enhanced screening from the polarization effect. Therefore, simulations based on the polarizable model may be analogous to simulations with the nonpolarizable model at higher temps. On the other hand, the enhanced intermol. interactions for the polarizable model at short-range due to the addnl. charge-dipole and dipole-dipole interactions result in a red shift of the intramol. C-H stretch spectrum and a higher degree of ion assocn., leading to a spectrum with enhanced cond. across the whole frequency range. The vibrational motion assocd. with the intermol. hydrogen bonding is highly IR active, highlighting the importance of hydrogen bond dynamics in ILs.
  31. 31
    Szabadi, A.; Elfgen, R.; Macchieraldo, R.; Kearns, F. L.; Lee Woodcock, H.; Kirchner, B.; Schröder, C. Comparison between ab initio and polarizable molecular dynamics simulations of 1-butyl-3-methylimidazolium tetrafluoroborate and chloride in water. J. Mol. Liq. 2021, 337, 116521,  DOI: 10.1016/j.molliq.2021.116521
    Google Scholar
    31
    Comparison between ab initio and polarizable molecular dynamics simulations of 1-butyl-3-methylimidazolium tetrafluoroborate and chloride in water
    Szabadi, Andras; Elfgen, Roman; Macchieraldo, Roberto; Kearns, Fiona L.; Lee Woodcock, H.; Kirchner, Barbara; Schroeder, Christian
    Journal of Molecular Liquids (2021), 337 (), 116521CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
    In this study we compare the results of three different polarizable mol. dynamics force fields with an ab initio trajectory of the aq. mixt. of 1-butyl-3-methylimidazolium tetrafluoroborate and chloride, esp. regarding their ability to describe static and dynamic phenomena. The discrepancies are discussed in terms of intra- and intermol. force field parameters as well as the system size. We report significant differences in the derived diffusion coeffs. and attribute them to system size, d. and general discrepancies between ab initio and classical mol. dynamics simulations. In most cases, radial distribution functions show qual. agreement; however, the overpolarization of chloride in the MD trajectories gives rises to unphys. results. Excellent agreement between dipolar distributions point out the importance of explicit polarizability in MD, while the comparison of computational and exptl. IR spectra highlights the similarities between classical and ab initio dynamics in the low-wave no. region and the differences around 1500 cm-1.
  32. 32
    Glielmo, A.; Sollich, P.; De Vita, A. Accurate interatomic force fields via machine learning with covariant kernels. Phys. Rev. B 2017, 95, 214302,  DOI: 10.1103/PhysRevB.95.214302
    Google Scholar
    32
    Accurate interatomic force fields via machine learning with covariant kernels
    Glielmo, Aldo; Sollich, Peter; De Vita, Alessandro
    Physical Review B (2017), 95 (21), 214302/1-214302/10CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    A review. We present a novel scheme to accurately predict at. forces as vector quantities, rather than sets of scalar components, by Gaussian process (GP) regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO(d) for the relevant dimensionality d. Remarkably, in specific cases the integration can be carried out anal. and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mech. forces in real materials is investigated by tests on pure and defective Ni, Fe, and Si cryst. systems.
  33. 33
    Chmiela, S.; Tkatchenko, A.; Sauceda, H. E.; Poltavsky, I.; Schütt, K. T.; Müller, K. R. Machine learning of accurate energy-conserving molecular force fields. Sci. Adv. 2017, 3, e1603015  DOI: 10.1126/sciadv.1603015
    Google Scholar
    33
    Machine learning of accurate energy-conserving molecular force fields
    Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.; Poltavsky, Igor; Schuett, Kristof T.; Mueller, Klaus-Robert
    Science Advances (2017), 3 (5), e1603015/1-e1603015/6CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
    Using conservation of energy-a fundamental property of closed classical and quantum mech. systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate mol. force fields using a restricted no. of samples from ab initio mol. dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized mols. with an accuracy of 0.3 kcal mol-1 for energies and 1 kcal mol-1 Å-1 for at. forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of mols., including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quant. mol. dynamics simulations for mols. at a fraction of cost of explicit AIMD calcns., thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.
  34. 34
    Chmiela, S.; Sauceda, H. E.; Müller, K. R.; Tkatchenko, A. Towards exact molecular dynamics simulations with machine-learned force fields. Nat. Commun. 2018, 9, 3887,  DOI: 10.1038/s41467-018-06169-2
    Google Scholar
    34
    Towards exact molecular dynamics simulations with machine-learned force fields
    Chmiela Stefan; Muller Klaus-Robert; Sauceda Huziel E; Muller Klaus-Robert; Muller Klaus-Robert; Tkatchenko Alexandre
    Nature communications (2018), 9 (1), 3887 ISSN:.
    Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as good as the underlying interatomic potential. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. Here we enable the direct construction of flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model in an automatic data-driven way. The developed sGDML approach faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged molecular dynamics simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations.
  35. 35
    Bartók, A. P.; Payne, M. C.; Kondor, R.; Csányi, G. Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons. Phys. Rev. Lett. 2010, 104, 136403,  DOI: 10.1103/PhysRevLett.104.136403
    Google Scholar
    35
    Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
    Bartok, Albert P.; Payne, Mike C.; Kondor, Risi; Csanyi, Gabor
    Physical Review Letters (2010), 104 (13), 136403/1-136403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We introduce a class of interat. potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mech. calcns. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calcg. properties at high temps. Using the interat. potential to generate the long mol. dynamics trajectories required for such calcns. saves orders of magnitude in computational cost.
  36. 36
    Behler, J.; Parrinello, M. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces. Phys. Rev. Lett. 2007, 98, 146401,  DOI: 10.1103/PhysRevLett.98.146401
    Google Scholar
    36
    Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
    Behler, Jorg; Parrinello, Michele
    Physical Review Letters (2007), 98 (14), 146401/1-146401/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The accurate description of chem. processes often requires the use of computationally demanding methods like d.-functional theory (DFT), making long simulations of large systems unfeasible. In this Letter we introduce a new kind of neural-network representation of DFT potential-energy surfaces, which provides the energy and forces as a function of all at. positions in systems of arbitrary size and is several orders of magnitude faster than DFT. The high accuracy of the method is demonstrated for bulk silicon and compared with empirical potentials and DFT. The method is general and can be applied to all types of periodic and nonperiodic systems.
  37. 37
    Behler, J. Representing potential energy surfaces by high-dimensional neural network potentials. J. Phys.: Condens. Matter 2014, 26, 183001,  DOI: 10.1088/0953-8984/26/18/183001
    Google Scholar
    37
    Representing potential energy surfaces by high-dimensional neural network potentials
    Behler, J.
    Journal of Physics: Condensed Matter (2014), 26 (18), 183001/1-183001/24, 24 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
    A review. The development of interat. potentials employing artificial neural networks has seen tremendous progress in recent years. While until recently the applicability of neural network potentials (NNPs) has been restricted to low-dimensional systems, this limitation has now been overcome and high-dimensional NNPs can be used in large-scale mol. dynamics simulations of thousands of atoms. NNPs are constructed by adjusting a set of parameters using data from electronic structure calcns. and in many cases energies and forces can be obtained with very high accuracy. Therefore, NNP-based simulation results are often very close to those gained by a direct application of first-principles methods. In this review, the basic methodol. of high-dimensional NNPs will be presented with a special focus on the scope and the remaining limitations of this approach. The development of NNPs requires substantial computational effort as typically thousands of ref. calcns. are required. Still, if the problem to be studied involves very large systems or long simulation times this overhead is regained quickly. Further, the method is still limited to systems contg. about three or four chem. elements due to the rapidly increasing complexity of the configuration space, although many atoms of each species can be present. Due to the ability of NNPs to describe even extremely complex at. configurations with excellent accuracy irresp. of the nature of the at. interactions, they represent a general and therefore widely applicable technique, e.g. for addressing problems in materials science, for investigating properties of interfaces and for studying solvation processes.
  38. 38
    Ghasemi, S. A.; Hofstetter, A.; Saha, S.; Goedecker, S. Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network. Phys. Rev. B 2015, 92, 045131,  DOI: 10.1103/PhysRevB.92.045131
    Google Scholar
    38
    Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network
    Ghasemi, S. Alireza; Hofstetter, Albert; Saha, Santanu; Goedecker, Stefan
    Physical Review B: Condensed Matter and Materials Physics (2015), 92 (4), 045131/1-045131/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    Based on an anal. of the short-range chem. environment of each atom in a system, std. machine-learning-based approaches to the construction of interat. potentials aim at detg. directly the central quantity, which is the total energy. This prevents, for instance, an accurate description of the energetics of systems in which long-range charge transfer or ionization is important. We propose therefore not to target directly with machine-learning methods the total energy but an intermediate phys. quantity, namely, the charge d., which then in turn allows us to det. the total energy. By allowing the electronic charge to distribute itself in an optimal way over the system, we can describe not only neutral but also ionized systems with unprecedented accuracy. We demonstrate the power of our approach for both neutral and ionized NaCl clusters where charge redistribution plays a decisive role for the energetics. We are able to obtain chem. accuracy, i.e., errors of less than a millihartree per atom compared to the ref. d. functional results for a huge data set of configurations with large structural variety. The introduction of phys. motivated quantities which are detd. by the short-range at. environment via a neural network also leads to an increased stability of the machine-learning process and transferability of the potential.
  39. 39
    Smith, J. S.; Isayev, O.; Roitberg, A. E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. Sci. 2017, 8, 3192– 3203,  DOI: 10.1039/C6SC05720A
    Google Scholar
    39
    ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost
    Smith, J. S.; Isayev, O.; Roitberg, A. E.
    Chemical Science (2017), 8 (4), 3192-3203CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    A review. Deep learning is revolutionizing many areas of science and technol., esp. image, text, and speech recognition. In this paper, we demonstrate how a deep neural network (NN) trained on quantum mech. (QM) DFT calcns. can learn an accurate and transferable potential for org. mols. We introduce ANAKIN-ME (Accurate NeurAl networK engINe for Mol. Energies) or ANI for short. ANI is a new method designed with the intent of developing transferable neural network potentials that utilize a highly-modified version of the Behler and Parrinello symmetry functions to build single-atom at. environment vectors (AEV) as a mol. representation. AEVs provide the ability to train neural networks to data that spans both configurational and conformational space, a feat not previously accomplished on this scale. We utilized ANI to build a potential called ANI-1, which was trained on a subset of the GDB databases with up to 8 heavy atoms in order to predict total energies for org. mols. contg. four atom types: H, C, N, and O. To obtain an accelerated but phys. relevant sampling of mol. potential surfaces, we also proposed a Normal Mode Sampling (NMS) method for generating mol. conformations. Through a series of case studies, we show that ANI-1 is chem. accurate compared to ref. DFT calcns. on much larger mol. systems (up to 54 atoms) than those included in the training data set.
  40. 40
    Yao, K.; Herr, J. E.; Toth, D. W.; Mckintyre, R.; Parkhill, J. The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics. Chem. Sci. 2018, 9, 2261– 2269,  DOI: 10.1039/C7SC04934J
    Google Scholar
    40
    The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics
    Yao, Kun; Herr, John E.; Toth, David W.; McKintyre, Ryker; Parkhill, John
    Chemical Science (2018), 9 (8), 2261-2269CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Traditional force fields cannot model chem. reactivity, and suffer from low generality without re-fitting. Neural network potentials promise to address these problems, offering energies and forces with near ab initio accuracy at low cost. However a data-driven approach is naturally inefficient for long-range interat. forces that have simple phys. formulas. In this manuscript we construct a hybrid model chem. consisting of a nearsighted neural network potential with screened long-range electrostatic and van der Waals physics. This trained potential, simply dubbed "TensorMol-0.1", is offered in an open-source Python package capable of many of the simulation types commonly used to study chem.: geometry optimizations, harmonic spectra, open or periodic mol. dynamics, Monte Carlo, and nudged elastic band calcns. We describe the robustness and speed of the package, demonstrating its millihartree accuracy and scalability to tens-of-thousands of atoms on ordinary laptops. We demonstrate the performance of the model by reproducing vibrational spectra, and simulating the mol. dynamics of a protein. Our comparisons with electronic structure theory and exptl. data demonstrate that neural network mol. dynamics is poised to become an important tool for mol. simulation, lowering the resource barrier to simulating chem.
  41. 41
    Schütt, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Müller, K. R. SchNet – A deep learning architecture for molecules and materials. J. Chem. Phys. 2018, 148, 241722,  DOI: 10.1063/1.5019779
    Google Scholar
    41
    SchNet - A deep learning architecture for molecules and materials
    Schuett, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Mueller, K.-R.
    Journal of Chemical Physics (2018), 148 (24), 241722/1-241722/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chem. physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mech. interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chem. compd. space. Here, we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chem. space for mols. and materials, where our model learns chem. plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for mol. dynamics simulations of small mols. and perform an exemplary study on the quantum-mech. properties of C20-fullerene that would have been infeasible with regular ab initio mol. dynamics. (c) 2018 American Institute of Physics.
  42. 42
    Han, J.; Zhang, L.; Car, R.; E, W. Deep Potential: A General Representation of a Many-Body Potential Energy Surface. Commun. Comput. Phys. 2018, 23, 629– 639,  DOI: 10.4208/cicp.oa-2017-0213
    Google Scholar
    There is no corresponding record for this reference.
  43. 43
    Unke, O. T.; Meuwly, M. PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges. J. Chem. Theory Comput. 2019, 15, 3678– 3693, PMID: 31042390  DOI: 10.1021/acs.jctc.9b00181
    Google Scholar
    43
    PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges
    Unke, Oliver T.; Meuwly, Markus
    Journal of Chemical Theory and Computation (2019), 15 (6), 3678-3693CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    In recent years, machine learning (ML) methods have become increasingly popular in computational chem. After being trained on appropriate ab initio ref. data, these methods allow for accurately predicting the properties of chem. systems, circumventing the need for explicitly solving the electronic Schrodinger equation. Because of their computational efficiency and scalability to large data sets, deep neural networks (DNNs) are a particularly promising ML algorithm for chem. applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces, and dipole moments of chem. systems. PhysNet achieves state-of-the-art performance on the QM9, MD17, and ISO17 benchmarks. Further, two new data sets are generated in order to probe the performance of ML models for describing chem. reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qual. correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala10): The optimized geometry of helical Ala10 predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 Å). By running unbiased mol. dynamics (MD) simulations of Ala10 on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala10 folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol-1 according to the ref. ab initio calcns.
  44. 44
    Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 2011, 134, 074106,  DOI: 10.1063/1.3553717
    Google Scholar
    44
    Atom-centered symmetry functions for constructing high-dimensional neural network potentials
    Behler, Joerg
    Journal of Chemical Physics (2011), 134 (7), 074106/1-074106/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calcns., and thus enable mol. dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the at. positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as mols., cryst. and amorphous solids, and liqs. (c) 2011 American Institute of Physics.
  45. 45
    Thompson, A.; Swiler, L.; Trott, C.; Foiles, S.; Tucker, G. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials. J. Comput. Phys. 2015, 285, 316– 330,  DOI: 10.1016/j.jcp.2014.12.018
    Google Scholar
    45
    Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials
    Thompson, A. P.; Swiler, L. P.; Trott, C. R.; Foiles, S. M.; Tucker, G. J.
    Journal of Computational Physics (2015), 285 (), 316-330CODEN: JCTPAH; ISSN:0021-9991. (Elsevier Inc.)
    We present a new interat. potential for solids and liqs. called Spectral Neighbor Anal. Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calcns. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor d. projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coeffs. are detd. using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calcn. of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel mol. dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calcns. by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calcd. properties of both the cryst. solid and the liq. phases. In addn., unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.
  46. 46
    Drautz, R. Atomic cluster expansion for accurate and transferable interatomic potentials. Phys. Rev. B 2019, 99, 014104,  DOI: 10.1103/PhysRevB.99.014104
    Google Scholar
    46
    Atomic cluster expansion for accurate and transferable interatomic potentials
    Drautz, Ralf
    Physical Review B (2019), 99 (1), 014104CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    The at. cluster expansion is developed as a complete descriptor of the local at. environment, including multicomponent materials, and its relation to a no. of other descriptors and potentials is discussed. The effort for evaluating the at. cluster expansion is shown to scale linearly with the no. of neighbors, irresp. of the order of the expansion. Application to small Cu clusters demonstrates smooth convergence of the at. cluster expansion to meV accuracy. By introducing nonlinear functions of the at. cluster expansion an interat. potential is obtained that is comparable in accuracy to state-of-the-art machine learning potentials. Because of the efficient convergence of the at. cluster expansion relevant subspaces can be sampled uniformly and exhaustively. This is demonstrated by testing against a large database of d. functional theory calcns. for copper.
  47. 47
    Batzner, S.; Musaelian, A.; Sun, L.; Geiger, M.; Mailoa, J. P.; Kornbluth, M.; Molinari, N.; Smidt, T. E.; Kozinsky, B. E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nat. Commun. 2022, 13, 2453,  DOI: 10.1038/s41467-022-29939-5
    Google Scholar
    47
    E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
    Batzner, Simon; Musaelian, Albert; Sun, Lixin; Geiger, Mario; Mailoa, Jonathan P.; Kornbluth, Mordechai; Molinari, Nicola; Smidt, Tess E.; Kozinsky, Boris
    Nature Communications (2022), 13 (1), 2453CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
    This work presents Neural Equivariant Interat. Potentials (NequIP), an E(3)-equivariant neural network approach for learning interat. potentials from ab-initio calcns. for mol. dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of at. environments. The method achieves state-of-the-art accuracy on a challenging and diverse set of mols. and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chem. level of theory as ref. and enables high-fidelity mol. dynamics simulations over long time scales.
  48. 48
    Schütt, K., Unke, O., Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. International Conference on Machine Learning 2021, 9377– 9388.
    Google Scholar
    There is no corresponding record for this reference.
  49. 49
    Haghighatlari, M.; Li, J.; Guan, X.; Zhang, O.; Das, A.; Stein, C. J.; Heidar-Zadeh, F.; Liu, M.; Head-Gordon, M.; Bertels, L.; Hao, H.; Leven, I.; Head-Gordon, T. NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces. Digital Discovery 2022, 1, 333– 343,  DOI: 10.1039/D2DD00008C
    Google Scholar
    49
    NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces
    Haghighatlari, Mojtaba; Li, Jie; Guan, Xingyi; Zhang, Oufan; Das, Akshaya; Stein, Christopher J.; Heidar-Zadeh, Farnaz; Liu, Meili; Head-Gordon, Martin; Bertels, Luke; Hao, Hongxia; Leven, Itai; Head-Gordon, Teresa
    Digital Discovery (2022), 1 (3), 333-343CODEN: DDIIAI; ISSN:2635-098X. (Royal Society of Chemistry)
    We report a new deep learning message passing network that takes inspiration from Newton's equations of motion to learn interat. potentials and forces. With the advantage of directional information from trainable force vectors, and physics-infused operators that are inspired by Newtonian physics, the entire model remains rotationally equivariant, and many-body interactions are inferred by more interpretable phys. features. We test NewtonNet on the prediction of several reactive and non-reactive high quality ab initio data sets including single small mols., a large set of chem. diverse mols., and methane and hydrogen combustion reactions, achieving state-of-the-art test performance on energies and forces with far greater data and computational efficiency than other deep learning models.
  50. 50
    Musaelian, A.; Batzner, S.; Johansson, A.; Sun, L.; Owen, C. J.; Kornbluth, M.; Kozinsky, B. Learning local equivariant representations for large-scale atomistic dynamics. Nat. Commun. 2023, 14, 579,  DOI: 10.1038/s41467-023-36329-y
    Google Scholar
    50
    Learning local equivariant representations for large-scale atomistic dynamics
    Musaelian, Albert; Batzner, Simon; Johansson, Anders; Sun, Lixin; Owen, Cameron J.; Kornbluth, Mordechai; Kozinsky, Boris
    Nature Communications (2023), 14 (1), 579CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
    A simultaneously accurate and computationally efficient parametrization of the potential energy surface of mols. and materials is a long-standing goal in the natural sciences. While atom-centered message passing neural networks (MPNNs) have shown remarkable accuracy, their information propagation has limited the accessible length-scales. Local methods, conversely, scale to large simulations but have suffered from inferior accuracy. This work introduces Allegro, a strictly local equivariant deep neural network interat. potential architecture that simultaneously exhibits excellent accuracy and scalability. Allegro represents a many-body potential using iterated tensor products of learned equivariant representations without atom-centered message passing. Allegro obtains improvements over state-of-the-art methods on QM9 and revMD17. A single tensor product layer outperforms existing deep MPNNs and transformers on QM9. Furthermore, Allegro displays remarkable generalization to out-of-distribution data. Mol. simulations using Allegro recover structural and kinetic properties of an amorphous electrolyte in excellent agreement with ab-initio simulations. Finally, we demonstrate parallelization with a simulation of 100 million atoms.
  51. 51
    Zhang, L.; Han, J.; Wang, H.; Saidi, W. A.; Car, R.; Weinan, E.: Red Hook, NY, USA, 2018, pp 4441– 4451. End-to-End Symmetry Preserving Inter-Atomic Potential Energy Model for Finite and Extended Systems Proceedings of the 32nd International Conference on Neural Information Processing Systems
    Google Scholar
    There is no corresponding record for this reference.
  52. 52
    Wang, H.; Zhang, L.; Han, J.; E, W. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun. 2018, 228, 178– 184,  DOI: 10.1016/j.cpc.2018.03.016
    Google Scholar
    52
    DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
    Wang, Han; Zhang, Linfeng; Han, Jiequn; E, Weinan
    Computer Physics Communications (2018), 228 (), 178-184CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    A review. Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-vs.-efficiency dilemma in mol. simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform mol. dynamics. Potential applications of DeePMD-kit span from finite mols. to extended systems and from metallic systems to chem. bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical mol. dynamics and quantum (path-integral) mol. dynamics packages, i.e., LAMMPS and the i-PI, resp. Thus, upon training, the potential energy and force field models can be used to perform efficient mol. simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interat. potential energy and forces of a water model using data obtained from d. functional theory. We demonstrate that the resulted mol. dynamics model reproduces accurately the structural information contained in the original model.Program Title: DeePMD-kitProgram Files doi:http://dx.doi.org/10.17632/hvfh9yvncf.1Licensing provisions: LGPLProgramming language: Python/C++Nature of problem: Modeling the many-body at. interactions by deep neural network models. Running mol. dynamics simulations with the models.Soln. method: The Deep Potential for Mol. Dynamics (DeePMD) method is implemented based on the deep learning framework TensorFlow. Supports for using a DeePMD model in LAMMPS and i-PI, for classical and quantum (path integral) mol. dynamics are provided.Addnl. comments including Restrictions and Unusual features: The code defines a data protocol such that the energy, force, and virial calcd. by different third-party mol. simulation packages can be easily processed and used as model training data.
  53. 53
    Kingma, D. P.; Ba, J. Adam: A Method for Stochastic Optimization. 2014, arXiv:1412.6980. https://arxiv.org/abs/1412.698web0.
    Google Scholar
    There is no corresponding record for this reference.
  54. 54
    Frauenheim, T.; Seifert, G.; Elsterner, M.; Hajnal, Z.; Jungnickel, G.; Porezag, D.; Suhai, S.; Scholz, R. A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology. Phys. Status Solidi B 2000, 217, 41– 62,  DOI: 10.1002/(SICI)1521-3951(200001)217:1<41::AID-PSSB41>3.0.CO;2-V
    Google Scholar
    54
    A self-consistent charge density-functional based tight-binding method for predictive materials simulations in physics, chemistry, and biology
    Frauenheim, T.; Seifert, G.; Elstner, M.; Hajnal, Z.; Jungnickel, G.; Porezag, D.; Suhai, S.; Scholz, R.
    Physica Status Solidi B: Basic Research (2000), 217 (1), 41-62CODEN: PSSBBD; ISSN:0370-1972. (Wiley-VCH Verlag Berlin GmbH)
    We outline recent developments in quantum mech. atomistic modeling of complex materials properties that combine the efficiency of semi-empirical quantum-chem. and tight-binding approaches with the accuracy and transferability of more sophisticated d.-functional and post-Hartree-Fock methods with the aim to perform highly predictive materials simulations of technol. relevant sizes in physics, chem., and biol. Following Harris, Foulkes, and Haydock, the methods are based on an expansion of the Kohn-Sham total energy in d.-functional theory (DFT) with respect to charge d. fluctuations at a given ref. d. While the zeroth order approach is equiv. to a common std. non-self-consistent tight-binding (TB) scheme, at 2nd order by variationally treating the approx. Kohn-Sham energy a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements may be derived. These matrix elements are modified by a self-consistent redistribution of Mulliken charges (SCC). Besides the usual band-structure and short-range repulsive terms the final approx. Kohn-Sham energy explicitly includes Coulomb interaction between charge fluctuations. The new SCC scheme is shown to successfully apply to problems, where deficiencies within the non-SCC std. TB-approach become obvious. These cover defect calcns. and surface studies in polar semiconductors (see M. Haugk et al. of this special issue), spectroscopic studies of org. light-emitting thin films, briefly outlined in the present article, and atomistic investigations of biomols. (see M. Elstner et al. of this special issue).
  55. 55
    VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 2005, 167, 103– 128,  DOI: 10.1016/j.cpc.2004.12.014
    Google Scholar
    55
    QUICKSTEP: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
    VandeVondele, Joost; Krack, Matthias; Mohamed, Fawzi; Parrinello, Michele; Chassaing, Thomas; Hutter, Juerg
    Computer Physics Communications (2005), 167 (2), 103-128CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    We present the Gaussian and plane waves (GPW) method and its implementation in which is part of the freely available program package CP2K. The GPW method allows for accurate d. functional calcns. in gas and condensed phases and can be effectively used for mol. dynamics simulations. We show how derivs. of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calcns. for single mols. and plane wave based calcns. in the condensed phase is excellent. Wave function optimization with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the d. matrix. We illustrate these findings with calcns. using commodity PCs as well as supercomputers.
  56. 56
    Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. cp2k: atomistic simulations of condensed matter systems. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4, 15– 25,  DOI: 10.1002/wcms.1159
    Google Scholar
    56
    cp2k: atomistic simulations of condensed matter systems
    Hutter, Juerg; Iannuzzi, Marcella; Schiffmann, Florian; VandeVondele, Joost
    Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (1), 15-25CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
    A review. Cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15-25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website.
  57. 57
    Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098– 3100,  DOI: 10.1103/PhysRevA.38.3098
    Google Scholar
    57
    Density-functional exchange-energy approximation with correct asymptotic behavior
    Becke, A. D.
    Physical Review A: Atomic, Molecular, and Optical Physics (1988), 38 (6), 3098-100CODEN: PLRAAN; ISSN:0556-2791.
    Current gradient-cor. d.-functional approxns. for the exchange energies of at. and mol. systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy d. A gradient-cor. exchange-energy functional is given with the proper asymptotic limit. This functional, contg. only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of at. systems with remarkable accuracy, surpassing the performance of previous functionals contg. two parameters or more.
