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C: Chemical and Catalytic Reactivity at Interfaces

Lateral Interactions of Dynamic Adlayer Structures from Artificial Neural Networks
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The Journal of Physical Chemistry C

Cite this: J. Phys. Chem. C 2022, 126, 12, 5529–5540
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https://doi.org/10.1021/acs.jpcc.1c10401
Published March 17, 2022

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Abstract

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Lateral interactions are a key factor in the correct description of adsorption isotherms relevant to heterogeneous catalytic reactions. To model these lateral interactions, a large number of monolayer structures have to be investigated, far exceeding the limitations of conventional techniques such as density functional theory. We have developed a new hybrid neural network model that can substitute the electronic structure calculations for these monolayer structures, without significant loss of accuracy. The low computational cost of this model allows the study of the adlayer structures close to industrial operating conditions. Lateral interactions are found to increase at elevated temperatures as a result of increased adsorbate mobility, and this contribution is found to be key in unifying theoretical and experimental observations. We show that the inclusion of dispersion interactions in stabilizing the adlayers is necessary to obtain correct predictions for both isotherms and adsorption site distributions.

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Introduction

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Microkinetic modeling allows us to describe the reaction rates of complex networks of chemical reactions. It is widely used in heterogeneous catalysis to describe the kinetics of surface reactions based on elementary reaction steps involving surface-adsorbed intermediates. (1,2) Typically, the reaction energetics (adsorption energies and activation barriers) are obtained from density functional theory (DFT) calculations of single adsorbates. However, in practice, surface coverages can be high due to mild reaction temperatures or high reaction pressures. Lateral interactions between adsorbed species cannot be neglected when the aim is to accurately predict the kinetics of the overall catalytic reaction. (3,4) Describing such lateral interactions at the DFT level is preferred but challenging because of the inherently high cost of DFT combined with the large number of adlayer configurations that must be studied.
Several notable advances have been made in deriving coverage-dependent reaction energetics. Within the microkinetic approach, coverage-dependent adsorption energies can be obtained through interpolation of DFT data. (4−17) Self-consistent feedback approaches have also been developed, wherein the DFT coverages are updated based on the results from the microkinetic simulations. (18−21) Adsorption rates can alternatively be obtained through kinetic Monte Carlo simulations. (3,22−26) Interactions between adsorbates are then described using sets of multibody interactions, which can again be determined by DFT. We observe that these state-of-the-art methods, while successful in reproducing experimental results, still rely on approximations. Microkinetic models utilize fixed interpolation functions. Multibody models are typically truncated to two-body terms to avoid tabulation of a large number of configurations. (3,22,23) Even for self-consistent approaches, computational limitations restrict the DFT model to discrete coverages, thereby limiting the resolution of coverages in the microkinetics. (18,22) To improve on existing modeling efforts, we therefore seek a method that can accurately describe lateral interactions without reliance on approximations.
Computational limitations in the scale-up of quantum chemical (QC) methods are common in many branches of computational chemistry. (27−29) Traditional solutions use semi-empirical models to extrapolate energy-structure relationships from available QC data, as with (reactive) force-fields and tight-binding models. (30−32) These methods are based on potential models, enhancing computational efficiency at the cost of accuracy relative to full electronic structure calculations. In recent years, data-driven machine learning (ML) approaches have emerged as an alternative to traditional force fields. (29,33,34) While the semi-empirical models are based on a set of rigorous equations wherein the parameters are tuned to provide a good fit with a given training set, data-driven methods do not a priori assume any kind of rigorous mathematical form. Instead, they utilize a flexible set of matrix equations that can adopt any kind of known mathematical function. (35) The rigorous mathematical form of semi-empirical methods leads to forms of descriptive biasing, which are absent in data-driven methods. From the user perspective, the data-driven nature lends to a more methodological approach of model construction. This shifts the investment cost to the data generation stage, facilitating better scalability.
Early examples of the use of ML in chemistry include the interpretation of experimental and spectroscopic data (36,37) and the discovery of new materials and chemicals by extraction of correlations between chemical properties. (38−40) The attention then shifted toward application in atomistic modeling. The initial focus on construction of ML-assisted semi-empirical models (41) has now been largely replaced by full reconstruction of potential energy surfaces (PES) determined by QC. (42,43) A breakthrough in this development can be attributed to high-dimensional neural network potential (HDNNP) (33,44−46) models, which facilitate tackling problems with higher degrees of freedom. (27−30,47−53) Recently, Gaussian approximation potentials (34,54,55) are increasing in popularity, boasting high accuracy and robustness, although at higher computational cost than HDNNP.
In this work, we present a hybrid ML model for the description of adlayer compositions in heterogeneous catalysis, which combines features from both kernel-based atomic potentials (such as HDNNP) and quantitative structure-property relationship (QSPR) networks. (38−40,56−58) A methodology based on molecular degrees of freedom allows for automated construction of small, cost-efficient datasets. The effectiveness of our method is shown for a model system composed of flat (001) and stepped (211) cobalt surfaces, allowing comparison to available experimental and theoretical data. (4,59) By leveraging the low computational cost of this workflow, we can critically assess how the choice of exchange-correlation functional and dispersion corrections in the development of the dataset influences the description of the adsorption layer in connection to the experiment. Furthermore, we show that the lateral interactions depend on temperature. Here, increased adsorbate mobility can create dynamic adlayer structures, affecting both adsorption site distributions and lateral interactions. This mobility effect is found to be a crucial aspect for correctly describing experimentally observed adsorption trends.

Methods

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Basis Functions and Network Architecture

The ML approach employed here is that of the artificial neural network (ANN). (60) The general mathematical expression of an ANN can be written in recursive form
(1)
The ANN entails a series of sequential, alternating basis (W̿) and non-linear (F) transformations of a set of input parameters o̅0. The basis transformations map the input space onto a new space spanned by compound variables. The non-linear transforms and bias shifts (b̅) are then used to connect the transformed input to the desired output. By tuning the transformations, the overall mapping between the network input and output can be defined to represent a correlation of the data. During this process, the network has the freedom to define its own intermediate compound variables and is therefore free from any framework bias. Chaining multiple transforms allows defining correlations as a series of connections between different sets of compound variables, increasing the complexity of the model. Because of the periodic linear transforms, linearized optimization of the ANN variables is possible, resulting in computationally efficient training algorithms.
The purpose of the ANN in the present study will be to predict the energy of the atomic configurations, i.e., of the adlayer structures, as is typically done using QC. As the number of adsorbates may vary, the dimensionality of the input space must be invariant to the number of atoms in the system. The system is therefore decomposed into a set of atomic ANN each describing the contribution to the system energy from a particular atom. One atomic ANN will be constructed per element to allow transferability between systems.
(2)
While it is possible to use traditional decomposition schemes (61) to determine the atomic energies EA, here, the choice of decomposition was integrated as a linear transform c̅ in the ANN to limit model bias.
To distinguish between different atomic configurations, it is necessary to include structural descriptors to the input space. In the literature, many successful approaches have been reported for the geometric description of adsorbates using ML. (27,54,62−66) A common factor between these approaches is their use of multibody interaction kernels as a basis for describing the interactions between atoms. This is seen with, e.g., the atom-centered symmetry function (ACSF) class of methods, (27,45,46,54,62) which employ interaction potentials based on modified atomic distribution functions, or methods such as the smooth overlap of atomic positions (SOAP), which employ expansions of coordination environments into more traditional basis functions (Gaussians and spherical harmonics). (54,55,63,66) Many further variations exist, e.g., partial radial distribution functions, (64) Coulomb matrices, (65) and internal coordinate descriptors. (42,65,66)
In this work, we employ an approach inspired by ACSF/SOAP. Orientational invariance is achieved by defining a basis sampling radial and angular distribution functions, which are evaluated per atom. The signal intensity per function can be used to define the relative atom density distribution around the reference atom, characterizing the coordination environment. This process is illustrated in Figure 1.

Figure 1

Figure 1. Illustration of radial (a) and angular (b) coordination descriptors. Radial distributions are defined with respect to the atom marked as (i), angular distributions relative to the axis between atoms (i,j). Different descriptors are shown using various colors. The graphs show the signal values as a function of the descriptor parameters. (a) Left: cutoff function gc for various cutoff radii. Right: radial coordinate descriptors Ri for various decay rates. (b) Angular coordinate descriptors Ai for various angular decay parameters.

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First, the distributions are limited to a local coordination environment by introducing a smooth cutoff function (34,62)
(3)
where r represents the interatomic distance and rc represents the radius of a cutoff sphere. For the radial sampling, this local environment is split into a set of subshells using a basis of Gaussians, defined by different decay rates η as given by
(4)
Within each radial shell, the distribution of angles between neighbors is sampled
(5)
with λ and ζ controlling the range of angles sampled by each descriptor. It is chosen here to omit the interaction of the neighbors gc(rjk) as it was found otherwise to result in low signal intensities for most angular functions. Compared to most ACSF methods, (45,46,62) these descriptors are not selective or weighted toward particular chemical elements.
A limitation of the described approach is the absence of explicit electronic information in the network input since the electronic effects must be learned implicitly as part of the atomic decomposition. To improve the network, the geometric description above is hybridized with a classical QSPR approach to allow better differentiation of local electronic character and to accelerate and improve the fitting procedure. The architecture of this hybrid network is shown in Figure 2. Within QSPR, the pattern-recognition capabilities of ML are used to find correlations directly between system properties without relying on atomistic models. The direct predictive quality of QSPR can now be leveraged to let the ANN make deductions on reactivity and stability based on physically relevant parameters, reminiscent of the force-field approaches. Several electronic parameters will be provided to supplement the structural descriptors. Two different forms for these electronic parameters were considered. First is the use of atomic parameters εi determined entirely by the nature of the atom, the common descriptors used in QSPR. Examples include atomic charge, magnetic moments, or electronegativity. Alongside these, effective local parameters are used that modify the atomic descriptors by accounting for the presence of the neighboring atoms in the local coordination environment. The latter therefore represents field- or density-averaged properties specific to the molecular environment. Different representations are used for scalar parameters
(6)
or vector properties
(7)
where H is the Heaviside function, which is used to limit the interaction range to the cutoff volume without introducing a radial dependence.
(8)

Figure 2

Figure 2. Schematic depiction of the hybrid network architecture. Separate geometric and electronic depictions of a molecular geometry are obtained, from which the atomic networks reconstruct the total energy. This compares to classical approaches in which only the geometric representation is used. Geometric and electronic information are communicated to the atomic networks using a set of basis functions, each represented as a single input node. One atomic network is constructed per chemically unique element (here shown in green, yellow, and red).

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For determining the network parameters, a training dataset is constructed for which the distribution of descriptor values can be analyzed. As the dataset only provides a finite representation of the full input space, it yields an approximation of the true descriptor distributions. This allows us to determine the contributions of the individual basis functions to the representations of our samples. Basis functions that do not contribute significantly to the resolution of the network can be filtered prior to the network fitting, allowing for fully automated construction of an optimized basis set specific to the system of interest: (I) Basis functions with low signal intensity, thus poor numerical resolution, are filtered first by imposing a minimum intensity requirement, which was chosen here to a value of 0.01 (corresponding to a minimum of 10% of the maximum signal intensity for the normalized descriptors); (II) sample homogeneity is restricted by imposing a minimum deviation of 2% of samples at 0.01 dispersity to avoid signals with poor differentiability; (III) to resolve overlapping signals, a continuous similarity recurrence (CSR) metric is introduced.
(9)
with two descriptors denoted as signals Ga and Gb for a dataset of size ζ. A large CSR overlap between two signals would indicate that their output differs significantly for most samples. Signals that have low CSR values for all descriptor pairs can be characterized as redundant and are removed from the basis set, while signals with high CSR values highlight symmetry classes that may require extension of the basis set. CSR thresholds of 5% were used in this work. This approach allows for informed construction and optimization of a basis set, without the need to repeatedly retrain the network.

Automated Dataset Generation

The quality of an ANN depends strongly on the dataset used for its construction. If segments of the configurational space are omitted, then extrapolations into this domain may result in unpredictable behavior. As such, when constructing a dataset, it is critical that all domains that will be accessed in target studies for the ANN have been explored. On the other hand, it is desirable to make the dataset as small as possible. Each sample point requires a DFT calculation to be performed, making this the computationally most expensive stage of the model construction. Because the networks are system-specific, requiring construction of a new network and corresponding dataset for each system, it is critical for this process to be as cheap as possible if widespread application is to be achieved.
To balance the dataset cost-effectiveness, a uniform sampling in feature space is proposed. Herein, the internal degrees of freedom of the molecular ensemble will be used to define the configurations for the dataset. This process is illustrated in Figure 3 with algorithmic details provided in the Supporting Information. Our method is system-independent, facilitating fully automated generation of datasets once a system is defined. By sampling the chemical configurational space, this should limit the overlap within the dataset as much as possible by eliminating symmetry-equivalent configurations and considering equal sampling of the translational, rotational, and vibrational subspaces. The latter is especially important considering that both single-adsorbate states and higher monolayer coverages will be included in the same dataset. Additionally, we can readily quantify the extent to which our model is applicable for a particular system. For example, if it is chosen to restrict sampling of vibrations up to a (small) maximum displacement, then the model should not be used in simulations involving stronger distortions of the molecular geometry.

Figure 3

Figure 3. Different stages of dataset construction: I. Translational states along a geometrically bounding potential surface. II. At each translational site, different rotations are obtained by rotating the molecule along two internal coordinates. III. Each rotation is expanded into a set of vibrational states. IV. Combinations of these states are used to construct a set of adlayers. At this step, translations are extended over a set of support grids to alleviate symmetry constraints. Note the sparser sample density over these extended surfaces.

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Results and Discussion

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We will first demonstrate the performance of our method for a well-defined system of CO adsorption on metallic hcp-cobalt (001) and (211) surfaces. Cobalt-catalyzed CO conversion is a crucial step for industrial processes such as FTS, and as such, both experimental and theoretical reference data are readily available. (1,4,59,67−69) Two different surface facets were considered to compare the effect of surface morphology and network performance. In the following segment, we will first validate the generated ANN models followed by a performance comparison against other methodologies. Afterward, we will apply our ANN to describe lateral interactions for CO adsorbed on Co(001) and Co(211) surfaces.

Machine Learning

Datasets were generated for both surfaces using the generation process described in the methods section, resulting in 551 samples for the (001) surface and 851 samples for the (211) surface. Herein, the larger size of the dataset of the (211) surface corresponds with the larger surface area for the primitive cell. DFT calculations were performed using a PBE exchange-correlation functional (70) to allow direct comparison to the literature. (4,5) The CSR was used to optimize the basis set followed by a hyperparameter screening to determine the network architecture. Details of these processes can be found in the Supporting Information.
The resulting networks reproduced the DFT data with root-mean-square-errors (RMSEs) of 0.22 meV/atom for Co(001) and 0.31 meV/atom for Co(211) and biases less than 0.01 meV/atom. This is well within the typical measure of chemical accuracy of 1 kcal/mol. This threshold is typically used in the context of comparing experimental and theoretical results, considering both numerical and experimental accuracy. As such, variations less than 4 kJ/mol will fall within the standard uncertainty of any theoretical method. For energy calculations, this corresponds with approximately 0.8 meV/atom for typical system sizes. Here, a per-atom accuracy metric is standard in ANN studies, given that the system sizes vary between samples. We see that our networks fall well within this margin.
Training, validation, and test subset error distributions have comparable mean and variance (shown in Table S1) indicating an absence of overfitting. The extrapolation behavior of our networks was tested by generating a secondary reference dataset with a sample density twice as large as the original set. The distribution of errors of this reference was found to be similar to that of the original dataset, even after filtering out samples shared between the datasets (0.24 meV/atom for Co(001) and 0.31 meV/atom for Co(211), see Table S2). This indicates correct extrapolation beyond the training set employed by the network. The RMSEs of the single-adsorbate and adlayer subsets were found to differ by less than 0.01 meV/atom, indicating that our models do not bias toward either set of samples.
The quality of an ANN is proportional to the amount of information contained in the training data. As both surface models contain the same chemical elements, we have explored the effect of combining both surfaces into a single network to benefit from an extended dataset. Similarly, we have explored addition of atomic carbon and oxygen data to observe if a similar trend holds for the adsorbate. The results are summarized in Tables S12–S14. A substantial improvement of the quality over the single-surface and single-adsorbate networks is observed. For the complete dataset, the overall RMSE decreases from 0.27 to only 0.18 meV/atom while subset biasing remains minimal. The skew is seen to decrease due to the smaller effective stepsize of the optimizer. This improvement in fit quality when adding additional adsorbates to the dataset follows as the distribution of coordination descriptors broadens. The effect levels off as the number of unique adsorbates increases, either due to the saturation of the distribution or numerical limitations in descriptor resolution. When adding different surfaces, the improvement in quality is more pronounced on account of the dissimilarity in descriptor distributions for either surface. The most prominent improvement is observed for the (211) surface. As the (211) dataset employs a sparser sampling than the (001) dataset (because of computational considerations), the former benefits the most from the extended number of samples. The combined datasets were also observed to improve the uniformity between training, validation, and test set error distributions owing to the more diverse array of chemical configurations in the input. This effect was most notable for CO as the addition of C and O data helps to establish atomic reference levels within the ANN framework.
Compared with the literature, other ANN methodologies have employed trajectory data from molecular dynamics (MD) as their training set, yielding on the order of 104 to 105 samples. (29,30,33) The approach taken in this work allows for much smaller datasets by exploiting chemical principles. The use of single-point calculations instead of local energy minima furthermore helps in capturing the rough features of the potential energy surfaces at lower sampling density by avoiding the bias induced by applying geometry optimizations. The more disperse sampling in our method avoids the existence of large extrapolation regimes, where the ANNs are known to perform poorly, (28,29,33) thereby obtaining solid predictive performance.

Effect of Network Hybridization

Key to supporting the small datasets is the proper mapping of the descriptor spaces as well as the resulting resolution for distinguishing samples. The hybridization of our networks was found to be the responsible factor in this regard. In Figure 4, we have compared the performance of our hybrid ANN to a selection of networks employing a purely structural basis set. Even after reoptimization of the network architecture, these models show notably larger errors. Increasing the size of the dataset used for training these networks does not significantly impact the observed error distributions, indicating that the network has reached a limit in its ability to learn additional details of the PES. Indeed, a more profound effect is observed when switching to an extended basis set (obtained by relaxing the CSR thresholds). Chemically accurate fit qualities are only obtained by combining both the extended basis set and extended dataset, in line with the other networks reported in the literature. (54,61) In the context of traditional HDNNP methods, increased architectural sizes and more narrow application foci of the datasets generated using MD suggest the presence of redundant parameters in the structural networks. (28−30,33,47) These networks require much larger datasets than the hybrid networks used here, partially on account of their larger size. The larger parameter set allows easier parametrization of the provided data but in turn increases the risk of overfitting that becomes critical once we exit the interpolation domain. This is supported by the trends observed here for the basis set size dependence and the observation of smaller extrapolation errors for the hybrid networks. The two network types therefore show different compatibilities with the small datasets.

Figure 4

Figure 4. Error distributions for a selection of CO/Co(001) networks. Model (II) is a purely structural network with the same architecture as the single-transform hybrid ANN detailed in the main text. Model (III) is a structural network with a reoptimized architecture with dimensionality 20 and 2 transforms. Model (IV) uses the reoptimized architecture but with the extended dataset (II) as the training dataset. Model (V) uses the reoptimized architecture along with an extended descriptor set (trained using dataset (I), parameters are provided in Figure S2). Model (VI) combines the extended dataset (II) with the extended descriptor set of model (V). Additional details are provided in Table S11.

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Comparing the descriptor distributions across the samples in our datasets, the electronic basis functions appear to do well in distinguishing the surface from bulk states and empty sites from adsorption sites based on the electronic environment. The electronic basis functions are largely uncoupled from the geometric ones, reducing underlying interdependencies between network inputs. As interactions of Co–CO can be traced specifically to surface states, electronic augmentation helps achieve the good predictive behavior and high accuracy of the hybrid networks.

Lateral Interactions

Using the ANN developed in the previous section to describe the potential energy as function of the adlayer configuration, we here demonstrate its application in describing the average adsorption energy of CO as function of the surface coverage, temperature, and pressure. Such a description aids in advancing microkinetic modeling studies by incorporation of lateral interactions, allowing for more realistic simulations under typical working conditions. For example, reaction barriers are conventionally treated in a static fashion in such simulations but can be made dependent on the coverage to model the effect of lateral interactions.
To compute the interaction energy at elevated temperature, Monte Carlo (MC) simulations were performed as detailed in the Supporting Information. Since the ANN is orders of magnitude cheaper to evaluate than DFT, it can easily serve as the underlying potential in these simulations. The ANN uses a 15 × 15 unit cell for Co(001) and a 20 × 20 unit cell for Co(211), in contrast to the 3 × 3 and 4 × 4 unit cells for DFT. These larger unit cells support a higher resolution of coverages. For our analysis, we have used PBE-DFT data to train our networks in line with earlier literature studies. (4,5) The effect of the exchange-correlation functional in experimental comparison will be revisited in the next section.
Figure 5 shows the results for the average adsorption energy of CO as a function of the coverage for the Co(001) and Co(211) surfaces at 0, 300, and 500 K. A comparison is made against DFT results from geometry optimizations, which corresponds to the 0 K system. From this figure, it can be seen that the ANN closely matches the result found by DFT. Additionally, the ANN has now provided us with the interaction energy at the intermediate coverages without resorting to interpolation methods.

Figure 5

Figure 5. ANN potentials for the CO adsorption energy in the presence of lateral interactions over the left (Co(001)) and middle (Co(211)). Profiles at 300 and 500 K are derived from temperature-corrected adlayer energies obtained through MC. Hexagonal markers represent reference DFT minimum energy points. Right: onset coverage at which temperature-dependent lateral interaction potentials deviate from the 0 K potential by >1 kJ/mol.

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At temperatures above 0 K, the adsorbates possess sufficient kinetic energy to traverse the PES, allowing them to access states above the energy minimum. This results in an increase in the average energy as readily seen in Figure 5. Below a fractional coverage of around 0.2 ML, the average energies at 0, 300, and 500 K are very similar. At low surface coverage, the distance between the neighboring adsorbates is too large for any noticeable lateral interactions. With increasing coverage, the distance between the adsorbates is smaller and an increased lateral interaction penalty is observed. This lateral interaction penalty increases with temperature as the adsorbates occupy a larger effective volume on the catalytic surface given their increased lateral mobility.
We can hence define a low and a high coverage domain, considering the temperature effect on the lateral interactions. In the low coverage domain, the distance between the adsorbates is sufficiently large that the increased occupational space of the adsorbates due to their enhanced mobility does not result in a noticeable difference in the lateral interactions as compared to the 0 K situation. The high coverage regime starts when this difference exceeds a set threshold. In Figure 5, this boundary surface coverage, marking the transition between the low and high coverage regimes, is shown as a function of temperature for a(n arbitrary) numerical threshold of 1.0 kJ/mol. The nonlinearity of these profiles relates to the exponential dependency of the hopping behavior of the adsorbates with temperature and the changes in the symmetry patterns of the adlayer with varying coverage.
Comparing the Co(001) and Co(211) surfaces, a few important differences can be observed, which can be directly attributed to the surface topology. Since the Co(001) surface is completely flat and rather homogeneous in terms of adsorption sites, we observe a gradual increase in the average adsorption energy as function of the coverage. For the Co(211) surface, which is more heterogeneous in terms of its adsorption site distribution, a more step-like curve is found. Below ∼0.35 ML coverage, the CO molecules can be distributed among a set of similar threefold adsorption sites (see Figure 6). Once these sites are all occupied, CO adsorbs on top sites in between the threefold sites, giving rise to a rapid decrease in the average adsorption energy. The next sharp increase is observed around 0.6 ML. Due to the large number of CO species adsorbed on the surface, the configuration where predominantly threefold sites are occupied becomes unfavorable as this configuration exhibits strong lateral repulsion. To mitigate this repulsion, the adlayer topology changes completely and predominantly bridge and on-top sites are occupied. A similar rapid change in the surface configuration is observed around 0.8 ML where the dominant adsorption mode changes from bridged to on-top.

