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ArticleJanuary 17, 2025

Accurately Computed Dimerization Trends of ALD Precursors and Their Impact on Surface Reactivity in Area-Selective Atomic Layer Deposition
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Patrick Maue
Patrick Maue
Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany
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Émilie Chantraine
Émilie Chantraine
Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany
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Fabian Pieck
Fabian Pieck
Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany
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https://orcid.org/0000-0001-6912-2725
Ralf Tonner-Zech*
Ralf Tonner-Zech
Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany
*Email: [email protected]
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https://orcid.org/0000-0002-6759-8559

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Chemistry of Materials

Cite this: Chem. Mater. 2025, XXXX, XXX, XXX-XXX

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https://doi.org/10.1021/acs.chemmater.4c02557

Published January 17, 2025

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Abstract

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The Lewis acidic nature of aluminum atoms in common precursors for the atomic layer deposition (ALD) of Al₂O₃ can lead to dimerization. This study investigates whether these compounds predominantly exist as monomers or dimers under ALD conditions. Understanding dimerization is crucial for discussing precursor reactivities and other properties, especially in the context of area-selective atomic layer deposition (AS-ALD). We employed a theoretical approach incorporating a conformer search, density functional theory, and coupled cluster calculations, to determine the dissociated dimer fraction for a range of precursors under typical ALD pressures and temperatures. The precursors studied include aluminum alkyls, chlorinated aluminum alkyls, dimethylaluminum isopropoxide (DMAI), and tris(dimethylamido)aluminum (TDMAA). Our findings indicate that aluminum alkyls are completely dissociated over the whole parameter range, while DMAI and TDMAA form stable dimers. Chlorinated precursors were found to exist in both monomeric and dimeric forms, depending on temperature and pressure.

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- Creative Commons (CC): This is a Creative Commons license.
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Subjects

1. Introduction

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Atomic layer deposition (ALD) is a technique for the deposition of thin-film structures based on sequential precursor pulses to a substrate surface where they react and form the desired material. (1−3) Applications of ALD include catalysts, (4) energy applications like fuel cells, (5) nanotechnology, (6) and semiconductor manufacturing. (1,2) A vital parameter in ALD processes is the choice of precursor molecules. (7,8) It has an influence on the deposition in many ways like differences in growth rates, (9) temperature and pressure at which ALD processes can be performed, (10) the quality of the deposited material, or the adsorption behavior. (11)

Recently, the area-selective variant of ALD (AS-ALD) has gained strong popularity. (3) Here, a material is controllably grown on one surface (the growth surface) while no deposition takes place on a second surface (the nongrowth surface). (12) A major challenge of AS-ALD is the loss of selectivity after a certain number of cycles. (3,13) Experiments have shown that the number of selective deposition steps before growth initiates on the nongrowth area often depends on the precursor molecule that is applied in the process. (14−16) This shows that the underlying precursor chemistry has an essential effect on the AS-ALD process. In case of the selective deposition of Al₂O₃, for example, a higher number of selective deposition steps was possible with dimethylaluminum isopropoxide (DMAI) compared to the most often used precursor trimethylaluminum (TMA). (15) In the same way, triethylaluminum (TEA) outperformed TMA and a set of alkyl aluminum chlorides in terms of achieved selectivity. (14,16) While the selectivity in AS-ALD thus obviously depends on the choice of the precursor, the underlying reactivity is not yet fully revealed for many processes. Consequently, a better understanding of precursor chemistry is desirable to improve the selectivity in current processes and to develop new AS-ALD processes.

The precursor chemistry is defined by the precursor size, its chemical reactivity, and physical properties like volatility and thermal stability. The chemical reactivity in AS-ALD, for example, can be determined by the accessibility to and reactivity with reactive surface sites on nongrowth areas, where effects of steric blocking (17) and therefore the size of precursors matter. For this reason, one crucial question is whether a precursor is present as a monomer or dimer under experimental ALD conditions (see Figure 1). Most ALD precursors are Lewis acids and thus form homomolecular dimers with the interdimer bond strength depending on their Lewis acidity and steric crowding.

Figure 1. Dimerization reaction of Al precursors shown at the example of TMA with the equilibrium constant K_diss for the dissociation defined via the partial pressures p_monomer and p_dimer and standard pressure p₀.

Dimers have bigger effective sizes and are less reactive than monomeric compounds. (14) Both effects can crucially influence the selectivity in AS-ALD. The effect of dimerization has been recently investigated for Ga precursors in the context of chemical vapor deposition of GaN. (18)

For Al-based precursors, the question of dimerization has been discussed in the past. It is known that compounds commonly used as Al precursors such as aluminum alkyls or alkyl aluminum chlorides (2,9,19−22) as well as DMAI (15,23) can dimerize. (14,19−23) To estimate the monomer-to-dimer ratio, dimerization enthalpies or energies have been determined either theoretically or experimentally. (14,20,21,24−26) However, the published values differ quite strongly: Hiraoka and Mashita (26) for example calculated a dissociation energy of 18 kJ·mol^–1 for TMA based on Hartree–Fock (HF) and Mo̷ller–Plesset perturbation theory (MP2), whereas Oh et al. (14) obtained a value of 77 kJ·mol^–1 based on density functional theory (DFT) calculations. One reason for the deviations is the use of computational methods with limited accuracy like DFT combined with moderately sized basis sets, which lead to considerable basis set superposition errors especially for association reactions. (27,28)

However, an accurate determination of Gibbs free energies of dissociation (ΔG_diss) is important because of its exponential relationship (29) to the dissociation equilibrium constant K_diss and thereby monomer-to-dimer ratio. Therefore, common errors of DFT calculations of 10 kJ·mol^–1 already change the dissociation constant by 1 order of magnitude (see eqs S1 and S2). Nevertheless, Marques et al. showed that DFT can often be used to predict equilibrium compositions. For temperature-dependent equilibrium compositions, however, only a qualitatively correct behavior has been predicted. (30) A further problem of calculated enthalpies or Gibbs energies (ΔG) is that they are computed at pressures and temperatures that are not common for ALD applications. Often, standard conditions of T = 25 °C and p = 1 bar or 1 atm are used, which are the default settings in common quantum chemistry software packages. This is not a problem when equilibrium constants are calculated, but when only the ΔG_diss values are considered to decide whether dissociation happens, more realistic conditions need to be chosen. ALD processes are usually performed at considerably higher temperatures and lower pressures (typical values are T = 100–300 °C (3) and p < 10^–2 bar (14,15,31,32)), causing strong changes in computed ΔG_diss values.