  58. 58
    Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785– 789,  DOI: 10.1103/PhysRevB.37.785
    Google Scholar
    58
    Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
    Lee, Chengteh; Yang, Weitao; Parr, Robert G.
    Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.
    A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
  59. 59
    Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
    Google Scholar
    59
    A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
    Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
    Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
  60. 60
    Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 1996, 54, 1703– 1710,  DOI: 10.1103/PhysRevB.54.1703
    Google Scholar
    60
    Separable dual-space Gaussian pseudopotentials
    Goedecker, S.; Teter, M.; Hutter, J.
    Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
  61. 61
    Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic separable dual-space Gaussian pseudopotentials from H to Rn. Phys. Rev. B 1998, 58, 3641– 3662,  DOI: 10.1103/PhysRevB.58.3641
    Google Scholar
    61
    Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
    Hartwigsen, C.; Goedecker, S.; Hutter, J.
    Physical Review B: Condensed Matter and Materials Physics (1998), 58 (7), 3641-3662CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole Periodic Table, and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real-space grid, it is highly accurate, and, due to its analytic form, it can be specified by a very small no. of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of mol. calcns.
  62. 62
    Smith, J. S.; Nebgen, B.; Lubbers, N.; Isayev, O.; Roitberg, A. E. Less is more: Sampling chemical space with active learning. J. Chem. Phys. 2018, 148, 241733,  DOI: 10.1063/1.5023802
    Google Scholar
    62
    Less is more: Sampling chemical space with active learning
    Smith, Justin S.; Nebgen, Ben; Lubbers, Nicholas; Isayev, Olexandr; Roitberg, Adrian E.
    Journal of Chemical Physics (2018), 148 (24), 241733/1-241733/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The development of accurate and transferable machine learning (ML) potentials for predicting mol. energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chem. space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach, we develop the COmprehensive Machine-learning Potential (COMP6) benchmark (publicly available on GitHub) which contains a diverse set of org. mols. Active learning-based ANI potentials outperform the original random sampled ANI-1 potential with only 10% of the data, while the final active learning-based model vastly outperforms ANI-1 on the COMP6 benchmark after training to only 25% of the data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single mols. or materials, while remaining applicable to the general class of org. mols. composed of the elements CHNO. (c) 2018 American Institute of Physics.
  63. 63
    Podryabinkin, E. V.; Shapeev, A. V. Active learning of linearly parametrized interatomic potentials. Comput. Mater. Sci. 2017, 140, 171– 180,  DOI: 10.1016/j.commatsci.2017.08.031
    Google Scholar
    63
    Active learning of linearly parametrized interatomic potentials
    Podryabinkin, Evgeny V.; Shapeev, Alexander V.
    Computational Materials Science (2017), 140 (), 171-180CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)
    This paper introduces an active learning approach to the fitting of machine learning interat. potentials. Our approach is based on the D-optimality criterion for selecting at. configurations on which the potential is fitted. It is shown that the proposed active learning approach is highly efficient in training potentials on the fly, ensuring that no extrapolation is attempted and leading to a completely reliable atomistic simulation without any significant decrease in accuracy. We apply our approach to mol. dynamics and structure relaxation, and we argue that it can be applied, in principle, to any other type of atomistic simulation. The software, test cases, and examples of usage are published at http://gitlab.skoltech.ru/shapeev/mlip/.
  64. 64
    Peterson, A. A.; Christensen, R.; Khorshidi, A. Addressing uncertainty in atomistic machine learning. Phys. Chem. Chem. Phys. 2017, 19, 10978– 10985,  DOI: 10.1039/C7CP00375G
    Google Scholar
    64
    Addressing uncertainty in atomistic machine learning
    Peterson, Andrew A.; Christensen, Rune; Khorshidi, Alireza
    Physical Chemistry Chemical Physics (2017), 19 (18), 10978-10985CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Machine-learning regression has been demonstrated to precisely emulate the potential energy and forces that are output from more expensive electronic-structure calcns. However, to predict new regions of the potential energy surface, an assessment must be made of the credibility of the predictions. In this perspective, we address the types of errors that might arise in atomistic machine learning, the unique aspects of atomistic simulations that make machine-learning challenging, and highlight how uncertainty anal. can be used to assess the validity of machine-learning predictions. We suggest this will allow researchers to more fully use machine learning for the routine acceleration of large, high-accuracy, or extended-time simulations. In our demonstrations, we use a bootstrap ensemble of neural network-based calculators, and show that the width of the ensemble can provide an est. of the uncertainty when the width is comparable to that in the training data. Intriguingly, we also show that the uncertainty can be localized to specific atoms in the simulation, which may offer hints for the generation of training data to strategically improve the machine-learned representation.
  65. 65
    Zhang, Y.; Wang, H.; Chen, W.; Zeng, J.; Zhang, L.; Wang, H. .. DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models. Comput. Phys. Commun. 2020, 253, 107206,  DOI: 10.1016/j.cpc.2020.107206
    Google Scholar
    65
    DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models
    Zhang, Yuzhi; Wang, Haidi; Chen, Weijie; Zeng, Jinzhe; Zhang, Linfeng; Wang, Han; E, Weinan
    Computer Physics Communications (2020), 253 (), 107206CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    In recent years, promising deep learning based interat. potential energy surface (PES) models have been proposed that can potentially allow us to perform mol. dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed "on-the-fly" learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN. Program Title: DP-GENProgram Files doi:http://dx.doi.org/10.17632/sxybkgc5xc.1Licensing provisions: LGPLProgramming language: PythonNature of problem: Generating reliable deep learning based potential energy models with minimal human intervention and computational cost. Soln. method: The concurrent learning scheme is implemented. Supports for sampling configuration space with LAMMPS, generating ab initio data with Quantum Espresso, VASP, CP2K and training potential models with DeePMD-kit are provided. Supports for different machines including workstations, high performance clusters and cloud machines are provided. Supports for job management tools including Slurm, PBS, LSF are provided.
  66. 66
    Thompson, A. P.; Aktulga, H. M.; Berger, R.; Bolintineanu, D. S.; Brown, W. M.; Crozier, P. S.; in ’t Veld, P. J.; Kohlmeyer, A.; Moore, S. G.; Nguyen, T. D.; Shan, R.; Stevens, M. J.; Tranchida, J.; Trott, C.; Plimpton, S. J. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 2022, 271, 108171,  DOI: 10.1016/j.cpc.2021.108171
    Google Scholar
    66
    LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales
    Thompson, Aidan P.; Aktulga, H. Metin; Berger, Richard; Bolintineanu, Dan S.; Brown, W. Michael; Crozier, Paul S.; in 't Veld, Pieter J.; Kohlmeyer, Axel; Moore, Stan G.; Nguyen, Trung Dac; Shan, Ray; Stevens, Mark J.; Tranchida, Julien; Trott, Christian; Plimpton, Steven J.
    Computer Physics Communications (2022), 271 (), 108171CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    Since the classical mol. dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from at. to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interat. potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interat. potentials.Program Title: Large-scale Atomic/Mol. Massively Parallel Simulator (LAMMPS)CPC Library link to program files:https://doi.org/10.17632/cxbxs9btsv.1Developer's repository link:https://github.com/lammps/lammpsLicensing provisions: GPLv2Programming language: C++, Python, C, FortranSupplementary material:https://www.lammps.orgNature of problem: Many science applications in physics, chem., materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from at. to mesoscale to macroscopic.Soln. method: The LAMMPS code uses parallel spatial decompn., distributed neighbor lists, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Stormer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addn., LAMMPS supports a wide range of interat. potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features.Addnl. comments including restrictions and unusual features: This paper serves as the definitive ref. for the LAMMPS code.S. Plimpton, Fast parallel algorithms for short-range mol. dynamics. Phys. 117 (1995) 1-19.L. Verlet, Computer expts. on classical fluids: I. Thermodynamical properties of Lennard-Jones mols., Phys. Rev. 159 (1967) 98-103.
  67. 67
    Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant pressure molecular dynamics algorithms. J. Chem. Phys. 1994, 101, 4177– 4189,  DOI: 10.1063/1.467468
    Google Scholar
    67
    Constant pressure molecular dynamics algorithms
    Martyna, Glenn J.; Tobias, Douglas J.; Klein, Michael L.
    Journal of Chemical Physics (1994), 101 (5), 4177-89CODEN: JCPSA6; ISSN:0021-9606.
    Modularly invariant equations of motion are derived that generate the isothermal-isobaric ensemble as their phase space avs. Isotropic vol. fluctuations and fully flexible simulation cells as well as a hybrid scheme that naturally combines the two motions are considered. The resulting methods are tested on two problems, a particle in a one-dimensional periodic potential and a spherical model of C60 in the solid/fluid phase.
  68. 68
    Agieienko, V.; Buchner, R. Densities, Viscosities, and Electrical Conductivities of Pure Anhydrous Reline and Its Mixtures with Water in the Temperature Range (293.15 to 338.15) K. J. Chem. Eng. Data 2019, 64, 4763– 4774,  DOI: 10.1021/acs.jced.9b00145
    Google Scholar
    68
    Densities, Viscosities, and Electrical Conductivities of Pure Anhydrous Reline and Its Mixtures with Water in the Temperature Range (293.15 to 338.15) K
    Agieienko, Vira; Buchner, Richard
    Journal of Chemical & Engineering Data (2019), 64 (11), 4763-4774CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
    D. (ρ), dynamic viscosity (η), and elec. cond. (κ) of the deep eutectic solvent (DES) reline, composed of choline chloride (ChCl) and urea in a 1:2 molar ratio, and its mixts. with water, covering the entire miscibility range, were studied at T = (293.15 to 338.15) K. Compared to many previous studies, reline purity was significantly improved by using ultrapure urea and ChCl recrystd. from ethanol. For the investigated DES samples the mass fraction of residual water was <0.00035. This allowed checking the influence of water traces and impurities on the physicochem. properties of pure reline. It was found that the presence of small amts. of water (w(H2O) < 0.0081) only negligibly decreased reline d., not exceeding 0.14% compared to the dry sample. However, for the same amt. of water η decreased by ∼36% at 298.15 K. The temp. dependence of ρ was well fitted by a quadratic expression, whereas η(T) and κ(T) were found to follow the empirical Vogel-Fulcher-Tammann equation. For the aq. mixts. excess properties of molar volume (VE) and viscosity (ηE) showed only minor variation with compn., suggesting rather weak interactions between water and the constituents of reline. However, VE and ηE depended significantly on temp., indicating a significant contribution of H-bonding to the inherent reline structure. Similar to conventional ionic liqs., the cond. of aq. reline showed a broad max. at the reline mole fraction of x1 ≈ 0.18 assocd. with the border between aq. solns. of individual reline components and reline/water mixts. The Walden plot classifies reline as a poor ionic liq.
  69. 69
    Fu, X.; Wu, Z.; Wang, W.; Xie, T.; Keten, S.; Gomez-Bombarelli, R.; Jaakkola, T. Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations. 2022, arXiv:2210.07237. https://arxiv.org/abs/2210.0723web7.
    Google Scholar
    There is no corresponding record for this reference.
  70. 70
    Stocker, S.; Gasteiger, J.; Becker, F.; Günnemann, S.; Margraf, J. T. How robust are modern graph neural network potentials in long and hot molecular dynamics simulations?. Machine Learning: Science and Technology 2022, 3, 045010,  DOI: 10.1088/2632-2153/ac9955
    Google Scholar
    There is no corresponding record for this reference.
  71. 71
    McDaniel, J. G.; Choi, E.; Son, C. Y.; Schmidt, J. R.; Yethiraj, A. Ab Initio Force Fields for Imidazolium-Based Ionic Liquids. J. Phys. Chem. B 2016, 120, 7024– 7036, PMID: 27352240  DOI: 10.1021/acs.jpcb.6b05328
    Google Scholar
    71
    Ab Initio Force Fields for Imidazolium-Based Ionic Liquids
    McDaniel, Jesse G.; Choi, Eunsong; Son, Chang Yun; Schmidt, J. R.; Yethiraj, Arun
    Journal of Physical Chemistry B (2016), 120 (28), 7024-7036CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    We develop ab initio force fields for alkylimidazolium-based ionic liqs. (ILs) that predict the d., heats of vaporization, diffusion, and cond. that are in semiquant. agreement with exptl. data. These predictions are useful in light of the scarcity of and sometimes inconsistency in exptl. heats of vaporization and diffusion coeffs. We illuminate phys. trends in the liq. cohesive energy with cation chain length and anion. These trends are different than those based on the exptl. heats of vaporization. Mol. dynamics prediction of the room temp. dynamics of such ILs is more difficult than is generally realized in the literature due to large statistical uncertainties and sensitivity to subtle force field details. We believe that our developed force fields will be useful for correctly detg. the physics responsible for the structure/property relationships in neat ILs.
  72. 72
    Yeh, I.-C.; Hummer, G. System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions. J. Phys. Chem. B 2004, 108, 15873– 15879,  DOI: 10.1021/jp0477147
    Google Scholar
    72
    System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions
    Yeh, In-Chul; Hummer, Gerhard
    Journal of Physical Chemistry B (2004), 108 (40), 15873-15879CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    We study the system-size dependence of translational diffusion coeffs. and viscosities in mol. dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coeffs. increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N-1/3, where N is the no. of particles. For a cubic simulation box of length L, the diffusion coeff. cor. for system-size effects is D0 = DPBC + 2.837297kBT/(6πηL), where DPBC is the diffusion coeff. calcd. in the simulation, kB the Boltzmann const., T the abs. temp., and η the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quant. accounts for the system-size dependence of the calcd. self-diffusion coeffs. In contrast to diffusion coeffs., the shear viscosities of water and the LJ fluid show no significant system-size dependences.
  73. 73
    D’Agostino, C.; Harris, R. C.; Abbott, A. P.; Gladden, L. F.; Mantle, M. D. Molecular motion and ion diffusion in choline chloride based deep eutectic solvents studied by 1H pulsed field gradient NMR spectroscopy. Phys. Chem. Chem. Phys. 2011, 13, 21383– 21391,  DOI: 10.1039/c1cp22554e
    Google Scholar
    73
    Molecular motion and ion diffusion in choline chloride based deep eutectic solvents studied by 1H pulsed field gradient NMR spectroscopy
    D'Agostino, Carmine; Harris, Robert C.; Abbott, Andrew P.; Gladden, Lynn F.; Mantle, Mick D.
    Physical Chemistry Chemical Physics (2011), 13 (48), 21383-21391CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Deep Eutectic Solvents (DESs) are a novel class of solvents with potential industrial applications in sepn. processes, chem. reactions, metal recovery and metal finishing processes such as electrodeposition and electropolishing. Macroscopic phys. properties such as viscosity, cond., eutectic compn. and surface tension are already available for several DESs, but the microscopic transport properties for this class of compds. are not well understood and the literature lacks exptl. data that could give a better insight into the understanding of such properties. This paper presents the first pulsed field gradient NMR (PFG-NMR) study of DESs. Several choline chloride based DESs were chosen as exptl. samples, each of them with a different assocd. hydrogen bond donor. The mol. equil. self-diffusion coeff. of both the choline cation and hydrogen bond donor was probed using a std. stimulated echo PFG-NMR pulse sequence. The increasing temp. leads to a weaker interaction between the choline cation and the correspondent hydrogen bond donor. The self-diffusion coeffs. of the samples obey an Arrhenius law temp.-dependence, with values of self-diffusivity in the range of [10-10-10-13 m2 s-1]. The results also highlight that the mol. structure of the hydrogen bond donor can greatly affect the mobility of the whole system. While for ethaline, glyceline and reline the choline cation diffuses slower than the assocd. hydrogen bond donor, reflecting the trend of mol. size and mol. wt., the opposite behavior is obsd. for maline, in which the hydrogen bond donor, i.e. malonic acid, diffuses slower than the choline cation, with self-diffusion coeffs. values of the order of 10-13 m2 s-1 at room temp., which are remarkably low values for a liq. This is believed to be due to the formation of extensive dimer chains between malonic acid mols., which restricts the mobility of the whole system at low temp. (<30 °C), with malonic acid and choline chloride having almost identical diffusivity values. Diffusion and viscosity data were combined together to gain insights into the diffusion mechanism, which is the same as for ionic liqs. with discrete anions.
  74. 74
    Balucani, U.; Vallauri, R.; Murthy, C. S. Interparticle velocity correlations in simple liquids. J. Chem. Phys. 1982, 77, 3233– 3237,  DOI: 10.1063/1.444199
    Google Scholar
    74
    Interparticle velocity correlations in simple liquids
    Balucani, U.; Vallauri, R.; Murthy, C. S.
    Journal of Chemical Physics (1982), 77 (6), 3233-7CODEN: JCPSA6; ISSN:0021-9606.
    The momentum transfer of a test particle to a cluster of atoms initially in the first shell of neighbors is investigated at liq. densities by mol. dynamics methods. The comparison of the results obtained for Lennard-Jones and soft spheres models is discussed. In the short time regime, the interpretation of the data parallels that of the single particle velocity autocorrelation function. At longer times, a simple phys. model can account for the decay of the cross correlation in terms of the increasing no. of atoms involved in the process.
  75. 75
    Verdaguer, A.; Padró, J. A.; Trullàs, J. Molecular dynamics study of the velocity cross-correlations in liquids. J. Chem. Phys. 1998, 109, 228– 234,  DOI: 10.1063/1.476555
    Google Scholar
    75
    Molecular dynamics study of the velocity cross-correlations in liquids
    Verdaguer, A.; Padro, J. A.; Trullas, J.
    Journal of Chemical Physics (1998), 109 (1), 228-234CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Velocity cross-correlations for both soft-sphere fluids at different densities and temps. and a simple molten salt are investigated by mol. dynamics simulation. Time correlation functions between the velocity of a tagged particle and velocities of particles within specified ranges of initial sepns. are calcd. In the case of the soft-sphere fluids, sepn. ranges corresponding to the first, second and third shells of neighbors are considered, whereas up to six different shells are analyzed for the molten salt. The calcd. functions allow us to build a picture of the spread of the initial momentum of a tagged particle over the successive shells of neighbors. It is obsd. that collisions with intermediate particles are the main mechanism for the transfer of momentum. A balance between the momentum exchanged by particles in a given shell with those in the two adjacent shells should be carried out in order to analyze the resulting velocity cross-correlation functions. The rate of transfer of momentum between distant particles increases with the d. and temp. of the liq. It has been noticed an incipient coherence, which is more marked for the ionic melt, between the motions of atoms in nonadjacent shells.
  76. 76
    Balucani, U.; Vallauri, R.; Murthy, C. Momentum transfer analysis in Lennard-Jones fluids. Phys. Lett. A 1981, 84, 133– 136,  DOI: 10.1016/0375-9601(81)90736-2
    Google Scholar
    76
    Momentum transfer analysis in Lennard-Jones fluids
    Balucani, U.; Vallauri, R.; Murthy, C. S.
    Physics Letters A (1981), 84A (3), 133-6CODEN: PYLAAG; ISSN:0375-9601.
    For Ar with the atoms interacting via a Lennard-Jones potential (a) near the triple point and (b) in the gas phase (at intermediate d.) at room temp., the cross-correlation functions and the velocity autocorrelation functions (vacf) were obtained in mol.-dynamics simulations (with 108 Ar atoms), and were used to analyze momentum transfer between a test atom and its neighbors. The anal. provided information on the dynamic processes leading to the decay of the single-particle vacf.
  77. 77
    Endo, Y.; Endo, H. Microscopic motions and the local environments of atoms in simple liquids. J. Chem. Phys. 1984, 80, 2087– 2091,  DOI: 10.1063/1.446974
    Google Scholar
    77
    Microscopic motions and the local environments of atoms in simple liquids
    Endo, Yoshikazu; Endo, Homare
    Journal of Chemical Physics (1984), 80 (5), 2087-91CODEN: JCPSA6; ISSN:0021-9606.
    Mol. dynamics simulations are carried out in order to understand the microscopic mechanism of at. motions in simple liqs. The radial distribution function is classified into subgroups by taking a partial av. over the atoms having the same coordination no. in the first shell. By considering this classified distribution of atoms as an initial one, the time evolution of the radial distribution function, and the velocity auto- and cross-correlation functions are calcd. in each subgroup. Investigation through these "microscopic" correlation functions reveals the details of at. motions which would be obscured if the totally averaged correlation functions were used. An atom in a region of low local d. oscillates weakly for a long period, because the low-d. region is surrounded, on the av., by the high d. region of atoms. An atom in a region of high local d. receives a strong rebound from the neighboring atoms, but behaves less oscillatory at subsequent times, because the neighboring atoms more toward the outer region of low d.
  78. 78
    Flener, P.; Vesely, F. J. Correlated motion of two particles in a fluid. Mol. Phys. 1992, 77, 601– 615,  DOI: 10.1080/00268979200102651
    Google Scholar
    78
    Correlated motion of two particles in fluid. II. Molecular-dynamics results
    Flener, Peter; Vesely, Franz J.
    Molecular Physics (1992), 77 (4), 601-15CODEN: MOPHAM; ISSN:0026-8976.
    Conditional velocity cross correlation function of the form 〈vi(0vj(t);rij(0)〉 in the Lennard-Jones fluid are investigated by mol. dynamics simulation. As shown in previous work, these cross correlation functions may be related to memory functions in a similar manner as the usual velocity auto-correlation function. To compute the memory functions, a modified version of Detyna and Singer's algorithm has been used.
  79. 79
    Balucani, U.; Zoppi, M. Dynamics of the Liquid State; Clarendon Press, 1995; Vol. 10.
    Google Scholar
    There is no corresponding record for this reference.
  80. 80
    Verdaguer, A.; Padró, J. A. Computer simulation study of the velocity cross correlations between neighboring atoms in simple liquid binary mixtures. J. Chem. Phys. 2001, 114, 2738– 2744,  DOI: 10.1063/1.1340581
    Google Scholar
    80
    Computer simulation study of the velocity cross correlations between neighboring atoms in simple liquid binary mixtures
    Verdaguer, A.; Padro, J. A.
    Journal of Chemical Physics (2001), 114 (6), 2738-2744CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The dynamic behavior of atoms in simple liq. binary mixts. is analyzed by mol. dynamic simulation. Time correlation functions between the initial velocity of a tagged particle and latter velocities of neighboring particles are calcd. for soft-sphere liq. mixts. of species with different mass and/or size. The transfer of momentum from a tagged particle to its neighbors as well as the differences between the velocity cross correlation between particles of the same or different species is discussed.
  81. 81
    Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids, 3rd ed.; Hansen, J.-P., McDonald, I. R., Eds.; Academic Press: Burlington, 2006; pp 291– 340.
    Google Scholar
    There is no corresponding record for this reference.
  82. 82
    Rey-Castro, C.; Vega, L. F. Transport Properties of the Ionic Liquid 1-Ethyl-3-Methylimidazolium Chloride from Equilibrium Molecular Dynamics Simulation. The Effect of Temperature. J. Phys. Chem. B 2006, 110, 14426– 14435, PMID: 16854152  DOI: 10.1021/jp062885s
    Google Scholar
    82
    Transport Properties of the Ionic Liquid 1-Ethyl-3-Methylimidazolium Chloride from Equilibrium Molecular Dynamics Simulation. The Effect of Temperature
    Rey-Castro, Carlos; Vega, Lourdes F.
    Journal of Physical Chemistry B (2006), 110 (29), 14426-14435CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    We present here equil. mol. dynamics simulation results for self-diffusion coeffs., shear viscosity, and elec. cond. in a model ionic liq. (1-ethyl-3-methylimidazolium chloride) at different temps. The Green-Kubo relations were employed to evaluate the transport coeffs. When compared with available exptl. data, the model underestimates the cond. and self-diffusion, whereas the viscosity is overpredicted, showing only a semiquant. agreement with exptl. data. These discrepancies are explained on the basis of the rigidity and lack of polarizability of the model. Despite this, the exptl. trends with temp. are remarkably well reproduced, with a good agreement on the activation energies when available. No significant deviations from the Nernst-Einstein relation can be assessed on the basis of the statistical uncertainty of the simulations, although the comparison between the elec. current and the velocity autocorrelation functions suggests some degree of cross-correlation among ions in a short time scale. The simulations reproduce remarkably well the slope of the Walden plots obtained from exptl. data of 1-ethyl-3-methylimidazolium chloride, confirming that temp. does not alter appreciably the extent of ion pairing.
  83. 83
    Reuter, D.; Binder, C.; Lunkenheimer, P.; Loidl, A. Ionic conductivity of deep eutectic solvents: the role of orientational dynamics and glassy freezing. Phys. Chem. Chem. Phys. 2019, 21, 6801– 6809,  DOI: 10.1039/C9CP00742C
    Google Scholar
    83
    Ionic conductivity of deep eutectic solvents: the role of orientational dynamics and glassy freezing
    Reuter, Daniel; Binder, Catharina; Lunkenheimer, Peter; Loidl, Alois
    Physical Chemistry Chemical Physics (2019), 21 (13), 6801-6809CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    We have performed a thorough examn. of the reorientational relaxation dynamics and the ionic charge transport of three typical deep eutectic solvents, ethaline, glyceline and reline, by using broadband dielec. spectroscopy. Our expts. cover a broad temp. range from the low-viscosity liq. down to the deeply supercooled state, allowing us to investigate the significant influence of glassy freezing on the ionic charge transport in these systems. In addn., we provide evidence for a close coupling of the ionic cond. in these materials to reorientational dipolar motions, which should be considered when searching for deep eutectic solvents optimized for electrochem. applications.
  84. 84
    Tan, A. R.; Urata, S.; Goldman, S.; Dietschreit, J. C. B.; Gómez-Bombarelli, R. Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles. 2023, arXiv:2305.01754 https://arxiv.org/abs/2305.0175web4.
    Google Scholar
    There is no corresponding record for this reference.
  85. 85
    Niblett, S. P.; Galib, M.; Limmer, D. T. Learning intermolecular forces at liquid–vapor interfaces. J. Chem. Phys. 2021, 155, 164101,  DOI: 10.1063/5.0067565
    Google Scholar
    85
    Learning intermolecular forces at liquid-vapor interfaces
    Niblett, Samuel P.; Galib, Mirza; Limmer, David T.
    Journal of Chemical Physics (2021), 155 (16), 164101CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    By adopting a perspective informed by contemporary liq.-state theory, we consider how to train an artificial neural network potential to describe inhomogeneous, disordered systems. We find that neural network potentials based on local representations of at. environments are capable of describing some properties of liq.-vapor interfaces but typically fail for properties that depend on unbalanced long-ranged interactions that build up in the presence of broken translation symmetry. These same interactions cancel in the translationally invariant bulk, allowing local neural network potentials to describe bulk properties correctly. By incorporating explicit models of the slowly varying long-ranged interactions and training neural networks only on the short-ranged components, we can arrive at potentials that robustly recover interfacial properties. We find that local neural network models can sometimes approx. a local mol. field potential to correct for the truncated interactions, but this behavior is variable and hard to learn. Generally, we find that models with explicit electrostatics are easier to train and have higher accuracy. We demonstrate this perspective in a simple model of an asym. dipolar fluid, where the exact long-ranged interaction is known, and in an ab initio water model, where it is approximated. (c) 2021 American Institute of Physics.
  86. 86
    Montes-Campos, H.; Carrete, J.; Bichelmaier, S.; Varela, L. M.; Madsen, G. K. H. A Differentiable Neural-Network Force Field for Ionic Liquids. J. Chem. Inf. Model. 2022, 62, 88– 101, PMID: 34941253  DOI: 10.1021/acs.jcim.1c01380
    Google Scholar
    86
    A Differentiable Neural-Network Force Field for Ionic Liquids
    Montes-Campos, Hadrian; Carrete, Jesus; Bichelmaier, Sebastian; Varela, Luis M.; Madsen, Georg K. H.
    Journal of Chemical Information and Modeling (2022), 62 (1), 88-101CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    We present NEURALIL, a model for the potential energy of an ionic liq. that accurately reproduces first-principles results with orders-of-magnitude savings in computational cost. Built on the basis of a multilayer perceptron and spherical Bessel descriptors of the at. environments, NEURALIL is implemented in such a way as to be fully automatically differentiable. It can thus be trained on ab initio forces instead of just energies, to make the most out of the available data, and can efficiently predict arbitrary derivs. of the potential energy. Using ethylammonium nitrate as the test system, we obtain out-of-sample accuracies better than 2 meV atom-1 ( < 0.05 kcal mol-1) in the energies and 70 meV Å-1 in the forces. We show that encoding the element-specific d. in the spherical Bessel descriptors is key to achieving this. Harnessing the information provided by the forces drastically reduces the amt. of at. configurations required to train a neural network force field based on atom-centered descriptors. We choose the Swish-1 activation function and discuss the role of this choice in keeping the neural network differentiable. Furthermore, the possibility of training on small data sets allows for an ensemble-learning approach to the detection of extrapolation. Finally, we find that a sep. treatment of long-range interactions is not required to achieve a high-quality representation of the potential energy surface of these dense ionic systems.