Figure 6

Figure 6. Minimum energy structures for CO/Co(211) predicted with the ANN. From left to right: 0.2, 0.4, 0.7, and 0.9 ML.

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The results as shown in Figure 5 can be directly utilized to describe lateral interactions in a mean-field manner, allowing these to be included in a microkinetic model. In Figure 7, the equilibrium CO coverage as function of temperature is shown. Herein, a comparison is made between our simulated results with and without the lateral correction potential and experimental data obtained from the literature both at ultrahigh vacuum and under atmospheric pressure. (59) Without lateral interactions at 1 bar, an unrealistic coverage of 1 ML is predicted below T = 700 K. Including the lateral interactions, the surface coverages modeled at p = 10–7 and 1 bar are in good agreement with experimental results. The deviation with the experiment at p = 10–7 bar in the temperature range near 200–350 K is highly sensitive to the calculated adsorption energy for CO. This deviation can be reduced by a small adjustment to the CO adsorption energy within the order of accuracy of MC.

Figure 7

Figure 7. Left: equilibrium CO coverage on the Co(001) surface, determined from a microkinetic model (MKM) composed of a single-reversible adsorption step with coverage-dependent adsorption energies. (Details are provided in the Supporting Information). The HK model omits lateral interactions. Markers show experimental data published by Weststrate et al. (59) Right: effect of the temperature correction applied to the lateral interaction model at 1 bar.

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The sharp drop from 0.7 to 0.5 ML coverage at T = ∼250 K at p = 10–7 bar and T = ∼350 K at p = 1 bar is attributed to a sudden rearrangement of the CO molecules due to a rapid increase in the lateral interactions as the result of the increasing temperature. Multibody decomposition of the ANN energies (Table S21) revealed that the adequate modeling of this transition requires including interactions between CO molecules over multiple coordination shells (nearest, next-nearest, and even further neighbors). Pair interactions were found to be sufficient at describing the system only at low coverages <0.2 ML, when the surface is sparsely occupied and clustering of adsorbates is rare. Successive addition of triplet- and quartet-interactions converges the model toward the full ANN solution at higher coverages >0.6 ML (Figure S16). Here, densely packed structures are formed, for which short-range interactions are expected to dominate. For an intermediate regime of 0.2–0.6 ML, however, accurate decomposition of the complex surface structures would require incorporation of many higher-order terms. This task has been successfully delegated to the ANN.
The decrease in binding of the adsorbates due to their increased mobility on the surface was shown to be strongly non-linear in the coverage as a result of changes in the occupation of different adsorption sites. This is why a simple shift of the 0 K interaction profiles (Figure 5) is not observed. It is noted that the temperature effect up to 500 K is only in the order of 10 kJ/mol, primarily at higher coverages. The electronic interaction between the surface and adsorbate remains dominant in controlling the adlayer structure, and thereby the energy, on account of the relatively strong binding of CO to the metal. The temperature effect does become stronger when considering higher temperatures (>500 K), although under these conditions, the surface is predicted to be largely depopulated and the adsorbate–metal interaction again remains leading. Nevertheless, we have seen that the temperature-dependent lateral interaction potentials are critical for the correct prediction of the characteristics of the coverage profiles. As noted in Figure 7, the strongest deviations are observed precisely in the catalytically active regime, emphasizing the importance of this effect in modeling heterogeneous catalysis. This effect has not been investigated before. It is made possible here due to the low computational cost of the ANN method.

Effect of Exchange-Correlation Functionals and Dispersion Interactions

In the foregoing discussions, we have employed the PBE functional (70) for the investigation of the lateral interactions. For CO adsorption over transition metals, PBE is known to exhibit an overbinding effect and hence an incorrect prediction of the adsorption sites. (4,71) It is therefore somewhat surprising that the correct lateral interactions are predicted for this system as co-adsorbate interactions depend strongly on the site locality. To investigate this, several alternative exchange-correlation functionals were considered (Tables S18 and S19). Of these, the AM (72) and PBEsol (73) functionals were quickly discarded as they showed comparatively large errors in the prediction of the Co-HCP lattice parameters. The revPBE (74) and rPBE (71) functionals yielded similar predictions for the Co-HCP lattice parameters as PBE. As the minimum energy structures and the lateral interactions for revPBE and rPBE are nearly identical (Figure 8 and Figures S11–S14), we chose revPBE for further analysis as it provided the closest agreement to experimental values.

Figure 8

Figure 8. Difference in the lateral interaction potentials for Co(001) predicted for different XC functionals at T = 0, 300, and 500 K. Average adsorption energies are expressed relative to the adsorption energy of CO on the empty surface.

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Using the revPBE functional, the experimentally observed top-adsorption below 0.4 ML is reproduced. Upon the increase in the monolayer coverage, a shift toward bridge states is found in contrast to experimental works, (59,68) which suggest a shift toward hollow sites first. However, it is noted that, depending on the degree of electron localization of the GGA, occupation of bridge-top and bridge-hollow intermediates can be observed, which matches the experimentally observed IR frequencies well (1820–1940 cm–1 compared to 1850–1910 cm–1). (59) At elevated coverages (0.5–0.75 ML), the non-temperature-corrected model predicts exclusively top sites, which are the dominant sites found in the experiment. With addition of finite temperature effects, CO is predicted to also adsorb on bridge sites, as is reflected by the peak broadening seen in the XPS signals at these coverages. (59,67,68)
While revPBE now produces an agreeable result for the monolayer geometries, the same cannot be said about the observed lateral interaction potentials. As seen previously in Figure 8, above 0.4 ML coverage, the lateral interaction penalty is now much larger than PBE. This is reflected in Figure 9, where the fractional monolayer coverage as function of temperature is shown, as lower surface coverages are obtained compared to the experiment. The difference between the revPBE and PBE functionals and thus between top–top and hollow–hollow interactions can be readily rationalized. For the hollow sites predicted with PBE, the surrounding cobalt atoms act to screen part of the lateral interactions. Hollow–hollow lateral interactions are much weaker than top–top lateral interactions (with two-body nearest-neighbor terms of ∼15 and ∼30 kJ/mol), yielding a stronger lateral effect for revPBE. The increased lateral interactions result in a shift toward lower coverages for the low-temperature regime, with the effect naturally leveling off as the surface depopulates.

Figure 9

Figure 9. Left: influence of different dispersion corrections on the revPBE lateral interaction potential for CO/Co(001). Integral adsorption energies have been expressed relative to the adsorption on the empty surface. Right: comparison of Grimme dispersion effects on the adsorption equilibrium for CO/Co(001) at 1 bar.

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This discrepancy with the experiment suggests that there might be a secondary stabilizing effect present at higher coverages. Dispersion interactions were therefore considered as a possible source. Different dispersion models have been tested (Table S20), which show a good deal of variability in their predictions for the co-adsorbate interactions (Figure 9). The best match with the experiment is observed in this case for the Grimme D3 models, for which both D3(0) and D3(BJ) variants were considered. (75) The corresponding lateral interaction potentials show behavior that is intermediate to those of the non-dispersion-corrected PBE and revPBE potentials, mimicking addition of the PBE screening effect to the geometric models of revPBE. As shown in Figure 9, combining revPBE with dispersion now reproduces the adsorption equilibrium observed in the experiment.
We note that the same effect would not have been achieved for rerevision of the PBE exchange locality or PBE + rPBE hybridization as this is seen to coincide with a corresponding top-hollow shift in site occupation. Comparative predictions of the different dispersion models appear to follow similar trends as found in the literature. (75,76) The absence of the stabilizing effect for non-Grimme models could be attributed to density dependence of their dispersion coupled with the enhanced non-locality of revPBE. (74,76) While this does not provide a conclusive acknowledgement that the stabilization originates from dispersion interactions, given the strong sensitivity to their theoretical treatment, we note that, at the very least, an experimentally satisfying result could be obtained.

Conclusions

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A novel machine learning approach has been illustrated for the study of adlayer structures and lateral interactions. We have critically assessed the accuracy of our method and identified the factors that control this accuracy. The most important factor was found to be the inclusion of electronic basis functions, which were shown to enhance the basis set resolution, thereby allowing much smaller DFT datasets to be used. We demonstrated how these datasets can be efficiently generated using an algorithm based on uniform sampling of the molecular degrees of freedom. The models can easily be extended to include multiple surfaces and adsorbates, making them exceptionally suited for the study of catalytic systems. To facilitate this scale-up, the importance of a proper balance of the representation of the different species within the dataset was highlighted. As the dataset is structured in a chemically intuitive manner, it is straightforward to analyze the extent to which the ANN has been trained and to a priori identify missing features in the datasets.
The low cost of the ANN as compared to DFT makes it possible to use stochastic methods for tackling problems, which suffer from combinatorial complexity. This feature was demonstrated by constructing an ANN to describe CO adlayer compositions of Co(001) and Co(211) surfaces. Inclusion of finite temperature effects allowed for accurate reproduction of experimental temperature-coverage curves by means of mean-field microkinetics. When extending these studies toward systems containing multiple adsorbates, it may become possible to also include non-mean-field organization of the adsorbates using this methodology, which would allow us to significantly enhance the level of detail incorporated in microkinetic models. These microkinetic simulations would lend themselves to incorporation in macroscale simulations, fully bridging the multiscale domains.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.1c10401.

  • Overview of dataset generation methods, ANN training statistics, computational methods for DFT, MC, and MKM, monolayer geometries, and lateral interaction potentials (PDF)

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Author Information

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  • Corresponding Author
  • Authors
    • Bart Klumpers - Laboratory of Inorganic Materials and Catalysis, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands;  Orcidhttps://orcid.org/0000-0001-9112-9069
    • Emiel J.M. Hensen - Laboratory of Inorganic Materials and Catalysis, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands;  Orcidhttps://orcid.org/0000-0002-9754-2417
  • Author Contributions

    The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by the Netherlands Center for Multiscale Catalytic Energy Conversion (MCEC), an NWO Gravitation program funded by the Ministry of Education, Culture and Science of the government of the Netherlands. The Netherlands Organization for Scientific Research is acknowledged for providing access to computational resources.

References

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This article references 76 other publications.