We thus set out to obtain accurate results by using highly accurate wave function based methods (CCSD(T), the so-called “gold standard”) together with a complete basis set (CBS) extrapolation scheme and several other methodological measures to derive accurate dimerization energies under typical ALD conditions. We use a set of contemporary Al precursors for ALD spanning a broad range of Lewis acids and steric crowding (Figure 2). Apart from the compound classes mentioned above, also tris(dimethylamido)aluminum (TDMAA) can be applied as an ALD precursor (33,17) and has been included in our set of precursors. The alkyl-aluminum compounds in this study include not only molecules with linear alkyl chains but also molecules with branched chains, in our case triisopropylaluminum (TiPA) and triisobutylaluminum (TiBA). The latter is an extensively studied precursor for the deposition of alumina films and has been discussed before in the context of chemical vapor deposition. (34) We derived dimerization fractions at different pressures and temperatures and analysed their trend comparing the different precursor classes. This will help to interpret ALD experiments as well as to choose ALD conditions to target a certain precursor state and can be crucial in AS-ALD where the dimerization can lead to increased selectivity. We show the impact of monomeric vs dimeric precursor exemplarily for a case study of surface adsorption on clean and SMI-covered SiO₂.

Figure 2. Set of aluminum precursors investigated in this study grouped in substance classes 1–4. Abbreviations used in the ALD literature are shown in parentheses where available.

2. Computational Details

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2.1. Molecular Calculations

2.1.1. Structural Optimizations

Calculations of the monomers and dimers for the thermochemical properties were done with ORCA 5.0.3. (35−42) Conformers were sampled with CREST (43,44) using standard settings, which include the iMTD-GC workflow and GFN2-xTB. The three conformers lowest in energy were selected and reoptimized with B3LYP-D3. The conformer with the lowest Gibbs free energy at 200 °C and 1.73 × 10^–4 bar (130 mTorr), a realistic set of conditions for ALD processes, (14) was then chosen for any further property calculations. No ensemble averages with multiple conformers were used in the calculation of the energies and enthalpies. The effect which Boltzmann averaging can have on the dimerization energies and why it has been neglected in this study is discussed in Table S2 in Section 3.1 in the SI. For all calculations with DFT, the B3LYP (45−47) exchange-correlation functional with DFT-D3 dispersion correction and a Becke-Johnson-type damping function (BJ) was applied. (38,39) This combination showed the best agreement with CCSD(T) calculations in our benchmark study (see Table S3). A def2-TZVPP (48) basis set together with the corresponding auxiliary basis set for the RI approximation (49) was applied. The densest Becke-Integration Grid (50) “defgrid3” was used in all DFT calculations. To obtain the thermodynamic correction terms and ensure that the obtained geometries correspond to minimum structures, frequency calculations (41) were performed. In all calculations, a convergence criterion for the self-consistent field (SCF) cycles of 10^–8 E_h for the change in energy was used. For optimizations, ORCA uses several criteria based on the change in energy (10^–6 E_h), the current gradient (root mean square: 3 × 10^–5 E_h·bohr^–1, largest value: 10^–4 E_h·bohr^–1), and the step size of the optimization step (root mean square: 6 × 10^–4 bohr, largest value: 10^–3 bohr). If imaginary frequencies were observed, the convergence criteria for optimizations were tightened to 2 × 10^–7 E_h, 8 × 10^–6 E_h·bohr^–1, 3 × 10^–5 E_h·bohr^–1, 10^–4 bohr, and 2 × 10^–4 bohr. For difficult cases, structures were distorted along imaginary modes, followed by structural optimizations until no imaginary modes were observed. The final electronic energy of each structure was obtained with a DLPNO-CCSD(T) (42,51) single-point calculation (in the following stated as CCSD(T)) including a CBS extrapolation (52) as implemented in ORCA. Here, the convergence of the HF energy to the basis set limit is extrapolated as

E_{SCF}^{(X)} = E_{SCF}^{(\infty)} + A \times e^{- α \sqrt X}

(1)

E_SCF^(X) is the SCF energy of a basis set cc-pVXZ, with X = 2 meaning a double-ζ, X = 3 meaning a triple-ζ basis, etc. E_SCF^(∞) is the basis set limit SCF energy, α is a basis set-specific constant, and A is the constant to be determined in the procedure.

The correlation energy contribution is extrapolated with β = 2.4 as

E_{corr}^{(\infty)} = \frac{X^{β} E_{corr}^{(X)} - Y^{β} E_{corr}^{(Y)}}{X^{β} - Y^{β}}

(2)

We used X = 3 and Y = 4, thus the cc-pVTZ and cc-pVQZ (49,53) basis sets. With these basis sets, the value for α is 5.46. Furthermore, for all DLPNO computations, default thresholds were used after testing (see Table S4 for a discussion of this choice).

Gibbs free energies were calculated by adding thermodynamic correction terms obtained at the B3LYP-D3 level of theory to CCSD(T) single point energies:

G = E (CCSD (T)) + G_{correction} (B 3 LYP - D 3)

(3)

Here, all thermodynamic corrections were calculated via statistical thermodynamic approaches in double harmonic approximation with T = −50–400 °C in steps of 50 °C and p = 1.013 × 10^–6 bar (10^–6 atm, 0.76 mTorr) to 1.013 bar (1 atm, 7.6 × 10⁵ mTorr) in steps of one order of magnitude.