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  • Abstract

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    Figure 1

    Figure 1. Schematic representation of choline chloride (left) and urea (right) with the corresponding atom labels used throughout this study.

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    Figure 2

    Figure 2. Reference DFT energies and atomic forces are compared to the predicted values by the ML model for 50 test structures of a system of 304 atoms (left) and 684 atoms (right). The reference (ref) and predicted (pred) energies are standardized by subtracting their mean value from them.

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    Figure 3

    Figure 3. Comparison of the redial distribution functions from the FPMD simulation (dashed lines) and simulations using the MLIP (solid lines) for interactions with H4 and N1 of choline (top) and hydrogen atoms of urea HU (bottom). Atom labels are given in Figure 1.

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    Figure 4

    Figure 4. Center-of-mass velocity autocorrelation functions A(t) for the three components of the reline mixture from the reference FPMD simulations (dashed lines) are compared to the MLIP simulations (solid lines) for a mixture of 18 ChCl and 36 urea molecules at 375 K.

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    Figure 5

    Figure 5. Calculated values of self-diffusion coefficients for the three components of reline mixture from MD simulations (filled symbols) are plotted against the inverse of the simulation temperature and compared to the experimental values (empty symbols) of ref (73). Lines are the best exponential fits to the data used to obtain the activation energies listed in Table 2.

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    Figure 6

    Figure 6. Velocity cross-correlation functions NC(t) for the cation as the central particle (top), anion as the central particle (middle), and urea as the central particle (bottom). The dashed lines are the velocity autocorrelation functions A(t) of the cation (gray), anion (green), and urea (red). The cross-correlation functions for longer correlation times are presented in Figures S8–S10.

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    Figure 7

    Figure 7. Calculated values of ionic conductivity from MD simulations using our ML potential are plotted against the inverse of the simulation temperature and compared to the experimental values from refs (1), (68), and (83). Lines are the VFT fits to the data.

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  • References

    This article references 86 other publications.