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    Getman, Rachel B.; Xu, Ye; Schneider, William F.
    Journal of Physical Chemistry C (2008), 112 (26), 9559-9572CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The reactivity of heterogeneous metal catalysts can be a strong function of the coverage of adsorbates. For example, Pt-catalyzed NO oxidn. to NO2 requires high concns. of chemisorbed (surface-bound) O, but the development of surface oxides is detrimental to reaction kinetics. Quantifying the structures, properties, and esp. the conditions that produce various adsorbate coverages is essential to developing qual. and quant. correct models of surface reactivity. In this work, we examine these ideas in the context of oxidn. reactions on Pt(111), the lowest energy face of bulk Pt. We use extensive supercell d. functional theory (DFT) calcns. to catalog and characterize the stable binding sites and arrangements of chemisorbed O on Pt(111), as a function of O coverage, θ. O atoms are found to uniformly prefer FCC binding sites and to arrange to minimize various destabilizing interactions with neighbor O. These destabilizing interactions are shown to have electronic and strain components that can either reinforce or oppose one another depending upon O-O sepn. Because of the nature and magnitudes of these lateral interactions, the thermodynamically stable O orderings partition into four coverage regimes of decreasing adsorption energy: 0 < θ ≤ 1/4 monolayer (ML), 1/4 < θ ≤ 1/2 ML, 1/2 < θ ≤ 2/3 ML, and 2/3 < θ ≤ 1 ML. We use equil. models to quantify the oxygen chem. potentials μO necessary to access each of these regimes. These equil. models can be used to relate surface coverage to various external environmental conditions and assumptions about relevant reaction equil.: dissociative equil. of the surface with O2 (g) can produce coverages up to 1/2 ML; either NO2 decompn. or "NO-assisted" O2 dissocn. can access coverages approaching 2/3 ML, as obsd. during NO oxidn. catalysis, and equil. with a solid-oxygen storage material, like ceria-zirconia, can buffer equil. coverages at a const. 1/4 ML O. These various oxidn. reaction energies can be summarized in a single "Ellingham" free energy diagram, providing a convenient representation of the relationship between surface coverage and reaction thermodn., and a useful guide toward relevant coverage regimes for more detailed study of reaction kinetics.
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  14. 14
    Bray, J. M.; Smith, J. L.; Schneider, W. F. Coverage-Dependent Adsorption at a Low Symmetry Surface: DFT and Statistical Analysis of Oxygen Chemistry on Kinked Pt(321). Top. Catal. 2014, 57, 89– 105,  DOI: 10.1007/s11244-013-0165-4
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    14
    Coverage-Dependent Adsorption at a Low Symmetry Surface: DFT and Statistical Analysis of Oxygen Chemistry on Kinked Pt(321)
    Bray, J. M.; Smith, J. L.; Schneider, W. F.
    Topics in Catalysis (2014), 57 (1-4), 89-105CODEN: TOCAFI; ISSN:1022-5528. (Springer)
    The authors explore the influence of adsorbate interactions on the thermodn. and spectroscopic properties of oxygen on the stepped, kinked Pt(321) surface. The ground state arrangements of at. oxygen are identified with the aid of a cluster expansion and analyzed for coverages up to one oxygen per surface Pt (1 ML). Oxygen prefers to bind in bridge sites at the step edge at coverages up to 0.2 ML, but at higher coverages oxygen atoms actually experience mild, localized attractions such that both bridge and 3-fold hollow sites are occupied to form square planar, 4-fold-coordinated PtO4-like structures. These structures progressively dominate the surface with increasing coverage up to 0.8 ML, at which point every kink Pt is satd. with four oxygens. The authors compute stability regions for these ground states with respect to gas-phase O2 and to NO/NO2 mixts. The ground state structures at 0.2, 0.6, and 0.8 ML dominate over a wide range of conditions, with the 0.6 ML structure being most prominent. The authors also explore site preferences for mol. O2 adsorbed on key O ground state structures. Calcns. of vibrational modes and core electron binding energy shifts allow the authors to relate both ground state and nonequil. structures to exptl. HREELS and XPS results. Adsorption sites are primarily characterized by their surface coordination, such that O in atop, bridge, and 3-fold hollow sites possess distinct and identifiable vibrational modes and core level shifts. However, within these broad categories, variability due to interactions with proximal adsorbates were found. Adsorption energies and vibrational modes of O2 are particularly sensitive to the local adsorption environment. Lastly, the authors develop a 1-dimensional adsorption model to understand and rationalize exptl. obsd. nonequil. behavior at low coverages.
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  15. 15
    Sutton, J. E.; Vlachos, D. G. Building Large Microkinetic Models with First-Principles’ Accuracy at Reduced Computational Cost. Chem. Eng. Sci. 2015, 121, 190– 199,  DOI: 10.1016/j.ces.2014.09.011
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    15
    Building large microkinetic models with first-principles' accuracy at reduced computational cost
    Sutton, Jonathan E.; Vlachos, Dionisios G.
    Chemical Engineering Science (2015), 121 (), 190-199CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
    We present a systematic hierarchical multiscale framework for parameterization of large microkinetic models that delivers first-principles' accuracy at significantly reduced computational cost. The framework leverages recently introduced first-principles-based semi-empirical methods (FPSEM), such as group additivity and Bronsted-Evans-Polanyi (BEP) relations, for surface reactions, local sensitivity anal., and a heuristic classification of the order of corrections to produce a hierarchy or family of models of improved accuracy. We demonstrate this approach to the moderate size ethanol steam reforming mechanism on Pt, consisting of 67 species (14 gas, 53 surface) and 160 reversible elementary-like reactions, for which the 'exact' d. functional theory (DFT)-based model is available. We find that the majority of refined parameters are surface species free energies and lateral interactions, underscoring the importance of thermodn. in kinetic mechanisms.
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  16. 16
    Sabbe, M. K.; Canduela-Rodriguez, G.; Joly, J.-F.; Reyniers, M.-F.; Marin, G. B. Ab Initio Coverage-Dependent Microkinetic Modeling of Benzene Hydrogenation on Pd(111). Catal. Sci. Technol. 2017, 7, 5267– 5283,  DOI: 10.1039/C7CY00962C
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    16
    Ab initio coverage-dependent microkinetic modeling of benzene hydrogenation on Pd(111)
    Sabbe, Maarten K.; Canduela-Rodriguez, Gonzalo; Joly, Jean-Francois; Reyniers, Marie-Francoise; Marin, Guy B.
    Catalysis Science & Technology (2017), 7 (22), 5267-5283CODEN: CSTAGD; ISSN:2044-4753. (Royal Society of Chemistry)
    The effect of hydrogen coverage on the kinetics of benzene hydrogenation on Pd(111) has been investigated with optPBE-vdW d. functional theory calcns. and a coverage-dependent microkinetic model. The dominant reaction path consists of the consecutive hydrogenation of carbon atoms located in ortho positions relative to the previously hydrogenated carbon atom, independent of the hydrogen coverage. Increasing the hydrogen coverage destabilizes all surface species, which leads to weaker adsorption and increased rate coeffs. for the hydrogenation steps due to stronger destabilization of reactants than transition states. The catalytic activities simulated using the constructed coverage-dependent microkinetic model exceed those obtained using a low-coverage microkinetic model by several orders of magnitude and are comparable to exptl. obsd. activities. The rate coeffs. to which the global rate is most sensitive depend on the reaction conditions and differ from those calcd. using low coverage kinetics. Therefore, properly accounting for coverage dependence on the kinetics and thermodn. of catalytic hydrogenation reactions is not only required for an accurate DFT-based prediction of the catalytic activity but also for a correct understanding of the reaction mechanism.
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  17. 17
    Liu, H.; Liu, J.; Yang, B. Modeling the Effect of Surface CO Coverage on the Electrocatalytic Reduction of CO2 to CO on Pd Surfaces. Phys. Chem. Chem. Phys. 2019, 21, 9876– 9882,  DOI: 10.1039/C8CP07427E
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    17
    Modeling the effect of surface CO coverage on the electrocatalytic reduction of CO2 to CO on Pd surfaces
    Liu, Hong; Liu, Jian; Yang, Bo
    Physical Chemistry Chemical Physics (2019), 21 (19), 9876-9882CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Electrocatalytic redn. of CO2 has attracted considerable attention recently, and it was found exptl. that Pd could show activity for the electroredn. of CO2 to CO. However, theor. studies showed that the adsorption of CO on Pd surfaces is strong and the coverage of CO is high, indicating that the interactions between the neighboring adsorbed CO and other reaction intermediates on the Pd surfaces cannot be neglected. Here, with d. functional theory calcns. and utilizing the Sabatier anal. method, we find that an adsorbate-adsorbate interaction is playing a crucial role in the modeling of the electrocatalytic redn. of CO2 to CO on Pd surfaces, while the reaction rates obtained by neglecting the interactions between the surface adsorbates are substantially lower than those reported in the expts. Upon analyzing the interactions quant. and using a self-consistent iterative microkinetic modeling method, we find that the active site for CO2 electroredn. is Pd(111) at different potentials applied. Our modeling results provide a reasonable computational interpretation for the electroredn. of CO2 to CO on Pd.
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  18. 18
    Wu, P.; Zeffron, J.; Xu, D.; Yang, B. First-Principles-Based Microkinetic Simulations of CO2 Hydrogenation to Methanol over Intermetallic GaPd2: Method Development to Include Complex Interactions between Surface Adsorbates. J. Phys. Chem. C 2020, 124, 15977– 15987,  DOI: 10.1021/acs.jpcc.0c03975
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    18
    First-Principles-Based Microkinetic Simulations of CO2 Hydrogenation to Methanol over Intermetallic GaPd2: Method Development to Include Complex Interactions between Surface Adsorbates
    Wu, Panpan; Zaffran, Jeremie; Xu, Dongyang; Yang, Bo
    Journal of Physical Chemistry C (2020), 124 (29), 15977-15987CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    To computationally design efficient solid catalysts, d. functional theory (DFT) calcns. are widely used in combination with microkinetic modeling (MKM). However, MKM results are often biased due to the overestimation of adsorption strength in DFT calcns. that are usually performed at an arbitrary low coverage of surface intermediates. We hereby developed a new iterative approach focusing on the main species present on the catalyst at the steady state, hence allowing adsorption energy calcn. only in the presence of relevant intermediates. In this way, the complex parametrization process to det. scaling relations between adsorption energies and coverages is avoided, which will increase the efficiency and accuracy of the iteration process. When applying this approach to CO2 hydrogenation over GaPd2, we found within few iterations that only when running DFT calcns. using the surface with both CO and HCOO precovered, the coverage of surface species obtained from MKM anal. can be consistent with that used in DFT calcns. It stems from our theor. study that all the species coverages must be self-consistent in order to predict methanol selectivity in fair agreement with expt.
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  19. 19
    Yao, Z.; Zhao, J.; Bunting, R. J.; Zhao, C.; Hu, P.; Wang, J. Quantitative Insights into the Reaction Mechanism for the Direct Synthesis of H2O2 over Transition Metals: Coverage-Dependent Microkinetic Modeling. ACS Catal. 2021, 11, 1202– 1221,  DOI: 10.1021/acscatal.0c04125
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    19
    Quantitative Insights into the Reaction Mechanism for the Direct Synthesis of H2O2 over Transition Metals: Coverage-Dependent Microkinetic Modeling
    Yao, Zihao; Zhao, Jinyan; Bunting, Rhys J.; Zhao, Chenxia; Hu, Peijun; Wang, Jianguo
    ACS Catalysis (2021), 11 (3), 1202-1221CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
    The direct synthesis is the most promising alternative method for the prodn. of hydrogen peroxide, and the bottleneck is still unsolved. The breakthrough lies in elusive reaction mechanism issues. In this work, advanced coverage-dependent kinetic modeling is combined with the energetics from first-principles calcns. to investigate the formation of H2O2 over transition metals. We show that the adsorbate-adsorbate interactions considerably affect the reaction mechanism of synthesis of hydrogen peroxide on Pd(111). Without the coverage effect, O2 is likely to go through the direct dissocn. mechanism, and water is the major product. When the coverage effects are included, the dissocns. of O-O and O-OH bonds are significantly inhibited, and on the contrary, the hydrogenations of O2 and OOH are promoted, leading to the prodn. of H2O2. We demonstrate that the reaction temp. induces strong variations in the coverage of intermediates, which in turn causes changes in product selectivity. Being consistent with the operando expt., our kinetic simulations indicate that the H2/O2 partial pressure ratio has great effects on H2O2 selectivity and the reaction rate of H2O2 is lower under hydrogen-rich (oxygen-lean) and oxygen-rich (hydrogen-lean) conditions, which is highly related to the intermediate coverage. The same approach is also applied to other important relevant metals, i.e., Cu(111), Au(111), PdAu, and PdHg alloys, and the trends of activity and selectivity have been obtained.
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  20. 20
    Yao, Z.; Guo, C.; Mao, Y.; Hu, P. Quantitative Determination of C-C Coupling Mechanisms and Detailed Analyses on the Activity and Selectivity for Fischer-Tropsch Synthesis on Co(0001): Microkinetic Modeling with Coverage Effects. ACS Catal. 2019, 9, 5957– 5973,  DOI: 10.1021/acscatal.9b01150
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    20
    Quantitative Determination of C-C Coupling Mechanisms and Detailed Analyses on the Activity and Selectivity for Fischer-Tropsch Synthesis on Co(0001): Microkinetic Modeling with Coverage Effects
    Yao, Zihao; Guo, Chenxi; Mao, Yu; Hu, P.
    ACS Catalysis (2019), 9 (7), 5957-5973CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
    The Fischer-Tropsch synthesis plays a significant role in re-forming natural resources to meet global demand for commodities, while there is ongoing oil depletion and population growth. Mechanisms have long been investigated, but they are still a heavily debated issue. In this work, all of the possible elementary reaction steps on a flat cobalt surface were calcd. using d. functional theory (DFT) with van der Waals interactions. Kinetic simulations using std. DFT data (free energies and barriers at low coverages), the so-called non-coverage-dependent kinetic model commonly used in the literature, are compared to those from a coverage-dependent kinetic model for the system. We show that the coverage-dependent kinetic model gives rise to a TOF which is approx. 6 orders of magnitude larger than the TOF calcd. using the non-coverage-dependent kinetic model. Furthermore, it is found that Co(0001) is highly selective to olefin prodn., and it is very likely to produce long-chain hydrocarbons. Both models demonstrate that the CO insertion mechanism is the dominant mechanism on Co(0001). Our calcns. also reveal that high coverage of CHx leads to the carbide mechanism being significant and low coverage of CHx results in the CO insertion mechanism being more favored. Direct CO dissocn. is difficult on Co(0001), which leads to monomers CHx being unable to occupy a certain amt. of surface coverage, causing the carbide mechanism to be inhibited. The reaction pathway through CO + H → CHO, CHO + H → CHOH, and CHOH → CH + OH is the main channel to form the monomer CH on the basis of the coverage-dependent kinetic model simulations. The temp. considerably affects the surface coverage and the total reaction rate, leading to the selectivity being highly temp. dependent. Our coverage-dependent kinetic model predicts that the selectivity of oxygenates is high in comparison to methane in the low-temp. region from 425 and 475 K. From 475 to 525 K, the selectivity toward CH4 increases. From 525 to 700 K, the selectivity of C2 decreases significantly and the selectivity of CH4 increases remarkably.
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  21. 21
    Ding, Y.; Xu, Y.; Song, Y.; Guo, C.; Hu, P. Quantitative Studies of the Coverage Effects on Microkinetic Simulations for NO Oxidation on Pt(111). J. Phys. Chem. C 2019, 123, 27594– 27602,  DOI: 10.1021/acs.jpcc.9b08208
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    21
    Quantitative Studies of the Coverage Effects on Microkinetic Simulations for NO Oxidation on Pt(111)
    Ding, Yunxuan; Xu, Yarong; Song, Yihui; Guo, Chenxi; Hu, P.
    Journal of Physical Chemistry C (2019), 123 (45), 27594-27602CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    To advance a reliable microkinetic modeling approach using d. functional theory (DFT) energies is of great importance to bridging between exptl. results and theor. calcns., and the current major issue is the coverage effect. A full microkinetic modeling for NO oxidn. using DFT energetics is developed. The calcd. turnover frequency (TOF) (0.22 s-1) agrees with the exptl. one (∼0.2 s-1) very well, if the coverage effects are properly incorporated. To include the interactions of adsorbates, namely, (i) O and O, NO and NO (self-interaction), and (ii) O and NO (cross-interaction), is important to obtain accurate kinetic results. Equally important, the interactions between the adsorbates and the transition states of O-O bond breaking and O-NO coupling are also crucial for achieving precise kinetics. A 2-line model can be used to describe accurately both the self and cross adsorbate-adsorbate interactions as well as the coverage effects on the transition states of O2 dissocn. and O-NO coupling. The various approxns. including Broensted-Evans-Polanyi (BEP) relations are carefully examd., and the errors involved are quantified. Also, a 1-line model is tested, which is a simplified approach but gives rise to a good agreement with exptl. results.
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  22. 22
    Prats, H.; Illas, F.; Sayós, R. General Concepts, Assumptions, Drawbacks, and Misuses in Kinetic Monte Carlo and Microkinetic Modeling Simulations Applied to Computational Heterogeneous Catalysis. Int. J. Quantum Chem. 2018, 118, 25518
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    Jørgenson, M.; Grönbeck, H. Selective Acetylene Hydrogenation over Single-Atom Alloy Nanoparticles by Kinetic Monte Carlo. J. Am. Chem. Soc. 2019, 141, 8541– 8549,  DOI: 10.1021/jacs.9b02132
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    There is no corresponding record for this reference.
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    Nagasaka, M.; Kondoh, H.; Nakai, I.; Ohta, T. CO Oxidation Reaction on Pt(111) Studied by the Dynamic Monte Carlo Method Including Lateral Interactions of Adsorbates. J. Chem. Phys. 2007, 126, 044704  DOI: 10.1063/1.2424705
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    24
    CO oxidation reaction on Pt(111) studied by the dynamic Monte Carlo method including lateral interactions of adsorbates
    Nagasaka, Masanari; Kondoh, Hiroshi; Nakai, Ikuyo; Ohta, Toshiaki
    Journal of Chemical Physics (2007), 126 (4), 044704/1-044704/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The dynamics of adsorbate structures during CO oxidn. on Pt(111) surfaces and its effects on the reaction were studied by the dynamic Monte Carlo method including lateral interactions of adsorbates. The lateral interaction energies between adsorbed species were calcd. by the d. functional theory method. Dynamic Monte Carlo simulations were performed for the oxidn. reaction over a mesoscopic scale, where the exptl. detd. activation energies of elementary paths were altered by the calcd. lateral interaction energies. The simulated results reproduced the characteristics of the microscopic and mesoscopic scale adsorbate structures formed during the reaction, and revealed that the complicated reaction kinetics is comprehensively explained by a single reaction path affected by the surrounding adsorbates. We also propose from the simulations that weakly adsorbed CO mols. at domain boundaries promote the island-periphery specific reaction.
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  25. 25
    Wu, C.; Schmidt, D. J.; Wolverton, C.; Schneider, W. F. Accurate Coverage-Dependence Incorporated into First-Principles Kinetic Models: Catalytic NO oxidation on Pt (111). J. Catal. 2012, 286, 88– 94,  DOI: 10.1016/j.jcat.2011.10.020
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    25
    Accurate coverage-dependence incorporated into first-principles kinetic models: Catalytic NO oxidation on Pt (1 1 1)
    Wu, C.; Schmidt, D. J.; Wolverton, C.; Schneider, W. F.
    Journal of Catalysis (2012), 286 (), 88-94CODEN: JCTLA5; ISSN:0021-9517. (Elsevier Inc.)
    The coverage of surface adsorbates influences both the no. and types of sites available for catalytic reactions at a heterogeneous surface, but accounting for adsorbate-adsorbate interactions and understanding their implications on obsd. rates remain challenges for simulation. Here, we demonstrate the use of a d. functional theory (DFT)-parameterized cluster expansion (CE) to incorporate accurate adsorbate-adsorbate interactions into a surface kinetic model. The distributions of adsorbates and reaction sites at a metal surface as a function of reaction conditions are obtained through Grand Canonical Monte Carlo simulations on the CE Hamiltonian. Reaction rates at those sites are obtained from the CE through a DFT-parameterized Bronsted-Evans-Polyani (BEP) relationship. The approach provides ready access both to steady-state rates and rate derivs. and further provides insight into the microscopic factors that influence obsd. rate behavior. We demonstrate the approach for steady-state O2 dissocn. at an O-covered Pt (1 1 1) surface-a model for catalytic NO oxidn. at this surface-and recover apparent activation energies and rate orders consistent with expt.
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  26. 26
    Yang, L.; Krim, A.; Muckerman, J. T. Density Functional Kinetic Monte Carlo Simulation of Water-Gas Shift Reaction on Cu/ZnO. J. Phys. Chem. C 2013, 117, 3414– 3425,  DOI: 10.1021/jp3114286
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    26
    Density Functional Kinetic Monte Carlo Simulation of Water-Gas Shift Reaction on Cu/ZnO
    Yang, Liu; Karim, Altaf; Muckerman, James T.
    Journal of Physical Chemistry C (2013), 117 (7), 3414-3425CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    We describe a d. functional theory based kinetic Monte Carlo study of the water-gas shift (WGS) reaction catalyzed by Cu nanoparticles supported on a ZnO surface. DFT calcns. were performed to obtain the energetics of the relevant atomistic processes. Subsequently, the DFT results were employed as an intrinsic database in kinetic Monte Carlo simulations that account for the spatial distribution, fluctuations, and evolution of chem. species under steady-state conditions. Our simulations show that, in agreement with expts., the H2 and CO2 prodn. rates strongly depend on the size and structure of the Cu nanoparticles, which are modeled by single-layer nano islands in the present work. The WGS activity varies linearly with the total no. of edge sites of Cu nano islands. In addn., examn. of different elementary processes has suggested competition between the carboxyl and the redox mechanisms, both of which contribute significantly to the WGS reactivity. Our results have also indicated that both edge sites and terrace sites are active and contribute to the obsd. H2 and CO2 productivity.
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    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, 7, 3192– 3203
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    There is no corresponding record for this reference.
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    Meyer, J.; Bukas, V. J.; Mitra, S.; Reuter, K. Fingerprints of Energy Dissipation for Exothermic Surface Chemical Reactions: O2 on Pd(100). J. Chem. Phys. 2015, 143, 2131– 2136,  DOI: 10.1063/1.4926989
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    Boes, J. R.; Kitchin, J. R. Neural Network Predictions of Oxygen Interactions on a Dynamic Pd Surface. Mol. Simul. 2017, 43, 346– 354,  DOI: 10.1080/08927022.2016.1274984
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    Neural network predictions of oxygen interactions on a dynamic Pd surface
    Boes, Jacob R.; Kitchin, John R.
    Molecular Simulation (2017), 43 (5-6), 346-354CODEN: MOSIEA; ISSN:0892-7022. (Taylor & Francis Ltd.)
    A review. Artificial neural networks (NNs) are increasingly common in quantum chem. applications. These models can be trained to higher-level ab-initio calcns. and are capable of achieving arbitrary levels of accuracy. The most common applications thus far have been specialised for either bulk or surface structures of up to two chem. components. However, very few of these studies utilize NNs trained to high-dimensional potential energy surfaces, and there are even fewer studies which examine adsorbate-adsorbate and adsorbate-surface interactions with those NNs. The goal of this work is to det. the feasibility of and develop methodologies for producing a high-dimensional NN capable of reproducing coverage-dependent oxygen interactions with a dynamic Pd fcc(1 1 1) surface. We utilize the atomistic machine-learning potential software package to generate a Behler-Parrinello local symmetry function NN trained on a large database of d. functional theory (DFT) calcns. These training methods are flexible, and thus easily expanded upon as demonstrated in previous work. This allows the database of high quality PdO DFT calcns. to be used as a basis for future work, such as the inclusion of a third chem. species, for example a binary Pd alloy, or another adsorbate atom such as hydrogen.
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    Boes, J. R.; Groenenboom, M. C.; Keith, J. A.; Kitchin, J. R. Neural Network and ReaxFF Comparison for Au Properties. Int. J. Quantum Chem. 2016, 116, 979– 987,  DOI: 10.1002/qua.25115
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    Neural network and ReaxFF comparison for Au properties
    Boes, Jacob R.; Groenenboom, Mitchell C.; Keith, John A.; Kitchin, John R.
    International Journal of Quantum Chemistry (2016), 116 (13), 979-987CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
    A review. We have studied how ReaxFF and Behler-Parrinello neural network (BPNN) atomistic potentials should be trained to be accurate and tractable across multiple structural regimes of Au as a representative example of a single-component material. We trained these potentials using subsets of 9,972 Kohn-Sham d. functional theory calcns. and then validated their predictions against the untrained data. Our best ReaxFF potential was trained from 848 data points and could reliably predict surface and bulk data; however, it was substantially less accurate for mol. clusters of 126 atoms or fewer. Training the ReaxFF potential to more data also resulted in overfitting and lower accuracy. In contrast, BPNN could be fit to 9,734 calcns., and this potential performed comparably or better than ReaxFF across all regimes. However, the BPNN potential in this implementation brings significantly higher computational cost. © 2016 Wiley Periodicals, Inc.
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    Density functional tight binding
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    This paper reviews the basic principles of the d.-functional tight-binding (DFTB) method, which is based on d.-functional theory as formulated by Hohenberg, Kohn and Sham (KS-DFT). DFTB consists of a series of models that are derived from a Taylor series expansion of the KS-DFT total energy. In the lowest order (DFTB1), densities and potentials are written as superpositions of at. densities and potentials. The Kohn-Sham orbitals are then expanded to a set of localized atom-centered functions, which are obtained for spherical sym. spin-unpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrixes contain one- and two-center contributions only. Therefore, they can be calcd. and tabulated in advance as functions of the distance between at. pairs. The second contributions to DFTB1, the DFT double counting terms, are summarized together with nuclear repulsion energy terms and can be rewritten as the sum of pairwise repulsive terms. The second-order (DFTB2) and third-order (DFTB3) terms in the energy expansion correspond to a self-consistent representation, where the deviation of the ground-state d. from the ref. d. is represented by charge monopoles only. This leads to a computationally efficient representation in terms of at. charges (Mulliken), chem. hardness (Hubbard) parameters and scaled Coulomb laws. Therefore, no addnl. adjustable parameters enter the DFTB2 and DFTB3 formalism. The handling of parameters, the efficiency, the performance and extensions of DFTB are briefly discussed.
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    van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A. ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105, 9396– 9409,  DOI: 10.1021/jp004368u
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    ReaxFF: A Reactive Force Field for Hydrocarbons
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    Journal of Physical Chemistry A (2001), 105 (41), 9396-9409CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    To make practical the mol. dynamics simulation of large scale reactive chem. systems (1000 s of atoms), the authors developed ReaxFF, a force field for reactive systems. ReaxFF uses a general relation between bond distance and bond order on one hand and between bond order and bond energy however, that leads to proper dissocn. of bonds to sepd. atoms. Other valence terms present in the force field (angle and torsion) are defined in terms of the same bond orders so that all these terms go to zero smoothly as bonds break. In addn., ReaxFF has Coulomb and Morse (van der Waals) potentials to describe nonbond interactions between all atoms (no exclusions). These nonbond interactions are shielded at short range so that the Coulomb and van der Waals interactions become const. as Rij → 0. The authors report here the ReaxFF for hydrocarbons. The parameters were derived from quantum chem. calcns. on bond dissocn. and reactions of small mols. plus heat of formation and geometry data for a no. of stable hydrocarbon compds. The ReaxFF provides a good description of these data. Generally, the results are of an accuracy similar or better than PM3, while ReaxFF is ∼100 times faster. In turn, the PM3 is ∼100 times faster than the QC calcns. Thus, with ReaxFF the authors hope to be able to study complex reactions in hydrocarbons.
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    Behler, J.; Parrinello, M. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces. Phys. Rev. Lett. 2007, 98, 146401– 146404,  DOI: 10.1103/PhysRevLett.98.146401
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    Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
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    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.
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    We present a swift walk-through of our recent work that uses machine learning to fit interat. potentials based on quantum mech. data. We describe our Gaussian approxn. potentials (GAP) framework, discuss a variety of descriptors, how to train the model on total energies and derivs., and the simultaneous use of multiple models of different complexity. We also show a small example using QUIP, the software sandbox implementation of GAP that is available for noncommercial use.
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    The title method was used to identify the spectra of 6 alditols including glucitol.
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    A feed-forward neural network was designed to classify low-resoln. mass spectra of unknown compds. according to the presence or absence of 100 org. substructures. The neural network, MSnet, was trained to compute a max.-likelihood est. of the probability that each substructure is present. Some design considerations and statistical properties of neural network classifiers, and the effect of various training regimes on generalization behavior are discussed. The MSnet classifies mass spectra more reliably than other methods reported in the literature, and has other desirable properties.
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    A new program was introduced to study the relationship between structure and biol. activity of org. mols. The computer-automated structure evaluation program automatically recognizes mol. structures from the KLN code, a mol. linear coding routine, and proceeds automatically to identify, tabulate, and statistically analyze biophores, i.e., substructures believed to be responsible for known or anticipated biol. activity of groups of mols. The method was applied to the study of the carcinogenicity of polycyclic arom. hydrocarbons, the carcinogenicity of N-nitrosamines in rats, and the pesticidal activity of some ketoxime carbamates.
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    Hopfinger, A. J.; Burke, B. J.; Dunn, W. J., III A Generalized Formalism of Three-Dimensional Quantitative Structure-Property Relationship Analysis for Flexible Molecules Using Tensor Representation. J. Med. Chem. 1994, 37, 3768– 3774,  DOI: 10.1021/jm00048a013
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    A general formalism, based upon tensor representation of multidimensional data blocks, is presented to express relationships between dependent properties and independent mol. feature measures. The solns. to these data set problems are three-dimensional quant. structure-property relationships, 3D-QSPRs. The mol. features are partitioned into the intrinsic mol. shape tensor, the mol. field tensor, a nonshape/field feature tensor, and an exptl. feature tensor. The intrinsic mol. shape tensor contains information on the shape of a mol. within the contact surface while the mol. field tensor contains information outside of the contact surface. Mol. features not directly related to mol. shape are put into the nonshape/field tensor. Exptl. measures not being used as dependent variables can be considered as independent mol. features in the exptl. feature tensor. The 3D-QSPR is realized by constructing the transformation tensor which optimizes the statistical significance between the dependent and independent variables. Repetitive use of partial least squares (PLS) regression permits the unfolding of the composite feature tensor and the identification of the optimum transformation tensor. It is pointed out that a variety of fragment, whole-mol.,two-dimensional, and/or three-dimensional features can be placed into a nonshape/field tensor.
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    A new computational scheme is developed to predict phys. properties of org. compds. on the basis of their mol. structure. The method uses graph theory to encode the structural information which is the numerical input for a neural network. Calcd. results for a series of satd. hydrocarbons demonstrate av. accuracies of 1-2% with max. deviations of 12-14%.