A detailed discussion of the conformer search (see Tables S2 and S5), the effect of density functionals (see Table S3) and basis sets (see Table S6) can be found in the Supporting Information. The effect of the basis set superposition error (BSSE) has been tested by the application of counterpoise (CP) correction (see Table S7) and can lead to errors of up to 4.2 kJ·mol^–1. However, the application of a CBS extrapolation for CCSD(T) calculations removes the problem of the BSSE. An overview of possible error sources and their estimated error is shown in Table S8.

2.1.2. Thermochemistry

With the inner energy U, and p and V for pressure and volume, respectively, the enthalpy H is defined as (29)

H = U + p \times V

(4)

The Gibbs energy G of a reaction at temperature T is related to the enthalpy H and entropy S by (29)

G = H - T \times S

(5)

Gibbs free energies of dissociation ΔG_diss were calculated as the difference between monomers and dimers for the reaction in the gas phase shown in Figure 1:

Δ G_{diss} = 2 \times G_{monomer} - G_{dimer}

(6)

ΔE_diss, ΔH_diss, and T·ΔS_diss were calculated analogously to eq 6. Differences between two ΔG_diss values, ΔG_diss1 and ΔG_diss2, were referred to as ΔΔG_diss:

Δ Δ G_{diss} = Δ G_{diss 1} - Δ G_{diss 2}

(7)

Other differences like ΔΔH_diss are defined as analogous.

In general, the equilibrium constant of a reaction can be derived from the standard Gibbs free energy of the reaction at standard pressure p₀. (29,54,55) In our case, this is a dissociation reaction of the dimer with 1.013 bar (1 atm) as standard pressure. Therefore, we use the calculated ΔG_diss(T) of 1 mol dimer at 1.013 bar (1 atm) pressure as Δ_rG^θ(T).

\ln (K) = \frac{- Δ_{r} G^{⊖} (T)}{R T} = \frac{- Δ G_{diss} (1.013 bar, T)}{R T}

(8)

With K, the pressure-dependent dissociated dimer fraction (DDF) can be determined, as shown in Section S6 in the SI by

K = \frac{(2 \times DDF)^{2}}{1 - {DDF}^{2}} \frac{p}{1.013 bar}

(9)

leading to

DDF = \sqrt{\frac{K}{K + 4 \times \frac{p}{1.013 bar}}}

(10)

G depends within our temperature window almost linearly on the temperature. Therefore, we interpolated the ΔG_diss values at different temperatures. The relationship between G and the pressure at constant temperature is

{(\frac{\partial G}{\partial p})}_{T} = V

(11)

Because the volume V is related to the pressure, it is not constant. Under ideal gas conditions (eq 12), V is inversely related to p, which results in a logarithmic dependence between G and p.

V = \frac{n R T}{p}

(12)

2.1.3. Energy Decomposition Analysis

Bonding analysis was performed with AMS 2023.101. (56) The fragmentation was chosen in a way that each molecule in the dimer structure was one fragment in the singlet ground state. The energy decomposition analysis (EDA) calculations were done with B3LYP (45−47) and a DFT-D3 (38,39) dispersion correction. The slater-type orbital (STO)-type basis TZ2P (57,58) was applied, and the parameters of the numerical quality level “good” were used. No relativistic effects were considered, and no frozen core approximation was applied.

The EDA scheme applied in this study was developed by Kitaura and Morokuma (59) and by Ziegler and Rauk. (60,61) The bond dissociation energy of two fragments A and B is the energy difference between the full molecule E_AB and the energies of the fragments in their relaxed geometry E_A^rel and E_B^rel:

E_{bond} = E_{AB} - E_{A}^{rel} - E_{B}^{rel}

(13)

The EDA scheme separates the bonding energy into the preparation energy ΔE_prep and the interaction energy ΔE_int. The preparation energy is the energy needed for the deformation of the fragments from the relaxed state as separated fragments with energy E_A^rel and E_B^rel into the associated structure they have in the molecule with energies E_A and E_B:

E_{bond} = Δ E_{prep} + Δ E_{int}

(14)

Δ E_{prep} = E_{A} + E_{B} - E_{A}^{rel} - E_{B}^{rel}

(15)

This is because the two fragments, here the two monomers, have a different structure as separated molecules compared to the dimer where they bond to each other. That means they need to be deformed from the monomer into the dimer structure, a step considered by the preparation energy (see Figure S12). Consequently, the preparation energy ΔE_prep was calculated as the energy difference between the fragments within the dimer geometry and the relaxed monomers. The interaction energy is further decomposed into a dispersion term ΔE_int (disp) and the electronic interaction energy ΔE_int (elec):

Δ E_{int} = Δ E_{int} (disp) + Δ E_{int} (elec)

(16)

The analysis finally decomposes the electronic interaction energy:

Δ E_{int} (elec) = Δ E_{Pauli} + Δ E_{elstat} + Δ E_{orb}

(17)

The electrostatic term ΔE_elstat comprises quasi-classical electrostatic interactions between the charge distributions and is usually attractive. The Pauli term ΔE_Pauli describes the repulsive effect due to normalization and anti-symmetrization of the resulting product wave function. The attractive orbital term ΔE_orb takes charge transfer and polarization effects into account. (62−64) More detailed information on the presented EDA scheme can be found in the literature. (65,66)