    1. 1
      Abbott, A. P.; Capper, G.; Davies, D. L.; Rasheed, R. K.; Tambyrajah, V. Novel solvent properties of choline chloride/urea mixturesElectronic supplementary information (ESI) available: spectroscopic data. See http://www.rsc.org/suppdata/cc/b2/b210714g/. Chem. Commun. 2002, 70– 71,  DOI: 10.1039/b210714g
      There is no corresponding record for this reference.
    2. 2
      Zhang, Q.; De Oliveira Vigier, K.; Royer, S.; Jérôme, F. Deep eutectic solvents: syntheses, properties and applications. Chem. Soc. Rev. 2012, 41, 7108– 7146,  DOI: 10.1039/c2cs35178a
      2
      Deep eutectic solvents: Syntheses, properties and applications
      Zhang, Qinghua; De Oliveira Vigier, Karine; Royer, Sebastien; Jerome, Francois
      Chemical Society Reviews (2012), 41 (21), 7108-7146CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review. Within the framework of green chem., solvents occupy a strategic place. To be qualified as a green medium, these solvents have to meet different criteria such as availability, non-toxicity, biodegradability, recyclability, flammability, and low price among others. Up to now, the no. of available green solvents are rather limited. Here we wish to discuss a new family of ionic fluids, so-called Deep Eutectic Solvents (DES), that are now rapidly emerging in the current literature. A DES is a fluid generally composed of two or three cheap and safe components that are capable of self-assocn., often through hydrogen bond interactions, to form a eutectic mixt. with a m.p. lower than that of each individual component. DESs are generally liq. at temps. lower than 100 °C. These DESs exhibit similar physico-chem. properties to the traditionally used ionic liqs., while being much cheaper and environmentally friendlier. Owing to these remarkable advantages, DESs are now of growing interest in many fields of research. In this review, we report the major contributions of DESs in catalysis, org. synthesis, dissoln. and extn. processes, electrochem. and material chem. All works discussed in this review aim at demonstrating that DESs not only allow the design of eco-efficient processes but also open a straightforward access to new chems. and materials.
    3. 3
      Smith, E. L.; Abbott, A. P.; Ryder, K. S. Deep Eutectic Solvents (DESs) and Their Applications. Chem. Rev. 2014, 114, 11060– 11082, PMID: 25300631  DOI: 10.1021/cr300162p
      3
      Deep Eutectic Solvents (DESs) and Their Applications
      Smith, Emma L.; Abbott, Andrew P.; Ryder, Karl S.
      Chemical Reviews (Washington, DC, United States) (2014), 114 (21), 11060-11082CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      This article describes the phys. and chem. properties of deep eutectic solvents (DESs) and ionic liq. (ILs), and how their applications differ. DESs are now widely acknowledged as a new class of IL analogs because they share many characteristics and properties with ILs. The terms DES and IL have been used interchangeably in the literature, though it is necessary to point out that these are actually two different types of solvent. DESs are systems formed from a eutectic mixt. of Lewis or Bronsted acids and bases which can contain a variety of anionic and/or cationic species; in contrast, ILs are formed from systems composed primarily of one type of discrete anion and cation.
    4. 4
      Hansen, B. B.; Spittle, S.; Chen, B.; Poe, D.; Zhang, Y.; Klein, J. M.; Horton, A.; Adhikari, L.; Zelovich, T.; Doherty, B. W.; Gurkan, B.; Maginn, E. J.; Ragauskas, A.; Dadmun, M.; Zawodzinski, T. A.; Baker, G. A.; Tuckerman, M. E.; Savinell, R. F.; Sangoro, J. R. Deep Eutectic Solvents: A Review of Fundamentals and Applications. Chem. Rev. 2021, 121, 1232– 1285, PMID: 33315380  DOI: 10.1021/acs.chemrev.0c00385
      4
      Deep Eutectic Solvents: A Review of Fundamentals and Applications
      Hansen, Benworth B.; Spittle, Stephanie; Chen, Brian; Poe, Derrick; Zhang, Yong; Klein, Jeffrey M.; Horton, Alexandre; Adhikari, Laxmi; Zelovich, Tamar; Doherty, Brian W.; Gurkan, Burcu; Maginn, Edward J.; Ragauskas, Arthur; Dadmun, Mark; Zawodzinski, Thomas A.; Baker, Gary A.; Tuckerman, Mark E.; Savinell, Robert F.; Sangoro, Joshua R.
      Chemical Reviews (Washington, DC, United States) (2021), 121 (3), 1232-1285CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. Deep eutectic solvents (DESs) are an emerging class of mixts. characterized by significant depressions in m.ps. compared to those of the neat constituent components. These materials are promising for applications as inexpensive "designer" solvents exhibiting a host of tunable physicochem. properties. A detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding is postulated as the root cause of their m.p. depressions and physicochem. properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and expts. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework needed for a deeper understanding of DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies promising research thrusts aligned with the advancement of the field toward predictive models and fundamental understanding of these solvents.
    5. 5
      Abbott, A. P.; Capper, G.; Davies, D. L.; McKenzie, K. J.; Obi, S. U. Solubility of Metal Oxides in Deep Eutectic Solvents Based on Choline Chloride. J. Chem. Eng. Data 2006, 51, 1280– 1282,  DOI: 10.1021/je060038c
      5
      Solubility of Metal Oxides in Deep Eutectic Solvents Based on Choline Chloride
      Abbott, Andrew P.; Capper, Glen; Davies, David L.; McKenzie, Katy J.; Obi, Stephen U.
      Journal of Chemical & Engineering Data (2006), 51 (4), 1280-1282CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
      The soly. of 17 commonly available metal oxides in the elemental mass series Ti through Zn have been detd. in three ionic liqs. based on choline chloride. The hydrogen bond donors used were urea, malonic acid, and ethylene glycol. The results obtained are compared with aq. solns. of HCl and NaCl. Some correlation is obsd. between the soly. in the deep eutectic solvents and that in aq. solns. but some significant exceptions offer an opportunity for novel extractive metallurgical processes.
    6. 6
      Jenkin, G. R.; Al-Bassam, A. Z.; Harris, R. C.; Abbott, A. P.; Smith, D. J.; Holwell, D. A.; Chapman, R. J.; Stanley, C. J. The application of deep eutectic solvent ionic liquids for environmentally-friendly dissolution and recovery of precious metals. Miner. Eng. 2016, 87, 18– 24, Processing of Precious Metal Ores  DOI: 10.1016/j.mineng.2015.09.026
      6
      The application of deep eutectic solvent ionic liquids for environmentally-friendly dissolution and recovery of precious metals
      Jenkin, Gawen R. T.; Al-Bassam, Ahmed Z. M.; Harris, Robert C.; Abbott, Andrew P.; Smith, Daniel J.; Holwell, David A.; Chapman, Robert J.; Stanley, Christopher J.
      Minerals Engineering (2016), 87 (), 18-24CODEN: MENGEB; ISSN:0892-6875. (Elsevier Ltd.)
      The processing of ore by hydrometallurgy or pyrometallurgy typically has a high energy demand, and assocd. release of carbon dioxide. Thus there is a need to develop more energy-efficient and environmentally-compatible processes. This article demonstrates that deep eutectic solvent (DES) ionic liqs. provide one such method since they can be used to selectively dissolve and recover native gold and tellurium, sulfides and tellurides. Ionic liqs. are anhyd. salts that are liq. at low temp. They are powerful solvents and electrolytes with potential for high selectivity in both dissoln. and recovery. Deep eutectic solvents are a form of ionic liq. that are mixts. of salts such as choline chloride with hydrogen-bond donors such as urea. DESs are environmentally benign, yet chem. stable and, furthermore, the components are already produced in large quantities at comparable costs to conventional reagents. Electrum, galena and chalcopyrite, as well as tellurobismuthite (Bi2Te3), were sol. in DES through an oxidative leach at 45-50°C. Leaching rates detd. by a novel technique employing an optical profiler were very favorable in comparison to the current industrial process of cyanidation. Pyrite was notably insol. by an oxidative leach. However, pyrite, and indeed any other sulfide, could be selectively dissolved by electrolysis in a DES, thus suggesting a protocol whereby target inclusions could be liberated by electrolysis and then dissolved by subsequent oxidn. Ionometallurgy could thus offer a new set of environmentally-benign process for metallurgy.
    7. 7
      Söldner, A.; Zach, J.; König, B. Deep eutectic solvents as extraction media for metal salts and oxides exemplarily shown for phosphates from incinerated sewage sludge ash. Green Chem. 2019, 21, 321– 328,  DOI: 10.1039/C8GC02702A
      There is no corresponding record for this reference.
    8. 8
      Chakrabarti, M. H.; Mjalli, F. S.; AlNashef, I. M.; Hashim, M. A.; Hussain, M. A.; Bahadori, L.; Low, C. T. J. Prospects of applying ionic liquids and deep eutectic solvents for renewable energy storage by means of redox flow batteries. Renew. Sustain. Energy Rev. 2014, 30, 254– 270,  DOI: 10.1016/j.rser.2013.10.004
      8
      Prospects of applying ionic liquids and deep eutectic solvents for renewable energy storage by means of redox flow batteries
      Chakrabarti, Mohammed Harun; Mjalli, Farouq Sabri; Al Nashef, Inas Muen; Hashim, Mohd. Ali; Hussain, Mohd. Azlan; Bahadori, Laleh; Low, Chee Tong John
      Renewable & Sustainable Energy Reviews (2014), 30 (), 254-270CODEN: RSERFH; ISSN:1364-0321. (Elsevier Ltd.)
      A review. Ionic liqs. (ILs) and deep eutectic solvents (DESs) have been applied in various fields such as electrolytes for lithium ion batteries, electrodeposition, electropolishing and even in fuel cells. ILs and molten salts have found some applications in redox flow batteries (RFBs) in the past and recently some metal ion based ILs have been proposed and used by Sandia National Labs. In addn., only two papers have very recently reported on the application of DESs for the same. This review gives an overview on DESs and discusses the possibility of employing them in RFBs for renewable energy storage and utility-scale load leveling applications. Commencing with a discussion on energy storage technologies and the RFB, this paper goes on to provide an account on ILs and DESs as well as their applications in electrochem. and energy conversion. A succinct discussion on the results of Sandia National Labs. on using ILs as electrolytes for RFBs is provided building onto the feasibility of replacing ILs with DESs in the near future (based upon recent publications on the topic).
    9. 9
      Cong, G.; Lu, Y.-C. Organic Eutectic Electrolytes for Future Flow Batteries. Chem 2018, 4, 2732– 2734,  DOI: 10.1016/j.chempr.2018.11.018
      9
      Organic Eutectic Electrolytes for Future Flow Batteries
      Cong, Guangtao; Lu, Yi-Chun
      Chem (2018), 4 (12), 2732-2734CODEN: CHEMVE; ISSN:2451-9294. (Cell Press)
      In this issue of Chem, Yu and coworkers report phthalimide-based eutectic anolytes, which achieved a high concn. and enhanced redox reversibility. The org.-mol.-based eutectic electrolytes take advantages of both the superior tunability of the org. mol. and the high molar concn. of the redox-active mols. of the eutectic solvents. With combined computational and exptl. anal., this work demonstrates that forming eutectic electrolytes with self-contg. redox-active orgs. is a promising strategy for the future development of high-energy-d. redox-flow batteries.
    10. 10
      Radošević, K.; Cvjetko Bubalo, M.; Gaurina Srček, V.; Grgas, D.; Landeka Dragičević, T.; Radojčić Redovniković, I. Evaluation of toxicity and biodegradability of choline chloride based deep eutectic solvents. Ecotoxicol. Environ. Saf. 2015, 112, 46– 53,  DOI: 10.1016/j.ecoenv.2014.09.034
      10
      Evaluation of toxicity and biodegradability of choline chloride based deep eutectic solvents
      Radosevic, Kristina; Cvjetko Bubalo, Marina; Gaurina Srcek, Visnje; Grgas, Dijana; Landeka Dragicevic, Tibela; Radojcic Redovnikovic, Ivana
      Ecotoxicology and Environmental Safety (2015), 112 (), 46-53CODEN: EESADV; ISSN:0147-6513. (Elsevier B.V.)
      Deep eutectic solvents (DESs) have been dramatically expanding in popularity as a new generation of environmentally friendly solvents with possible applications in various industrial fields, but their ecol. footprint has not yet been thoroughly investigated. In the present study, three choline chloride-based DESs with glucose, glycerol and oxalic acid as hydrogen bond donors were evaluated for in vitro toxicity using fish and human cell line, phytotoxicity using wheat and biodegradability using wastewater microorganisms through closed bottle test. Obtained in vitro toxicity data on cell lines indicate that choline chloride: glucose and choline chloride:glycerol possess low cytotoxicity (EC50>10 mM for both cell lines) while choline chloride:oxalic acid possess moderate cytotoxicity (EC50 value 1.64 mM and 4.19 mM for fish and human cell line, resp.). Results on phytotoxicity imply that tested DESs are non-toxic with seed germination EC50 values higher than 5000 mg L-1. All tested DESs were classified as'readily biodegradable' based on their high levels of mineralization (68-96%). These findings indicate that DESs have a green profile and a good prospect for a wider use in the field of green technologies.
    11. 11
      Halder, A. K.; Cordeiro, M. N. D. S. Probing the Environmental Toxicity of Deep Eutectic Solvents and Their Components: An In Silico Modeling Approach. ACS Sustain. Chem. Eng. 2019, 7, 10649– 10660,  DOI: 10.1021/acssuschemeng.9b01306
      11
      Probing the Environmental Toxicity of Deep Eutectic Solvents and Their Components: An In Silico Modeling Approach
      Halder, Amit Kumar; Cordeiro, M. Natalia D. S.
      ACS Sustainable Chemistry & Engineering (2019), 7 (12), 10649-10660CODEN: ASCECG; ISSN:2168-0485. (American Chemical Society)
      Because of the increasing demand of greener solvents, deep eutectic solvents (DES) have just emerged as low-cost alternative solvents for a broad range of applications. However, recent toxicity assay studies showed a non-negligible toxic behavior for these solvents and their components. Alternative in silico-based approaches such as the one proposed here, multitasking-Quant. Structure Toxicity Relationships (mtk-QSTR), are increasingly used for risk assessment of chems. to speed up policy decisions. This work reports a mtk-QSTR modeling of 572 DES and their components under multiple exptl. conditions. To set up a reliable model from such data, the authors examd. here the use of 0D-2D descriptors along with classification anal., and the Box-Jenkins approach. This procedure led to a final mtk-QSTR model with high overall accuracy and predictivity (∼90%). The model highlights also the crucial role that polarizability, electronegativity, hydrogen-bond donor (HBD), and topol. properties play into the DES toxicity. Furthermore, with the help of the derived mtk-QSTR model, 30 different HBD components were ranked on the basis of their toxic contributions to DES. More importantly, the proposed in silico modeling approach is shown to be a valuable tool to mine relevant STR information, therefore guiding the rational design of potentially safe DES.
    12. 12
      Khandelwal, S.; Tailor, Y. K.; Kumar, M. Deep eutectic solvents (DESs) as eco-friendly and sustainable solvent/catalyst systems in organic transformations. J. Mol. Liq. 2016, 215, 345– 386,  DOI: 10.1016/j.molliq.2015.12.015
      12
      Deep eutectic solvents (DESs) as eco-friendly and sustainable solvent/catalyst systems in organic transformations
      Khandelwal, Sarita; Tailor, Yogesh Kumar; Kumar, Mahendra
      Journal of Molecular Liquids (2016), 215 (), 345-386CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
      A review. The use of environmentally benign and inexpensive DES as solvent and catalyst in the field of org. chem was discussed.
    13. 13
      Zahn, S. Deep eutectic solvents: similia similibus solvuntur?. Phys. Chem. Chem. Phys. 2017, 19, 4041– 4047,  DOI: 10.1039/C6CP08017K
      13
      Deep eutectic solvents: similia similibus solvuntur?
      Zahn, Stefan
      Physical Chemistry Chemical Physics (2017), 19 (5), 4041-4047CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Deep eutectic solvents, mixts. of an org. compd. and a salt with a deep eutectic m.p., are promising cheap and eco-friendly alternatives to ionic liqs. Ab initio mol. dynamics simulations of reline, a mixt. consisting of urea and choline chloride, reveal that not solely hydrogen bonds allow similar interactions between both constituents. The chloride anion and the oxygen atom of urea also show a similar spatial distribution close to the cationic core of choline due to a similar charge located on both atoms. As a result of multiple similar interactions, clusters migrating together cannot be obsd. in reline which supports the hypothesis similia similibus solvuntur. In contrast to previous suggestions, the interaction of the hydroxyl group of choline with a hydrogen bond acceptor is overall rigid. Fast hydrogen bond acceptor dynamics is facilitated by the hydrogen atoms in the trans position to the carbonyl group of urea which contributes to the low m.p. of reline.
    14. 14
      Stefanovic, R.; Ludwig, M.; Webber, G. B.; Atkin, R.; Page, A. J. Nanostructure, hydrogen bonding and rheology in choline chloride deep eutectic solvents as a function of the hydrogen bond donor. Phys. Chem. Chem. Phys. 2017, 19, 3297– 3306,  DOI: 10.1039/C6CP07932F
      14
      Nanostructure, hydrogen bonding and rheology in choline chloride deep eutectic solvents as a function of the hydrogen bond donor
      Stefanovic, Ryan; Ludwig, Michael; Webber, Grant B.; Atkin, Rob; Page, Alister J.
      Physical Chemistry Chemical Physics (2017), 19 (4), 3297-3306CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Deep eutectic solvents (DESs) are a mixt. of a salt and a mol. hydrogen bond donor, which form a eutectic liq. with a depressed m.p. Quantum mech. mol. dynamics (QM/MD) simulations were used to probe the 1 : 2 choline chloride-urea (ChCl : U), choline chloride-ethylene glycol (ChCl : EG) and choline chloride-glycerol (ChCl : Gly) DESs. DES nanostructure and interactions between the ions is used to rationalise differences in DES eutectic point temps. and viscosity. Simulations show that the structure of the bulk hydrogen bond donor is largely preserved for hydroxyl based hydrogen bond donors (ChCl:Gly and ChCl:EG), resulting in a smaller m.p. depression. By contrast, ChCl:U exhibits a well-established hydrogen bond network between the salt and hydrogen bond donor, leading to a larger m.p. depression. This extensive hydrogen bond network in ChCl:U also leads to substantially higher viscosity, compared to ChCl:EG and ChCl:Gly. Of the two hydroxyl based DESs, ChCl:Gly also exhibits a higher viscosity than ChCl:EG. This is attributed to the over-satn. of hydrogen bond donor groups in the ChCl:Gly bulk, which leads to more extensive hydrogen bond donor self-interaction and hence higher cohesive forces within the bulk liq.
    15. 15
      Fetisov, E. O.; Harwood, D. B.; Kuo, I.-F. W.; Warrag, S. E. E.; Kroon, M. C.; Peters, C. J.; Siepmann, J. I. First-Principles Molecular Dynamics Study of a Deep Eutectic Solvent: Choline Chloride/Urea and Its Mixture with Water. J. Phys. Chem. B 2018, 122, 1245– 1254, PMID: 29200290  DOI: 10.1021/acs.jpcb.7b10422
      15
      First-Principles Molecular Dynamics Study of a Deep Eutectic Solvent: Choline Chloride/Urea and Its Mixture with Water
      Fetisov, Evgenii O.; Harwood, David B.; Kuo, I-Feng William; Warrag, Samah E. E.; Kroon, Maaike C.; Peters, Cor J.; Siepmann, J. Ilja
      Journal of Physical Chemistry B (2018), 122 (3), 1245-1254CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      First principles mol. dynamics simulations in the canonical ensemble at temps. of 333 and 363 K and at the corresponding exptl. densities are carried out to investigate the behavior of the 1:2 choline chloride/urea (reline) deep eutectic solvent and its equimolar mixt. with water. Anal. of atom-atom radial and spatial distribution functions and of the H-bond network reveals the microheterogeneous structure of these complex liq. mixts. In neat reline, the structure is governed by strong H-bonds of the trans- and cis-H atoms of urea to the chloride ion. In hydrous reline, water competes for the anions, and the H atoms of urea have similar propensities to bond to the chloride ions and the O atoms of urea and water. The vibrational spectra exhibit relatively broad peaks reflecting the heterogeneity of the environment. Although the 100-ps trajectories allow only for a qual. assessment of transport properties, the simulations indicate that water is more mobile than the other species and its addn. also fosters faster motion of urea.
    16. 16
      Perkins, S. L.; Painter, P.; Colina, C. M. Molecular Dynamic Simulations and Vibrational Analysis of an Ionic Liquid Analogue. J. Phys. Chem. B 2013, 117, 10250– 10260, PMID: 23915257  DOI: 10.1021/jp404619x
      16
      Molecular Dynamic Simulations and Vibrational Analysis of an Ionic Liquid Analogue
      Perkins, Sasha L.; Painter, Paul; Colina, Coray M.
      Journal of Physical Chemistry B (2013), 117 (35), 10250-10260CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Atomistic mol. dynamics simulations have been performed over a range of temps. for the 1:2 choline chloride-urea mixt. using different force field modifications. Good agreement was achieved between simulated d., vol. expansion coeff., heat capacity, and diffusion coeffs. and exptl. values in order to validate the best performing force field. Atom-atom and center-of-mass radial distribution functions are discussed in order to understand the atomistic interactions involved in this eutectic mixt. Exptl. IR spectra are also reported for choline chloride-urea mixts., and band assignments are discussed. The distribution of hydrogen-bond interactions from mol. simulations is correlated to curve-resolved bands from the IR spectra. This work suggests that there is a strong interaction between the NH2 of urea and the chlorine anion where the system wants to maximize the no. of hydrogen bonds to the anion. Addnl., the disappearance of free carbonyl groups upon increasing concns. of urea suggests that at low urea concns., urea will preferentially interact with the anion through the NH2 groups. As this concn. increases, the complex remains but with addnl. interactions that remove the free carbonyl band from the spectra. The results from both mol. simulations and exptl. IR spectroscopy support the idea that key interactions between the moieties in the eutectic mixt. interrupt the main interactions within the parent substances and are responsible for the decrease in f.p.