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    Journal of Chemical Physics (1995), 103 (10), 4129-37CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Neural networks provide an efficient, general interpolation method for nonlinear functions of several variables. This paper describes the use of feed-forward neural networks to model global properties of potential energy surfaces from information available at a limited no. of configurations. As an initial demonstration of the method, several fits are made to data derived from an empirical potential model of CO adsorbed on Ni(111). The data are error-free and geometries are selected from uniform grids of two and three dimensions. The neural network model predicts the potential to within a few hundredths of a kcal/mol at arbitrary geometries. The accuracy and efficiency of the neural network in practical calcns. are demonstrated in quantum transition state theory rate calcns. for surface diffusion of CO/Ni(111) using a Monte Carlo/path integral method. The network model is much faster to evaluate than the original potential from which it is derived. As a more complex test of the method, the interaction potential of H2 with the Si(100)-2 × 1 surface is detd. as a function of 12 degrees of freedom from energies calcd. with the local d. functional method at 750 geometries. The training examples are not uniformly spaces and they depend weakly on variables not included in the fit. The neural net model predicts the potential at geometries outside the training set with a mean abs. deviation of 2.1 kcal/mol.
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    Brown, D. F. R.; Gibbs, M. N.; Clary, D. C. Combining Ab Initio Computations, Neural Networks, and Diffusion Monte Carlo: An Efficient Method to Treat Weakly Bound Molecules. J. Chem. Phys. 1996, 105, 7597– 7604,  DOI: 10.1063/1.472596
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    Combining ab initio computations, neural networks, and diffusion Monte Carlo: an efficient method to treat weakly bound molecules
    Brown, David F. R.; Gibbs, Mark N.; Clary, David C.
    Journal of Chemical Physics (1996), 105 (17), 7597-7604CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We describe a new method to calc. the vibrational ground-state properties of weakly bound mol. systems, and apply it to (HF)2 and HF-HCl. A Bayesian inference neural network is used to fit an analytic function to a set of ab-initio data points, which may then be employed by the quantum-diffusion-Monte-Carlo method to produce ground-state vibrational wave functions and properties. The method is general and relatively simple to implement, and will be attractive for calcns. on systems for which no analytic potential energy surface exists.
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    Behler, J. Representing Potential Energy Surfaces by High-Dimensional Neural Network Potentials. Condens. Matter 2014, 26, 183001,  DOI: 10.1088/0953-8984/26/18/183001
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    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.
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    Behler, J. Atom-Centered Symmetry Functions for Constructing High-Dimensional Neural Network Potentials. J. Chem. Phys. 2011, 134, 074106  DOI: 10.1063/1.3553717
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    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.
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    Jose, K. V. J.; Artrith, A.; Behler, J. Construction of High-Dimensional Neural Network Potentials Using Environment-Dependent Atom Pairs. J. Chem. Phys. 2012, 136, 194111,  DOI: 10.1063/1.4712397
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    Construction of high-dimensional neural network potentials using environment-dependent atom pairs
    Jose, K. V. Jovan; Artrith, Nongnuch; Behler, Joerg
    Journal of Chemical Physics (2012), 136 (19), 194111/1-194111/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    An accurate detn. of the potential energy is the crucial step in computer simulations of chem. processes, but using electronic structure methods on-the-fly in mol. dynamics (MD) is computationally too demanding for many systems. Constructing more efficient interat. potentials becomes intricate with increasing dimensionality of the potential-energy surface (PES), and for numerous systems the accuracy that can be achieved is still not satisfying and far from the reliability of 1st-principles calcns. Feed-forward neural networks (NNs) have a very flexible functional form, and in recent years they were shown to be an accurate tool to construct efficient PESs. High-dimensional NN potentials based on environment-dependent at. energy contributions were presented for a no. of materials. Still, these potentials may be improved by a more detailed structural description, e.g., in form of atom pairs, which directly reflect the at. interactions and take the chem. environment into account. We present an implementation of an NN method based on atom pairs, and its accuracy and performance are compared to the atom-based NN approach using 2 very different systems, the MeOH mol. and metallic Cu. We find that both types of NN potentials provide an excellent description of both PESs, with the pair-based method yielding a slightly higher accuracy making it a competitive alternative for addressing complex systems in MD simulations. (c) 2012 American Institute of Physics.
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    Shakouri, K.; Behler, J.; Meyer, J.; Kroes, G.-J. Accurate Neural Network Description of Surface Phonons in Reactive Gas–Surface Dynamics: N2 + Ru(0001). J. Phys. Chem. Lett. 2017, 8, 2131– 2136,  DOI: 10.1021/acs.jpclett.7b00784
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    Accurate Neural Network Description of Surface Phonons in Reactive Gas-Surface Dynamics: N2 + Ru(0001)
    Shakouri, Khosrow; Behler, Joerg; Meyer, Joerg; Kroes, Geert-Jan
    Journal of Physical Chemistry Letters (2017), 8 (10), 2131-2136CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Ab initio mol. dynamics (AIMD) simulations enable the accurate description of reactive mol.-surface scattering esp. if energy transfer involving surface phonons is important. However, presently, the computational expense of AIMD rules out its application to systems where reaction probabilities are smaller than about 1%. Here we show that this problem can be overcome by a high-dimensional neural network fit of the mol.-surface interaction potential, which also incorporates the dependence on phonons by taking into account all degrees of freedom of the surface explicitly. As shown for N2 + Ru(0001), which is a prototypical case for highly activated dissociative chemisorption, the method allows an accurate description of the coupling of mol. and surface atom motion and accurately accounts for vibrational properties of the employed slab model of Ru(0001). The neural network potential allows reaction probabilities as low as 10-5 to be computed, showing good agreement with exptl. results.
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    Gao, T.; Kitchin, J. R. Modeling Palladium Surfaces with Density Functional Theory, Neural Networks and Molecular Dynamics. Catal. Today 2018, 312, 132– 140,  DOI: 10.1016/j.cattod.2018.03.045
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    Modeling palladium surfaces with density functional theory, neural networks and molecular dynamics
    Gao, Tianyu; Kitchin, John R.
    Catalysis Today (2018), 312 (), 132-140CODEN: CATTEA; ISSN:0920-5861. (Elsevier B.V.)
    In this work, we have constructed a high dimensional neural network (NN) potential energy function for simulating palladium surface properties. The NN potential was trained with 3035 d. functional theory (DFT) calcns., and was shown to be nearly as accurate as DFT in mol. simulations. Important properties including lattice consts., elastic properties and surface energies as well as transition state energies and adatom diffusion barriers were predicted by the NN and were found to be in excellent agreement with DFT results. The computational time to run the NN was compared to DFT calcn. time, and we found this implementation of the NN is roughly four orders of magnitude faster than DFT. This approach is general and applicable to other systems and may have applications in modeling catalytic processes at surfaces.
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    Wang, C.; Tharval, A.; Kitchin, J. R. A Density Functional Theory Parameterised Neural Network Model of Zirconia. Mol. Simul. 2018, 44, 623– 630,  DOI: 10.1080/08927022.2017.1420185
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    A density functional theory parameterised neural network model of zirconia
    Wang, Chen; Tharval, Akshay; Kitchin, John R.
    Molecular Simulation (2018), 44 (8), 623-630CODEN: MOSIEA; ISSN:0892-7022. (Taylor & Francis Ltd.)
    A review. We have developed a Behler-Parrinello Neural Network (BPNN) that can be employed to calc. energies and forces of zirconia bulk structures with oxygen vacancies with similar accuracy as that of the d. functional theory (DFT) calcns. that were used to train the BPNN. In this work, we have trained the BPNN potential with a ref. set of 2178 DFT calcns. and validated it against a dataset of untrained data. We have shown that the bulk structural parameters, equation of states, oxygen vacancy formation energies and diffusion barriers predicted by the BPNN potential are in good agreement with the ref. DFT data. The transferability of the BPNN potential has also been benchmarked with the prediction of structures that were not included in the ref. set. The evaluation time of the BPNN is orders of magnitude less than corresponding DFT calcns., although the training process of the BPNN potential requires non-negligible amt. of computational resources to prep. the dataset. The computational efficiency of the NN enabled it to be used in mol. dynamics simulations of the temp.-dependent diffusion of an oxygen vacancy and the corresponding diffusion activation energy.
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    Eckhoff, M.; Behler, J. From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5. J. Chem. Theory Comput. 2019, 15, 3793– 3809,  DOI: 10.1021/acs.jctc.8b01288
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    From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5
    Eckhoff, Marco; Behler, Joerg
    Journal of Chemical Theory and Computation (2019), 15 (6), 3793-3809CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The development of first-principles-quality reactive atomistic potentials for org.-inorg. hybrid materials is still a substantial challenge because of the very different physics of the at. interactions-from covalent via ionic bonding to dispersion-that have to be described in an accurate and balanced way. In this work we used a prototypical metal-org. framework, MOF-5, as a benchmark case to investigate the applicability of high-dimensional neural network potentials (HDNNPs) to this class of materials. In HDNNPs, which belong to the class of machine learning potentials, the energy is constructed as a sum of environment-dependent at. energy contributions. We demonstrate that by the use of this approach it is possible to obtain a high-quality potential for the periodic MOF-5 crystal using d. functional theory (DFT) ref. calcns. of small mol. fragments only. The resulting HDNNP, which has a root-mean-square error (RMSE) of 1.6 meV/atom for the energies of mol. fragments not included in the training set, is able to provide the equil. lattice const. of the bulk MOF-5 structure with an error of about 0.1% relative to DFT, and also, the neg. thermal expansion behavior is accurately predicted. The total energy RMSE of periodic structures that are completely absent in the training set is about 6.5 meV/atom, with errors on the order of 2 meV/atom for energy differences. We show that in contrast to energy differences, achieving a high accuracy for total energies requires careful variation of the stoichiometries of the training structures to avoid energy offsets, as at. energies are not phys. observables. The forces, which have RMSEs of about 94 meV/a0 for the mol. fragments and 130 meV/a0 for bulk structures not included in the training set, are insensitive to such offsets. Therefore, forces, which are the relevant properties for mol. dynamics simulations, provide a realistic est. of the accuracy of atomistic potentials.
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  51. 51
    Schran, C.; Uhl, F.; Behler, J.; Marx, D. High-Dimensional Neural Network Potentials for Solvation: The Case of Protonated Water Clusters in Helium. J. Chem. Phys. 2018, 148, 102310,  DOI: 10.1063/1.4996819
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    51
    High-dimensional neural network potentials for solvation: The case of protonated water clusters in helium
    Schran, Christoph; Uhl, Felix; Behler, Joerg; Marx, Dominik
    Journal of Chemical Physics (2018), 148 (10), 102310/1-102310/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The design of accurate helium-solute interaction potentials for the simulation of chem. complex mols. solvated in superfluid helium has long been a cumbersome task due to the rather weak but strongly anisotropic nature of the interactions. We show that this challenge can be met by using a combination of an effective pair potential for the He-He interactions and a flexible high-dimensional neural network potential (NNP) for describing the complex interaction between helium and the solute in a pairwise additive manner. This approach yields an excellent agreement with a mean abs. deviation as small as 0.04 kJ mol-1 for the interaction energy between helium and both hydronium and Zundel cations compared with coupled cluster ref. calcns. with an energetically converged basis set. The construction and improvement of the potential can be performed in a highly automated way, which opens the door for applications to a variety of reactive mols. to study the effect of solvation on the solute as well as the solute-induced structuring of the solvent. Furthermore, we show that this NNP approach yields convincing agreement with the coupled cluster ref. for properties like many-body spatial and radial distribution functions. This holds for the microsolvation of the protonated water monomer and dimer by a few helium atoms up to their solvation in bulk helium as obtained from path integral simulations at ∼1 K. (c) 2018 American Institute of Physics.
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  52. 52
    Lahey, S.-H. J.; Rowley, C. N. Simulating Protein–Ligand Binding with Neural Network Potentials. Chem. Sci. 2020, 11, 2362– 2368,  DOI: 10.1039/C9SC06017K
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    Simulating protein-ligand binding with neural network potentials
    Lahey, Shae-Lynn J.; Rowley, Christopher N.
    Chemical Science (2020), 11 (9), 2362-2368CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Drug mols. adopt a range of conformations both in soln. and in their protein-bound state. The strain and reduced flexibility of bound drugs can partially counter the intermol. interactions that drive protein-ligand binding. To make accurate computational predictions of drug binding affinities, computational chemists have attempted to develop efficient empirical models of these interactions, although these methods are not always reliable. Machine learning has allowed the development of highly-accurate neural-network potentials (NNPs), which are capable of predicting the stability of mol. conformations with accuracy comparable to state-of-the-art quantum chem. calcns. but at a billionth of the computational cost. Here, we demonstrate that these methods can be used to represent the intramol. forces of protein-bound drugs within mol. dynamics simulations. These simulations are shown to be capable of predicting the protein-ligand binding pose and conformational component of the abs. Gibbs energy of binding for a set of drug mols. Notably, the conformational energy for anti-cancer drug erlotinib binding to its target was found to be considerably overestimated by a mol. mech. model, while the NNP predicts a more moderate value. Although the ANI-1ccX NNP was not trained to describe ionic mols., reasonable binding poses are predicted for charged ligands, but this method is not suitable for modeling charged ligands in soln.
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    Sun, G.; Sautet, P. Metastable Structures in Cluster Catalysis from First-Principles: Structural Ensemble in Reaction Conditions and Metastability Triggered Reactivity. J. Am. Chem. Soc. 2018, 140, 2812– 2820,  DOI: 10.1021/jacs.7b11239
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    53
    Metastable Structures in Cluster Catalysis from First-Principles: Structural Ensemble in Reaction Conditions and Metastability Triggered Reactivity
    Sun, Geng; Sautet, Philippe
    Journal of the American Chemical Society (2018), 140 (8), 2812-2820CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Reactivity studies on catalytic transition metal clusters are usually performed on a single global min. structure. With the example of a Pt13 cluster under a pressure of hydrogen, we show from first-principle calcns. that low energy metastable structures of the cluster can play a major role for catalytic reactivity and that hence consideration of the global min. structure alone can severely underestimate the activity. The catalyst is fluxional with an ensemble of metastable structures energetically accessible at reaction conditions. A modified genetic algorithm is proposed to comprehensively search for the low energy metastable ensemble (LEME) structures instead of merely the global min. structure. In order to reduce the computational cost of d. functional calcns., a high dimensional neural network potential is employed to accelerate the exploration. The presence and influence of LEME structures during catalysis is discussed by the example of H covered Pt13 clusters for two reactions of major importance: hydrogen evolution reaction and methane activation. The results demonstrate that although the no. of accessible metastable structures is reduced under reaction condition for Pt13 clusters, these metastable structures can exhibit high activity and dominate the obsd. activity due to their unique electronic or structural properties. This underlines the necessity of thoroughly exploring the LEME structures in catalysis simulations. The approach enables one to systematically address the impact of isomers in catalysis studies, taking into account the high adsorbate coverage induced by reaction conditions.
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    Zuo, Y.; Chen, C.; Li, X.; Deng, Z.; Chen, Y.; Behler, J.; Csányi, G.; Shapeev, A. V.; Thompson, A. P.; Wood, A. M.; Ong, S. P. A Performance and Cost Assessment of Machine Learning Interatomic Potentials. J. Phys. Chem. A 2020, 124, 731– 745,  DOI: 10.1021/acs.jpca.9b08723
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    Performance and Cost Assessment of Machine Learning Interatomic Potentials
    Zuo, Yunxing; Chen, Chi; Li, Xiangguo; Deng, Zhi; Chen, Yiming; Behler, Jorg; Csanyi, Gabor; Shapeev, Alexander V.; Thompson, Aidan P.; Wood, Mitchell A.; Ong, Shyue Ping
    Journal of Physical Chemistry A (2020), 124 (4), 731-745CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    Machine learning of the quant. relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interat. potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors-atom-centered symmetry functions (ACSF), smooth overlap of at. positions (SOAP), the spectral neighbor anal. potential (SNAP) bispectrum components, and moment tensors-using a diverse data set generated using high-throughput d. functional theory (DFT) calcns. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic consts. and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for mol. dynamics and other applications.
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    Bartók, A. P.; Gillan, M. J.; Manby, F. R.; Csányi, G. Machine-Learning Approach for One- and Two-Body Corrections to Density Functional Theory: Applications to Molecular and Condensed Water. Phys. Rev. B 2013, 88, 054104,  DOI: 10.1103/PhysRevB.87.184115
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    Machine-learning approach for one- and two-body corrections to density functional theory: applications to molecular and condensed water
    Bartok, Albert P.; Gillan, Michael J.; Manby, Frederick R.; Csanyi, Gabor
    Physical Review B: Condensed Matter and Materials Physics (2013), 88 (5), 054104/1-054104/12CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    We show how machine learning techniques based on Bayesian inference can be used to enhance the computer simulation of mol. materials, focusing here on water. We train our machine-learning algorithm using accurate, correlated quantum chem., and predict energies and forces in mol. aggregates ranging from clusters to solid and liq. phases. The widely used electronic-structure methods based on d. functional theory (DFT) by themselves give poor accuracy for mol. materials like water, and we show how our techniques can be used to generate systematically improvable one- and two-body corrections to DFT with modest extra resources. The resulting cor. DFT scheme is considerably more accurate than uncorrected DFT for the relative energies of small water clusters and different ice structures and significantly improves the description of the structure and dynamics of liq. water. However, our results for ice structures and the liq. indicate that beyond-two-body DFT errors cannot be ignored, and we suggest how our machine-learning methods can be further developed to correct these errors.
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    Hanse, K.; Montavon, G.; Biegler, F.; Fazli, S.; Rupp, M.; Scheffler, M.; von Lilienfeld, O. A.; Tkatchenko, A.; Müller, K.-R. Assessment and Validation of Machine Learning Methods for Predicting Molecular Atomization Energies. J. Chem. Theory Comput. 2013, 9, 3404– 3419,  DOI: 10.1021/ct400195d
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    Montavon, G.; Rupp, M.; Gobre, V.; Vazquez-Mayagoitia, A.; Hansen, K.; Tkatchenko, A.; Müller, K.-R.; von Lilienfeld, O. A. Machine Learning of Molecular Electronic Properties in Chemical Compound Space. New J. Phys. 2013, 15, 095003  DOI: 10.1088/1367-2630/15/9/095003
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    Machine learning of molecular electronic properties in chemical compound space
    Montavon, Gregoire; Rupp, Matthias; Gobre, Vivekanand; Vazquez-Mayagoitia, Alvaro; Hansen, Katja; Tkatchenko, Alexandre; Mueller, Klaus-Robert; von Lilienfeld, O. Anatole
    New Journal of Physics (2013), 15 (Sept.), 095003CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
    The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amt. of data amenable to intelligent data anal. for the identification of meaningful, novel and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compds. that are synthetically accessible. Here, we present a machine learning model, trained on a database of ab initio calcn. results for thousands of org. mols., that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity and excitation energies. The machine learning model is based on a deep multi-task artificial neural network, exploiting the underlying correlations between various mol. properties. The input is identical to ab initio methods, i.e. nuclear charges and Cartesian coordinates of all atoms. For small org. mols., the accuracy of such a 'quantum machine' is similar, and sometimes superior, to modern quantum-chem. methods-at negligible computational cost.
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    Rupp, M.; Ramakrishnan, R.; von Lilienfeld, O. A. Machine Learning for Quantum Mechanical Properties of Atoms in Molecules. J. Phys. Chem. Lett. 2015, 6, 3309– 3313,  DOI: 10.1021/acs.jpclett.5b01456
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    Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
    Rupp, Matthias; Ramakrishnan, Raghunathan; von Lilienfeld, O. Anatole
    Journal of Physical Chemistry Letters (2015), 6 (16), 3309-3313CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    We introduce machine learning models of quantum mech. observables of atoms in mols. Instant out-of-sample predictions for proton and carbon nuclear chem. shifts, at. core level excitations, and forces on atoms reach accuracies on par with d. functional theory ref. Locality is exploited within nonlinear regression via local atom-centered coordinate systems. The approach is validated on a diverse set of 9 k small org. mols. Linear scaling of computational cost in system size is demonstrated for satd. polymers with up to submesoscale lengths.
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    Weststrate, C. J.; van de Loosdrecht, J.; Niemantsverdriet, J. W. Spectroscopic Insights into Cobalt-Catalyzed Fischer-Tropsch Synthesis: A Review of the Carbon Monoxide Interaction with Single Crystalline Surfaces of Cobalt. J. Catal. 2016, 342, 1– 16,  DOI: 10.1016/j.jcat.2016.07.010
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    Spectroscopic insights into cobalt-catalyzed Fischer-Tropsch synthesis: A review of the carbon monoxide interaction with single crystalline surfaces of cobalt
    Weststrate, C. J.; van de Loosdrecht, J.; Niemantsverdriet, J. W.
    Journal of Catalysis (2016), 342 (), 1-16CODEN: JCTLA5; ISSN:0021-9517. (Elsevier Inc.)
    The present article summarizes exptl. findings of the interaction of CO with single crystal surfaces of cobalt. We first provide a quant. study of non-dissociative CO adsorption on Co(0001) and establish a quant. correlation between θCO and adsorption site occupation. In light of these findings we revisit the structure of previously reported ordered CO/Co(0001) adsorbate layers. Measurements of the CO coverage at equil. conditions are used to derive a phase diagram for CO on Co(0001). For low temp. Fischer-Tropsch synthesis conditions the CO coverage is predicted to be ≈0.5 ML, a value that hardly changes with pCO. The CO desorption temp. found in temp. programmed desorption is practically structure-independent, despite structure-dependent heats of adsorption reported in the literature. This mismatch is attributed to a structure-dependent pre-exponential factor for desorption. IR spectra reported throughout this study provide a ref. point for IR studies on cobalt catalysts. Results for CO adsorbed on flat and defect-rich Co surfaces as well as particular, CO adsorbed on top sites, and in addn. affect the distribution of COad over the various possible adsorption sites.
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    Werbos, P. J. Generalization of Backpropagation with Application to a Recurrent Gas Market Model. Neural Networks 1988, 1, 339– 356,  DOI: 10.1016/0893-6080(88)90007-X
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    Huang, Y.; Kang, J.; Goddard, W. A.; Wang, L.-W. Density Functional Theory Based Neural Network Force Fields from Energy Decompositions. Phys. Rev. B 2019, 99, 064103  DOI: 10.1103/PhysRevB.99.064103
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    Density functional theory based neural network force fields from energy decompositions
    Huang, Yufeng; Kang, Jun; Goddard, William A. III; Wang, Lin-Wang
    Physical Review B (2019), 99 (6), 064103/1-064103/11CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    In order to develop force fields (FF) for mol. dynamics simulations that retain the accuracy of ab initio d. functional theory (DFT), we developed a machine learning protocol based on an energy decompn. scheme that exts. at. energies from DFT calcns. Our DFT to FF (DFT2FF) approach provides almost hundreds of times more data for the DFT energies, which dramatically improves accuracy with less DFT calcns. In addn., we use piecewise cosine basis functions to systematically construct symmetry invariant features into the neural network model. We illustrate this DFT2FF approach for amorphous silicon where only 800 DFT configurations are sufficient to achieve an accuracy of 1 meV/atom for energy and 0.1 eV/A for forces. We then use the resulting FF model to calc. the thermal cond. of amorphous Si based on long mol. dynamics simulations. The dramatic speedup in training in our DFT2FF protocol allows the adoption of a simulation paradigm where an accurate and problem specific FF for a given physics phenomenon is trained on-the-spot through a quick DFT precalcn. and FF training.
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    Gastegger, M.; Schwiedrzik, L.; Bittermann, M.; Berzsenyi, F.; Marquetand, P. wACSF - Weighted Atom-Centered Symmetry Functions as Descriptors in Machine Learning Potentials. J. Chem. Phys. 2018, 148, 241709,  DOI: 10.1063/1.5019667
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    wACSF-Weighted atom-centered symmetry functions as descriptors in machine learning potentials
    Gastegger, M.; Schwiedrzik, L.; Bittermann, M.; Berzsenyi, F.; Marquetand, P.
    Journal of Chemical Physics (2018), 148 (24), 241709/1-241709/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We introduce weighted atom-centered symmetry functions (wACSFs) as descriptors of a chem. system's geometry for use in the prediction of chem. properties such as enthalpies or potential energies via machine learning. The wACSFs are based on conventional atom-centered symmetry functions (ACSFs) but overcome the undesirable scaling of the latter with an increasing no. of different elements in a chem. system. The performance of these two descriptors is compared using them as inputs in high-dimensional neural network potentials (HDNNPs), employing the mol. structures and assocd. enthalpies of the 133 855 mols. contg. up to five different elements reported in the QM9 database as ref. data. A substantially smaller no. of wACSFs than ACSFs is needed to obtain a comparable spatial resoln. of the mol. structures. At the same time, this smaller set of wACSFs leads to a significantly better generalization performance in the machine learning potential than the large set of conventional ACSFs. Furthermore, we show that the intrinsic parameters of the descriptors can in principle be optimized with a genetic algorithm in a highly automated manner. For the wACSFs employed here, we find however that using a simple empirical parametrization scheme is sufficient in order to obtain HDNNPs with high accuracy. (c) 2018 American Institute of Physics.
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    Artrith, N.; Urban, A.; Ceder, G. Efficient and Accurate Machine-Learning Interpolation of Atomic Energies in Compositions with Many Species. Phys. Rev. B 2017, 96, 014112  DOI: 10.1103/PhysRevB.96.014112
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    Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species
    Artrith, Nongnuch; Urban, Alexander; Ceder, Gerbrand
    Physical Review B (2017), 96 (1), 014112/1-014112/5CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    Machine-learning potentials (MLPs) for atomistic simulations are a promising alternative to conventional classical potentials. Current approaches rely on descriptors of the local at. environment with dimensions that increase quadratically with the no. of chem. species. In this paper, we demonstrate that such a scaling can be avoided in practice. We show that a math. simple and computationally efficient descriptor with const. complexity is sufficient to represent transition-metal oxide compns. and biomols. contg. 11 chem. species with a precision of around 3 meV/atom. This insight removes a perceived bound on the utility of MLPs and paves the way to investigate the physics of previously inaccessible materials with more than ten chem. species.
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    Seko, A.; Hayashi, H.; Nakayama, K.; Takahashi, A.; Tanaka, I. Representation of Compounds for Machine-Learning Prediction of Physical Properties. Phys. Rev. B 2017, 95, 144110,  DOI: 10.1103/PhysRevB.95.144110
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    Representation of compounds for machine-learning prediction of physical properties
    Seko, Atsuto; Hayashi, Hiroyuki; Nakayama, Keita; Takahashi, Akira; Tanaka, Isao
    Physical Review B (2017), 95 (14), 144110/1-144110/11CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    The representations of a compd., called "descriptors" or "features", play an essential role in constructing a machine-learning model of its phys. properties. In this study, we adopt a procedure for generating a set of descriptors from simple elemental and structural representations. First, it is applied to a large data set composed of the cohesive energy for about 18 000 compds. computed by d. functional theory calcn. As a result, we obtain a kernel ridge prediction model with a prediction error of 0.041 eV/atom, which is close to the "chem. accuracy" of 1 kcal/mol (0.043 eV/atom). A prediction model with an error of 0.071 eV/atom of the cohesive energy is obtained for the normalized prototype structures, which can be used for the practical purpose of searching for as-yet-unknown structures. The procedure is also applied to two smaller data sets, i.e., a data set of the lattice thermal cond. for 110 compds. computed by d. functional theory calcn. and a data set of the exptl. melting temp. for 248 compds. We examine the effect of the descriptor sets on the efficiency of Bayesian optimization in addn. to the accuracy of the kernel ridge regression models. They exhibit good predictive performances.
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    Huang, B.; von Lilienfeld, O. A. Communication: Understanding Molecular Representations in Machine Learning: The Role of Uniqueness and Target Similarity. J. Chem. Phys. 2016, 145, 161102,  DOI: 10.1063/1.4964627
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    Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity
    Huang, Bing; von Lilienfeld, O. Anatole
    Journal of Chemical Physics (2016), 145 (16), 161102/1-161102/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The predictive accuracy of Machine Learning (ML) models of mol. properties depends on the choice of the mol. representation. Inspired by the postulates of quantum mechanics, we introduce a hierarchy of representations which meet uniqueness and target similarity criteria. To systematically control target similarity, we simply rely on interat. many body expansions, as implemented in universal force-fields, including Bonding, Angular (BA), and higher order terms. Addn. of higher order contributions systematically increases similarity to the true potential energy and predictive accuracy of the resulting ML models. We report numerical evidence for the performance of BAML models trained on mol. properties pre-calcd. at electron-correlated and d. functional theory level of theory for thousands of small org. mols. Properties studied include enthalpies and free energies of atomization, heat capacity, zero-point vibrational energies, dipole-moment, polarizability, HOMO/LUMO energies and gap, ionization potential, electron affinity, and electronic excitations. After training, BAML predicts energies or electronic properties of out-of-sample mols. with unprecedented accuracy and speed. (c) 2016 American Institute of Physics.
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    Handley, C. M.; Popelier, P. L. A. Potential Energy Surfaces Fitted by Artificial Neural Networks. J. Phys. Chem. A 2010, 114, 3371– 3383,  DOI: 10.1021/jp9105585
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    Potential Energy Surfaces Fitted by Artificial Neural Networks
    Handley, Chris M.; Popelier, Paul L. A.
    Journal of Physical Chemistry A (2010), 114 (10), 3371-3383CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    A review. Mol. mechanics is the tool of choice for the modeling of systems that are so large or complex that it is impractical or impossible to model them by ab initio methods. For this reason there is a need for accurate potentials that are able to quickly reproduce ab initio quality results at the fraction of the cost. The interactions within force fields are represented by a no. of functions. Some interactions are well understood and can be represented by simple math. functions while others are not so well understood and their functional form is represented in a simplistic manner or not even known. In the last 20 years there have been the first examples of a new design ethic, where novel and contemporary methods using machine learning, in particular, artificial neural networks, have been used to find the nature of the underlying functions of a force field. Here we appraise what has been achieved over this time and what requires further improvements, while offering some insight and guidance for the development of future force fields.
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    Ramsvik, T.; Borg, A.; Kildemo, M.; Raaen, S.; Matsuura, A.; Jaworowski, A. J.; Worren, T.; Leandersson, M. Molecular Vibrations in Core-Ionised CO Adsorbed on Co(0001) and Rh(100). Surf. Sci. 2001, 492, 152– 160,  DOI: 10.1016/S0039-6028(01)01446-7
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    Molecular vibrations in core-ionised CO adsorbed on Co(0 0 0 1) and Rh(1 0 0)
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  • Abstract