2.2. Computations for Extended Systems

Periodic slab calculations were performed with VASP 5.4.4, (67−71) the PBE functional (72) with D3(BJ) (38,39) dispersion correction, and a plane wave cutoff of 450 eV using standard PAWs. (73) The Brillouin zone was sampled with a gamma-centered Γ(2 × 2 × 1) Monkhorst–Pack (74,75) mesh. The plane wave cutoff, k-grid, and vacuum above the slab were determined in a convergence test to an accuracy of 1 kJ·mol^–1 (see Figures S3 and S4). The surface model was a crystalline, 3 × 3 α-quartz slab consisting of three O–Si-layers where the bottom layer of silicon was H-terminated and kept frozen during the optimization. The top oxygen layer was saturated by hydrogen, resulting in a hydroxylated silica surface. The cell parameters of the periodic cell are a = 16.550 Å, b = 12.820 Å, and c = 52.000 Å. The vacuum above the slab was set at 45 Å. Minima were optimized with a conjugate gradient algorithm with a convergence criterium for the energy difference of the SCF cycle of 10^–5 eV. The convergence criterium for the forces within the geometry optimization was set to 10^–2 eV·Å^–1 for all optimizations. The slab was derived from an optimized SiO₂ bulk cell containing three silicon atoms and six oxygen atoms and cut along the (001) plane using VESTA 3.5.5. (76) The bulk structure for optimization was obtained from the Crystallography Open Database. (77,78) The parameters of the original bulk cell were a = b = 4.892 Å and c = 5.389 Å. The bulk was optimized with an energy cutoff of 500 eV and Γ(5 × 5 × 5) k-point mesh. The parameters of the optimized bulk cell in the α-quartz phase were a = b = 4.934 Å and c = 5.436 Å.

Reaction paths were calculated with the nudged elastic band (NEB) method and transition states determined in a subsequent climbing image calculation (NEB-CI). (79,80) Different to the optimization of minima, NEBs were optimized with the fast inertial relaxation engine (FIRE) (81) and a tightened convergence criterium for the SCF cycle of 10^–7 eV. To obtain the initial interpolation for the minimum energy path (MEP) as a starting point for the NEB, the image-dependent-pair-potential method (82) (IDPP) was used. To check that the transition state had only one imaginary mode, a numeric frequency calculation was performed with finite differences of 0.015 Å and an SCF convergence criterium of 10^–5 eV·Å^–1.

3. Results and Discussion

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In the first section, we want to introduce the structures of the optimized dimers, which are used in the second section to obtain accurate Gibbs free energies. Based on these, DDFs under varying pressures and temperatures for each molecule are derived. In the third section, we will discuss the thermochemistry at typical ALD conditions in detail. Here, results from our study are also compared with previous data from the literature. To understand the observed trends of dimerization and allow predictions on the dimerization of Al precursors, we will then discuss a bonding analysis of the bridging dimer bond for all precursor classes in the fifth section. Finally, the adsorption behavior of dimers compared to monomers and the possibility of dimer opening is tested on SiO₂.

3.1. Structures of Dimerized Precursors

Figure 3 shows one representative example of the dimer structures from each substance class. The general structure of the dimerized precursors is the same for all molecules: All dimers show a four-membered ring that connects the two fragments containing the two aluminum atoms and two atoms from the ligands. The Al atom is either bonded to carbon (1) or to heteroatoms such as chlorine (2), nitrogen (3), and oxygen (4).

Figure 3. Dimer structures with one example of each substance class.

Structural parameters for the central 4-ring of the dimers are listed in Table 1. The distance between the Al atoms varies between 2.6 Å (1-iPr) and 3.3 Å (2-Me₂Cl). Here, the differences within each substance class are small and the Al–Al distance varies only by up to 0.1 Å. The distance between Al and the second atom can be either the same, i.e., differences of less than 0.001 Å, such as in the case of (1-Me)₂, or different by 1.6 Å as with (1-iPr)₂ and (1-iBu)₂. If the distances are the same, it shows that the difference between the bond within one fragment and the bridging bond between the fragments has disappeared and the dimer has taken a symmetric form. As expected, this can be observed for the smaller dimers such as (1-Me)₂ and (2-Cl)₂ while the molecules with sterically more demanding groups such as 1-iPr cannot approach each other close enough for the dimer to take a symmetric form. Consequently, this comparison of the bond distances shows that not only the atoms directly involved in the bridging bonds but also the other atoms of the dimer have a significant influence on the dimer bond due to their steric demand.

Table 1. Structural Parameters of the Al-X-Al-X (X = C, Cl, O, N) Four-Membered Rings of the Calculated Precursor Dimers^a

precursor	d(Al–Al)	d(Al-X)^b
1-Me	2.596	2.144	2.144
1-Et	2.578	2.189	2.142
1-Pr	2.576	2.199	2.134
1-iPr	2.567	2.317	2.153
1-iBu	2.627	2.254	2.092
2-Me₂Cl	3.281	2.332	2.331
2-MeCl₂	3.237	2.304	2.304
2-Cl	3.185	2.279	2.279
3	2.823	1.854	1.853
4	2.805	1.984	1.968

^{^a}

All bond distances in Å. Structures optimized at B3LYP-D3/def2-TZVPP.

^{^b}

Some dimers exhibit asymmetric structures leading to two different bond lengths.

3.2. Pressure Dependence of Dimer Dissociation

To analyze whether precursors are preferably monomeric or dimeric at certain conditions, the ΔG_diss values of the dimers were computed. If ΔG_diss is positive, the dimers are thermodynamically favored, while a negative value shows a thermodynamic driving force for dissociation. The DDFs were derived from ΔG_diss, as described in Section 2.1.2. Figure 4 shows the DDF dependent on the pressure. Figure S5 in the SI shows ΔG_diss in dependence of the pressure to better see the effect of the ligands. Here, a range of typical ALD pressures (“ALD window”) from 10^–4 to 10^–2 bar (14,15,31,32) is highlighted.

Figure 4. Dissociated dimer fraction (DDF) as a function of total pressure of the system at 200 °C for the tested set of Al precursors. Common ALD pressures from 10^–4 to 10^–2 bar are highlighted in gray.