    17. 17
      Doherty, B.; Acevedo, O. OPLS Force Field for Choline Chloride-Based Deep Eutectic Solvents. J. Phys. Chem. B 2018, 122, 9982– 9993, PMID: 30125108  DOI: 10.1021/acs.jpcb.8b06647
      17
      OPLS Force Field for Choline Chloride-Based Deep Eutectic Solvents
      Doherty, Brian; Acevedo, Orlando
      Journal of Physical Chemistry B (2018), 122 (43), 9982-9993CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Deep eutectic solvents (DES) are a class of solvents frequently composed of choline chloride and a neutral hydrogen bond donor (HBD) at ratios of 1:1, 1:2, or 1:3, resp. As cost-effective and eco-friendly solvents, DESs have gained considerable popularity in multiple fields, including materials, sepns., and nanotechnol. In the present work, a comprehensive set of transferable parameters have been fine-tuned to accurately reproduce bulk-phase phys. properties and local intermol. interactions for 8 different choline chloride-based DESs. This nonpolarizable force field, OPLS-DES, gave near quant. agreement at multiple temps. for exptl. densities, viscosities, heat capacities, and surface tensions yielding overall mean abs. errors (MAEs) of ca. 1.1%, 1.6%, 5.5%, and 1.5%, resp. Local interactions and solvent structuring between the ions and HBDs, including urea, glycerol, phenol, ethylene glycol, levulinic acid, oxalic acid, and malonic acid, were accurately reproduced when compared to radial distribution functions and coordination nos. derived from exptl. liq.-phase neutron diffraction data and from first-principles mol. dynamics simulations. The reprodn. of transport properties presented a considerable challenge and behaved more like a supercooled liq. near room temp.; higher-temp. simulations, e.g., 400-500 K, or an alternative polarizable force field is recommended when computing self-diffusion coeffs.
    18. 18
      Nandy, A.; Smiatek, J. Mixtures of LiTFSI and urea: ideal thermodynamic behavior as key to the formation of deep eutectic solvents?. Phys. Chem. Chem. Phys. 2019, 21, 12279– 12287,  DOI: 10.1039/C9CP01440C
      18
      Mixtures of LiTFSI and urea: ideal thermodynamic behavior as key to the formation of deep eutectic solvents?
      Nandy, Aniruddha; Smiatek, Jens
      Physical Chemistry Chemical Physics (2019), 21 (23), 12279-12287CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      At certain mixing ratios, urea and lithium bis(trifluorosulfonyl)imide (LiTFSI) form deep eutectic solvents with a pronounced lowering of the melting temp. when compared to the individual components. Using atomistic mol. dynamics (MD) simulations and d. functional theory (DFT) calcns., we study the structural and dynamic properties of these mixts. at various urea concns. Our findings show that the diffusivity of all species increases linearly with the urea mole fraction which can be explained by a successive replacement of TFSI- ions from the first coordination shell around lithium ions. A comparable linear change is also obsd. for the interaction energies between the individual components. Broad electrochem. stability windows in combination with high lithium ion transport nos. are brought into agreement with electronic reshuffling mechanisms between the interacting species. Further calcns. of chem. potential derivs. and transfer free energies highlight an ideal thermodn. behavior for certain LiTFSI/urea mixing ratios. Our findings thus provide a rationale for the unique properties of these mixts. in reasonable agreement with exptl. outcomes.
    19. 19
      Zhang, Y.; Poe, D.; Heroux, L.; Squire, H.; Doherty, B. W.; Long, Z.; Dadmun, M.; Gurkan, B.; Tuckerman, M. E.; Maginn, E. J. Liquid Structure and Transport Properties of the Deep Eutectic Solvent Ethaline. J. Phys. Chem. B 2020, 124, 5251– 5264, PMID: 32464060  DOI: 10.1021/acs.jpcb.0c04058
      19
      Liquid Structure and Transport Properties of the Deep Eutectic Solvent Ethaline
      Zhang, Yong; Poe, Derrick; Heroux, Luke; Squire, Henry; Doherty, Brian W.; Long, Zhuoran; Dadmun, Mark; Gurkan, Burcu; Tuckerman, Mark E.; Maginn, Edward J.
      Journal of Physical Chemistry B (2020), 124 (25), 5251-5264CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      A range of techniques including phys. property measurements, neutron scattering expts., ab initio mol. dynamics, and classical mol. dynamics simulations are used to probe the structural, thermodn., and transport properties of a deep eutectic solvent comprised of a 1:2 molar ratio of choline chloride and ethylene glycol. This mixt., known as Ethaline, has many desirable properties for use in a range of applications, and therefore, understanding its liq. structure and transport properties is of interest. Simulation results are able to capture exptl. densities, diffusivities, viscosities, and structure factors extremely well. The solvation environment is dynamic and dominated by different hydrogen bonding interactions. Dynamic heterogeneities resulting from hydrogen bonding interactions are quantified. Rotational dynamics of mol. dipole moments of choline and ethylene glycol are computed and found to exhibit a fast and slow mode.
    20. 20
      Shayestehpour, O.; Zahn, S. Molecular Features of Reline and Homologous Deep Eutectic Solvents Contributing to Nonideal Mixing Behavior. J. Phys. Chem. B 2020, 124, 7586– 7597, PMID: 32790398  DOI: 10.1021/acs.jpcb.0c03091
      20
      Molecular Features of Reline and Homologous Deep Eutectic Solvents Contributing to Nonideal Mixing Behavior
      Shayestehpour, Omid; Zahn, Stefan
      Journal of Physical Chemistry B (2020), 124 (35), 7586-7597CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Deep eutectic solvents based on choline chloride and a series of urea derivs. are studied by mol. dynamics simulations with the aim to identify mol. features contributing to nonideal mixing behavior of these compds. In case of reline, a mixt. of choline chloride and urea in 1:2 ratio, urea mols. provide sufficient hydrogen bond donor sites to take up the chloride anions into their polar network. Replacing any of the hydrogen atoms of urea by a Me group strongly pushes the anion to interact with these alkyl chains, resulting in a pos. deviation of the activity coeffs. of choline chloride compared to reline. Furthermore, the oxygen atom of urea can interact with the nitrogen atom of the cation. This enables the chloride anion to move off-center of the cation toward the hydrogen atom of its hydroxyl group, possessing stronger directional Coulomb interactions than the nitrogen atom of the cation. The substitution of urea's hydrogen atoms in cis position to the carbonyl group as in 1,3-dimethylurea, pushes the newly introduced nonpolar alkyl chains toward the nitrogen atom of the cation. This effect can be responsible for the exptl. obsd. increase of the activity coeff. of the urea deriv. compared to urea. Addnl., indications for formation of nonpolar domains within the liq. and, thus, nanoscale segregation is visible as soon as one hydrogen atom of urea is replaced by an alkyl group.
    21. 21
      Goloviznina, K.; Gong, Z.; Costa Gomes, M. F.; Pádua, A. A. H. Extension of the CL&Pol Polarizable Force Field to Electrolytes, Protic Ionic Liquids, and Deep Eutectic Solvents. J. Chem. Theory Comput. 2021, 17, 1606– 1617, PMID: 33555860  DOI: 10.1021/acs.jctc.0c01002
      21
      Extension of the CL&Pol Polarizable Force Field to Electrolytes, Protic Ionic Liquids, and Deep Eutectic Solvents
      Goloviznina, Kateryna; Gong, Zheng; Costa Gomes, Margarida F.; Padua, Agilio A. H.
      Journal of Chemical Theory and Computation (2021), 17 (3), 1606-1617CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The polarizable CL and Pol force field presented in our previous study, Transferable, Polarizable Force Field for Ionic Liqs. (J. Chem. Theory Comput.2019,15, 5858, DOI: http://doi.org/10.1021/acs.jctc.9b0068910.1021/acs.jctc.9b00689), is extended to electrolytes, protic ionic liqs. (PIL), deep eutectic solvents (DES), and glycols. These systems are problematic in polarizable simulations because they contain either small, highly charged ions or strong hydrogen bonds, which cause trajectory instabilities due to the pull exerted on the induced dipoles. We use a Tang-Toennies (TT) function to dampen, or smear, the interactions between charges and induced dipole at a short range involving small, highly charged atoms (such as hydrogen or lithium), thus preventing the "polarization catastrophe". The new force field gives stable trajectories and is validated through comparison with exptl. data on d., viscosity, and ion diffusion coeffs. of liq. systems of the above-mentioned classes. The results also shed light on the hydrogen-bonding pattern in ethylammonium nitrate, a PIL, for which the literature contains conflicting views. We describe the implementation of the TT damping function, of the temp.-grouped Nose-Hoover thermostat for polarizable mol. dynamics (MD) and of the periodic perturbation method for viscosity evaluation from non-equil. trajectories in the LAMMPS MD code. The main result of this work is the wider applicability of the CL and Pol polarizable force field to new, important classes of fluids, achieving robust trajectories and a good description of equil. and transport properties in challenging systems. The fragment-based approach of CL and Pol will allow ready extension to a wide variety of PILs, DES, and electrolytes.
    22. 22
      Jeong, K.-j.; McDaniel, J. G.; Yethiraj, A. Deep Eutectic Solvents: Molecular Simulations with a First-Principles Polarizable Force Field. J. Phys. Chem. B 2021, 125, 7177– 7186, PMID: 34181852  DOI: 10.1021/acs.jpcb.1c01692
      22
      Deep Eutectic Solvents: Molecular Simulations with a First-Principles Polarizable Force Field
      Jeong, Kyeong-jun; McDaniel, Jesse G.; Yethiraj, Arun
      Journal of Physical Chemistry B (2021), 125 (26), 7177-7186CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      The unique properties of deep eutectic solvents make them useful in a variety of applications. In this work we develop a first-principles force field for reline, which is composed of choline chloride and urea in the molar ratio 1:2. We start with the symmetry adapted perturbation theory (SAPT) protocol and then make adjustments to better reproduce the structure and dynamics of the liq. when compared to first-principles mol. dynamics (FPMD) simulations. The resulting force field is in good agreement with expts. in addn. to being consistent with the FPMD simulations. The simulations show that primitive mol. clusters are preferentially formed with choline-chloride ionic pairs bound with a hydrogen bond in the hydroxyl group and that urea mols. coordinate the chloride mainly via the trans-H chelating hydrogen bonds. Incorporating polarizability qual. influences the radial distributions and lifetimes of hydrogen bonds and affects long-range structural order and dynamics. The polarizable force field predicts a diffusion const. about an order of magnitude larger than the nonpolarizable force field and is therefore less computationally intensive. We hope this study paves the way for studying complex hydrogen-bonding liqs. from a first-principles approach.
    23. 23
      Shayestehpour, O.; Zahn, S. Ion Correlation in Choline Chloride–Urea Deep Eutectic Solvent (Reline) from Polarizable Molecular Dynamics Simulations. J. Phys. Chem. B 2022, 126, 3439– 3449, PMID: 35500254  DOI: 10.1021/acs.jpcb.1c10671
      23
      Ion Correlation in Choline Chloride-Urea Deep Eutectic Solvent (Reline) from Polarizable Molecular Dynamics Simulations
      Shayestehpour, Omid; Zahn, Stefan
      Journal of Physical Chemistry B (2022), 126 (18), 3439-3449CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      In recent years, deep eutectic solvents (DESs) emerged as highly tunable and environmentally friendly alternatives to common ionic liqs. and org. solvents. In this work, a polarizable model based on the CHARMM Drude polarizable force field is developed for a 1:2 ratio mixt. of choline chloride/urea (reline) DES. To successfully reproduce the structure of the liq. as compared to first-principles mol. dynamics simulations, a damping factor was introduced to correct the obsd. over-binding between the chloride and the hydrogen bonding site of choline. Investigated radial distributions reveal the formation of hydrogen bonds between all the constituents of reline and similar interactions for chloride and urea's oxygen atoms, which could contribute to the m.p. depression of the mixt. Predicted dynamic properties from our polarizable force field are in good agreement with expts., showing significant improvements over nonpolarizable models. Similar to some ionic liqs., an oscillatory behavior in the velocity autocorrelation function of the anion is visible, which can be interpreted as a rattling motion of the lighter anion surrounded by the heavier cations. The obtained results for ionic cond. of reline show some degree of correlated ion motion in this DES. However, a joint diffusion of ion pairs cannot be obsd. during the simulations.
    24. 24
      Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133– A1138,  DOI: 10.1103/PhysRev.140.A1133
      There is no corresponding record for this reference.
    25. 25
      Goedecker, S. Linear scaling electronic structure methods. Rev. Mod. Phys. 1999, 71, 1085– 1123,  DOI: 10.1103/RevModPhys.71.1085
      25
      Linear scaling electronic structure methods
      Goedecker, Stefan
      Reviews of Modern Physics (1999), 71 (4), 1085-1123CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
      A review with many refs. Methods exhibiting linear scaling with respect to the size of the system, the so-called O(N) methods, are an essential tool for the calcn. of the electronic structure of large systems contg. many atoms. They are based on algorithms that take advantage of the decay properties of the d. matrix. In this article the phys. decay properties of the d. matrix are be studied for both metals and insulators. Several strategies for constructing O(N) algorithms are presented and critically examd. Some issues that are relevant only for self-consistent O(N) methods, such as the calcn. of the Hartree potential and mixing issues, are also discussed. Some typical applications of O(N) methods are briefly described.
    26. 26
      Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225– 11236,  DOI: 10.1021/ja9621760
      26
      Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids
      Jorgensen, William L.; Maxwell, David S.; Tirado-Rives, Julian
      Journal of the American Chemical Society (1996), 118 (45), 11225-11236CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The parametrization and testing of the OPLS all-atom force field for org. mols. and peptides are described. Parameters for both torsional and nonbonded energetics have been derived, while the bond stretching and angle bending parameters have been adopted mostly from the AMBER all-atom force field. The torsional parameters were detd. by fitting to rotational energy profiles obtained from ab initio MO calcns. at the RHF/6-31G*//RHF/6-31G* level for more than 50 org. mols. and ions. The quality of the fits was high with av. errors for conformational energies of less than 0.2 kcal/mol. The force-field results for mol. structures are also demonstrated to closely match the ab initio predictions. The nonbonded parameters were developed in conjunction with Monte Carlo statistical mechanics simulations by computing thermodn. and structural properties for 34 pure org. liqs. including alkanes, alkenes, alcs., ethers, acetals, thiols, sulfides, disulfides, aldehydes, ketones, and amides. Av. errors in comparison with exptl. data are 2% for heats of vaporization and densities. The Monte Carlo simulations included sampling all internal and intermol. degrees of freedom. It is found that such non-polar and monofunctional systems do not show significant condensed-phase effects on internal energies in going from the gas phase to the pure liqs.
    27. 27
      Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J. Comput. Chem. 2010, 31, 671– 690,  DOI: 10.1002/jcc.21367
      27
      CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields
      Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D., Jr.
      Journal of Computational Chemistry (2010), 31 (4), 671-690CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The widely used CHARMM additive all-atom force field includes parameters for proteins, nucleic acids, lipids, and carbohydrates. In the present article, an extension of the CHARMM force field to drug-like mols. is presented. The resulting CHARMM General Force Field (CGenFF) covers a wide range of chem. groups present in biomols. and drug-like mols., including a large no. of heterocyclic scaffolds. The parametrization philosophy behind the force field focuses on quality at the expense of transferability, with the implementation concg. on an extensible force field. Statistics related to the quality of the parametrization with a focus on exptl. validation are presented. Addnl., the parametrization procedure, described fully in the present article in the context of the model systems, pyrrolidine, and 3-phenoxymethyl-pyrrolidine will allow users to readily extend the force field to chem. groups that are not explicitly covered in the force field as well as add functional groups to and link together mols. already available in the force field. CGenFF thus makes it possible to perform "all-CHARMM" simulations on drug-target interactions thereby extending the utility of CHARMM force fields to medicinally relevant systems. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2010.
    28. 28
      Cadena, C.; Zhao, Q.; Snurr, R. Q.; Maginn, E. J. Molecular Modeling and Experimental Studies of the Thermodynamic and Transport Properties of Pyridinium-Based Ionic Liquids. J. Phys. Chem. B 2006, 110, 2821– 2832, PMID: 16471891  DOI: 10.1021/jp056235k
      28
      Molecular Modeling and Experimental Studies of the Thermodynamic and Transport Properties of Pyridinium-Based Ionic Liquids
      Cadena, Cesar; Zhao, Qi; Snurr, Randall Q.; Maginn, Edward J.
      Journal of Physical Chemistry B (2006), 110 (6), 2821-2832CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      A combined exptl. and mol. dynamics study has been performed on the following pyridinium-based ionic liqs.: 1-n-hexyl-3-methylpyridinium bis(trifluoromethanesulfonyl)imide ([hmpy][Tf2N]), 1-n-octyl-3-methylpyridinium bis(trifluoromethanesulfonyl)imide ([ompy][Tf2N]), and 1-n-hexyl-3,5-dimethylpyridinium bis(trifluoromethanesulfonyl)imide ([hdmpy][Tf2N]). Pulsed field gradient NMR spectroscopy was used to det. the self-diffusivities of the individual cations and anions as a function of temp. Exptl. self-diffusivities range from 10-11 to 10-10 m2/s. Activation energies for diffusion are 44-49 kJ/mol. A classical force field was developed for these compds., and mol. dynamics simulations were performed to compute dynamic as well as thermodn. properties. Evidence of glassy dynamics was found, preventing accurate detn. of self-diffusivities over mol. dynamics time scales. Volumetric properties such as d., isothermal compressibility, and volumetric expansivity agree well with expt. Simulated heat capacities are within 2% of exptl. values.
    29. 29
      Rajput, N. N.; Murugesan, V.; Shin, Y.; Han, K. S.; Lau, K. C.; Chen, J.; Liu, J.; Curtiss, L. A.; Mueller, K. T.; Persson, K. A. Elucidating the Solvation Structure and Dynamics of Lithium Polysulfides Resulting from Competitive Salt and Solvent Interactions. Chem. Mater. 2017, 29, 3375– 3379,  DOI: 10.1021/acs.chemmater.7b00068
      29
      Elucidating the Solvation Structure and Dynamics of Lithium Polysulfides Resulting from Competitive Salt and Solvent Interactions
      Rajput, Nav Nidhi; Murugesan, Vijayakumar; Shin, Yongwoo; Han, Kee Sung; Lau, Kah Chun; Chen, Junzheng; Liu, Jun; Curtiss, Larry A.; Mueller, Karl T.; Persson, Kristin A.
      Chemistry of Materials (2017), 29 (8), 3375-3379CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Fundamental mol. level understanding of functional properties of liq. solns. provides an important basis for designing optimized electrolytes for numerous applications. In particular, exhaustive knowledge of solvation structure, stability and transport properties is crit. for developing stable electrolytes for fast charging and high energy d. next-generation energy storage systems. Here we report the correlation between soly., solvation structure and translational dynamics of a lithium salt (Li-TFSI) and polysulfides species using well-benchmarked classical mol. dynamics simulations combined with NMR. It is obsd. that the polysulfide chain length has a significant effect on the ion-ion and ion-solvent interaction as well as on the diffusion coeff. of the ionic species in soln. In particular, extensive cluster formation is obsd. in lower order polysulfides (Sx2-; x≤4), whereas the longer poly-sulfides (Sx2-; x>4) show high soly. and slow dynamics in the soln. It is obsd. that optimal solvent/salt ratio is essential to control the soly. and cond. as the addn. of Li salt increases the soly. but decreases the mobility of the ionic species. This work provides a coupled theor. and exptl. study of bulk solvation structure and transport properties of multi-component electrolyte systems, yielding design metrics for developing optimal electrolytes with improved stability and soly.
    30. 30
      Yan, T.; Wang, Y.; Knox, C. On the Dynamics of Ionic Liquids: Comparisons between Electronically Polarizable and Nonpolarizable Models II. J. Phys. Chem. B 2010, 114, 6886– 6904, PMID: 20443608  DOI: 10.1021/jp908914d
      30
      On the Dynamics of Ionic Liquids: Comparisons between Electronically Polarizable and Nonpolarizable Models II
      Yan, Tianying; Wang, Yanting; Knox, Craig