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    Figure 1

    Figure 1. Illustration of radial (a) and angular (b) coordination descriptors. Radial distributions are defined with respect to the atom marked as (i), angular distributions relative to the axis between atoms (i,j). Different descriptors are shown using various colors. The graphs show the signal values as a function of the descriptor parameters. (a) Left: cutoff function gc for various cutoff radii. Right: radial coordinate descriptors Ri for various decay rates. (b) Angular coordinate descriptors Ai for various angular decay parameters.

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    Figure 2

    Figure 2. Schematic depiction of the hybrid network architecture. Separate geometric and electronic depictions of a molecular geometry are obtained, from which the atomic networks reconstruct the total energy. This compares to classical approaches in which only the geometric representation is used. Geometric and electronic information are communicated to the atomic networks using a set of basis functions, each represented as a single input node. One atomic network is constructed per chemically unique element (here shown in green, yellow, and red).

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    Figure 3

    Figure 3. Different stages of dataset construction: I. Translational states along a geometrically bounding potential surface. II. At each translational site, different rotations are obtained by rotating the molecule along two internal coordinates. III. Each rotation is expanded into a set of vibrational states. IV. Combinations of these states are used to construct a set of adlayers. At this step, translations are extended over a set of support grids to alleviate symmetry constraints. Note the sparser sample density over these extended surfaces.

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    Figure 4

    Figure 4. Error distributions for a selection of CO/Co(001) networks. Model (II) is a purely structural network with the same architecture as the single-transform hybrid ANN detailed in the main text. Model (III) is a structural network with a reoptimized architecture with dimensionality 20 and 2 transforms. Model (IV) uses the reoptimized architecture but with the extended dataset (II) as the training dataset. Model (V) uses the reoptimized architecture along with an extended descriptor set (trained using dataset (I), parameters are provided in Figure S2). Model (VI) combines the extended dataset (II) with the extended descriptor set of model (V). Additional details are provided in Table S11.

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    Figure 5

    Figure 5. ANN potentials for the CO adsorption energy in the presence of lateral interactions over the left (Co(001)) and middle (Co(211)). Profiles at 300 and 500 K are derived from temperature-corrected adlayer energies obtained through MC. Hexagonal markers represent reference DFT minimum energy points. Right: onset coverage at which temperature-dependent lateral interaction potentials deviate from the 0 K potential by >1 kJ/mol.

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    Figure 6

    Figure 6. Minimum energy structures for CO/Co(211) predicted with the ANN. From left to right: 0.2, 0.4, 0.7, and 0.9 ML.

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    Figure 7

    Figure 7. Left: equilibrium CO coverage on the Co(001) surface, determined from a microkinetic model (MKM) composed of a single-reversible adsorption step with coverage-dependent adsorption energies. (Details are provided in the Supporting Information). The HK model omits lateral interactions. Markers show experimental data published by Weststrate et al. (59) Right: effect of the temperature correction applied to the lateral interaction model at 1 bar.

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    Figure 8

    Figure 8. Difference in the lateral interaction potentials for Co(001) predicted for different XC functionals at T = 0, 300, and 500 K. Average adsorption energies are expressed relative to the adsorption energy of CO on the empty surface.

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    Figure 9

    Figure 9. Left: influence of different dispersion corrections on the revPBE lateral interaction potential for CO/Co(001). Integral adsorption energies have been expressed relative to the adsorption on the empty surface. Right: comparison of Grimme dispersion effects on the adsorption equilibrium for CO/Co(001) at 1 bar.