In the relevant range of pressures from 1 × 10^–4 to 1 × 10^–2 bar, no dissociation of dimers of precursors 3 and 4 is visible. The aluminum alkyls of group 1 are completely dissociated, and dimers begin to form only at pressures close to atmospheric conditions, which is far beyond common ALD conditions. The chlorinated compounds of group 2 make a transition from almost complete dissociation at 10^–6 bar to almost undissociated dimers under atmospheric conditions. At 10^–3 bar, the DDF of the chlorinated dimers ranges from 19% (2-Me₂Cl) to 33% (2-Cl). It is worth mentioning that in the case of 2-Cl and 2-MeCl₂, the transition from a majority to a minority of dissociated dimers happens in the ALD window between 10^–4 and 10^–2 bar.

3.3. Temperature Dependence of Dimer Dissociation

Apart from the pressure dependency of the dissociation, also the temperature dependency was investigated. Figure 5 shows the DDF for all of the precursor dimers. Figure S6 in the SI shows ΔG_diss in dependence of the temperature to better see the effect of the ligands. Again, a typical range of ALD temperatures from 100 to 300 °C (3) is highlighted.

Figure 5. Dissociated dimer fraction (DDF) versus temperature at total pressure of the system of 1.73 × 10^–4 bar (130 mTorr) for the tested set of Al precursors. A common temperature range for ALD is highlighted in gray.

The result shows that the alkyl-based precursors of group 1 undergo the transition from dimer to monomer before the typical ALD window whereas the chlorinated precursors of group 2 show this transition within the ALD window. 4 remains stable as a dimer over the whole temperature range whereas 3 starts to dissociate at above 250 °C. It needs to be considered that the pressure in our study is far below standard pressures of 1.013 bar (1 atm). At a higher pressure, dimerization becomes more favorable, as shown in Section 3.2, enabling dimerization at even higher temperatures. Consequently, this explains that dimers of 1-Me have been identified in experiment at higher pressures and temperatures below 100 °C. (22,83)

The general relation between the calculated ΔG_diss values at p = 1.013 bar and temperature T in °C that were used to derive the temperature-dependent DDFs can be described by the following formula:

Δ G_{diss} [\frac{kJ}{mol}] = - a \times T + b

(18)

The parameters a and b are shown in Table S9 in the Supporting Information for each precursor. This enables the derivation of ΔG_diss for other temperature values.

3.4. Thermochemistry for Typical ALD Conditions

After presenting the temperature and pressure dependence of ΔG_diss and the DDFs for a range of temperatures and pressures, a detailed analysis of all relevant parameters (ΔE_diss, ΔH_diss, ΔG_diss, ΔS_diss, DDF) for one set of temperature (200 °C) and pressure (1.73 × 10^–4 bar, 130 mTorr) is presented in Table 2.

Table 2. Compiled Thermochemical Data of the Dissociation Reaction of the Dimers at ALD Conditions of T = 200°C and p = 1.73 × 10^–4 bar (130 mTorr)^a

	1-iBu	1-iPr	1-Me	1-Et	1-Pr	2-Me₂Cl	2-MeCl₂	2-Cl	3	4
ΔE_diss	80.0	46.3	91.1	94.9	88.0	132.4	129.0	127.9	205.8	266.6
ΔH_diss	65.1	28.1	80.5	81.8	73.8	124.2	121.2	120.3	194.9	257.1
–T·ΔS_diss	–144.5	–159.0	–133.8	–141.6	–140.2	–123.7	–123.8	–124.5	–140.1	–133.5
ΔG_diss	–79.4	–130.9	–53.2	–59.7	–66.4	0.5	–2.6	–4.2	54.8	123.6
DDF	100.00%	100.00%	100.00%	100.00%	100.00%	40.72%	55.78%	64.37%	0.05%	0.00%

^{^a}

All ΔE, ΔH, ΔG, and −T·ΔS values in kJ·mol^–1, as defined in Section 2.1.2.

As previously discussed, all dimers of the precursors of group 1 are dissociated at the selected conditions. In the same way, all of the dimers of 4 are intact. 3 also remains largely undissociated with only 0.05% DDF according to the calculation. Whether the monomeric form would already play a role with such a degree of dissociation in the experiment or be negligible cannot be predicted easily. At least the values show that the dimers of 4 are slightly more stable than the dimers of 3.

Furthermore, the table gives insight into the different terms of ΔG_diss and one may ask which are decisive to explain the trends found in ΔG_diss. Considering ΔH_diss, it is evident that almost the same trend as that of ΔG_diss is observed. The only exceptions are the ordering of 1-Me and 1-Et. Here, the ΔH_diss of 1-Me is slightly higher by ΔΔH_diss = 1.3 kJ·mol^–1 compared to 1-Et. The corresponding ΔG_diss of 1-Me is lower by ΔΔG_diss = 6.5 kJ·mol^–1 compared to that of 1-Et. The entropy term −T·ΔS_diss correlates less negatively with ΔG_diss. For example, the same order for −T·ΔS_diss and ΔG_diss is observed within group 2, while −T·ΔS_diss for 3 and 4 is lower than for any precursor of group 2 and is thereby in contrast to the trend of ΔG_diss. Consequently, the enthalpy ΔH_diss is a better measure for the dimer stability than the entropy term −T·ΔS_diss and allows more predictions on the relative stability of dimers. Still, both terms are essential to predicting whether a compound is monomeric or dimeric under certain conditions.

From a computational point of view, the data in Table 2 greatly show the need for accurate computational methods. While the dimers of 2-Me₂Cl and 2-Cl differ only by ΔΔG_diss = 3.7 kJ·mol^–1, a qualitative difference in the DDF value is present as it is changing from 41% in the case of 2-Me₂Cl to 64% for 2-Cl. Thus, a difference of ΔΔG_diss < 4 kJ·mol^–1 leads to a difference of more than 20% in the DDF. This sensitivity of the DDF on the ΔG_diss value is a consequence of the exponential relationship between ΔG_diss and K (see eq 8), which is used for the calculation of the DDFs (eq 10). Table S10 in the Supporting Information further supports this finding as it shows a comparison of the values presented above to values derived with DFT instead of CCSD(T) energies.