      Journal of Physical Chemistry B (2010), 114 (20), 6886-6904CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      An electronically polarizable model has been developed for the ionic liq. (IL) 1-ethyl-3-methyl-imidazolium nitrate (EMIM+/NO3-). Mol. dynamics simulations were then performed with both the polarizable and nonpolarizable models. Both models exhibited certain properties that are similar to a supercooled liq. behavior even though the simulations were run at 400 K (89 K above the m.p. of EMIM+/NO3-). The ionic mean-squared displacement and transverse current correlation function of both models were well represented by a memory function with a fast Gaussian initial relaxation followed by the two-step exponential functions for β- and α- structural relaxations. Another feature shared by both models is the dynamic heterogeneity, which highlights the complex dynamic behavior of ILs. Apart from the overall slow dynamics, the relaxation of the H-atoms attached to the Me group demonstrates a "free rotor" type of motion. Also, the Et group shows the fastest overall relaxation, due to the weak electrostatic interactions on it. Such flexibility enhances the entropic effect and thus favors the liq. state at room temp. For the dynamical properties reported in this paper, the polarizable model consistently exhibited faster relaxations (including translational and reorientational motions), higher self-diffusion and ionic cond., and lower shear viscosity than the nonpolarizable model. The faster relaxations of the polarizable model result from attenuated long-range electrostatic interactions caused by enhanced screening from the polarization effect. Therefore, simulations based on the polarizable model may be analogous to simulations with the nonpolarizable model at higher temps. On the other hand, the enhanced intermol. interactions for the polarizable model at short-range due to the addnl. charge-dipole and dipole-dipole interactions result in a red shift of the intramol. C-H stretch spectrum and a higher degree of ion assocn., leading to a spectrum with enhanced cond. across the whole frequency range. The vibrational motion assocd. with the intermol. hydrogen bonding is highly IR active, highlighting the importance of hydrogen bond dynamics in ILs.
    31. 31
      Szabadi, A.; Elfgen, R.; Macchieraldo, R.; Kearns, F. L.; Lee Woodcock, H.; Kirchner, B.; Schröder, C. Comparison between ab initio and polarizable molecular dynamics simulations of 1-butyl-3-methylimidazolium tetrafluoroborate and chloride in water. J. Mol. Liq. 2021, 337, 116521,  DOI: 10.1016/j.molliq.2021.116521
      31
      Comparison between ab initio and polarizable molecular dynamics simulations of 1-butyl-3-methylimidazolium tetrafluoroborate and chloride in water
      Szabadi, Andras; Elfgen, Roman; Macchieraldo, Roberto; Kearns, Fiona L.; Lee Woodcock, H.; Kirchner, Barbara; Schroeder, Christian
      Journal of Molecular Liquids (2021), 337 (), 116521CODEN: JMLIDT; ISSN:0167-7322. (Elsevier B.V.)
      In this study we compare the results of three different polarizable mol. dynamics force fields with an ab initio trajectory of the aq. mixt. of 1-butyl-3-methylimidazolium tetrafluoroborate and chloride, esp. regarding their ability to describe static and dynamic phenomena. The discrepancies are discussed in terms of intra- and intermol. force field parameters as well as the system size. We report significant differences in the derived diffusion coeffs. and attribute them to system size, d. and general discrepancies between ab initio and classical mol. dynamics simulations. In most cases, radial distribution functions show qual. agreement; however, the overpolarization of chloride in the MD trajectories gives rises to unphys. results. Excellent agreement between dipolar distributions point out the importance of explicit polarizability in MD, while the comparison of computational and exptl. IR spectra highlights the similarities between classical and ab initio dynamics in the low-wave no. region and the differences around 1500 cm-1.
    32. 32
      Glielmo, A.; Sollich, P.; De Vita, A. Accurate interatomic force fields via machine learning with covariant kernels. Phys. Rev. B 2017, 95, 214302,  DOI: 10.1103/PhysRevB.95.214302
      32
      Accurate interatomic force fields via machine learning with covariant kernels
      Glielmo, Aldo; Sollich, Peter; De Vita, Alessandro
      Physical Review B (2017), 95 (21), 214302/1-214302/10CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      A review. We present a novel scheme to accurately predict at. forces as vector quantities, rather than sets of scalar components, by Gaussian process (GP) regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO(d) for the relevant dimensionality d. Remarkably, in specific cases the integration can be carried out anal. and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mech. forces in real materials is investigated by tests on pure and defective Ni, Fe, and Si cryst. systems.
    33. 33
      Chmiela, S.; Tkatchenko, A.; Sauceda, H. E.; Poltavsky, I.; Schütt, K. T.; Müller, K. R. Machine learning of accurate energy-conserving molecular force fields. Sci. Adv. 2017, 3, e1603015  DOI: 10.1126/sciadv.1603015
      33
      Machine learning of accurate energy-conserving molecular force fields
      Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.; Poltavsky, Igor; Schuett, Kristof T.; Mueller, Klaus-Robert
      Science Advances (2017), 3 (5), e1603015/1-e1603015/6CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
      Using conservation of energy-a fundamental property of closed classical and quantum mech. systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate mol. force fields using a restricted no. of samples from ab initio mol. dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized mols. with an accuracy of 0.3 kcal mol-1 for energies and 1 kcal mol-1 Å-1 for at. forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of mols., including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quant. mol. dynamics simulations for mols. at a fraction of cost of explicit AIMD calcns., thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.
    34. 34
      Chmiela, S.; Sauceda, H. E.; Müller, K. R.; Tkatchenko, A. Towards exact molecular dynamics simulations with machine-learned force fields. Nat. Commun. 2018, 9, 3887,  DOI: 10.1038/s41467-018-06169-2
      34
      Towards exact molecular dynamics simulations with machine-learned force fields
      Chmiela Stefan; Muller Klaus-Robert; Sauceda Huziel E; Muller Klaus-Robert; Muller Klaus-Robert; Tkatchenko Alexandre
      Nature communications (2018), 9 (1), 3887 ISSN:.
      Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as good as the underlying interatomic potential. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. Here we enable the direct construction of flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model in an automatic data-driven way. The developed sGDML approach faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged molecular dynamics simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations.
    35. 35
      Bartók, A. P.; Payne, M. C.; Kondor, R.; Csányi, G. Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons. Phys. Rev. Lett. 2010, 104, 136403,  DOI: 10.1103/PhysRevLett.104.136403
      35
      Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
      Bartok, Albert P.; Payne, Mike C.; Kondor, Risi; Csanyi, Gabor
      Physical Review Letters (2010), 104 (13), 136403/1-136403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We introduce a class of interat. potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mech. calcns. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calcg. properties at high temps. Using the interat. potential to generate the long mol. dynamics trajectories required for such calcns. saves orders of magnitude in computational cost.
    36. 36
      Behler, J.; Parrinello, M. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces. Phys. Rev. Lett. 2007, 98, 146401,  DOI: 10.1103/PhysRevLett.98.146401
      36
      Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
      Behler, Jorg; Parrinello, Michele
      Physical Review Letters (2007), 98 (14), 146401/1-146401/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The accurate description of chem. processes often requires the use of computationally demanding methods like d.-functional theory (DFT), making long simulations of large systems unfeasible. In this Letter we introduce a new kind of neural-network representation of DFT potential-energy surfaces, which provides the energy and forces as a function of all at. positions in systems of arbitrary size and is several orders of magnitude faster than DFT. The high accuracy of the method is demonstrated for bulk silicon and compared with empirical potentials and DFT. The method is general and can be applied to all types of periodic and nonperiodic systems.
    37. 37
      Behler, J. Representing potential energy surfaces by high-dimensional neural network potentials. J. Phys.: Condens. Matter 2014, 26, 183001,  DOI: 10.1088/0953-8984/26/18/183001
      37
      Representing potential energy surfaces by high-dimensional neural network potentials
      Behler, J.
      Journal of Physics: Condensed Matter (2014), 26 (18), 183001/1-183001/24, 24 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
      A review. The development of interat. potentials employing artificial neural networks has seen tremendous progress in recent years. While until recently the applicability of neural network potentials (NNPs) has been restricted to low-dimensional systems, this limitation has now been overcome and high-dimensional NNPs can be used in large-scale mol. dynamics simulations of thousands of atoms. NNPs are constructed by adjusting a set of parameters using data from electronic structure calcns. and in many cases energies and forces can be obtained with very high accuracy. Therefore, NNP-based simulation results are often very close to those gained by a direct application of first-principles methods. In this review, the basic methodol. of high-dimensional NNPs will be presented with a special focus on the scope and the remaining limitations of this approach. The development of NNPs requires substantial computational effort as typically thousands of ref. calcns. are required. Still, if the problem to be studied involves very large systems or long simulation times this overhead is regained quickly. Further, the method is still limited to systems contg. about three or four chem. elements due to the rapidly increasing complexity of the configuration space, although many atoms of each species can be present. Due to the ability of NNPs to describe even extremely complex at. configurations with excellent accuracy irresp. of the nature of the at. interactions, they represent a general and therefore widely applicable technique, e.g. for addressing problems in materials science, for investigating properties of interfaces and for studying solvation processes.
    38. 38
      Ghasemi, S. A.; Hofstetter, A.; Saha, S.; Goedecker, S. Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network. Phys. Rev. B 2015, 92, 045131,  DOI: 10.1103/PhysRevB.92.045131
      38
      Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network
      Ghasemi, S. Alireza; Hofstetter, Albert; Saha, Santanu; Goedecker, Stefan
      Physical Review B: Condensed Matter and Materials Physics (2015), 92 (4), 045131/1-045131/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Based on an anal. of the short-range chem. environment of each atom in a system, std. machine-learning-based approaches to the construction of interat. potentials aim at detg. directly the central quantity, which is the total energy. This prevents, for instance, an accurate description of the energetics of systems in which long-range charge transfer or ionization is important. We propose therefore not to target directly with machine-learning methods the total energy but an intermediate phys. quantity, namely, the charge d., which then in turn allows us to det. the total energy. By allowing the electronic charge to distribute itself in an optimal way over the system, we can describe not only neutral but also ionized systems with unprecedented accuracy. We demonstrate the power of our approach for both neutral and ionized NaCl clusters where charge redistribution plays a decisive role for the energetics. We are able to obtain chem. accuracy, i.e., errors of less than a millihartree per atom compared to the ref. d. functional results for a huge data set of configurations with large structural variety. The introduction of phys. motivated quantities which are detd. by the short-range at. environment via a neural network also leads to an increased stability of the machine-learning process and transferability of the potential.
    39. 39
      Smith, J. S.; Isayev, O.; Roitberg, A. E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. Sci. 2017, 8, 3192– 3203,  DOI: 10.1039/C6SC05720A
      39
      ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost
      Smith, J. S.; Isayev, O.; Roitberg, A. E.
      Chemical Science (2017), 8 (4), 3192-3203CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      A review. Deep learning is revolutionizing many areas of science and technol., esp. image, text, and speech recognition. In this paper, we demonstrate how a deep neural network (NN) trained on quantum mech. (QM) DFT calcns. can learn an accurate and transferable potential for org. mols. We introduce ANAKIN-ME (Accurate NeurAl networK engINe for Mol. Energies) or ANI for short. ANI is a new method designed with the intent of developing transferable neural network potentials that utilize a highly-modified version of the Behler and Parrinello symmetry functions to build single-atom at. environment vectors (AEV) as a mol. representation. AEVs provide the ability to train neural networks to data that spans both configurational and conformational space, a feat not previously accomplished on this scale. We utilized ANI to build a potential called ANI-1, which was trained on a subset of the GDB databases with up to 8 heavy atoms in order to predict total energies for org. mols. contg. four atom types: H, C, N, and O. To obtain an accelerated but phys. relevant sampling of mol. potential surfaces, we also proposed a Normal Mode Sampling (NMS) method for generating mol. conformations. Through a series of case studies, we show that ANI-1 is chem. accurate compared to ref. DFT calcns. on much larger mol. systems (up to 54 atoms) than those included in the training data set.
    40. 40
      Yao, K.; Herr, J. E.; Toth, D. W.; Mckintyre, R.; Parkhill, J. The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics. Chem. Sci. 2018, 9, 2261– 2269,  DOI: 10.1039/C7SC04934J
      40
      The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics
      Yao, Kun; Herr, John E.; Toth, David W.; McKintyre, Ryker; Parkhill, John
      Chemical Science (2018), 9 (8), 2261-2269CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      Traditional force fields cannot model chem. reactivity, and suffer from low generality without re-fitting. Neural network potentials promise to address these problems, offering energies and forces with near ab initio accuracy at low cost. However a data-driven approach is naturally inefficient for long-range interat. forces that have simple phys. formulas. In this manuscript we construct a hybrid model chem. consisting of a nearsighted neural network potential with screened long-range electrostatic and van der Waals physics. This trained potential, simply dubbed "TensorMol-0.1", is offered in an open-source Python package capable of many of the simulation types commonly used to study chem.: geometry optimizations, harmonic spectra, open or periodic mol. dynamics, Monte Carlo, and nudged elastic band calcns. We describe the robustness and speed of the package, demonstrating its millihartree accuracy and scalability to tens-of-thousands of atoms on ordinary laptops. We demonstrate the performance of the model by reproducing vibrational spectra, and simulating the mol. dynamics of a protein. Our comparisons with electronic structure theory and exptl. data demonstrate that neural network mol. dynamics is poised to become an important tool for mol. simulation, lowering the resource barrier to simulating chem.
    41. 41
      Schütt, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Müller, K. R. SchNet – A deep learning architecture for molecules and materials. J. Chem. Phys. 2018, 148, 241722,  DOI: 10.1063/1.5019779
      41
      SchNet - A deep learning architecture for molecules and materials
      Schuett, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Mueller, K.-R.
      Journal of Chemical Physics (2018), 148 (24), 241722/1-241722/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chem. physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mech. interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chem. compd. space. Here, we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chem. space for mols. and materials, where our model learns chem. plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for mol. dynamics simulations of small mols. and perform an exemplary study on the quantum-mech. properties of C20-fullerene that would have been infeasible with regular ab initio mol. dynamics. (c) 2018 American Institute of Physics.
    42. 42
      Han, J.; Zhang, L.; Car, R.; E, W. Deep Potential: A General Representation of a Many-Body Potential Energy Surface. Commun. Comput. Phys. 2018, 23, 629– 639,  DOI: 10.4208/cicp.oa-2017-0213
      There is no corresponding record for this reference.
    43. 43
      Unke, O. T.; Meuwly, M. PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges. J. Chem. Theory Comput. 2019, 15, 3678– 3693, PMID: 31042390  DOI: 10.1021/acs.jctc.9b00181
      43
      PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges
      Unke, Oliver T.; Meuwly, Markus
      Journal of Chemical Theory and Computation (2019), 15 (6), 3678-3693CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      In recent years, machine learning (ML) methods have become increasingly popular in computational chem. After being trained on appropriate ab initio ref. data, these methods allow for accurately predicting the properties of chem. systems, circumventing the need for explicitly solving the electronic Schrodinger equation. Because of their computational efficiency and scalability to large data sets, deep neural networks (DNNs) are a particularly promising ML algorithm for chem. applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces, and dipole moments of chem. systems. PhysNet achieves state-of-the-art performance on the QM9, MD17, and ISO17 benchmarks. Further, two new data sets are generated in order to probe the performance of ML models for describing chem. reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qual. correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala10): The optimized geometry of helical Ala10 predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 Å). By running unbiased mol. dynamics (MD) simulations of Ala10 on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala10 folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol-1 according to the ref. ab initio calcns.
    44. 44
      Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 2011, 134, 074106,  DOI: 10.1063/1.3553717
      44
      Atom-centered symmetry functions for constructing high-dimensional neural network potentials
      Behler, Joerg
      Journal of Chemical Physics (2011), 134 (7), 074106/1-074106/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calcns., and thus enable mol. dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the at. positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as mols., cryst. and amorphous solids, and liqs. (c) 2011 American Institute of Physics.
    45. 45
      Thompson, A.; Swiler, L.; Trott, C.; Foiles, S.; Tucker, G. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials. J. Comput. Phys. 2015, 285, 316– 330,  DOI: 10.1016/j.jcp.2014.12.018
      45
      Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials
      Thompson, A. P.; Swiler, L. P.; Trott, C. R.; Foiles, S. M.; Tucker, G. J.
      Journal of Computational Physics (2015), 285 (), 316-330CODEN: JCTPAH; ISSN:0021-9991. (Elsevier Inc.)
      We present a new interat. potential for solids and liqs. called Spectral Neighbor Anal. Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calcns. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor d. projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coeffs. are detd. using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calcn. of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel mol. dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calcns. by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calcd. properties of both the cryst. solid and the liq. phases. In addn., unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.
    46. 46
      Drautz, R. Atomic cluster expansion for accurate and transferable interatomic potentials. Phys. Rev. B 2019, 99, 014104,  DOI: 10.1103/PhysRevB.99.014104
      46
      Atomic cluster expansion for accurate and transferable interatomic potentials
      Drautz, Ralf
      Physical Review B (2019), 99 (1), 014104CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      The at. cluster expansion is developed as a complete descriptor of the local at. environment, including multicomponent materials, and its relation to a no. of other descriptors and potentials is discussed. The effort for evaluating the at. cluster expansion is shown to scale linearly with the no. of neighbors, irresp. of the order of the expansion. Application to small Cu clusters demonstrates smooth convergence of the at. cluster expansion to meV accuracy. By introducing nonlinear functions of the at. cluster expansion an interat. potential is obtained that is comparable in accuracy to state-of-the-art machine learning potentials. Because of the efficient convergence of the at. cluster expansion relevant subspaces can be sampled uniformly and exhaustively. This is demonstrated by testing against a large database of d. functional theory calcns. for copper.
    47. 47