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  • References

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      Kinetic Monte Carlo Simulations Unveil Synergic Effects at Work on Bifunctional Catalysts
      Prats, Hector; Posada-Perez, Sergio; Rodriguez, Jose A.; Sayos, Ramon; Illas, Francesc
      ACS Catalysis (2019), 9 (10), 9117-9126CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
      The interaction between metal particles and the support in heterogeneous catalysis was the subject of a large no. of studies. While strong metal-support interactions can lead to deleterious catalyst deactivation and the underlying mechanism is well understood, in other cases the effect may beneficially enhance the catalytic activity and/or selectivity with no clear picture of the chem. involved. Strong metal-support interactions make Au nanoparticles dispersed on MoC a highly active catalyst for the low-temp. H2O-gas shift reaction (WGSR). By using kinetic Monte Carlo (kMC) simulations, the authors unravel the origin of the exptl. obsd. high WGSR activity of Au/MoC. The kMC simulations provide strong evidence for a cooperative effect between the different regions of the catalyst: the clean MoC regions are responsible for adsorbing and dissocg. H2O mols., and the vicinity of the Au adclusters contributes to COOH formation. The information thus obtained goes beyond that obtained solely from free-energy landscapes and constitutes a step forward toward the rational design of catalysts. The simulations and anal. described here are general and can be applied to other complex systems involving different catalytic regions and a large no. of surface processes.
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    4. 4
      Zijlstra, B.; Broos, R. J. P.; Chen, W.; Oosterbeek, H.; Filot, I. A. W.; Hensen, E. J. M. Coverage Effects in CO Dissociation on Metallic Cobalt Nanoparticles. ACS Catal. 2019, 9, 7365– 7372,  DOI: 10.1021/acscatal.9b01967
      4
      Coverage Effects in CO Dissociation on Metallic Cobalt Nanoparticles
      Zijlstra, Bart; Broos, Robin J. P.; Chen, Wei; Oosterbeek, Heiko; Filot, Ivo A. W.; Hensen, Emiel J. M.
      ACS Catalysis (2019), 9 (8), 7365-7372CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
      The active site of CO dissocn. on a cobalt nanoparticle, relevant to the Fischer-Tropsch reaction, can be computed directly using d. functional theory. We investigate how the activation barrier for direct CO dissocn. depends on CO coverage for step-edge and terrace cobalt sites. Whereas on terrace sites increasing coverage results in a substantial increase of the direct CO dissocn. barrier, we find that this barrier is nearly independent of CO coverage for the step-edge sites on corrugated surfaces. A detailed electronic anal. shows that this difference is due to the flexibility of the adsorbed layer, minimizing Pauli repulsion during the carbon-oxygen bond dissocn. reaction on the step-edge site. We constructed a simple first-principles microkinetic model that not only reproduces exptl. obsd. rates but also shows how migration of carbon species between step-edge and terrace sites contributes to methane formation.
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    5. 5
      Zijlstra, B.; Broos, R. J. P.; Chen, W.; Bezemer, G. L.; Filot, I. A. W.; Hensen, E. J. M. The Vital Role of Step-Edge Sites for Both CO Activation and Chain Growth on Cobalt Fischer–Tropsch Catalysts Revealed through First-Principles-Based Microkinetic Modeling Including Lateral Interactions. ACS Catal. 2020, 10, 9376– 9400,  DOI: 10.1021/acscatal.0c02420
      5
      The Vital Role of Step-Edge Sites for Both CO Activation and Chain Growth on Cobalt Fischer-Tropsch Catalysts Revealed through First-Principles-Based Microkinetic Modeling Including Lateral Interactions
      Zijlstra, Bart; Broos, Robin J. P.; Chen, Wei; Bezemer, G. Leendert; Filot, Ivo A. W.; Hensen, Emiel J. M.
      ACS Catalysis (2020), 10 (16), 9376-9400CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
      Microkinetic modeling is employed to predict catalytic turnover rates, product distributions, preferred mechanistic pathways, and rate- and selectivity-controlling elementary reaction steps for the Fischer-Tropsch (FT) reaction. We considered all relevant elementary reaction steps on Co(11‾21) step-edge and Co(0001) terrace sites as well as such important aspects as coverage-related lateral interactions, different chain-growth mechanisms, and the migration of adsorbed species between the two surfaces in the dual-site model. CHx-CHy coupling pathways relevant to the carbide mechanism have favorable barriers in comparison to the overall barriers for the CO insertion mechanism. A comparison of reaction barriers indicates why cobalt is such a good FT catalyst: CO bond scission and chain growth compete, while termination to olefins has a slightly higher barrier. The predicted kinetic parameters correspond well with exptl. kinetic data. The Co(11‾21) model surface is highly active and selective for the FT reaction. Adding terrace Co(0001) sites in a dual-site model approach leads to a substantially higher CH4 selectivity at the expense of the C2+-hydrocarbons selectivity. The chain-growth probability decreases with increasing temp. and H2/CO ratio, caused by faster hydrogenation of the hydrocarbon chains. The elementary reaction steps for O removal and CO dissocn. significantly control the overall CO consumption rate. Chain growth occurs almost exclusively at step-edge sites, while addnl. CH4 stems from CH and CH3 migration from step-edge to terrace sites. Replacing CO by CO2 as the reactant shifts the product distribution nearly completely to CH4, which is related to the much higher H/CO coverage ratio during CO2 hydrogenation in comparison to CO hydrogenation. These findings highlight the importance of a proper balance of CO and H surface species during the FT reaction and pinpoint step-edge sites as the locus of the FT reaction with low-reactive terrace sites near step-edge sites being the origin of unwanted CH4.
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    6. 6
      Grabow, L. C.; Hvolbæk, B.; Nørskov, J. K. Understanding Trends in Catalytic Activity: The Effect of Adsorbate–Adsorbate Interactions for CO Oxidation Over Transition Metals. Top. Catal. 2010, 53, 298– 310,  DOI: 10.1007/s11244-010-9455-2
      6
      Understanding Trends in Catalytic Activity: The Effect of Adsorbate-Adsorbate Interactions for CO Oxidation Over Transition Metals
      Grabow, Lars C.; Hvolbaek, Britt; Noerskov, Jens K.
      Topics in Catalysis (2010), 53 (5-6), 298-310CODEN: TOCAFI; ISSN:1022-5528. (Springer)
      Using high temp. CO oxidn. as the example, trends in the reactivity of transition metals are discussed on the basis of d. functional theory (DFT) calcns. Volcano type relations between the catalytic rate and adsorption energies of important intermediates are introduced and the effect of adsorbate-adsorbate interaction on the trends is discussed. We find that adsorbate-adsorbate interactions significantly increase the activity of strong binding metals (left side of the volcano) but the interactions do not change the relative activity of different metals and have a very small influence on the position of the top of the volcano, i.e., on which metal is the best catalyst.
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    7. 7
      Lausche, A. C.; Medford, A. J.; Khan, T. S.; Xu, Y.; Bligaard, T.; Abild-Pedersen, F.; Nørskov, J. K.; Studt, F. On the Effect of Coverage-Dependent Adsorbate-Adsorbate Interactions for CO Methanation on Transition Metal Surfaces. J. Catal. 2013, 307, 275– 282,  DOI: 10.1016/j.jcat.2013.08.002
      7
      On the effect of coverage-dependent adsorbate-adsorbate interactions for CO methanation on transition metal surfaces
      Lausche, Adam C.; Medford, Andrew J.; Khan, Tuhin Suvra; Xu, Yue; Bligaard, Thomas; Abild-Pedersen, Frank; Noerskov, Jens K.; Studt, Felix
      Journal of Catalysis (2013), 307 (), 275-282CODEN: JCTLA5; ISSN:0021-9517. (Elsevier Inc.)
      Heterogeneously catalyzed reactions involving the dissocn. of strongly bonded mols. typically need quite reactive catalysts with high coverages of intermediate mols. Methanation of carbon monoxide is one example, where CO dissocn. has been reported to take place on step sites with a high coverage of CO. At these high coverages, reaction intermediates experience interaction effects that typically reduce their adsorption energies. Herein, the effect of these interactions on the activities of transition metals for CO methanation is investigated. For transition metals that have low coverages of reactants, the effect is minimal. But for materials with high coverages under reaction conditions, rates can change by several orders of magnitude. Nevertheless, the position of the max. of the activity volcano does not shift significantly, and the rates at the max. are only slightly perturbed by adsorbate-adsorbate interactions. In order to accurately describe selectivities, however, adsorbate-adsorbate interactions will likely need to be included.
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    8. 8
      Grabow, L. C.; Gokhale, A. A.; Evans, S. T.; Dumesic, J. A.; Mavrikakis, M. Mechanism of the Water Gas Shift Reaction on Pt: First Principles, Experiments, and Microkinetic Modeling. J. Phys. Chem. C 2008, 112, 4608– 4617,  DOI: 10.1021/jp7099702
      8
      Mechanism of the Water Gas Shift Reaction on Pt: First Principles, Experiments, and Microkinetic Modeling
      Grabow, Lars C.; Gokhale, Amit A.; Evans, Steven T.; Dumesic, James A.; Mavrikakis, Manos
      Journal of Physical Chemistry C (2008), 112 (12), 4608-4617CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      We present a microkinetic model as well as exptl. data for the low-temp. water gas shift (WGS) reaction catalyzed by Pt at temps. from 523 to 573 K and for various gas compns. at a pressure of 1 atm. Thermodn. and kinetic parameters for the model are derived from periodic, self-consistent d. functional theory (DFT-GGA) calcns. on Pt(111). The destabilizing effect of high CO surface coverage on the binding energies of surface species is quantified through DFT calcns. and accounted for in the microkinetic model. Deviations of specific fitted model parameters from DFT calcd. parameters on Pt(111) point to the possible role of steps/defects in this reaction. Our model predicts reaction rates and reaction orders in good agreement with our expts. The calcd. and exptl. apparent activation energies are 67.8 kJ/mol and 71.4 kJ/mol, resp. The model shows that the most significant reaction channel proceeds via a carboxyl (COOH) intermediate. Formate (HCOO), which has been exptl. obsd. and thought to be the key WGS intermediate in the literature, is shown to act only as a spectator species.
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    9. 9
      Bajpai, A.; Frey, K.; Schneider, W. F. Comparison of Coverage-Dependent Binding Energy Models for Mean-Field Microkinetic Rate Predictions. Langmuir 2020, 36, 465– 474,  DOI: 10.1021/acs.langmuir.9b03563
      9
      Comparison of Coverage-Dependent Binding Energy Models for Mean-Field Microkinetic Rate Predictions
      Bajpai, Anshumaan; Frey, Kurt; Schneider, William F.
      Langmuir (2020), 36 (1), 465-474CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      The binding energies of adsorbates at catalytic surfaces are in general functions of adsorbate coverage, with corresponding consequences for equil. surface coverages and reaction rates under relevant conditions. This coverage dependence is commonly incorporated into mean-field microkinetic models by writing adsorption energies as an algebraic function of coverage and parametrizing against d. functional theory models. In this work, we compare the performance of three different anal. coverage-dependent forms, including linear and piecewise models and a logarithmic form inspired by Wilson's activity model, against accurate results obtained from a lattice-based cluster expansion (CE) representation of adsorbate interactions combined with a Monte Carlo evaluation of reaction rates. We take as a model system O2 dissocn.-limited NO oxidn. to NO2 over Pt(111), parametrize all models against the same set of previously reported coverage-dependent NO and O binding energies, and solve kinetic models under the same set of assumptions. Steady-state coverages from the anal. models are similar to each other and the ensemble-averaged CE result, other than the discontinuities in O and NO coverages that appear in the piecewise model. Predicted steady-state rates differ more substantially, reflecting the sensitivity of the O2 dissocn. activation energy to coverage-dependent binding energies. The activity model predicts reaction rates reliably at low temps. and systematically deviates from CE rates at high temps., where minority surface sites, having low local coverage around vacant pairs, dominate overall reaction rates. The results highlight the challenges of developing coverage-dependent microkinetic models that are reliable across a range of conditions.
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    10. 10
      Mhadeshwar, A. B.; Kitchin, J. R.; Barteau, M. A.; Vlachos, D. G. The Role of Adsorbate–Adsorbate Interactions in the Rate Controlling Step and the Most Abundant Reaction Intermediate of NH3 Decomposition on Ru. Catal. Lett. 2004, 96, 13– 22,  DOI: 10.1023/B:CATL.0000029523.22277.e1
      10
      The Role of Adsorbate-adsorbate Interactions in the Rate Controlling Step and the Most Abundant Reaction Intermediate of NH3 Decomposition on Ru
      Mhadeshwar, A. B.; Kitchin, J. R.; Barteau, M. A.; Vlachos, D. G.
      Catalysis Letters (2004), 96 (1-2), 13-22CODEN: CALEER; ISSN:1011-372X. (Kluwer Academic/Plenum Publishers)
      N-N adsorbate-adsorbate interactions on a Ru(0001) surface are first estd. using quantum mech. d. functional theory (DFT) calcns., and subsequently incorporated, for the first time, in a detailed microkinetic model for NH3 decompn. on Ru using the unity bond index-quadratic exponential potential (UBI-QEP) method. DFT simulations indicate that the cross N-H interactions are relatively small. Microkinetic model predictions are compared to ultra-high vacuum temp. programmed desorption and atm. fixed bed reactor data. The microkinetic model with N-N interactions captures the exptl. features quant. It is shown that the N-N interactions significantly alter the rate detg. step, the most abundant reaction intermediate, and the max. N*-coverage, compared to mechanisms that ignore adsorbate-adsorbate interactions.
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    11. 11
      Miller, S. D.; Pushkarev, V. V.; Gellman, A. J.; Kitchin, J. R. Simulating Temperature Programmed Desorption of Oxygen on Pt(111) Using DFT Derived Coverage Dependent Desorption Barriers. Top. Catal. 2013, 57, 106– 117
      There is no corresponding record for this reference.
    12. 12
      Getman, R. B.; Schneider, W. F. DFT-Based Coverage-Dependent Model of Pt-Catalyzed NO-Oxidation. ChemCatChem 2010, 2, 1450– 1460,  DOI: 10.1002/cctc.201000146
      12
      DFT-based coverage-dependent model of Pt-catalyzed NO oxidation
      Getman, Rachel B.; Schneider, William F.
      ChemCatChem (2010), 2 (11), 1450-1460CODEN: CHEMK3; ISSN:1867-3880. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A coverage-dependent, mean-field microkinetic model of catalytic NO oxidn., NO+0.5 O2.dblharw.NO2, at a Pt(111) surface was developed, based on large supercell d. functional theory (DFT) calcns. DFT is used to det. the overall energetics and activation energies of candidate reaction steps as a function of surface coverage. Surface coverage is found to have a significant but non-uniform effect on the energetics, pathways, and activation energies of reaction steps involving formation or cleavage of ON-O and O-O bonds, and inclusion of this coverage dependence is essential for obtaining a qual. correct representation of the catalysis. Correlations were used to express all reaction parameters in terms of a single coverage variable θ and steady-state solns. to the resultant mean-field models are obtained in the method of DeDonder relations. At conditions representative of NO oxidn. catalysis, the surface coverage is predicted to be 0.25 ≤ θ < 0.4 ML and to be controlled by equil. between gas-phase NO and NO2 and chemisorbed O. O2 dissociative adsorption (O2(g)→ 2O*) is rate limiting in the model. The DFT-based mean-field model captures many features of the exptl. obsd. catalysis, and its short-comings point the way toward more robust models of coverage-dependent kinetics.
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    13. 13
      Getman, R. B.; Xu, Y.; Schneider, W. F. Thermodynamics of Environment-Dependent Oxygen Chemisorption on Pt(111). J. Phys. Chem. C 2008, 112, 9559– 9572,  DOI: 10.1021/jp800905a
      13
      Thermodynamics of Environment-Dependent Oxygen Chemisorption on Pt(111)
      Getman, Rachel B.; Xu, Ye; Schneider, William F.
      Journal of Physical Chemistry C (2008), 112 (26), 9559-9572CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The reactivity of heterogeneous metal catalysts can be a strong function of the coverage of adsorbates. For example, Pt-catalyzed NO oxidn. to NO2 requires high concns. of chemisorbed (surface-bound) O, but the development of surface oxides is detrimental to reaction kinetics. Quantifying the structures, properties, and esp. the conditions that produce various adsorbate coverages is essential to developing qual. and quant. correct models of surface reactivity. In this work, we examine these ideas in the context of oxidn. reactions on Pt(111), the lowest energy face of bulk Pt. We use extensive supercell d. functional theory (DFT) calcns. to catalog and characterize the stable binding sites and arrangements of chemisorbed O on Pt(111), as a function of O coverage, θ. O atoms are found to uniformly prefer FCC binding sites and to arrange to minimize various destabilizing interactions with neighbor O. These destabilizing interactions are shown to have electronic and strain components that can either reinforce or oppose one another depending upon O-O sepn. Because of the nature and magnitudes of these lateral interactions, the thermodynamically stable O orderings partition into four coverage regimes of decreasing adsorption energy: 0 < θ ≤ 1/4 monolayer (ML), 1/4 < θ ≤ 1/2 ML, 1/2 < θ ≤ 2/3 ML, and 2/3 < θ ≤ 1 ML. We use equil. models to quantify the oxygen chem. potentials μO necessary to access each of these regimes. These equil. models can be used to relate surface coverage to various external environmental conditions and assumptions about relevant reaction equil.: dissociative equil. of the surface with O2 (g) can produce coverages up to 1/2 ML; either NO2 decompn. or "NO-assisted" O2 dissocn. can access coverages approaching 2/3 ML, as obsd. during NO oxidn. catalysis, and equil. with a solid-oxygen storage material, like ceria-zirconia, can buffer equil. coverages at a const. 1/4 ML O. These various oxidn. reaction energies can be summarized in a single "Ellingham" free energy diagram, providing a convenient representation of the relationship between surface coverage and reaction thermodn., and a useful guide toward relevant coverage regimes for more detailed study of reaction kinetics.
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    14. 14
      Bray, J. M.; Smith, J. L.; Schneider, W. F. Coverage-Dependent Adsorption at a Low Symmetry Surface: DFT and Statistical Analysis of Oxygen Chemistry on Kinked Pt(321). Top. Catal. 2014, 57, 89– 105,  DOI: 10.1007/s11244-013-0165-4
      14
      Coverage-Dependent Adsorption at a Low Symmetry Surface: DFT and Statistical Analysis of Oxygen Chemistry on Kinked Pt(321)
      Bray, J. M.; Smith, J. L.; Schneider, W. F.
      Topics in Catalysis (2014), 57 (1-4), 89-105CODEN: TOCAFI; ISSN:1022-5528. (Springer)
      The authors explore the influence of adsorbate interactions on the thermodn. and spectroscopic properties of oxygen on the stepped, kinked Pt(321) surface. The ground state arrangements of at. oxygen are identified with the aid of a cluster expansion and analyzed for coverages up to one oxygen per surface Pt (1 ML). Oxygen prefers to bind in bridge sites at the step edge at coverages up to 0.2 ML, but at higher coverages oxygen atoms actually experience mild, localized attractions such that both bridge and 3-fold hollow sites are occupied to form square planar, 4-fold-coordinated PtO4-like structures. These structures progressively dominate the surface with increasing coverage up to 0.8 ML, at which point every kink Pt is satd. with four oxygens. The authors compute stability regions for these ground states with respect to gas-phase O2 and to NO/NO2 mixts. The ground state structures at 0.2, 0.6, and 0.8 ML dominate over a wide range of conditions, with the 0.6 ML structure being most prominent. The authors also explore site preferences for mol. O2 adsorbed on key O ground state structures. Calcns. of vibrational modes and core electron binding energy shifts allow the authors to relate both ground state and nonequil. structures to exptl. HREELS and XPS results. Adsorption sites are primarily characterized by their surface coordination, such that O in atop, bridge, and 3-fold hollow sites possess distinct and identifiable vibrational modes and core level shifts. However, within these broad categories, variability due to interactions with proximal adsorbates were found. Adsorption energies and vibrational modes of O2 are particularly sensitive to the local adsorption environment. Lastly, the authors develop a 1-dimensional adsorption model to understand and rationalize exptl. obsd. nonequil. behavior at low coverages.
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    15. 15
      Sutton, J. E.; Vlachos, D. G. Building Large Microkinetic Models with First-Principles’ Accuracy at Reduced Computational Cost. Chem. Eng. Sci. 2015, 121, 190– 199,  DOI: 10.1016/j.ces.2014.09.011
      15
      Building large microkinetic models with first-principles' accuracy at reduced computational cost
      Sutton, Jonathan E.; Vlachos, Dionisios G.
      Chemical Engineering Science (2015), 121 (), 190-199CODEN: CESCAC; ISSN:0009-2509. (Elsevier Ltd.)
      We present a systematic hierarchical multiscale framework for parameterization of large microkinetic models that delivers first-principles' accuracy at significantly reduced computational cost. The framework leverages recently introduced first-principles-based semi-empirical methods (FPSEM), such as group additivity and Bronsted-Evans-Polanyi (BEP) relations, for surface reactions, local sensitivity anal., and a heuristic classification of the order of corrections to produce a hierarchy or family of models of improved accuracy. We demonstrate this approach to the moderate size ethanol steam reforming mechanism on Pt, consisting of 67 species (14 gas, 53 surface) and 160 reversible elementary-like reactions, for which the 'exact' d. functional theory (DFT)-based model is available. We find that the majority of refined parameters are surface species free energies and lateral interactions, underscoring the importance of thermodn. in kinetic mechanisms.
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    16. 16
      Sabbe, M. K.; Canduela-Rodriguez, G.; Joly, J.-F.; Reyniers, M.-F.; Marin, G. B. Ab Initio Coverage-Dependent Microkinetic Modeling of Benzene Hydrogenation on Pd(111). Catal. Sci. Technol. 2017, 7, 5267– 5283,  DOI: 10.1039/C7CY00962C
      16
      Ab initio coverage-dependent microkinetic modeling of benzene hydrogenation on Pd(111)
      Sabbe, Maarten K.; Canduela-Rodriguez, Gonzalo; Joly, Jean-Francois; Reyniers, Marie-Francoise; Marin, Guy B.
      Catalysis Science & Technology (2017), 7 (22), 5267-5283CODEN: CSTAGD; ISSN:2044-4753. (Royal Society of Chemistry)
      The effect of hydrogen coverage on the kinetics of benzene hydrogenation on Pd(111) has been investigated with optPBE-vdW d. functional theory calcns. and a coverage-dependent microkinetic model. The dominant reaction path consists of the consecutive hydrogenation of carbon atoms located in ortho positions relative to the previously hydrogenated carbon atom, independent of the hydrogen coverage. Increasing the hydrogen coverage destabilizes all surface species, which leads to weaker adsorption and increased rate coeffs. for the hydrogenation steps due to stronger destabilization of reactants than transition states. The catalytic activities simulated using the constructed coverage-dependent microkinetic model exceed those obtained using a low-coverage microkinetic model by several orders of magnitude and are comparable to exptl. obsd. activities. The rate coeffs. to which the global rate is most sensitive depend on the reaction conditions and differ from those calcd. using low coverage kinetics. Therefore, properly accounting for coverage dependence on the kinetics and thermodn. of catalytic hydrogenation reactions is not only required for an accurate DFT-based prediction of the catalytic activity but also for a correct understanding of the reaction mechanism.
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    17. 17
      Liu, H.; Liu, J.; Yang, B. Modeling the Effect of Surface CO Coverage on the Electrocatalytic Reduction of CO2 to CO on Pd Surfaces. Phys. Chem. Chem. Phys. 2019, 21, 9876– 9882,  DOI: 10.1039/C8CP07427E
      17
      Modeling the effect of surface CO coverage on the electrocatalytic reduction of CO2 to CO on Pd surfaces
      Liu, Hong; Liu, Jian; Yang, Bo
      Physical Chemistry Chemical Physics (2019), 21 (19), 9876-9882CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Electrocatalytic redn. of CO2 has attracted considerable attention recently, and it was found exptl. that Pd could show activity for the electroredn. of CO2 to CO. However, theor. studies showed that the adsorption of CO on Pd surfaces is strong and the coverage of CO is high, indicating that the interactions between the neighboring adsorbed CO and other reaction intermediates on the Pd surfaces cannot be neglected. Here, with d. functional theory calcns. and utilizing the Sabatier anal. method, we find that an adsorbate-adsorbate interaction is playing a crucial role in the modeling of the electrocatalytic redn. of CO2 to CO on Pd surfaces, while the reaction rates obtained by neglecting the interactions between the surface adsorbates are substantially lower than those reported in the expts. Upon analyzing the interactions quant. and using a self-consistent iterative microkinetic modeling method, we find that the active site for CO2 electroredn. is Pd(111) at different potentials applied. Our modeling results provide a reasonable computational interpretation for the electroredn. of CO2 to CO on Pd.
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    18. 18
      Wu, P.; Zeffron, J.; Xu, D.; Yang, B. First-Principles-Based Microkinetic Simulations of CO2 Hydrogenation to Methanol over Intermetallic GaPd2: Method Development to Include Complex Interactions between Surface Adsorbates. J. Phys. Chem. C 2020, 124, 15977– 15987,  DOI: 10.1021/acs.jpcc.0c03975
      18
      First-Principles-Based Microkinetic Simulations of CO2 Hydrogenation to Methanol over Intermetallic GaPd2: Method Development to Include Complex Interactions between Surface Adsorbates
      Wu, Panpan; Zaffran, Jeremie; Xu, Dongyang; Yang, Bo
      Journal of Physical Chemistry C (2020), 124 (29), 15977-15987CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      To computationally design efficient solid catalysts, d. functional theory (DFT) calcns. are widely used in combination with microkinetic modeling (MKM). However, MKM results are often biased due to the overestimation of adsorption strength in DFT calcns. that are usually performed at an arbitrary low coverage of surface intermediates. We hereby developed a new iterative approach focusing on the main species present on the catalyst at the steady state, hence allowing adsorption energy calcn. only in the presence of relevant intermediates. In this way, the complex parametrization process to det. scaling relations between adsorption energies and coverages is avoided, which will increase the efficiency and accuracy of the iteration process. When applying this approach to CO2 hydrogenation over GaPd2, we found within few iterations that only when running DFT calcns. using the surface with both CO and HCOO precovered, the coverage of surface species obtained from MKM anal. can be consistent with that used in DFT calcns. It stems from our theor. study that all the species coverages must be self-consistent in order to predict methanol selectivity in fair agreement with expt.
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    19. 19
      Yao, Z.; Zhao, J.; Bunting, R. J.; Zhao, C.; Hu, P.; Wang, J. Quantitative Insights into the Reaction Mechanism for the Direct Synthesis of H2O2 over Transition Metals: Coverage-Dependent Microkinetic Modeling. ACS Catal. 2021, 11, 1202– 1221,  DOI: 10.1021/acscatal.0c04125
      19
      Quantitative Insights into the Reaction Mechanism for the Direct Synthesis of H2O2 over Transition Metals: Coverage-Dependent Microkinetic Modeling
      Yao, Zihao; Zhao, Jinyan; Bunting, Rhys J.; Zhao, Chenxia; Hu, Peijun; Wang, Jianguo
      ACS Catalysis (2021), 11 (3), 1202-1221CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
      The direct synthesis is the most promising alternative method for the prodn. of hydrogen peroxide, and the bottleneck is still unsolved. The breakthrough lies in elusive reaction mechanism issues. In this work, advanced coverage-dependent kinetic modeling is combined with the energetics from first-principles calcns. to investigate the formation of H2O2 over transition metals. We show that the adsorbate-adsorbate interactions considerably affect the reaction mechanism of synthesis of hydrogen peroxide on Pd(111). Without the coverage effect, O2 is likely to go through the direct dissocn. mechanism, and water is the major product. When the coverage effects are included, the dissocns. of O-O and O-OH bonds are significantly inhibited, and on the contrary, the hydrogenations of O2 and OOH are promoted, leading to the prodn. of H2O2. We demonstrate that the reaction temp. induces strong variations in the coverage of intermediates, which in turn causes changes in product selectivity. Being consistent with the operando expt., our kinetic simulations indicate that the H2/O2 partial pressure ratio has great effects on H2O2 selectivity and the reaction rate of H2O2 is lower under hydrogen-rich (oxygen-lean) and oxygen-rich (hydrogen-lean) conditions, which is highly related to the intermediate coverage. The same approach is also applied to other important relevant metals, i.e., Cu(111), Au(111), PdAu, and PdHg alloys, and the trends of activity and selectivity have been obtained.
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    20. 20
      Yao, Z.; Guo, C.; Mao, Y.; Hu, P. Quantitative Determination of C-C Coupling Mechanisms and Detailed Analyses on the Activity and Selectivity for Fischer-Tropsch Synthesis on Co(0001): Microkinetic Modeling with Coverage Effects. ACS Catal. 2019, 9, 5957– 5973,  DOI: 10.1021/acscatal.9b01150
      20
      Quantitative Determination of C-C Coupling Mechanisms and Detailed Analyses on the Activity and Selectivity for Fischer-Tropsch Synthesis on Co(0001): Microkinetic Modeling with Coverage Effects
      Yao, Zihao; Guo, Chenxi; Mao, Yu; Hu, P.
      ACS Catalysis (2019), 9 (7), 5957-5973CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
      The Fischer-Tropsch synthesis plays a significant role in re-forming natural resources to meet global demand for commodities, while there is ongoing oil depletion and population growth. Mechanisms have long been investigated, but they are still a heavily debated issue. In this work, all of the possible elementary reaction steps on a flat cobalt surface were calcd. using d. functional theory (DFT) with van der Waals interactions. Kinetic simulations using std. DFT data (free energies and barriers at low coverages), the so-called non-coverage-dependent kinetic model commonly used in the literature, are compared to those from a coverage-dependent kinetic model for the system. We show that the coverage-dependent kinetic model gives rise to a TOF which is approx. 6 orders of magnitude larger than the TOF calcd. using the non-coverage-dependent kinetic model. Furthermore, it is found that Co(0001) is highly selective to olefin prodn., and it is very likely to produce long-chain hydrocarbons. Both models demonstrate that the CO insertion mechanism is the dominant mechanism on Co(0001). Our calcns. also reveal that high coverage of CHx leads to the carbide mechanism being significant and low coverage of CHx results in the CO insertion mechanism being more favored. Direct CO dissocn. is difficult on Co(0001), which leads to monomers CHx being unable to occupy a certain amt. of surface coverage, causing the carbide mechanism to be inhibited. The reaction pathway through CO + H → CHO, CHO + H → CHOH, and CHOH → CH + OH is the main channel to form the monomer CH on the basis of the coverage-dependent kinetic model simulations. The temp. considerably affects the surface coverage and the total reaction rate, leading to the selectivity being highly temp. dependent. Our coverage-dependent kinetic model predicts that the selectivity of oxygenates is high in comparison to methane in the low-temp. region from 425 and 475 K. From 475 to 525 K, the selectivity toward CH4 increases. From 525 to 700 K, the selectivity of C2 decreases significantly and the selectivity of CH4 increases remarkably.
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    21. 21
      Ding, Y.; Xu, Y.; Song, Y.; Guo, C.; Hu, P. Quantitative Studies of the Coverage Effects on Microkinetic Simulations for NO Oxidation on Pt(111). J. Phys. Chem. C 2019, 123, 27594– 27602,  DOI: 10.1021/acs.jpcc.9b08208
      21
      Quantitative Studies of the Coverage Effects on Microkinetic Simulations for NO Oxidation on Pt(111)
      Ding, Yunxuan; Xu, Yarong; Song, Yihui; Guo, Chenxi; Hu, P.