3.5. Comparison with Previous Data on Precursor Dimerization

To evaluate the impact of an improved theoretical approach and reasonable ALD pressures on the thermochemistry predictions, a comparison with previous calculations is made. Oh et al. (14) determined the thermochemistry for 1-Me, 1-Et, 2-Me₂Cl, 2-MeCl₂, and 2-Cl using DFT approaches. A comparison of the ΔG_diss and the DDF values to our results is shown in Table 3. It needs to be noted that the formula for the calculation of the DDF from the equilibrium constant applied by Oh et al. (14) (S13) and also more recently by Kim and Shong (84) is only valid under very specific assumptions under which it is equivalent to our more general approach shown in (eq 9) (discussion see SI Section 7). When dissociation profiles at different p and T like those of Kim and Shong are calculated, the two formulas lead to different results, however. (S12 The rather limited impact on the DDF results at p=p₀is discussed in the SI (see Figure S9). Due to the different approach we limit the comparison here to the ΔG_diss values.

Table 3. Comparison of Calculated ΔG_diss of the Chlorinated Precursors of Group 2 as well as 1-Me and 1-Et to Literature Data^a

value	reference	method	p	2-Cl	2-MeCl₂	2-Me₂Cl	1-Me	1-Et
ΔG_diss	Oh et al.^b	DFT	1.013 bar	25.6	18.3	22.9	–31.0	–29.7
	this study^c	DFT	1.013 bar	31.5	30.7	31.3	–27.9	–33.9
	this study^d	CCSD(T)	1.013 bar	29.9	31.5	34.6	–19.1	–25.6
	this study^d	CCSD(T)	1.73 × 10^–4 bar	–4.2	–2.6	0.5	–53.2	–59.7

^{^a}

All ΔG values in kJ·mol^–1.

^{^b}

Values derived at 200 °C 1.013 bar, 75.98 × 10⁴ mTorr using B3LYP-D3/6-311G**.

^{^c}

Values calculated with B3LYP-D3/def2-TZVPP.

^{^d}

Values calculated based on the CCSD(T)-based protocol outlined above.

Our most accurate values for the ΔG_diss at 1.73 × 10^–4 bar (130 mTorr) differ significantly from the literature values . For 2-Cl, for example, a ΔG_diss value of −4.2 kJ·mol^–1 was determined in our study compared to a value of 25.6 kJ·mol^–1 by Oh et al. (14) which sums to a difference of 29.8 kJ·mol^–1.

The pressure values used in the calculations are the main reason to explain the observed differences. If 1.013 bar (75.98 × 10⁴ mTorr) is used instead of typical ALD pressures, ΔG_diss becomes closer to the values from Oh et al. (14) This is especially the case for chlorinated precursors. At standard pressure, a ΔG_diss value of 29.9 kJ·mol^–1 has been obtained for 2-Cl in our study compared to 25.6 kJ·mol^–1 by Oh et al. (14) This makes an absolute difference of only ΔΔG_diss = 4.3 kJ·mol^–1 compared to a difference of ΔΔG_diss = 29.8 kJ·mol^–1 when lower pressures of 1.73 × 10^–4 bar (130 mTorr) are applied.

The use of B3LYP-D3 only instead of the combined approach with CCSD(T) did not always lead to results that were closer to those in the literature. Only for 1-Me is the value of −27.9 kJ·mol^–1 considerably closer to the value of -31.0 kJ·mol^–1 calculated by Oh et al. (14) compared to −19.1 kJ·mol^–1 with the combined approach. We attribute the remaining differences between our calculations and those of Oh et al. to different conformers and the different basis sets. Table S8 shows an overview of common errors from DFT calculations, and the errors estimated from the method tests that are described in Section 3 in the Supporting Information. The comparison shows how the methodology of ab initio calculations on dimerization can affect the predicted dissociation. The application of typical ALD pressures and a refined methodology gives considerably different results. A further comparison between the method applied in the study presented here and a “standard” DFT approach is shown in Table S10 in the SI.

While the comparison above includes only the precursors of classes 1 and 2, also theoretical data on the dissociation of (4)₂ are available. Kim et al. (85) calculated the dimerization energy (ΔE_dim) of 1-Me and 4 with machine-learning potentials (MLPs) and compared the result with DFT calculations using the PBE functional. In the same way, the Gibbs free energy for the dimerization (ΔG_dim) was calculated and compared for a temperature range of −73 to 473 °C (200 to 600 K) at 1.33 × 10^–3 bar (1000 mTorr).

An electronic energy of −104 kJ·mol^–1 (−1.08 eV) for the dimerization of 1-Me and of −250 kJ·mol^–1 (−2.59 eV) for the dimerization of 4 was calculated with the MLP. The dimerization energies from PBE were slightly different with −94 kJ·mol^–1 (−0.97 eV) in the case of 1-Me and −239 kJ·mol^–1 (−2.48 eV) in the case of 4. In our study, the dimerization energies of 1-Me are −91 and −267 kJ·mol^–1 for 4 what makes the 1-Me dimer slightly weaker (−10 kJ·mol^–1 difference) associated compared to the MLP result and the 4 dimer slightly stronger (+17 kJ·mol^–1 difference) associated. The general chemical trend is the same, however. Table 4 shows the comparison of the electronic dimerization energies of our study with those calculated by Kim et al. (85) The differences from our values can be explained by the use of a different calculation method; the MLP had been trained on the basis of PBE-results. With B3LYP-D3 and CCSD(T), the results from the study presented in our paper can be assumed to be more accurate.

Table 4. Dimerization Energies (ΔE_dim) of 1-Me and 4^a

reference	method	1-Me	4
this study^b	CCSD(T)	–91	–267
Kim et al.^c	MLP	–104	–250
Kim et al.^d	DFT	–94	–239

^{^a}

All values in kJ·mol^–1.