      Batzner, S.; Musaelian, A.; Sun, L.; Geiger, M.; Mailoa, J. P.; Kornbluth, M.; Molinari, N.; Smidt, T. E.; Kozinsky, B. E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nat. Commun. 2022, 13, 2453,  DOI: 10.1038/s41467-022-29939-5
      47
      E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
      Batzner, Simon; Musaelian, Albert; Sun, Lixin; Geiger, Mario; Mailoa, Jonathan P.; Kornbluth, Mordechai; Molinari, Nicola; Smidt, Tess E.; Kozinsky, Boris
      Nature Communications (2022), 13 (1), 2453CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
      This work presents Neural Equivariant Interat. Potentials (NequIP), an E(3)-equivariant neural network approach for learning interat. potentials from ab-initio calcns. for mol. dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of at. environments. The method achieves state-of-the-art accuracy on a challenging and diverse set of mols. and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chem. level of theory as ref. and enables high-fidelity mol. dynamics simulations over long time scales.
    48. 48
      Schütt, K., Unke, O., Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. International Conference on Machine Learning 2021, 9377– 9388.
      There is no corresponding record for this reference.
    49. 49
      Haghighatlari, M.; Li, J.; Guan, X.; Zhang, O.; Das, A.; Stein, C. J.; Heidar-Zadeh, F.; Liu, M.; Head-Gordon, M.; Bertels, L.; Hao, H.; Leven, I.; Head-Gordon, T. NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces. Digital Discovery 2022, 1, 333– 343,  DOI: 10.1039/D2DD00008C
      49
      NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces
      Haghighatlari, Mojtaba; Li, Jie; Guan, Xingyi; Zhang, Oufan; Das, Akshaya; Stein, Christopher J.; Heidar-Zadeh, Farnaz; Liu, Meili; Head-Gordon, Martin; Bertels, Luke; Hao, Hongxia; Leven, Itai; Head-Gordon, Teresa
      Digital Discovery (2022), 1 (3), 333-343CODEN: DDIIAI; ISSN:2635-098X. (Royal Society of Chemistry)
      We report a new deep learning message passing network that takes inspiration from Newton's equations of motion to learn interat. potentials and forces. With the advantage of directional information from trainable force vectors, and physics-infused operators that are inspired by Newtonian physics, the entire model remains rotationally equivariant, and many-body interactions are inferred by more interpretable phys. features. We test NewtonNet on the prediction of several reactive and non-reactive high quality ab initio data sets including single small mols., a large set of chem. diverse mols., and methane and hydrogen combustion reactions, achieving state-of-the-art test performance on energies and forces with far greater data and computational efficiency than other deep learning models.
    50. 50
      Musaelian, A.; Batzner, S.; Johansson, A.; Sun, L.; Owen, C. J.; Kornbluth, M.; Kozinsky, B. Learning local equivariant representations for large-scale atomistic dynamics. Nat. Commun. 2023, 14, 579,  DOI: 10.1038/s41467-023-36329-y
      50
      Learning local equivariant representations for large-scale atomistic dynamics
      Musaelian, Albert; Batzner, Simon; Johansson, Anders; Sun, Lixin; Owen, Cameron J.; Kornbluth, Mordechai; Kozinsky, Boris
      Nature Communications (2023), 14 (1), 579CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
      A simultaneously accurate and computationally efficient parametrization of the potential energy surface of mols. and materials is a long-standing goal in the natural sciences. While atom-centered message passing neural networks (MPNNs) have shown remarkable accuracy, their information propagation has limited the accessible length-scales. Local methods, conversely, scale to large simulations but have suffered from inferior accuracy. This work introduces Allegro, a strictly local equivariant deep neural network interat. potential architecture that simultaneously exhibits excellent accuracy and scalability. Allegro represents a many-body potential using iterated tensor products of learned equivariant representations without atom-centered message passing. Allegro obtains improvements over state-of-the-art methods on QM9 and revMD17. A single tensor product layer outperforms existing deep MPNNs and transformers on QM9. Furthermore, Allegro displays remarkable generalization to out-of-distribution data. Mol. simulations using Allegro recover structural and kinetic properties of an amorphous electrolyte in excellent agreement with ab-initio simulations. Finally, we demonstrate parallelization with a simulation of 100 million atoms.
    51. 51
      Zhang, L.; Han, J.; Wang, H.; Saidi, W. A.; Car, R.; Weinan, E.: Red Hook, NY, USA, 2018, pp 4441– 4451. End-to-End Symmetry Preserving Inter-Atomic Potential Energy Model for Finite and Extended Systems Proceedings of the 32nd International Conference on Neural Information Processing Systems
      There is no corresponding record for this reference.
    52. 52
      Wang, H.; Zhang, L.; Han, J.; E, W. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun. 2018, 228, 178– 184,  DOI: 10.1016/j.cpc.2018.03.016
      52
      DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
      Wang, Han; Zhang, Linfeng; Han, Jiequn; E, Weinan
      Computer Physics Communications (2018), 228 (), 178-184CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      A review. Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-vs.-efficiency dilemma in mol. simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform mol. dynamics. Potential applications of DeePMD-kit span from finite mols. to extended systems and from metallic systems to chem. bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical mol. dynamics and quantum (path-integral) mol. dynamics packages, i.e., LAMMPS and the i-PI, resp. Thus, upon training, the potential energy and force field models can be used to perform efficient mol. simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interat. potential energy and forces of a water model using data obtained from d. functional theory. We demonstrate that the resulted mol. dynamics model reproduces accurately the structural information contained in the original model.Program Title: DeePMD-kitProgram Files doi:http://dx.doi.org/10.17632/hvfh9yvncf.1Licensing provisions: LGPLProgramming language: Python/C++Nature of problem: Modeling the many-body at. interactions by deep neural network models. Running mol. dynamics simulations with the models.Soln. method: The Deep Potential for Mol. Dynamics (DeePMD) method is implemented based on the deep learning framework TensorFlow. Supports for using a DeePMD model in LAMMPS and i-PI, for classical and quantum (path integral) mol. dynamics are provided.Addnl. comments including Restrictions and Unusual features: The code defines a data protocol such that the energy, force, and virial calcd. by different third-party mol. simulation packages can be easily processed and used as model training data.
    53. 53
      Kingma, D. P.; Ba, J. Adam: A Method for Stochastic Optimization. 2014, arXiv:1412.6980. https://arxiv.org/abs/1412.698web0.
      There is no corresponding record for this reference.
    54. 54
      Frauenheim, T.; Seifert, G.; Elsterner, M.; Hajnal, Z.; Jungnickel, G.; Porezag, D.; Suhai, S.; Scholz, R. A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology. Phys. Status Solidi B 2000, 217, 41– 62,  DOI: 10.1002/(SICI)1521-3951(200001)217:1<41::AID-PSSB41>3.0.CO;2-V
      54
      A self-consistent charge density-functional based tight-binding method for predictive materials simulations in physics, chemistry, and biology
      Frauenheim, T.; Seifert, G.; Elstner, M.; Hajnal, Z.; Jungnickel, G.; Porezag, D.; Suhai, S.; Scholz, R.
      Physica Status Solidi B: Basic Research (2000), 217 (1), 41-62CODEN: PSSBBD; ISSN:0370-1972. (Wiley-VCH Verlag Berlin GmbH)
      We outline recent developments in quantum mech. atomistic modeling of complex materials properties that combine the efficiency of semi-empirical quantum-chem. and tight-binding approaches with the accuracy and transferability of more sophisticated d.-functional and post-Hartree-Fock methods with the aim to perform highly predictive materials simulations of technol. relevant sizes in physics, chem., and biol. Following Harris, Foulkes, and Haydock, the methods are based on an expansion of the Kohn-Sham total energy in d.-functional theory (DFT) with respect to charge d. fluctuations at a given ref. d. While the zeroth order approach is equiv. to a common std. non-self-consistent tight-binding (TB) scheme, at 2nd order by variationally treating the approx. Kohn-Sham energy a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements may be derived. These matrix elements are modified by a self-consistent redistribution of Mulliken charges (SCC). Besides the usual band-structure and short-range repulsive terms the final approx. Kohn-Sham energy explicitly includes Coulomb interaction between charge fluctuations. The new SCC scheme is shown to successfully apply to problems, where deficiencies within the non-SCC std. TB-approach become obvious. These cover defect calcns. and surface studies in polar semiconductors (see M. Haugk et al. of this special issue), spectroscopic studies of org. light-emitting thin films, briefly outlined in the present article, and atomistic investigations of biomols. (see M. Elstner et al. of this special issue).
    55. 55
      VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 2005, 167, 103– 128,  DOI: 10.1016/j.cpc.2004.12.014
      55
      QUICKSTEP: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
      VandeVondele, Joost; Krack, Matthias; Mohamed, Fawzi; Parrinello, Michele; Chassaing, Thomas; Hutter, Juerg
      Computer Physics Communications (2005), 167 (2), 103-128CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      We present the Gaussian and plane waves (GPW) method and its implementation in which is part of the freely available program package CP2K. The GPW method allows for accurate d. functional calcns. in gas and condensed phases and can be effectively used for mol. dynamics simulations. We show how derivs. of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calcns. for single mols. and plane wave based calcns. in the condensed phase is excellent. Wave function optimization with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the d. matrix. We illustrate these findings with calcns. using commodity PCs as well as supercomputers.
    56. 56
      Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. cp2k: atomistic simulations of condensed matter systems. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4, 15– 25,  DOI: 10.1002/wcms.1159
      56
      cp2k: atomistic simulations of condensed matter systems
      Hutter, Juerg; Iannuzzi, Marcella; Schiffmann, Florian; VandeVondele, Joost
      Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (1), 15-25CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
      A review. Cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15-25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website.
    57. 57
      Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098– 3100,  DOI: 10.1103/PhysRevA.38.3098
      57
      Density-functional exchange-energy approximation with correct asymptotic behavior
      Becke, A. D.
      Physical Review A: Atomic, Molecular, and Optical Physics (1988), 38 (6), 3098-100CODEN: PLRAAN; ISSN:0556-2791.
      Current gradient-cor. d.-functional approxns. for the exchange energies of at. and mol. systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy d. A gradient-cor. exchange-energy functional is given with the proper asymptotic limit. This functional, contg. only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of at. systems with remarkable accuracy, surpassing the performance of previous functionals contg. two parameters or more.
    58. 58
      Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785– 789,  DOI: 10.1103/PhysRevB.37.785
      58
      Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
      Lee, Chengteh; Yang, Weitao; Parr, Robert G.
      Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.
      A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
    59. 59
      Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
      59
      A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
      Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
      Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
    60. 60
      Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 1996, 54, 1703– 1710,  DOI: 10.1103/PhysRevB.54.1703
      60
      Separable dual-space Gaussian pseudopotentials
      Goedecker, S.; Teter, M.; Hutter, J.
      Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
    61. 61
      Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic separable dual-space Gaussian pseudopotentials from H to Rn. Phys. Rev. B 1998, 58, 3641– 3662,  DOI: 10.1103/PhysRevB.58.3641
      61
      Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
      Hartwigsen, C.; Goedecker, S.; Hutter, J.
      Physical Review B: Condensed Matter and Materials Physics (1998), 58 (7), 3641-3662CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole Periodic Table, and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real-space grid, it is highly accurate, and, due to its analytic form, it can be specified by a very small no. of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of mol. calcns.
    62. 62
      Smith, J. S.; Nebgen, B.; Lubbers, N.; Isayev, O.; Roitberg, A. E. Less is more: Sampling chemical space with active learning. J. Chem. Phys. 2018, 148, 241733,  DOI: 10.1063/1.5023802
      62
      Less is more: Sampling chemical space with active learning
      Smith, Justin S.; Nebgen, Ben; Lubbers, Nicholas; Isayev, Olexandr; Roitberg, Adrian E.
      Journal of Chemical Physics (2018), 148 (24), 241733/1-241733/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The development of accurate and transferable machine learning (ML) potentials for predicting mol. energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chem. space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach, we develop the COmprehensive Machine-learning Potential (COMP6) benchmark (publicly available on GitHub) which contains a diverse set of org. mols. Active learning-based ANI potentials outperform the original random sampled ANI-1 potential with only 10% of the data, while the final active learning-based model vastly outperforms ANI-1 on the COMP6 benchmark after training to only 25% of the data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single mols. or materials, while remaining applicable to the general class of org. mols. composed of the elements CHNO. (c) 2018 American Institute of Physics.
    63. 63
      Podryabinkin, E. V.; Shapeev, A. V. Active learning of linearly parametrized interatomic potentials. Comput. Mater. Sci. 2017, 140, 171– 180,  DOI: 10.1016/j.commatsci.2017.08.031
      63
      Active learning of linearly parametrized interatomic potentials
      Podryabinkin, Evgeny V.; Shapeev, Alexander V.
      Computational Materials Science (2017), 140 (), 171-180CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)
      This paper introduces an active learning approach to the fitting of machine learning interat. potentials. Our approach is based on the D-optimality criterion for selecting at. configurations on which the potential is fitted. It is shown that the proposed active learning approach is highly efficient in training potentials on the fly, ensuring that no extrapolation is attempted and leading to a completely reliable atomistic simulation without any significant decrease in accuracy. We apply our approach to mol. dynamics and structure relaxation, and we argue that it can be applied, in principle, to any other type of atomistic simulation. The software, test cases, and examples of usage are published at http://gitlab.skoltech.ru/shapeev/mlip/.
    64. 64
      Peterson, A. A.; Christensen, R.; Khorshidi, A. Addressing uncertainty in atomistic machine learning. Phys. Chem. Chem. Phys. 2017, 19, 10978– 10985,  DOI: 10.1039/C7CP00375G
      64
      Addressing uncertainty in atomistic machine learning
      Peterson, Andrew A.; Christensen, Rune; Khorshidi, Alireza
      Physical Chemistry Chemical Physics (2017), 19 (18), 10978-10985CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Machine-learning regression has been demonstrated to precisely emulate the potential energy and forces that are output from more expensive electronic-structure calcns. However, to predict new regions of the potential energy surface, an assessment must be made of the credibility of the predictions. In this perspective, we address the types of errors that might arise in atomistic machine learning, the unique aspects of atomistic simulations that make machine-learning challenging, and highlight how uncertainty anal. can be used to assess the validity of machine-learning predictions. We suggest this will allow researchers to more fully use machine learning for the routine acceleration of large, high-accuracy, or extended-time simulations. In our demonstrations, we use a bootstrap ensemble of neural network-based calculators, and show that the width of the ensemble can provide an est. of the uncertainty when the width is comparable to that in the training data. Intriguingly, we also show that the uncertainty can be localized to specific atoms in the simulation, which may offer hints for the generation of training data to strategically improve the machine-learned representation.
    65. 65
      Zhang, Y.; Wang, H.; Chen, W.; Zeng, J.; Zhang, L.; Wang, H. .. DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models. Comput. Phys. Commun. 2020, 253, 107206,  DOI: 10.1016/j.cpc.2020.107206
      65
      DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models
      Zhang, Yuzhi; Wang, Haidi; Chen, Weijie; Zeng, Jinzhe; Zhang, Linfeng; Wang, Han; E, Weinan
      Computer Physics Communications (2020), 253 (), 107206CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      In recent years, promising deep learning based interat. potential energy surface (PES) models have been proposed that can potentially allow us to perform mol. dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed "on-the-fly" learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN. Program Title: DP-GENProgram Files doi:http://dx.doi.org/10.17632/sxybkgc5xc.1Licensing provisions: LGPLProgramming language: PythonNature of problem: Generating reliable deep learning based potential energy models with minimal human intervention and computational cost. Soln. method: The concurrent learning scheme is implemented. Supports for sampling configuration space with LAMMPS, generating ab initio data with Quantum Espresso, VASP, CP2K and training potential models with DeePMD-kit are provided. Supports for different machines including workstations, high performance clusters and cloud machines are provided. Supports for job management tools including Slurm, PBS, LSF are provided.
    66. 66
      Thompson, A. P.; Aktulga, H. M.; Berger, R.; Bolintineanu, D. S.; Brown, W. M.; Crozier, P. S.; in ’t Veld, P. J.; Kohlmeyer, A.; Moore, S. G.; Nguyen, T. D.; Shan, R.; Stevens, M. J.; Tranchida, J.; Trott, C.; Plimpton, S. J. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 2022, 271, 108171,  DOI: 10.1016/j.cpc.2021.108171
      66
      LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales
      Thompson, Aidan P.; Aktulga, H. Metin; Berger, Richard; Bolintineanu, Dan S.; Brown, W. Michael; Crozier, Paul S.; in 't Veld, Pieter J.; Kohlmeyer, Axel; Moore, Stan G.; Nguyen, Trung Dac; Shan, Ray; Stevens, Mark J.; Tranchida, Julien; Trott, Christian; Plimpton, Steven J.
      Computer Physics Communications (2022), 271 (), 108171CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      Since the classical mol. dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from at. to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interat. potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interat. potentials.Program Title: Large-scale Atomic/Mol. Massively Parallel Simulator (LAMMPS)CPC Library link to program files:https://doi.org/10.17632/cxbxs9btsv.1Developer's repository link:https://github.com/lammps/lammpsLicensing provisions: GPLv2Programming language: C++, Python, C, FortranSupplementary material:https://www.lammps.orgNature of problem: Many science applications in physics, chem., materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from at. to mesoscale to macroscopic.Soln. method: The LAMMPS code uses parallel spatial decompn., distributed neighbor lists, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Stormer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addn., LAMMPS supports a wide range of interat. potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features.Addnl. comments including restrictions and unusual features: This paper serves as the definitive ref. for the LAMMPS code.S. Plimpton, Fast parallel algorithms for short-range mol. dynamics. Phys. 117 (1995) 1-19.L. Verlet, Computer expts. on classical fluids: I. Thermodynamical properties of Lennard-Jones mols., Phys. Rev. 159 (1967) 98-103.
    67. 67
      Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant pressure molecular dynamics algorithms. J. Chem. Phys. 1994, 101, 4177– 4189,  DOI: 10.1063/1.467468
      67
      Constant pressure molecular dynamics algorithms
      Martyna, Glenn J.; Tobias, Douglas J.; Klein, Michael L.
      Journal of Chemical Physics (1994), 101 (5), 4177-89CODEN: JCPSA6; ISSN:0021-9606.
      Modularly invariant equations of motion are derived that generate the isothermal-isobaric ensemble as their phase space avs. Isotropic vol. fluctuations and fully flexible simulation cells as well as a hybrid scheme that naturally combines the two motions are considered. The resulting methods are tested on two problems, a particle in a one-dimensional periodic potential and a spherical model of C60 in the solid/fluid phase.
    68. 68
      Agieienko, V.; Buchner, R. Densities, Viscosities, and Electrical Conductivities of Pure Anhydrous Reline and Its Mixtures with Water in the Temperature Range (293.15 to 338.15) K. J. Chem. Eng. Data 2019, 64, 4763– 4774,  DOI: 10.1021/acs.jced.9b00145
      68