      Journal of Physical Chemistry C (2019), 123 (45), 27594-27602CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      To advance a reliable microkinetic modeling approach using d. functional theory (DFT) energies is of great importance to bridging between exptl. results and theor. calcns., and the current major issue is the coverage effect. A full microkinetic modeling for NO oxidn. using DFT energetics is developed. The calcd. turnover frequency (TOF) (0.22 s-1) agrees with the exptl. one (∼0.2 s-1) very well, if the coverage effects are properly incorporated. To include the interactions of adsorbates, namely, (i) O and O, NO and NO (self-interaction), and (ii) O and NO (cross-interaction), is important to obtain accurate kinetic results. Equally important, the interactions between the adsorbates and the transition states of O-O bond breaking and O-NO coupling are also crucial for achieving precise kinetics. A 2-line model can be used to describe accurately both the self and cross adsorbate-adsorbate interactions as well as the coverage effects on the transition states of O2 dissocn. and O-NO coupling. The various approxns. including Broensted-Evans-Polanyi (BEP) relations are carefully examd., and the errors involved are quantified. Also, a 1-line model is tested, which is a simplified approach but gives rise to a good agreement with exptl. results.
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    22. 22
      Prats, H.; Illas, F.; Sayós, R. General Concepts, Assumptions, Drawbacks, and Misuses in Kinetic Monte Carlo and Microkinetic Modeling Simulations Applied to Computational Heterogeneous Catalysis. Int. J. Quantum Chem. 2018, 118, 25518
      There is no corresponding record for this reference.
    23. 23
      Jørgenson, M.; Grönbeck, H. Selective Acetylene Hydrogenation over Single-Atom Alloy Nanoparticles by Kinetic Monte Carlo. J. Am. Chem. Soc. 2019, 141, 8541– 8549,  DOI: 10.1021/jacs.9b02132
      There is no corresponding record for this reference.
    24. 24
      Nagasaka, M.; Kondoh, H.; Nakai, I.; Ohta, T. CO Oxidation Reaction on Pt(111) Studied by the Dynamic Monte Carlo Method Including Lateral Interactions of Adsorbates. J. Chem. Phys. 2007, 126, 044704  DOI: 10.1063/1.2424705
      24
      CO oxidation reaction on Pt(111) studied by the dynamic Monte Carlo method including lateral interactions of adsorbates
      Nagasaka, Masanari; Kondoh, Hiroshi; Nakai, Ikuyo; Ohta, Toshiaki
      Journal of Chemical Physics (2007), 126 (4), 044704/1-044704/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The dynamics of adsorbate structures during CO oxidn. on Pt(111) surfaces and its effects on the reaction were studied by the dynamic Monte Carlo method including lateral interactions of adsorbates. The lateral interaction energies between adsorbed species were calcd. by the d. functional theory method. Dynamic Monte Carlo simulations were performed for the oxidn. reaction over a mesoscopic scale, where the exptl. detd. activation energies of elementary paths were altered by the calcd. lateral interaction energies. The simulated results reproduced the characteristics of the microscopic and mesoscopic scale adsorbate structures formed during the reaction, and revealed that the complicated reaction kinetics is comprehensively explained by a single reaction path affected by the surrounding adsorbates. We also propose from the simulations that weakly adsorbed CO mols. at domain boundaries promote the island-periphery specific reaction.
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    25. 25
      Wu, C.; Schmidt, D. J.; Wolverton, C.; Schneider, W. F. Accurate Coverage-Dependence Incorporated into First-Principles Kinetic Models: Catalytic NO oxidation on Pt (111). J. Catal. 2012, 286, 88– 94,  DOI: 10.1016/j.jcat.2011.10.020
      25
      Accurate coverage-dependence incorporated into first-principles kinetic models: Catalytic NO oxidation on Pt (1 1 1)
      Wu, C.; Schmidt, D. J.; Wolverton, C.; Schneider, W. F.
      Journal of Catalysis (2012), 286 (), 88-94CODEN: JCTLA5; ISSN:0021-9517. (Elsevier Inc.)
      The coverage of surface adsorbates influences both the no. and types of sites available for catalytic reactions at a heterogeneous surface, but accounting for adsorbate-adsorbate interactions and understanding their implications on obsd. rates remain challenges for simulation. Here, we demonstrate the use of a d. functional theory (DFT)-parameterized cluster expansion (CE) to incorporate accurate adsorbate-adsorbate interactions into a surface kinetic model. The distributions of adsorbates and reaction sites at a metal surface as a function of reaction conditions are obtained through Grand Canonical Monte Carlo simulations on the CE Hamiltonian. Reaction rates at those sites are obtained from the CE through a DFT-parameterized Bronsted-Evans-Polyani (BEP) relationship. The approach provides ready access both to steady-state rates and rate derivs. and further provides insight into the microscopic factors that influence obsd. rate behavior. We demonstrate the approach for steady-state O2 dissocn. at an O-covered Pt (1 1 1) surface-a model for catalytic NO oxidn. at this surface-and recover apparent activation energies and rate orders consistent with expt.
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    26. 26
      Yang, L.; Krim, A.; Muckerman, J. T. Density Functional Kinetic Monte Carlo Simulation of Water-Gas Shift Reaction on Cu/ZnO. J. Phys. Chem. C 2013, 117, 3414– 3425,  DOI: 10.1021/jp3114286
      26
      Density Functional Kinetic Monte Carlo Simulation of Water-Gas Shift Reaction on Cu/ZnO
      Yang, Liu; Karim, Altaf; Muckerman, James T.
      Journal of Physical Chemistry C (2013), 117 (7), 3414-3425CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      We describe a d. functional theory based kinetic Monte Carlo study of the water-gas shift (WGS) reaction catalyzed by Cu nanoparticles supported on a ZnO surface. DFT calcns. were performed to obtain the energetics of the relevant atomistic processes. Subsequently, the DFT results were employed as an intrinsic database in kinetic Monte Carlo simulations that account for the spatial distribution, fluctuations, and evolution of chem. species under steady-state conditions. Our simulations show that, in agreement with expts., the H2 and CO2 prodn. rates strongly depend on the size and structure of the Cu nanoparticles, which are modeled by single-layer nano islands in the present work. The WGS activity varies linearly with the total no. of edge sites of Cu nano islands. In addn., examn. of different elementary processes has suggested competition between the carboxyl and the redox mechanisms, both of which contribute significantly to the WGS reactivity. Our results have also indicated that both edge sites and terrace sites are active and contribute to the obsd. H2 and CO2 productivity.
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    27. 27
      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, 7, 3192– 3203
      There is no corresponding record for this reference.
    28. 28
      Meyer, J.; Bukas, V. J.; Mitra, S.; Reuter, K. Fingerprints of Energy Dissipation for Exothermic Surface Chemical Reactions: O2 on Pd(100). J. Chem. Phys. 2015, 143, 2131– 2136,  DOI: 10.1063/1.4926989
      There is no corresponding record for this reference.
    29. 29
      Boes, J. R.; Kitchin, J. R. Neural Network Predictions of Oxygen Interactions on a Dynamic Pd Surface. Mol. Simul. 2017, 43, 346– 354,  DOI: 10.1080/08927022.2016.1274984
      29
      Neural network predictions of oxygen interactions on a dynamic Pd surface
      Boes, Jacob R.; Kitchin, John R.
      Molecular Simulation (2017), 43 (5-6), 346-354CODEN: MOSIEA; ISSN:0892-7022. (Taylor & Francis Ltd.)
      A review. Artificial neural networks (NNs) are increasingly common in quantum chem. applications. These models can be trained to higher-level ab-initio calcns. and are capable of achieving arbitrary levels of accuracy. The most common applications thus far have been specialised for either bulk or surface structures of up to two chem. components. However, very few of these studies utilize NNs trained to high-dimensional potential energy surfaces, and there are even fewer studies which examine adsorbate-adsorbate and adsorbate-surface interactions with those NNs. The goal of this work is to det. the feasibility of and develop methodologies for producing a high-dimensional NN capable of reproducing coverage-dependent oxygen interactions with a dynamic Pd fcc(1 1 1) surface. We utilize the atomistic machine-learning potential software package to generate a Behler-Parrinello local symmetry function NN trained on a large database of d. functional theory (DFT) calcns. These training methods are flexible, and thus easily expanded upon as demonstrated in previous work. This allows the database of high quality PdO DFT calcns. to be used as a basis for future work, such as the inclusion of a third chem. species, for example a binary Pd alloy, or another adsorbate atom such as hydrogen.
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    30. 30
      Boes, J. R.; Groenenboom, M. C.; Keith, J. A.; Kitchin, J. R. Neural Network and ReaxFF Comparison for Au Properties. Int. J. Quantum Chem. 2016, 116, 979– 987,  DOI: 10.1002/qua.25115
      30
      Neural network and ReaxFF comparison for Au properties
      Boes, Jacob R.; Groenenboom, Mitchell C.; Keith, John A.; Kitchin, John R.
      International Journal of Quantum Chemistry (2016), 116 (13), 979-987CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
      A review. We have studied how ReaxFF and Behler-Parrinello neural network (BPNN) atomistic potentials should be trained to be accurate and tractable across multiple structural regimes of Au as a representative example of a single-component material. We trained these potentials using subsets of 9,972 Kohn-Sham d. functional theory calcns. and then validated their predictions against the untrained data. Our best ReaxFF potential was trained from 848 data points and could reliably predict surface and bulk data; however, it was substantially less accurate for mol. clusters of 126 atoms or fewer. Training the ReaxFF potential to more data also resulted in overfitting and lower accuracy. In contrast, BPNN could be fit to 9,734 calcns., and this potential performed comparably or better than ReaxFF across all regimes. However, the BPNN potential in this implementation brings significantly higher computational cost. © 2016 Wiley Periodicals, Inc.
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    31. 31
      Elstner, M.; Seifert, G. Density Functional Tight Binding. Philos. Trans. R. Soc., A 2014, 372, 20120483,  DOI: 10.1098/rsta.2012.0483
      31
      Density functional tight binding
      Elstner, Marcus; Seifert, Gotthard
      Philosophical Transactions of the Royal Society, A: Mathematical, Physical & Engineering Sciences (2014), 372 (2011), 20120483/1-20120483/12CODEN: PTRMAD; ISSN:1364-503X. (Royal Society)
      This paper reviews the basic principles of the d.-functional tight-binding (DFTB) method, which is based on d.-functional theory as formulated by Hohenberg, Kohn and Sham (KS-DFT). DFTB consists of a series of models that are derived from a Taylor series expansion of the KS-DFT total energy. In the lowest order (DFTB1), densities and potentials are written as superpositions of at. densities and potentials. The Kohn-Sham orbitals are then expanded to a set of localized atom-centered functions, which are obtained for spherical sym. spin-unpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrixes contain one- and two-center contributions only. Therefore, they can be calcd. and tabulated in advance as functions of the distance between at. pairs. The second contributions to DFTB1, the DFT double counting terms, are summarized together with nuclear repulsion energy terms and can be rewritten as the sum of pairwise repulsive terms. The second-order (DFTB2) and third-order (DFTB3) terms in the energy expansion correspond to a self-consistent representation, where the deviation of the ground-state d. from the ref. d. is represented by charge monopoles only. This leads to a computationally efficient representation in terms of at. charges (Mulliken), chem. hardness (Hubbard) parameters and scaled Coulomb laws. Therefore, no addnl. adjustable parameters enter the DFTB2 and DFTB3 formalism. The handling of parameters, the efficiency, the performance and extensions of DFTB are briefly discussed.
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    32. 32
      van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A. ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105, 9396– 9409,  DOI: 10.1021/jp004368u
      32
      ReaxFF: A Reactive Force Field for Hydrocarbons
      van Duin, Adri C. T.; Dasgupta, Siddharth; Lorant, Francois; Goddard, William A., III
      Journal of Physical Chemistry A (2001), 105 (41), 9396-9409CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      To make practical the mol. dynamics simulation of large scale reactive chem. systems (1000 s of atoms), the authors developed ReaxFF, a force field for reactive systems. ReaxFF uses a general relation between bond distance and bond order on one hand and between bond order and bond energy however, that leads to proper dissocn. of bonds to sepd. atoms. Other valence terms present in the force field (angle and torsion) are defined in terms of the same bond orders so that all these terms go to zero smoothly as bonds break. In addn., ReaxFF has Coulomb and Morse (van der Waals) potentials to describe nonbond interactions between all atoms (no exclusions). These nonbond interactions are shielded at short range so that the Coulomb and van der Waals interactions become const. as Rij → 0. The authors report here the ReaxFF for hydrocarbons. The parameters were derived from quantum chem. calcns. on bond dissocn. and reactions of small mols. plus heat of formation and geometry data for a no. of stable hydrocarbon compds. The ReaxFF provides a good description of these data. Generally, the results are of an accuracy similar or better than PM3, while ReaxFF is ∼100 times faster. In turn, the PM3 is ∼100 times faster than the QC calcns. Thus, with ReaxFF the authors hope to be able to study complex reactions in hydrocarbons.
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    33. 33
      Behler, J.; Parrinello, M. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces. Phys. Rev. Lett. 2007, 98, 146401– 146404,  DOI: 10.1103/PhysRevLett.98.146401
      33
      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.
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    34. 34
      Bartók, A. P.; Csanyi, G. Gaussian Approximation Potentials: A Brief Tutorial Introduction. Int. J. Quantum Chem. 2015, 115, 1051– 1057,  DOI: 10.1002/qua.24927
      34
      Gaussian approximation potentials: A brief tutorial introduction
      Bartok, Albert P.; Csanyi, Gabor
      International Journal of Quantum Chemistry (2015), 115 (16), 1051-1057CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
      We present a swift walk-through of our recent work that uses machine learning to fit interat. potentials based on quantum mech. data. We describe our Gaussian approxn. potentials (GAP) framework, discuss a variety of descriptors, how to train the model on total energies and derivs., and the simultaneous use of multiple models of different complexity. We also show a small example using QUIP, the software sandbox implementation of GAP that is available for noncommercial use.
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    35. 35
      Leshno, M.; Lin, V. Y.; Pinkus, A.; Schocken, S. Multilayer Feedforward Networks with a Nonpolynomial Activation Function Can Approximate Any Function. Neural Networks 1993, 6, 861– 867,  DOI: 10.1016/S0893-6080(05)80131-5
      There is no corresponding record for this reference.
    36. 36
      Thomsen, J. U.; Meyer, B. Pattern Recognition of the 1H NMR Spectra of Sugar Alditols Using a Neural Network. J. Magn. Reson. 1989, 84, 212– 217
      36
      Pattern recognition of the proton NMR spectra of sugar alditols using a neural network
      Thomsen, J. U.; Meyer, B.
      Journal of Magnetic Resonance (1969-1992) (1989), 84 (1), 212-17CODEN: JOMRA4; ISSN:0022-2364.
      The title method was used to identify the spectra of 6 alditols including glucitol.
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    37. 37
      Curry, B.; Rumelhart, D. E. MSnet: A Neural Network which Classifies Mass Spectra. Tetrahedron Comput. Methodol. 1990, 3, 213– 237,  DOI: 10.1016/0898-5529(90)90053-B
      37
      MSnet: a neural network which classifies mass spectra
      Curry, Bo; Rumelhart, David E.
      Tetrahedron Computer Methodology (1990), 3 (3-4), 213-37CODEN: TCMTE6; ISSN:0898-5529.
      A feed-forward neural network was designed to classify low-resoln. mass spectra of unknown compds. according to the presence or absence of 100 org. substructures. The neural network, MSnet, was trained to compute a max.-likelihood est. of the probability that each substructure is present. Some design considerations and statistical properties of neural network classifiers, and the effect of various training regimes on generalization behavior are discussed. The MSnet classifies mass spectra more reliably than other methods reported in the literature, and has other desirable properties.
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    38. 38
      Klopman, G. Artificial Intelligence Approach to Structure-Activity Studies. Computer Automated Structure Evaluation of Biological Activity of Organic Molecules. J. Am. Chem. Soc. 1984, 106, 7315– 7321,  DOI: 10.1021/ja00336a004
      38
      Artificial intelligence approach to structure-activity studies. Computer automated structure evaluation of biological activity of organic molecules
      Klopman, Gilles
      Journal of the American Chemical Society (1984), 106 (24), 7315-21CODEN: JACSAT; ISSN:0002-7863.
      A new program was introduced to study the relationship between structure and biol. activity of org. mols. The computer-automated structure evaluation program automatically recognizes mol. structures from the KLN code, a mol. linear coding routine, and proceeds automatically to identify, tabulate, and statistically analyze biophores, i.e., substructures believed to be responsible for known or anticipated biol. activity of groups of mols. The method was applied to the study of the carcinogenicity of polycyclic arom. hydrocarbons, the carcinogenicity of N-nitrosamines in rats, and the pesticidal activity of some ketoxime carbamates.
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    39. 39
      Hopfinger, A. J.; Burke, B. J.; Dunn, W. J., III A Generalized Formalism of Three-Dimensional Quantitative Structure-Property Relationship Analysis for Flexible Molecules Using Tensor Representation. J. Med. Chem. 1994, 37, 3768– 3774,  DOI: 10.1021/jm00048a013
      39
      A generalized formalism of three-dimensional quantitative structure-property relationship analysis for flexible molecules using tensor representation
      Hopfinger, A. J.; Burke, Benjamin J.; Dunn, William J., III
      Journal of Medicinal Chemistry (1994), 37 (22), 3768-74CODEN: JMCMAR; ISSN:0022-2623.
      A general formalism, based upon tensor representation of multidimensional data blocks, is presented to express relationships between dependent properties and independent mol. feature measures. The solns. to these data set problems are three-dimensional quant. structure-property relationships, 3D-QSPRs. The mol. features are partitioned into the intrinsic mol. shape tensor, the mol. field tensor, a nonshape/field feature tensor, and an exptl. feature tensor. The intrinsic mol. shape tensor contains information on the shape of a mol. within the contact surface while the mol. field tensor contains information outside of the contact surface. Mol. features not directly related to mol. shape are put into the nonshape/field tensor. Exptl. measures not being used as dependent variables can be considered as independent mol. features in the exptl. feature tensor. The 3D-QSPR is realized by constructing the transformation tensor which optimizes the statistical significance between the dependent and independent variables. Repetitive use of partial least squares (PLS) regression permits the unfolding of the composite feature tensor and the identification of the optimum transformation tensor. It is pointed out that a variety of fragment, whole-mol.,two-dimensional, and/or three-dimensional features can be placed into a nonshape/field tensor.
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    40. 40
      Gakh, A. A.; Gakh, E. G.; Sumpter, B. G.; Noid, D. W. Neural Network-Graph Theory Approach to the Prediction of the Physical Properties of Organic Compounds. J. Chem. Inf. Comput. Sci. 1994, 34, 832– 839,  DOI: 10.1021/ci00020a017
      40
      Neural Network-Graph Theory Approach to the Prediction of the Physical Properties of Organic Compounds
      Gakh, Andrei A.; Gakh, Elena G.; Sumpter, Bobby G.; Noid, Donald W.
      Journal of Chemical Information and Computer Sciences (1994), 34 (4), 832-9CODEN: JCISD8; ISSN:0095-2338.
      A new computational scheme is developed to predict phys. properties of org. compds. on the basis of their mol. structure. The method uses graph theory to encode the structural information which is the numerical input for a neural network. Calcd. results for a series of satd. hydrocarbons demonstrate av. accuracies of 1-2% with max. deviations of 12-14%.
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    41. 41
      Sumpter, B. G.; Noid, D. W. Potential Energy Surfaces for Macromolecules. A Neural Network Technique. Chem. Phys. Lett. 1992, 192, 79– 86,  DOI: 10.1016/0009-2614(92)85498-Y
      There is no corresponding record for this reference.
    42. 42
      Blank, T. B.; Brown, S. D.; Calhoun, A. W.; Doren, D. J. Neural Network Models of Potential Energy Surfaces. J. Chem. Phys. 1995, 103, 4129– 4137,  DOI: 10.1063/1.469597
      42
      Neural network models of potential energy surfaces
      Blank, Thomas B.; Brown, Steven D.; Calhoun, August W.; Doren, Douglas J.
      Journal of Chemical Physics (1995), 103 (10), 4129-37CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Neural networks provide an efficient, general interpolation method for nonlinear functions of several variables. This paper describes the use of feed-forward neural networks to model global properties of potential energy surfaces from information available at a limited no. of configurations. As an initial demonstration of the method, several fits are made to data derived from an empirical potential model of CO adsorbed on Ni(111). The data are error-free and geometries are selected from uniform grids of two and three dimensions. The neural network model predicts the potential to within a few hundredths of a kcal/mol at arbitrary geometries. The accuracy and efficiency of the neural network in practical calcns. are demonstrated in quantum transition state theory rate calcns. for surface diffusion of CO/Ni(111) using a Monte Carlo/path integral method. The network model is much faster to evaluate than the original potential from which it is derived. As a more complex test of the method, the interaction potential of H2 with the Si(100)-2 × 1 surface is detd. as a function of 12 degrees of freedom from energies calcd. with the local d. functional method at 750 geometries. The training examples are not uniformly spaces and they depend weakly on variables not included in the fit. The neural net model predicts the potential at geometries outside the training set with a mean abs. deviation of 2.1 kcal/mol.
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    43. 43
      Brown, D. F. R.; Gibbs, M. N.; Clary, D. C. Combining Ab Initio Computations, Neural Networks, and Diffusion Monte Carlo: An Efficient Method to Treat Weakly Bound Molecules. J. Chem. Phys. 1996, 105, 7597– 7604,  DOI: 10.1063/1.472596
      43
      Combining ab initio computations, neural networks, and diffusion Monte Carlo: an efficient method to treat weakly bound molecules
      Brown, David F. R.; Gibbs, Mark N.; Clary, David C.
      Journal of Chemical Physics (1996), 105 (17), 7597-7604CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We describe a new method to calc. the vibrational ground-state properties of weakly bound mol. systems, and apply it to (HF)2 and HF-HCl. A Bayesian inference neural network is used to fit an analytic function to a set of ab-initio data points, which may then be employed by the quantum-diffusion-Monte-Carlo method to produce ground-state vibrational wave functions and properties. The method is general and relatively simple to implement, and will be attractive for calcns. on systems for which no analytic potential energy surface exists.
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    44. 44
      Behler, J. Representing Potential Energy Surfaces by High-Dimensional Neural Network Potentials. Condens. Matter 2014, 26, 183001,  DOI: 10.1088/0953-8984/26/18/183001
      44
      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.
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    45. 45
      Behler, J. Atom-Centered Symmetry Functions for Constructing High-Dimensional Neural Network Potentials. J. Chem. Phys. 2011, 134, 074106  DOI: 10.1063/1.3553717
      45
      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.
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    46. 46
      Jose, K. V. J.; Artrith, A.; Behler, J. Construction of High-Dimensional Neural Network Potentials Using Environment-Dependent Atom Pairs. J. Chem. Phys. 2012, 136, 194111,  DOI: 10.1063/1.4712397
      46
      Construction of high-dimensional neural network potentials using environment-dependent atom pairs
      Jose, K. V. Jovan; Artrith, Nongnuch; Behler, Joerg
      Journal of Chemical Physics (2012), 136 (19), 194111/1-194111/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      An accurate detn. of the potential energy is the crucial step in computer simulations of chem. processes, but using electronic structure methods on-the-fly in mol. dynamics (MD) is computationally too demanding for many systems. Constructing more efficient interat. potentials becomes intricate with increasing dimensionality of the potential-energy surface (PES), and for numerous systems the accuracy that can be achieved is still not satisfying and far from the reliability of 1st-principles calcns. Feed-forward neural networks (NNs) have a very flexible functional form, and in recent years they were shown to be an accurate tool to construct efficient PESs. High-dimensional NN potentials based on environment-dependent at. energy contributions were presented for a no. of materials. Still, these potentials may be improved by a more detailed structural description, e.g., in form of atom pairs, which directly reflect the at. interactions and take the chem. environment into account. We present an implementation of an NN method based on atom pairs, and its accuracy and performance are compared to the atom-based NN approach using 2 very different systems, the MeOH mol. and metallic Cu. We find that both types of NN potentials provide an excellent description of both PESs, with the pair-based method yielding a slightly higher accuracy making it a competitive alternative for addressing complex systems in MD simulations. (c) 2012 American Institute of Physics.
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    47. 47
      Shakouri, K.; Behler, J.; Meyer, J.; Kroes, G.-J. Accurate Neural Network Description of Surface Phonons in Reactive Gas–Surface Dynamics: N2 + Ru(0001). J. Phys. Chem. Lett. 2017, 8, 2131– 2136,  DOI: 10.1021/acs.jpclett.7b00784
      47
      Accurate Neural Network Description of Surface Phonons in Reactive Gas-Surface Dynamics: N2 + Ru(0001)
      Shakouri, Khosrow; Behler, Joerg; Meyer, Joerg; Kroes, Geert-Jan
      Journal of Physical Chemistry Letters (2017), 8 (10), 2131-2136CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Ab initio mol. dynamics (AIMD) simulations enable the accurate description of reactive mol.-surface scattering esp. if energy transfer involving surface phonons is important. However, presently, the computational expense of AIMD rules out its application to systems where reaction probabilities are smaller than about 1%. Here we show that this problem can be overcome by a high-dimensional neural network fit of the mol.-surface interaction potential, which also incorporates the dependence on phonons by taking into account all degrees of freedom of the surface explicitly. As shown for N2 + Ru(0001), which is a prototypical case for highly activated dissociative chemisorption, the method allows an accurate description of the coupling of mol. and surface atom motion and accurately accounts for vibrational properties of the employed slab model of Ru(0001). The neural network potential allows reaction probabilities as low as 10-5 to be computed, showing good agreement with exptl. results.
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    48. 48
      Gao, T.; Kitchin, J. R. Modeling Palladium Surfaces with Density Functional Theory, Neural Networks and Molecular Dynamics. Catal. Today 2018, 312, 132– 140,  DOI: 10.1016/j.cattod.2018.03.045
      48
      Modeling palladium surfaces with density functional theory, neural networks and molecular dynamics
      Gao, Tianyu; Kitchin, John R.
      Catalysis Today (2018), 312 (), 132-140CODEN: CATTEA; ISSN:0920-5861. (Elsevier B.V.)
      In this work, we have constructed a high dimensional neural network (NN) potential energy function for simulating palladium surface properties. The NN potential was trained with 3035 d. functional theory (DFT) calcns., and was shown to be nearly as accurate as DFT in mol. simulations. Important properties including lattice consts., elastic properties and surface energies as well as transition state energies and adatom diffusion barriers were predicted by the NN and were found to be in excellent agreement with DFT results. The computational time to run the NN was compared to DFT calcn. time, and we found this implementation of the NN is roughly four orders of magnitude faster than DFT. This approach is general and applicable to other systems and may have applications in modeling catalytic processes at surfaces.
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    49. 49
      Wang, C.; Tharval, A.; Kitchin, J. R. A Density Functional Theory Parameterised Neural Network Model of Zirconia. Mol. Simul. 2018, 44, 623– 630,  DOI: 10.1080/08927022.2017.1420185
      49
      A density functional theory parameterised neural network model of zirconia
      Wang, Chen; Tharval, Akshay; Kitchin, John R.
      Molecular Simulation (2018), 44 (8), 623-630CODEN: MOSIEA; ISSN:0892-7022. (Taylor & Francis Ltd.)
      A review. We have developed a Behler-Parrinello Neural Network (BPNN) that can be employed to calc. energies and forces of zirconia bulk structures with oxygen vacancies with similar accuracy as that of the d. functional theory (DFT) calcns. that were used to train the BPNN. In this work, we have trained the BPNN potential with a ref. set of 2178 DFT calcns. and validated it against a dataset of untrained data. We have shown that the bulk structural parameters, equation of states, oxygen vacancy formation energies and diffusion barriers predicted by the BPNN potential are in good agreement with the ref. DFT data. The transferability of the BPNN potential has also been benchmarked with the prediction of structures that were not included in the ref. set. The evaluation time of the BPNN is orders of magnitude less than corresponding DFT calcns., although the training process of the BPNN potential requires non-negligible amt. of computational resources to prep. the dataset. The computational efficiency of the NN enabled it to be used in mol. dynamics simulations of the temp.-dependent diffusion of an oxygen vacancy and the corresponding diffusion activation energy.
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    50. 50
      Eckhoff, M.; Behler, J. From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5. J. Chem. Theory Comput. 2019, 15, 3793– 3809,  DOI: 10.1021/acs.jctc.8b01288
      50
      From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5
      Eckhoff, Marco; Behler, Joerg
      Journal of Chemical Theory and Computation (2019), 15 (6), 3793-3809CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The development of first-principles-quality reactive atomistic potentials for org.-inorg. hybrid materials is still a substantial challenge because of the very different physics of the at. interactions-from covalent via ionic bonding to dispersion-that have to be described in an accurate and balanced way. In this work we used a prototypical metal-org. framework, MOF-5, as a benchmark case to investigate the applicability of high-dimensional neural network potentials (HDNNPs) to this class of materials. In HDNNPs, which belong to the class of machine learning potentials, the energy is constructed as a sum of environment-dependent at. energy contributions. We demonstrate that by the use of this approach it is possible to obtain a high-quality potential for the periodic MOF-5 crystal using d. functional theory (DFT) ref. calcns. of small mol. fragments only. The resulting HDNNP, which has a root-mean-square error (RMSE) of 1.6 meV/atom for the energies of mol. fragments not included in the training set, is able to provide the equil. lattice const. of the bulk MOF-5 structure with an error of about 0.1% relative to DFT, and also, the neg. thermal expansion behavior is accurately predicted. The total energy RMSE of periodic structures that are completely absent in the training set is about 6.5 meV/atom, with errors on the order of 2 meV/atom for energy differences. We show that in contrast to energy differences, achieving a high accuracy for total energies requires careful variation of the stoichiometries of the training structures to avoid energy offsets, as at. energies are not phys. observables. The forces, which have RMSEs of about 94 meV/a0 for the mol. fragments and 130 meV/a0 for bulk structures not included in the training set, are insensitive to such offsets. Therefore, forces, which are the relevant properties for mol. dynamics simulations, provide a realistic est. of the accuracy of atomistic potentials.
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    51. 51
      Schran, C.; Uhl, F.; Behler, J.; Marx, D. High-Dimensional Neural Network Potentials for Solvation: The Case of Protonated Water Clusters in Helium. J. Chem. Phys. 2018, 148, 102310,  DOI: 10.1063/1.4996819
      51
      High-dimensional neural network potentials for solvation: The case of protonated water clusters in helium
      Schran, Christoph; Uhl, Felix; Behler, Joerg; Marx, Dominik