^{^b}

Values calculated based on the CCSD(T)-based protocol outlined above.

^{^c}

Values calculated with a universal MLP (PreFerredPotential) trained on data from PBE-D3 and the PAW approach.

^{^d}

Values calculated with PBE-D3 and the PAW approach.

The ΔG values for the dimerization (ΔG_dim) from MLP calculated by Kim et al. (85) predict 4 to be dimeric at the whole temperature range from −73 to 473 °C (200 to 600 K) at 1.33 × 10^–3 bar (1000 Torr). Only the DFT results predict a transition from the dimeric to the monomeric form at about 473 °C, where ΔG gets slightly positive. 1-Me has a positive ΔG_dim above 27 °C (300 K), which means that the monomer is preferred and a negative ΔG_dim below that temperature according to MLP and DFT results. Our study predicts (4)₂ to be dimeric over the range of −50 to 400 °C (see Figure 5) as well and 1-Me to make a transition from dimer to monomer between −50 and +100 °C and being completely dissociated above 100 °C. ΔG_dim changes sign between 5 and 10 °C according to our results, which is at lower temperatures than in the study of Kim et al. (85) The earlier dissociation of 1-Me is not in contradiction with their results because the pressure at which the thermochemistry was calculated was with 1.73 × 10^–4 bar lower in our study and therefore the equilibrium is shifted toward the monomer. With this, both studies gave the same qualitative predictions for the given range of temperatures.

Furthermore, to check whether the calculations make realistic predictions about dimerization, a comparison to experimental results on dimer dissociation is made. According to Almenningen et al., (22) 1-Me is 97% dimeric at 0.04 bar (30,000 mTorr) and 60 °C while it is 96% monomeric at 215 °C. The DDF in our approach according to eq 9 is 41% at 60 °C and 0.04 bar and 100% at 215 °C and 0.04 bar (30,000 mTorr). The qualitative transition from a majority of dimer to almost complete dissociation agrees with the experimental result, whereas the degree of dissociation that is predicted is different. This could be either due to limitations of the theoretical method, like approximations made in the calculation of the thermochemistry, or due to inaccuracies of the experiment. Henrickson and Eyman (86) also experimentally determined the equilibrium constant for the dimer dissociation of (1-Me)₂, from which we calculated the DDF from −50 to 400 °C at a pressure of 1.73 × 10^–4 bar (130 mTorr). The comparison of the experimental and our dissociation profile of (1-Me)₂ is shown in Figure S10.

It can be seen from the graphs that our approach predicts the dimer dissociation to take place earlier than the experimental data. The temperatures by which certain degrees of dissociation are reached are with our approach: >1% DDF at −40 °C; >50% at 15 °C; >90% at 40 °C; >99% DDF at 65 °C. With the result from Henrickson and Eyman, (86) these are >1% DDF at 0 °C; >50% at 70 °C; >90% at 100 °C; and >99% DDF at 140 °C. That means, the starting point of dissociation is shifted by 40 °C, the point where half of the dimers are dissociated by 55 °C and the point at which 99% of all dimers are dissociated by 75 °C.

Also, the comparison with the results for (1-Me)₂ from Almenningen et al. (22) resulted in an earlier start of dissociation in our approach, which indicates that the theoretical approach predicts an earlier dissociation compared to the experiment. If we assume that the experimental values are reliable and the calculated dissociation curves are systematically shifted by roughly 50 °C, as in the example above, the corresponding error in the ΔG_diss values would be around 10 kJ·mol^–1. This is not unexpected for theoretical thermochemistry calculations, which contain several approximations for the calculation of the correction terms based on standard statistical thermodynamics. As a consequence, we conclude that our theoretical predictions can estimate the starting point of dissociation of the different compound classes by roughly 50 °C accuracy and compare the effect of the different ligands. This would not change our overall conclusion that (4)₂ and (3)₂ are stable dimers at ALD conditions (assuming that our approach overestimates the dissociation at a specific temperature), the chlorinated precursors undergo a transition from monomer to dimer in the ALD temperature range, and the alkyl substituted precursors are mainly dissociated at ALD conditions.

A further comparison with experiment is done on the structure of the dimers on the example of (1-Me)₂ in the SI (see Figure S11 and Table S11).

3.6. EDA on Dimer Bond

To get an understanding of the chemical origin of the differences in dimerization degree for the investigated set of precursors, EDA calculations were performed on the dimer bond. The EDA should help to identify reasons and trends for the different bond strengths to make predictions about the dimerization of new precursor compounds or compound classes. Figure 6 shows the most important result of the EDA calculations on the dimer bond for each class of precursor. The complete data set is shown in Table S12 and Figure S13 in the Supporting Information.

Figure 6. EDA on the dimer bond of the Al precursors. All energy terms are given in kJ·mol^–1.

The preparation energy (ΔE_prep) in general increases by the order 2 < 1 ≈ 4 < 3. With an increasing ΔE_prep term, more energy is needed to deform the monomer fragments into dimer geometry. The preparation energy of 1-Me is the highest compared to the other precursors of class 1. That means that the larger bulkiness of the alkyl groups does not necessarily lead to a higher ΔE_prep, as one might have expected.

The Pauli repulsion (ΔE_Pauli) of the chlorinated precursors of group 2 is smaller than that of the other compounds. It is highest in the case of 3. It is worth mentioning that ΔE_Pauli in substance class 1 is strongest for 1-Me again. 1-iBu in contrast has the lowest ΔE_Pauli of precursor class 1. The bulkiness of the alkyl ligands leads not to a higher Pauli repulsion. This can be explained by increasing bond lengths (see Table 1) of the dimers with branched alkyl chains. The bulkiness of the ligands increases the length of the dimer bond and, thereby, minimizes ΔE_Pauli. Similarly to the Pauli repulsion, the electrostatic interaction (ΔE_elstat) is strongest in the case of 3. This compensates for the high ΔE_Pauli and allows for the formation of a stable dimer bond. Both 4 and 3 show with −705 and −882 kJ·mol^–1 of ΔE_elstat a stronger electrostatic attraction than all other precursors that reach only values of up to −570 kJ·mol^–1 (1-Me). The orbital terms, in contrast, are rather similar for all compound classes, with −305 (1-iBu) to −435 kJ·mol^–1 (3).