      Densities, Viscosities, and Electrical Conductivities of Pure Anhydrous Reline and Its Mixtures with Water in the Temperature Range (293.15 to 338.15) K
      Agieienko, Vira; Buchner, Richard
      Journal of Chemical & Engineering Data (2019), 64 (11), 4763-4774CODEN: JCEAAX; ISSN:0021-9568. (American Chemical Society)
      D. (ρ), dynamic viscosity (η), and elec. cond. (κ) of the deep eutectic solvent (DES) reline, composed of choline chloride (ChCl) and urea in a 1:2 molar ratio, and its mixts. with water, covering the entire miscibility range, were studied at T = (293.15 to 338.15) K. Compared to many previous studies, reline purity was significantly improved by using ultrapure urea and ChCl recrystd. from ethanol. For the investigated DES samples the mass fraction of residual water was <0.00035. This allowed checking the influence of water traces and impurities on the physicochem. properties of pure reline. It was found that the presence of small amts. of water (w(H2O) < 0.0081) only negligibly decreased reline d., not exceeding 0.14% compared to the dry sample. However, for the same amt. of water η decreased by ∼36% at 298.15 K. The temp. dependence of ρ was well fitted by a quadratic expression, whereas η(T) and κ(T) were found to follow the empirical Vogel-Fulcher-Tammann equation. For the aq. mixts. excess properties of molar volume (VE) and viscosity (ηE) showed only minor variation with compn., suggesting rather weak interactions between water and the constituents of reline. However, VE and ηE depended significantly on temp., indicating a significant contribution of H-bonding to the inherent reline structure. Similar to conventional ionic liqs., the cond. of aq. reline showed a broad max. at the reline mole fraction of x1 ≈ 0.18 assocd. with the border between aq. solns. of individual reline components and reline/water mixts. The Walden plot classifies reline as a poor ionic liq.
    69. 69
      Fu, X.; Wu, Z.; Wang, W.; Xie, T.; Keten, S.; Gomez-Bombarelli, R.; Jaakkola, T. Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations. 2022, arXiv:2210.07237. https://arxiv.org/abs/2210.0723web7.
      There is no corresponding record for this reference.
    70. 70
      Stocker, S.; Gasteiger, J.; Becker, F.; Günnemann, S.; Margraf, J. T. How robust are modern graph neural network potentials in long and hot molecular dynamics simulations?. Machine Learning: Science and Technology 2022, 3, 045010,  DOI: 10.1088/2632-2153/ac9955
      There is no corresponding record for this reference.
    71. 71
      McDaniel, J. G.; Choi, E.; Son, C. Y.; Schmidt, J. R.; Yethiraj, A. Ab Initio Force Fields for Imidazolium-Based Ionic Liquids. J. Phys. Chem. B 2016, 120, 7024– 7036, PMID: 27352240  DOI: 10.1021/acs.jpcb.6b05328
      71
      Ab Initio Force Fields for Imidazolium-Based Ionic Liquids
      McDaniel, Jesse G.; Choi, Eunsong; Son, Chang Yun; Schmidt, J. R.; Yethiraj, Arun
      Journal of Physical Chemistry B (2016), 120 (28), 7024-7036CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      We develop ab initio force fields for alkylimidazolium-based ionic liqs. (ILs) that predict the d., heats of vaporization, diffusion, and cond. that are in semiquant. agreement with exptl. data. These predictions are useful in light of the scarcity of and sometimes inconsistency in exptl. heats of vaporization and diffusion coeffs. We illuminate phys. trends in the liq. cohesive energy with cation chain length and anion. These trends are different than those based on the exptl. heats of vaporization. Mol. dynamics prediction of the room temp. dynamics of such ILs is more difficult than is generally realized in the literature due to large statistical uncertainties and sensitivity to subtle force field details. We believe that our developed force fields will be useful for correctly detg. the physics responsible for the structure/property relationships in neat ILs.
    72. 72
      Yeh, I.-C.; Hummer, G. System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions. J. Phys. Chem. B 2004, 108, 15873– 15879,  DOI: 10.1021/jp0477147
      72
      System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions
      Yeh, In-Chul; Hummer, Gerhard
      Journal of Physical Chemistry B (2004), 108 (40), 15873-15879CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      We study the system-size dependence of translational diffusion coeffs. and viscosities in mol. dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coeffs. increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N-1/3, where N is the no. of particles. For a cubic simulation box of length L, the diffusion coeff. cor. for system-size effects is D0 = DPBC + 2.837297kBT/(6πηL), where DPBC is the diffusion coeff. calcd. in the simulation, kB the Boltzmann const., T the abs. temp., and η the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quant. accounts for the system-size dependence of the calcd. self-diffusion coeffs. In contrast to diffusion coeffs., the shear viscosities of water and the LJ fluid show no significant system-size dependences.
    73. 73
      D’Agostino, C.; Harris, R. C.; Abbott, A. P.; Gladden, L. F.; Mantle, M. D. Molecular motion and ion diffusion in choline chloride based deep eutectic solvents studied by 1H pulsed field gradient NMR spectroscopy. Phys. Chem. Chem. Phys. 2011, 13, 21383– 21391,  DOI: 10.1039/c1cp22554e
      73
      Molecular motion and ion diffusion in choline chloride based deep eutectic solvents studied by 1H pulsed field gradient NMR spectroscopy
      D'Agostino, Carmine; Harris, Robert C.; Abbott, Andrew P.; Gladden, Lynn F.; Mantle, Mick D.
      Physical Chemistry Chemical Physics (2011), 13 (48), 21383-21391CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Deep Eutectic Solvents (DESs) are a novel class of solvents with potential industrial applications in sepn. processes, chem. reactions, metal recovery and metal finishing processes such as electrodeposition and electropolishing. Macroscopic phys. properties such as viscosity, cond., eutectic compn. and surface tension are already available for several DESs, but the microscopic transport properties for this class of compds. are not well understood and the literature lacks exptl. data that could give a better insight into the understanding of such properties. This paper presents the first pulsed field gradient NMR (PFG-NMR) study of DESs. Several choline chloride based DESs were chosen as exptl. samples, each of them with a different assocd. hydrogen bond donor. The mol. equil. self-diffusion coeff. of both the choline cation and hydrogen bond donor was probed using a std. stimulated echo PFG-NMR pulse sequence. The increasing temp. leads to a weaker interaction between the choline cation and the correspondent hydrogen bond donor. The self-diffusion coeffs. of the samples obey an Arrhenius law temp.-dependence, with values of self-diffusivity in the range of [10-10-10-13 m2 s-1]. The results also highlight that the mol. structure of the hydrogen bond donor can greatly affect the mobility of the whole system. While for ethaline, glyceline and reline the choline cation diffuses slower than the assocd. hydrogen bond donor, reflecting the trend of mol. size and mol. wt., the opposite behavior is obsd. for maline, in which the hydrogen bond donor, i.e. malonic acid, diffuses slower than the choline cation, with self-diffusion coeffs. values of the order of 10-13 m2 s-1 at room temp., which are remarkably low values for a liq. This is believed to be due to the formation of extensive dimer chains between malonic acid mols., which restricts the mobility of the whole system at low temp. (<30 °C), with malonic acid and choline chloride having almost identical diffusivity values. Diffusion and viscosity data were combined together to gain insights into the diffusion mechanism, which is the same as for ionic liqs. with discrete anions.
    74. 74
      Balucani, U.; Vallauri, R.; Murthy, C. S. Interparticle velocity correlations in simple liquids. J. Chem. Phys. 1982, 77, 3233– 3237,  DOI: 10.1063/1.444199
      74
      Interparticle velocity correlations in simple liquids
      Balucani, U.; Vallauri, R.; Murthy, C. S.
      Journal of Chemical Physics (1982), 77 (6), 3233-7CODEN: JCPSA6; ISSN:0021-9606.
      The momentum transfer of a test particle to a cluster of atoms initially in the first shell of neighbors is investigated at liq. densities by mol. dynamics methods. The comparison of the results obtained for Lennard-Jones and soft spheres models is discussed. In the short time regime, the interpretation of the data parallels that of the single particle velocity autocorrelation function. At longer times, a simple phys. model can account for the decay of the cross correlation in terms of the increasing no. of atoms involved in the process.
    75. 75
      Verdaguer, A.; Padró, J. A.; Trullàs, J. Molecular dynamics study of the velocity cross-correlations in liquids. J. Chem. Phys. 1998, 109, 228– 234,  DOI: 10.1063/1.476555
      75
      Molecular dynamics study of the velocity cross-correlations in liquids
      Verdaguer, A.; Padro, J. A.; Trullas, J.
      Journal of Chemical Physics (1998), 109 (1), 228-234CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Velocity cross-correlations for both soft-sphere fluids at different densities and temps. and a simple molten salt are investigated by mol. dynamics simulation. Time correlation functions between the velocity of a tagged particle and velocities of particles within specified ranges of initial sepns. are calcd. In the case of the soft-sphere fluids, sepn. ranges corresponding to the first, second and third shells of neighbors are considered, whereas up to six different shells are analyzed for the molten salt. The calcd. functions allow us to build a picture of the spread of the initial momentum of a tagged particle over the successive shells of neighbors. It is obsd. that collisions with intermediate particles are the main mechanism for the transfer of momentum. A balance between the momentum exchanged by particles in a given shell with those in the two adjacent shells should be carried out in order to analyze the resulting velocity cross-correlation functions. The rate of transfer of momentum between distant particles increases with the d. and temp. of the liq. It has been noticed an incipient coherence, which is more marked for the ionic melt, between the motions of atoms in nonadjacent shells.
    76. 76
      Balucani, U.; Vallauri, R.; Murthy, C. Momentum transfer analysis in Lennard-Jones fluids. Phys. Lett. A 1981, 84, 133– 136,  DOI: 10.1016/0375-9601(81)90736-2
      76
      Momentum transfer analysis in Lennard-Jones fluids
      Balucani, U.; Vallauri, R.; Murthy, C. S.
      Physics Letters A (1981), 84A (3), 133-6CODEN: PYLAAG; ISSN:0375-9601.
      For Ar with the atoms interacting via a Lennard-Jones potential (a) near the triple point and (b) in the gas phase (at intermediate d.) at room temp., the cross-correlation functions and the velocity autocorrelation functions (vacf) were obtained in mol.-dynamics simulations (with 108 Ar atoms), and were used to analyze momentum transfer between a test atom and its neighbors. The anal. provided information on the dynamic processes leading to the decay of the single-particle vacf.
    77. 77
      Endo, Y.; Endo, H. Microscopic motions and the local environments of atoms in simple liquids. J. Chem. Phys. 1984, 80, 2087– 2091,  DOI: 10.1063/1.446974
      77
      Microscopic motions and the local environments of atoms in simple liquids
      Endo, Yoshikazu; Endo, Homare
      Journal of Chemical Physics (1984), 80 (5), 2087-91CODEN: JCPSA6; ISSN:0021-9606.
      Mol. dynamics simulations are carried out in order to understand the microscopic mechanism of at. motions in simple liqs. The radial distribution function is classified into subgroups by taking a partial av. over the atoms having the same coordination no. in the first shell. By considering this classified distribution of atoms as an initial one, the time evolution of the radial distribution function, and the velocity auto- and cross-correlation functions are calcd. in each subgroup. Investigation through these "microscopic" correlation functions reveals the details of at. motions which would be obscured if the totally averaged correlation functions were used. An atom in a region of low local d. oscillates weakly for a long period, because the low-d. region is surrounded, on the av., by the high d. region of atoms. An atom in a region of high local d. receives a strong rebound from the neighboring atoms, but behaves less oscillatory at subsequent times, because the neighboring atoms more toward the outer region of low d.
    78. 78
      Flener, P.; Vesely, F. J. Correlated motion of two particles in a fluid. Mol. Phys. 1992, 77, 601– 615,  DOI: 10.1080/00268979200102651
      78
      Correlated motion of two particles in fluid. II. Molecular-dynamics results
      Flener, Peter; Vesely, Franz J.
      Molecular Physics (1992), 77 (4), 601-15CODEN: MOPHAM; ISSN:0026-8976.
      Conditional velocity cross correlation function of the form 〈vi(0vj(t);rij(0)〉 in the Lennard-Jones fluid are investigated by mol. dynamics simulation. As shown in previous work, these cross correlation functions may be related to memory functions in a similar manner as the usual velocity auto-correlation function. To compute the memory functions, a modified version of Detyna and Singer's algorithm has been used.
    79. 79
      Balucani, U.; Zoppi, M. Dynamics of the Liquid State; Clarendon Press, 1995; Vol. 10.
      There is no corresponding record for this reference.
    80. 80
      Verdaguer, A.; Padró, J. A. Computer simulation study of the velocity cross correlations between neighboring atoms in simple liquid binary mixtures. J. Chem. Phys. 2001, 114, 2738– 2744,  DOI: 10.1063/1.1340581
      80
      Computer simulation study of the velocity cross correlations between neighboring atoms in simple liquid binary mixtures
      Verdaguer, A.; Padro, J. A.
      Journal of Chemical Physics (2001), 114 (6), 2738-2744CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The dynamic behavior of atoms in simple liq. binary mixts. is analyzed by mol. dynamic simulation. Time correlation functions between the initial velocity of a tagged particle and latter velocities of neighboring particles are calcd. for soft-sphere liq. mixts. of species with different mass and/or size. The transfer of momentum from a tagged particle to its neighbors as well as the differences between the velocity cross correlation between particles of the same or different species is discussed.
    81. 81
      Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids, 3rd ed.; Hansen, J.-P., McDonald, I. R., Eds.; Academic Press: Burlington, 2006; pp 291– 340.
      There is no corresponding record for this reference.
    82. 82
      Rey-Castro, C.; Vega, L. F. Transport Properties of the Ionic Liquid 1-Ethyl-3-Methylimidazolium Chloride from Equilibrium Molecular Dynamics Simulation. The Effect of Temperature. J. Phys. Chem. B 2006, 110, 14426– 14435, PMID: 16854152  DOI: 10.1021/jp062885s
      82
      Transport Properties of the Ionic Liquid 1-Ethyl-3-Methylimidazolium Chloride from Equilibrium Molecular Dynamics Simulation. The Effect of Temperature
      Rey-Castro, Carlos; Vega, Lourdes F.
      Journal of Physical Chemistry B (2006), 110 (29), 14426-14435CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      We present here equil. mol. dynamics simulation results for self-diffusion coeffs., shear viscosity, and elec. cond. in a model ionic liq. (1-ethyl-3-methylimidazolium chloride) at different temps. The Green-Kubo relations were employed to evaluate the transport coeffs. When compared with available exptl. data, the model underestimates the cond. and self-diffusion, whereas the viscosity is overpredicted, showing only a semiquant. agreement with exptl. data. These discrepancies are explained on the basis of the rigidity and lack of polarizability of the model. Despite this, the exptl. trends with temp. are remarkably well reproduced, with a good agreement on the activation energies when available. No significant deviations from the Nernst-Einstein relation can be assessed on the basis of the statistical uncertainty of the simulations, although the comparison between the elec. current and the velocity autocorrelation functions suggests some degree of cross-correlation among ions in a short time scale. The simulations reproduce remarkably well the slope of the Walden plots obtained from exptl. data of 1-ethyl-3-methylimidazolium chloride, confirming that temp. does not alter appreciably the extent of ion pairing.
    83. 83
      Reuter, D.; Binder, C.; Lunkenheimer, P.; Loidl, A. Ionic conductivity of deep eutectic solvents: the role of orientational dynamics and glassy freezing. Phys. Chem. Chem. Phys. 2019, 21, 6801– 6809,  DOI: 10.1039/C9CP00742C
      83
      Ionic conductivity of deep eutectic solvents: the role of orientational dynamics and glassy freezing
      Reuter, Daniel; Binder, Catharina; Lunkenheimer, Peter; Loidl, Alois
      Physical Chemistry Chemical Physics (2019), 21 (13), 6801-6809CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      We have performed a thorough examn. of the reorientational relaxation dynamics and the ionic charge transport of three typical deep eutectic solvents, ethaline, glyceline and reline, by using broadband dielec. spectroscopy. Our expts. cover a broad temp. range from the low-viscosity liq. down to the deeply supercooled state, allowing us to investigate the significant influence of glassy freezing on the ionic charge transport in these systems. In addn., we provide evidence for a close coupling of the ionic cond. in these materials to reorientational dipolar motions, which should be considered when searching for deep eutectic solvents optimized for electrochem. applications.
    84. 84
      Tan, A. R.; Urata, S.; Goldman, S.; Dietschreit, J. C. B.; Gómez-Bombarelli, R. Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles. 2023, arXiv:2305.01754 https://arxiv.org/abs/2305.0175web4.
      There is no corresponding record for this reference.
    85. 85
      Niblett, S. P.; Galib, M.; Limmer, D. T. Learning intermolecular forces at liquid–vapor interfaces. J. Chem. Phys. 2021, 155, 164101,  DOI: 10.1063/5.0067565
      85
      Learning intermolecular forces at liquid-vapor interfaces
      Niblett, Samuel P.; Galib, Mirza; Limmer, David T.
      Journal of Chemical Physics (2021), 155 (16), 164101CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      By adopting a perspective informed by contemporary liq.-state theory, we consider how to train an artificial neural network potential to describe inhomogeneous, disordered systems. We find that neural network potentials based on local representations of at. environments are capable of describing some properties of liq.-vapor interfaces but typically fail for properties that depend on unbalanced long-ranged interactions that build up in the presence of broken translation symmetry. These same interactions cancel in the translationally invariant bulk, allowing local neural network potentials to describe bulk properties correctly. By incorporating explicit models of the slowly varying long-ranged interactions and training neural networks only on the short-ranged components, we can arrive at potentials that robustly recover interfacial properties. We find that local neural network models can sometimes approx. a local mol. field potential to correct for the truncated interactions, but this behavior is variable and hard to learn. Generally, we find that models with explicit electrostatics are easier to train and have higher accuracy. We demonstrate this perspective in a simple model of an asym. dipolar fluid, where the exact long-ranged interaction is known, and in an ab initio water model, where it is approximated. (c) 2021 American Institute of Physics.
    86. 86
      Montes-Campos, H.; Carrete, J.; Bichelmaier, S.; Varela, L. M.; Madsen, G. K. H. A Differentiable Neural-Network Force Field for Ionic Liquids. J. Chem. Inf. Model. 2022, 62, 88– 101, PMID: 34941253  DOI: 10.1021/acs.jcim.1c01380
      86
      A Differentiable Neural-Network Force Field for Ionic Liquids
      Montes-Campos, Hadrian; Carrete, Jesus; Bichelmaier, Sebastian; Varela, Luis M.; Madsen, Georg K. H.
      Journal of Chemical Information and Modeling (2022), 62 (1), 88-101CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      We present NEURALIL, a model for the potential energy of an ionic liq. that accurately reproduces first-principles results with orders-of-magnitude savings in computational cost. Built on the basis of a multilayer perceptron and spherical Bessel descriptors of the at. environments, NEURALIL is implemented in such a way as to be fully automatically differentiable. It can thus be trained on ab initio forces instead of just energies, to make the most out of the available data, and can efficiently predict arbitrary derivs. of the potential energy. Using ethylammonium nitrate as the test system, we obtain out-of-sample accuracies better than 2 meV atom-1 ( < 0.05 kcal mol-1) in the energies and 70 meV Å-1 in the forces. We show that encoding the element-specific d. in the spherical Bessel descriptors is key to achieving this. Harnessing the information provided by the forces drastically reduces the amt. of at. configurations required to train a neural network force field based on atom-centered descriptors. We choose the Swish-1 activation function and discuss the role of this choice in keeping the neural network differentiable. Furthermore, the possibility of training on small data sets allows for an ensemble-learning approach to the detection of extrapolation. Finally, we find that a sep. treatment of long-range interactions is not required to achieve a high-quality representation of the potential energy surface of these dense ionic systems.

  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00944.

    • Details of the DFTB-based MD simulations, additional radial and angular distribution functions, simulation box sizes and viscosities, mean-square displacement plots and self-diffusion coefficients from the Green–Kubo approach with details of the correction term for the finite-size effects, and velocity cross-correlation functions for longer correlation times (PDF)


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