      Journal of Chemical Physics (2018), 148 (10), 102310/1-102310/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The design of accurate helium-solute interaction potentials for the simulation of chem. complex mols. solvated in superfluid helium has long been a cumbersome task due to the rather weak but strongly anisotropic nature of the interactions. We show that this challenge can be met by using a combination of an effective pair potential for the He-He interactions and a flexible high-dimensional neural network potential (NNP) for describing the complex interaction between helium and the solute in a pairwise additive manner. This approach yields an excellent agreement with a mean abs. deviation as small as 0.04 kJ mol-1 for the interaction energy between helium and both hydronium and Zundel cations compared with coupled cluster ref. calcns. with an energetically converged basis set. The construction and improvement of the potential can be performed in a highly automated way, which opens the door for applications to a variety of reactive mols. to study the effect of solvation on the solute as well as the solute-induced structuring of the solvent. Furthermore, we show that this NNP approach yields convincing agreement with the coupled cluster ref. for properties like many-body spatial and radial distribution functions. This holds for the microsolvation of the protonated water monomer and dimer by a few helium atoms up to their solvation in bulk helium as obtained from path integral simulations at ∼1 K. (c) 2018 American Institute of Physics.
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    52. 52
      Lahey, S.-H. J.; Rowley, C. N. Simulating Protein–Ligand Binding with Neural Network Potentials. Chem. Sci. 2020, 11, 2362– 2368,  DOI: 10.1039/C9SC06017K
      52
      Simulating protein-ligand binding with neural network potentials
      Lahey, Shae-Lynn J.; Rowley, Christopher N.
      Chemical Science (2020), 11 (9), 2362-2368CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      Drug mols. adopt a range of conformations both in soln. and in their protein-bound state. The strain and reduced flexibility of bound drugs can partially counter the intermol. interactions that drive protein-ligand binding. To make accurate computational predictions of drug binding affinities, computational chemists have attempted to develop efficient empirical models of these interactions, although these methods are not always reliable. Machine learning has allowed the development of highly-accurate neural-network potentials (NNPs), which are capable of predicting the stability of mol. conformations with accuracy comparable to state-of-the-art quantum chem. calcns. but at a billionth of the computational cost. Here, we demonstrate that these methods can be used to represent the intramol. forces of protein-bound drugs within mol. dynamics simulations. These simulations are shown to be capable of predicting the protein-ligand binding pose and conformational component of the abs. Gibbs energy of binding for a set of drug mols. Notably, the conformational energy for anti-cancer drug erlotinib binding to its target was found to be considerably overestimated by a mol. mech. model, while the NNP predicts a more moderate value. Although the ANI-1ccX NNP was not trained to describe ionic mols., reasonable binding poses are predicted for charged ligands, but this method is not suitable for modeling charged ligands in soln.
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    53. 53
      Sun, G.; Sautet, P. Metastable Structures in Cluster Catalysis from First-Principles: Structural Ensemble in Reaction Conditions and Metastability Triggered Reactivity. J. Am. Chem. Soc. 2018, 140, 2812– 2820,  DOI: 10.1021/jacs.7b11239
      53
      Metastable Structures in Cluster Catalysis from First-Principles: Structural Ensemble in Reaction Conditions and Metastability Triggered Reactivity
      Sun, Geng; Sautet, Philippe
      Journal of the American Chemical Society (2018), 140 (8), 2812-2820CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Reactivity studies on catalytic transition metal clusters are usually performed on a single global min. structure. With the example of a Pt13 cluster under a pressure of hydrogen, we show from first-principle calcns. that low energy metastable structures of the cluster can play a major role for catalytic reactivity and that hence consideration of the global min. structure alone can severely underestimate the activity. The catalyst is fluxional with an ensemble of metastable structures energetically accessible at reaction conditions. A modified genetic algorithm is proposed to comprehensively search for the low energy metastable ensemble (LEME) structures instead of merely the global min. structure. In order to reduce the computational cost of d. functional calcns., a high dimensional neural network potential is employed to accelerate the exploration. The presence and influence of LEME structures during catalysis is discussed by the example of H covered Pt13 clusters for two reactions of major importance: hydrogen evolution reaction and methane activation. The results demonstrate that although the no. of accessible metastable structures is reduced under reaction condition for Pt13 clusters, these metastable structures can exhibit high activity and dominate the obsd. activity due to their unique electronic or structural properties. This underlines the necessity of thoroughly exploring the LEME structures in catalysis simulations. The approach enables one to systematically address the impact of isomers in catalysis studies, taking into account the high adsorbate coverage induced by reaction conditions.
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    54. 54
      Zuo, Y.; Chen, C.; Li, X.; Deng, Z.; Chen, Y.; Behler, J.; Csányi, G.; Shapeev, A. V.; Thompson, A. P.; Wood, A. M.; Ong, S. P. A Performance and Cost Assessment of Machine Learning Interatomic Potentials. J. Phys. Chem. A 2020, 124, 731– 745,  DOI: 10.1021/acs.jpca.9b08723
      54
      Performance and Cost Assessment of Machine Learning Interatomic Potentials
      Zuo, Yunxing; Chen, Chi; Li, Xiangguo; Deng, Zhi; Chen, Yiming; Behler, Jorg; Csanyi, Gabor; Shapeev, Alexander V.; Thompson, Aidan P.; Wood, Mitchell A.; Ong, Shyue Ping
      Journal of Physical Chemistry A (2020), 124 (4), 731-745CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      Machine learning of the quant. relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interat. potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors-atom-centered symmetry functions (ACSF), smooth overlap of at. positions (SOAP), the spectral neighbor anal. potential (SNAP) bispectrum components, and moment tensors-using a diverse data set generated using high-throughput d. functional theory (DFT) calcns. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic consts. and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for mol. dynamics and other applications.
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    55. 55
      Bartók, A. P.; Gillan, M. J.; Manby, F. R.; Csányi, G. Machine-Learning Approach for One- and Two-Body Corrections to Density Functional Theory: Applications to Molecular and Condensed Water. Phys. Rev. B 2013, 88, 054104,  DOI: 10.1103/PhysRevB.87.184115
      55
      Machine-learning approach for one- and two-body corrections to density functional theory: applications to molecular and condensed water
      Bartok, Albert P.; Gillan, Michael J.; Manby, Frederick R.; Csanyi, Gabor
      Physical Review B: Condensed Matter and Materials Physics (2013), 88 (5), 054104/1-054104/12CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      We show how machine learning techniques based on Bayesian inference can be used to enhance the computer simulation of mol. materials, focusing here on water. We train our machine-learning algorithm using accurate, correlated quantum chem., and predict energies and forces in mol. aggregates ranging from clusters to solid and liq. phases. The widely used electronic-structure methods based on d. functional theory (DFT) by themselves give poor accuracy for mol. materials like water, and we show how our techniques can be used to generate systematically improvable one- and two-body corrections to DFT with modest extra resources. The resulting cor. DFT scheme is considerably more accurate than uncorrected DFT for the relative energies of small water clusters and different ice structures and significantly improves the description of the structure and dynamics of liq. water. However, our results for ice structures and the liq. indicate that beyond-two-body DFT errors cannot be ignored, and we suggest how our machine-learning methods can be further developed to correct these errors.
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    56. 56
      Hanse, K.; Montavon, G.; Biegler, F.; Fazli, S.; Rupp, M.; Scheffler, M.; von Lilienfeld, O. A.; Tkatchenko, A.; Müller, K.-R. Assessment and Validation of Machine Learning Methods for Predicting Molecular Atomization Energies. J. Chem. Theory Comput. 2013, 9, 3404– 3419,  DOI: 10.1021/ct400195d
      There is no corresponding record for this reference.
    57. 57
      Montavon, G.; Rupp, M.; Gobre, V.; Vazquez-Mayagoitia, A.; Hansen, K.; Tkatchenko, A.; Müller, K.-R.; von Lilienfeld, O. A. Machine Learning of Molecular Electronic Properties in Chemical Compound Space. New J. Phys. 2013, 15, 095003  DOI: 10.1088/1367-2630/15/9/095003
      57
      Machine learning of molecular electronic properties in chemical compound space
      Montavon, Gregoire; Rupp, Matthias; Gobre, Vivekanand; Vazquez-Mayagoitia, Alvaro; Hansen, Katja; Tkatchenko, Alexandre; Mueller, Klaus-Robert; von Lilienfeld, O. Anatole
      New Journal of Physics (2013), 15 (Sept.), 095003CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
      The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amt. of data amenable to intelligent data anal. for the identification of meaningful, novel and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compds. that are synthetically accessible. Here, we present a machine learning model, trained on a database of ab initio calcn. results for thousands of org. mols., that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity and excitation energies. The machine learning model is based on a deep multi-task artificial neural network, exploiting the underlying correlations between various mol. properties. The input is identical to ab initio methods, i.e. nuclear charges and Cartesian coordinates of all atoms. For small org. mols., the accuracy of such a 'quantum machine' is similar, and sometimes superior, to modern quantum-chem. methods-at negligible computational cost.
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    58. 58
      Rupp, M.; Ramakrishnan, R.; von Lilienfeld, O. A. Machine Learning for Quantum Mechanical Properties of Atoms in Molecules. J. Phys. Chem. Lett. 2015, 6, 3309– 3313,  DOI: 10.1021/acs.jpclett.5b01456
      58
      Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
      Rupp, Matthias; Ramakrishnan, Raghunathan; von Lilienfeld, O. Anatole
      Journal of Physical Chemistry Letters (2015), 6 (16), 3309-3313CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      We introduce machine learning models of quantum mech. observables of atoms in mols. Instant out-of-sample predictions for proton and carbon nuclear chem. shifts, at. core level excitations, and forces on atoms reach accuracies on par with d. functional theory ref. Locality is exploited within nonlinear regression via local atom-centered coordinate systems. The approach is validated on a diverse set of 9 k small org. mols. Linear scaling of computational cost in system size is demonstrated for satd. polymers with up to submesoscale lengths.
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    59. 59
      Weststrate, C. J.; van de Loosdrecht, J.; Niemantsverdriet, J. W. Spectroscopic Insights into Cobalt-Catalyzed Fischer-Tropsch Synthesis: A Review of the Carbon Monoxide Interaction with Single Crystalline Surfaces of Cobalt. J. Catal. 2016, 342, 1– 16,  DOI: 10.1016/j.jcat.2016.07.010
      59
      Spectroscopic insights into cobalt-catalyzed Fischer-Tropsch synthesis: A review of the carbon monoxide interaction with single crystalline surfaces of cobalt
      Weststrate, C. J.; van de Loosdrecht, J.; Niemantsverdriet, J. W.
      Journal of Catalysis (2016), 342 (), 1-16CODEN: JCTLA5; ISSN:0021-9517. (Elsevier Inc.)
      The present article summarizes exptl. findings of the interaction of CO with single crystal surfaces of cobalt. We first provide a quant. study of non-dissociative CO adsorption on Co(0001) and establish a quant. correlation between θCO and adsorption site occupation. In light of these findings we revisit the structure of previously reported ordered CO/Co(0001) adsorbate layers. Measurements of the CO coverage at equil. conditions are used to derive a phase diagram for CO on Co(0001). For low temp. Fischer-Tropsch synthesis conditions the CO coverage is predicted to be ≈0.5 ML, a value that hardly changes with pCO. The CO desorption temp. found in temp. programmed desorption is practically structure-independent, despite structure-dependent heats of adsorption reported in the literature. This mismatch is attributed to a structure-dependent pre-exponential factor for desorption. IR spectra reported throughout this study provide a ref. point for IR studies on cobalt catalysts. Results for CO adsorbed on flat and defect-rich Co surfaces as well as particular, CO adsorbed on top sites, and in addn. affect the distribution of COad over the various possible adsorption sites.
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    60. 60
      Werbos, P. J. Generalization of Backpropagation with Application to a Recurrent Gas Market Model. Neural Networks 1988, 1, 339– 356,  DOI: 10.1016/0893-6080(88)90007-X
      There is no corresponding record for this reference.
    61. 61
      Huang, Y.; Kang, J.; Goddard, W. A.; Wang, L.-W. Density Functional Theory Based Neural Network Force Fields from Energy Decompositions. Phys. Rev. B 2019, 99, 064103  DOI: 10.1103/PhysRevB.99.064103
      61
      Density functional theory based neural network force fields from energy decompositions
      Huang, Yufeng; Kang, Jun; Goddard, William A. III; Wang, Lin-Wang
      Physical Review B (2019), 99 (6), 064103/1-064103/11CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      In order to develop force fields (FF) for mol. dynamics simulations that retain the accuracy of ab initio d. functional theory (DFT), we developed a machine learning protocol based on an energy decompn. scheme that exts. at. energies from DFT calcns. Our DFT to FF (DFT2FF) approach provides almost hundreds of times more data for the DFT energies, which dramatically improves accuracy with less DFT calcns. In addn., we use piecewise cosine basis functions to systematically construct symmetry invariant features into the neural network model. We illustrate this DFT2FF approach for amorphous silicon where only 800 DFT configurations are sufficient to achieve an accuracy of 1 meV/atom for energy and 0.1 eV/A for forces. We then use the resulting FF model to calc. the thermal cond. of amorphous Si based on long mol. dynamics simulations. The dramatic speedup in training in our DFT2FF protocol allows the adoption of a simulation paradigm where an accurate and problem specific FF for a given physics phenomenon is trained on-the-spot through a quick DFT precalcn. and FF training.
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    62. 62
      Gastegger, M.; Schwiedrzik, L.; Bittermann, M.; Berzsenyi, F.; Marquetand, P. wACSF - Weighted Atom-Centered Symmetry Functions as Descriptors in Machine Learning Potentials. J. Chem. Phys. 2018, 148, 241709,  DOI: 10.1063/1.5019667
      62
      wACSF-Weighted atom-centered symmetry functions as descriptors in machine learning potentials
      Gastegger, M.; Schwiedrzik, L.; Bittermann, M.; Berzsenyi, F.; Marquetand, P.
      Journal of Chemical Physics (2018), 148 (24), 241709/1-241709/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We introduce weighted atom-centered symmetry functions (wACSFs) as descriptors of a chem. system's geometry for use in the prediction of chem. properties such as enthalpies or potential energies via machine learning. The wACSFs are based on conventional atom-centered symmetry functions (ACSFs) but overcome the undesirable scaling of the latter with an increasing no. of different elements in a chem. system. The performance of these two descriptors is compared using them as inputs in high-dimensional neural network potentials (HDNNPs), employing the mol. structures and assocd. enthalpies of the 133 855 mols. contg. up to five different elements reported in the QM9 database as ref. data. A substantially smaller no. of wACSFs than ACSFs is needed to obtain a comparable spatial resoln. of the mol. structures. At the same time, this smaller set of wACSFs leads to a significantly better generalization performance in the machine learning potential than the large set of conventional ACSFs. Furthermore, we show that the intrinsic parameters of the descriptors can in principle be optimized with a genetic algorithm in a highly automated manner. For the wACSFs employed here, we find however that using a simple empirical parametrization scheme is sufficient in order to obtain HDNNPs with high accuracy. (c) 2018 American Institute of Physics.
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    63. 63
      Artrith, N.; Urban, A.; Ceder, G. Efficient and Accurate Machine-Learning Interpolation of Atomic Energies in Compositions with Many Species. Phys. Rev. B 2017, 96, 014112  DOI: 10.1103/PhysRevB.96.014112
      63
      Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species
      Artrith, Nongnuch; Urban, Alexander; Ceder, Gerbrand
      Physical Review B (2017), 96 (1), 014112/1-014112/5CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      Machine-learning potentials (MLPs) for atomistic simulations are a promising alternative to conventional classical potentials. Current approaches rely on descriptors of the local at. environment with dimensions that increase quadratically with the no. of chem. species. In this paper, we demonstrate that such a scaling can be avoided in practice. We show that a math. simple and computationally efficient descriptor with const. complexity is sufficient to represent transition-metal oxide compns. and biomols. contg. 11 chem. species with a precision of around 3 meV/atom. This insight removes a perceived bound on the utility of MLPs and paves the way to investigate the physics of previously inaccessible materials with more than ten chem. species.
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    64. 64
      Seko, A.; Hayashi, H.; Nakayama, K.; Takahashi, A.; Tanaka, I. Representation of Compounds for Machine-Learning Prediction of Physical Properties. Phys. Rev. B 2017, 95, 144110,  DOI: 10.1103/PhysRevB.95.144110
      64
      Representation of compounds for machine-learning prediction of physical properties
      Seko, Atsuto; Hayashi, Hiroyuki; Nakayama, Keita; Takahashi, Akira; Tanaka, Isao
      Physical Review B (2017), 95 (14), 144110/1-144110/11CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      The representations of a compd., called "descriptors" or "features", play an essential role in constructing a machine-learning model of its phys. properties. In this study, we adopt a procedure for generating a set of descriptors from simple elemental and structural representations. First, it is applied to a large data set composed of the cohesive energy for about 18 000 compds. computed by d. functional theory calcn. As a result, we obtain a kernel ridge prediction model with a prediction error of 0.041 eV/atom, which is close to the "chem. accuracy" of 1 kcal/mol (0.043 eV/atom). A prediction model with an error of 0.071 eV/atom of the cohesive energy is obtained for the normalized prototype structures, which can be used for the practical purpose of searching for as-yet-unknown structures. The procedure is also applied to two smaller data sets, i.e., a data set of the lattice thermal cond. for 110 compds. computed by d. functional theory calcn. and a data set of the exptl. melting temp. for 248 compds. We examine the effect of the descriptor sets on the efficiency of Bayesian optimization in addn. to the accuracy of the kernel ridge regression models. They exhibit good predictive performances.
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    65. 65
      Huang, B.; von Lilienfeld, O. A. Communication: Understanding Molecular Representations in Machine Learning: The Role of Uniqueness and Target Similarity. J. Chem. Phys. 2016, 145, 161102,  DOI: 10.1063/1.4964627
      65
      Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity
      Huang, Bing; von Lilienfeld, O. Anatole
      Journal of Chemical Physics (2016), 145 (16), 161102/1-161102/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The predictive accuracy of Machine Learning (ML) models of mol. properties depends on the choice of the mol. representation. Inspired by the postulates of quantum mechanics, we introduce a hierarchy of representations which meet uniqueness and target similarity criteria. To systematically control target similarity, we simply rely on interat. many body expansions, as implemented in universal force-fields, including Bonding, Angular (BA), and higher order terms. Addn. of higher order contributions systematically increases similarity to the true potential energy and predictive accuracy of the resulting ML models. We report numerical evidence for the performance of BAML models trained on mol. properties pre-calcd. at electron-correlated and d. functional theory level of theory for thousands of small org. mols. Properties studied include enthalpies and free energies of atomization, heat capacity, zero-point vibrational energies, dipole-moment, polarizability, HOMO/LUMO energies and gap, ionization potential, electron affinity, and electronic excitations. After training, BAML predicts energies or electronic properties of out-of-sample mols. with unprecedented accuracy and speed. (c) 2016 American Institute of Physics.
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    66. 66
      Handley, C. M.; Popelier, P. L. A. Potential Energy Surfaces Fitted by Artificial Neural Networks. J. Phys. Chem. A 2010, 114, 3371– 3383,  DOI: 10.1021/jp9105585
      66
      Potential Energy Surfaces Fitted by Artificial Neural Networks
      Handley, Chris M.; Popelier, Paul L. A.
      Journal of Physical Chemistry A (2010), 114 (10), 3371-3383CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      A review. Mol. mechanics is the tool of choice for the modeling of systems that are so large or complex that it is impractical or impossible to model them by ab initio methods. For this reason there is a need for accurate potentials that are able to quickly reproduce ab initio quality results at the fraction of the cost. The interactions within force fields are represented by a no. of functions. Some interactions are well understood and can be represented by simple math. functions while others are not so well understood and their functional form is represented in a simplistic manner or not even known. In the last 20 years there have been the first examples of a new design ethic, where novel and contemporary methods using machine learning, in particular, artificial neural networks, have been used to find the nature of the underlying functions of a force field. Here we appraise what has been achieved over this time and what requires further improvements, while offering some insight and guidance for the development of future force fields.
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    67. 67
      Ramsvik, T.; Borg, A.; Kildemo, M.; Raaen, S.; Matsuura, A.; Jaworowski, A. J.; Worren, T.; Leandersson, M. Molecular Vibrations in Core-Ionised CO Adsorbed on Co(0001) and Rh(100). Surf. Sci. 2001, 492, 152– 160,  DOI: 10.1016/S0039-6028(01)01446-7
      67
      Molecular vibrations in core-ionised CO adsorbed on Co(0 0 0 1) and Rh(1 0 0)
      Ramsvik, T.; Borg, A.; Kildemo, M.; Raaen, S.; Matsuura, A.; Jaworowski, A. J.; Worren, T.; Leandersson, M.
      Surface Science (2001), 492 (1-2), 152-160CODEN: SUSCAS; ISSN:0039-6028. (Elsevier Science B.V.)
      Previous studies of CO on Ni(1 0 0) by Fohlisch et al. [Phys. Rev. Lett. 81 (1998) 1730] have shown that the intramol. stretch vibration mode obsd. in the C 1s photoelectron lines depends strongly on the chem. state of the adsorbate. In the current investigation analogous analyses were done for CO on Co(0 0 0 1) and Rh(1 0 0). CO adsorbs in on-top sites on Co(0 0 0 1) resulting in a vibrational splitting of (210 ± 3) meV from the adiabatic C 1s peak. Including the measured intensities and comparing with similar data from electron energy loss spectroscopy expts. the change in the equil. distance between the initial state and the ionized state was deduced to be (4.2 ± 0.2) pm. For CO on Rh(1 0 0) two adsorption sites, on-top and bridge, are populated. Similar anal. of the vibrational fine structure gives a vibrational splitting of (221 ± 4) meV for the on-top site and (174±11) meV for the bridge site. The resp. changes in the equil. distances are (3.8 ± 0.2) and (5.6 ± 0.3) pm. These results are compared with available data in literature.
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    68. 68
      Lahtinen, J.; Vaari, J.; Kauraala, K. Adsorption and Structure Dependent Desorption of CO on Co(0001). Surf. Sci. 1998, 418, 502– 510,  DOI: 10.1016/S0039-6028(98)00711-0
      68
      Adsorption and structure dependent desorption of CO on Co(0001)
      Lahtinen, J.; Vaari, J.; Kauraala, K.
      Surface Science (1998), 418 (3), 502-510CODEN: SUSCAS; ISSN:0039-6028. (Elsevier Science B.V.)
      The adsorption of CO on the Co(0001) surface at room temp. and at 180 K has been studied using work function measurements, XPS, thermal desorption spectroscopy (TDS) and LEED. At low coverages and at room temp. the std. (√3×√3)R30°-CO structure was obsd. By decreasing the temp. and increasing the CO exposure, other stable structures were found on the surface. The (√7/3×√7/3)R10.9°-CO structure was found in a small coverage range around θ=0.43 ML and the (√12/7×√12/7)R10.9° structure with θ=0.58 at satn. exposures. Each of the structures were attached to a specific desorption regime in the TDS spectrum. The position of the C 1s and O 1s core levels indicate single adsorption site in the two lower coverage structure and two different adsorption sites for the most dense adsorption layer.
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    69. 69
      Joos, L.; Filot, I. A. W.; Cottenier, S.; Hensen, E. J. M.; Waroquier, M.; Van Speybroeck, V.; van Santen, R. A. Reactivity of CO on Carbon-Covered Cobalt Surfaces in Fischer-Tropsch Synthesis. J. Phys. Chem. C 2014, 118, 5317– 5327,  DOI: 10.1021/jp4109706
      69
      Reactivity of CO on Carbon-Covered Cobalt Surfaces in Fischer-Tropsch Synthesis
      Joos, Lennart; Filot, Ivo A. W.; Cottenier, Stefaan; Hensen, Emiel J. M.; Waroquier, Michel; Van Speybroeck, Veronique; van Santen, Rutger A.
      Journal of Physical Chemistry C (2014), 118 (10), 5317-5327CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Fischer-Tropsch synthesis is an attractive process to convert alternative carbon sources, such as biomass, natural gas, or coal, to fuels and chems. Deactivation of the catalyst is obviously undesirable, and for a com. plant it is of high importance to keep the catalyst active as long as possible during operating conditions. In this study, the reactivity of CO on carbon-covered cobalt surfaces was investigated by d. functional theory (DFT). An attempt is made to provide insight into the role of carbon deposition on the deactivation of two cobalt surfaces: the closed-packed Co(0001) surface and the corrugated Co(1121) surface. We also analyzed the adsorption and diffusion of carbon atoms on both surfaces and compared the mobility. Finally, the results for Co(0001) and Co(1121) are compared, and the influence of the surface topol. is assessed.
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    70. 70
      Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865
      70
      Generalized gradient approximation made simple
      Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    71. 71
      Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved Adsorption Energetics within Density-Functional Theory using Revised Perdew-Burke-Ernzerhof Functionals. Phys. Rev. B 1999, 59, 7413– 7421,  DOI: 10.1103/PhysRevB.59.7413
      71
      Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals
      Hammer, B.; Hansen, L. B.; Norskov, J. K.
      Physical Review B: Condensed Matter and Materials Physics (1999), 59 (11), 7413-7421CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      A simple formulation of a generalized gradient approxn. for the exchange and correlation energy of electrons has been proposed by J. Perdew et al. (1996). Subsequently, Y. Zhang and W. Wang (1998) have shown that a slight revision of the Perdew-Burke-Ernzerhof (PBE) functional systematically improves the atomization energies for a large database of small mols. In the present work, we show that the Zhang and Yang functional (revPBE) also improves the chemisorption energetics of atoms and mols. on transition-metal surfaces. Our test systems comprise at. and mol. adsorption of oxygen, CO, and NO on Ni(100), Ni(111), Rh(100), Pd(100), and Pd(111) surfaces. As the revPBE functional may locally violate the Lieb-Oxford criterion, we further develop an alternative revision of the PBE functional, RPBE, which gives the same improvement of the chemisorption energies as the revPBE functional at the same time as it fulfills the Lieb-Oxford criterion locally.
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    72. 72
      Mattsson, A. E.; Armiento, R.; Paier, J.; Kresse, G.; Wills, J. M.; Mattsson, T. R. The AM05 Density Functional Applied to Solids. J. Chem. Phys. 2008, 128, 084714,  DOI: 10.1063/1.2835596
      72
      The AM05 density functional applied to solids
      Mattsson, Ann E.; Armiento, Rickard; Paier, Joachim; Kresse, Georg; Wills, John M.; Mattsson, Thomas R.
      Journal of Chemical Physics (2008), 128 (8), 084714/1-084714/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We show that the AM05 functional has the same excellent performance for solids as the hybrid d. functionals tested in Paier et al. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calcns. are typically an order of magnitude slower than local or semilocal d. functionals such as AM05, which is of a regular semilocal generalized gradient approxn. form. The performance of AM05 is on av. found to be superior to selecting the best of local d. approxn. and PBE for each solid. By comparing data from several different electronic-structure codes, we have detd. that the numerical errors in this study are equal to or smaller than the corresponding exptl. uncertainties. (c) 2008 American Institute of Physics.
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    73. 73
      Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406,  DOI: 10.1103/PhysRevLett.100.136406
      73
      Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
      Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gabor I.; Vydrov, Oleg A.; Scuseria, Gustavo E.; Constantin, Lucian A.; Zhou, Xiaolan; Burke, Kieron
      Physical Review Letters (2008), 100 (13), 136406/1-136406/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Popular modern generalized gradient approxns. are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of d. gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approxn. that improves equil. properties of densely packed solids and their surfaces.
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    74. 74
      Zhang, Y.; Yang, W. Comment on “Generalized Gradient Approximation Made Simple”. Phys. Rev. Lett. 1998, 80, 890,  DOI: 10.1103/PhysRevLett.80.890
      74
      Comment on "Generalized Gradient Approximation Made Simple"
      Zhang, Yingkai; Yang, Weitao
      Physical Review Letters (1998), 80 (4), 890CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      A Comment on the Letter by John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. 77, 3865 (1996). The authors of the Letter offer a Reply.
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    75. 75
      Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456– 1465,  DOI: 10.1002/jcc.21759
      75
      Effect of the damping function in dispersion corrected density functional theory
      Grimme, Stefan; Ehrlich, Stephan; Goerigk, Lars
      Journal of Computational Chemistry (2011), 32 (7), 1456-1465CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      It is shown by an extensive benchmark on mol. energy data that the math. form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a std. "zero-damping" formula and rational damping to finite values for small interat. distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coeffs. is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interat. forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramol. dispersion in four representative mol. structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermol. distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of cor. GGAs for non-covalent interactions. According to the thermodn. benchmarks BJ-damping is more accurate esp. for medium-range electron correlation problems and only small and practically insignificant double-counting effects are obsd. It seems to provide a phys. correct short-range behavior of correlation/dispersion even with unmodified std. functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying d. functional. © 2011 Wiley Periodicals, Inc.; J. Comput. Chem., 2011.
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    76. 76
      Grimme, S.; Hansen, A.; Brandenburg, J. G.; Bannwarth, C. Dispersion-Corrected Mean-Field Electronic Structure Methods. Chem. Rev. 2016, 116, 5105– 5154,  DOI: 10.1021/acs.chemrev.5b00533
      76
      Dispersion-Corrected Mean-Field Electronic Structure Methods
      Grimme, Stefan; Hansen, Andreas; Brandenburg, Jan Gerit; Bannwarth, Christoph
      Chemical Reviews (Washington, DC, United States) (2016), 116 (9), 5105-5154CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. Mean-field electronic structure methods like Hartree-Fock, semilocal d. functional approxns., or semiempirical MO theories do not account for long-range electron correlation (London dispersion interaction). Inclusion of these effects is mandatory for realistic calcns. on large or condensed chem. systems and for various intramol. phenomena (thermochem.). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes are classified into three groups: (i) nonlocal, d.-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on mol. complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energies with a typical relative error of 5%. For many chem. problems, this accuracy is higher compared to that of the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP).
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