A diagram with all terms of the EDA is shown in Figure S13. As a sum of all terms, the absolute value of the bonding energy (ΔE_bond) increases as expected by the order 1 < 2 < 3 < 4. The dispersion term (ΔE_disp) is relatively small compared to the other terms, therefore not decisive, and is not discussed here. Therefore, the terms shown in Figure 6 are mainly responsible for the observed trend in ΔE_bond and, with that, the dimer stability of the different substance classes.

From EDA, the following conclusions about the stability of the dimer bonds are drawn: First, alkyl groups are unfavorable as bridging ligands because of their high ΔE_Pauli and ΔE_prep. This affects not only relatively bulky ligands such as isobutyl but also small ligands like methyl. A stable dimer bond can be achieved with heteroatoms containing a free electron pair as O and N that stabilizes the bond to Al due to ΔE_elstat. Chlorine, as a bigger atom of the third period, behaves differently, however. This is explained by the larger size of the atom, leading to a more diffuse electron density. Another difference to the other groups is that no deformation of chlorine as a single atom is possible, different from ligands that consist of more atoms. This explains the low ΔE_prep value of the chlorinated precursors. With chlorine, all terms except ΔE_orb, including the attractive ΔE_elstat as well as the terms that weaken the bond, are comparably small. This leads to ΔE_bond between that of the precursor class 1 and the precursors of 3 and 4. As a conclusion, the substance class and thereby the atoms involved in the bridging dimer bond determine the nature and strength of the dimer bond, while the substitution within a class is less relevant. Consequently, to predict whether a precursor is dimeric, the bridging atoms are decisive rather than the absolute size or bulkiness of the ligands.

3.7. Dimer versus Monomer Adsorption

Finally, after determining which precursor is prevalent in which form, the question of which impact the dimerization has on ALD processes was addressed. A first consequence of dimerization is the higher effective size, which affects the steric hindrance by inhibitors in AS-ALD. Several studies, using experimental and theoretical methods, demonstrate the effect of precursor size on the steric hindrance by inhibitors. (14,87,17,15) Because dimers are larger, they would have it more difficult to diffuse into the inhibitor layer on the nongrowth surface, and therefore, a lower reactivity of dimers on the NGS can be expected. Apart from the size, the adsorption energies and reactivity with certain groups are important for AS-ALD. As shown by Oh et al., (14) the selectivity with chlorinated precursors compared to other precursors like 1-Me could be significantly improved by longer purging times, which can be explained by their stronger physisorption. Xu et al. (88) detected a more persistent adsorption of 1-Me compared to 4 on an SMI-inhibited SiO₂ surface. The examples given show that in some cases, the adsorption energetics needs to be considered to explain different selectivities in experiment. In AS-ALD, every adsorption of precursors on the nongrowth surface, even physisorption might lead to undesired nucleation of material. (89) Therefore, the question of which influence dimerization has on the adsorption is relevant. The same applies to the reactivity of precursors, because it can be expected that dimers do not react the same way as monomers. For these reasons, we briefly address the different behaviors of monomers and dimers on the surface.

To get an impression about the adsorption of dimers compared to that of the corresponding monomers, calculations including a hydroxylated silica surface model were performed. The structures of 1-Me, 2-Cl, and 4 as representative examples for the different substances and their dimers above the surface were calculated. Because precursors of the same class are chemically similar, we selected one alkyl-substituted precursor, one chlorine-substituted precursor, and one with oxygen as heteroatom of the second period.

Here, monomers and dimers were considered independent of their likelihood to be present in the experiment to compare their reactivities and explore the impact of the dimerization on surface reactivity. Understanding this dimerization–reactivity relation in combination with the knowledge of the preferred form under common ALD conditions can help to understand why certain precursors are rather reactive or unreactive in AS-ALD applications. Furthermore, as in the case of the chlorinated precursors, knowledge of the conditions for dimerization could even allow to influence their reactivities by choosing the desired precursor form by tuning the process conditions. While this study gives a limited impression on the reactivity of dimers, further investigations will be necessary to confirm what chemical intuition and adsorption structures on the surface indicate. Figure 7 shows the adsorbing dimers and monomers, including bond length and adsorption energies.

Figure 7. Adsorption of dimers (a) (2-Cl)₂, (b) (4)₂, and (c) (1-Me)₂ and monomers (d) 2-Cl, (e) 4, and (f) 1-Me on SiO₂. Bond lengths are shown in Å, and adsorption energies in kJ·mol^–1. The dispersion contribution to the adsorption energy is shown in brackets. Color code: (soft) pink─Al, green─Cl, black─C, red─O, and white─H. All hydrogens attached to carbon are omitted for clarity.

The absolute value of adsorption energy (E_ads) is higher for the monomers than for the dimers in all three cases with a difference exceeding 40 kJ·mol^–1 for all molecules. In terms of bond strength, 2-Cl (Figure 7d) adsorbs strongest with an E_ads of −148 kJ·mol^–1 whereas its dimer is adsorbed with only −91 kJ·mol^–1 (Figure 7a). In comparison, 4 and 1-Me adsorb with slightly higher adsorption energies of −90 kJ·mol^–1 each while their dimers are only weakly bound by dispersion interactions, leading to E_ads of −47 kJ·mol^–1 for (4)₂ and −32 kJ·mol^–1 with (1-Me)₂, respectively.

The trend in the adsorption energies is also reflected in the adsorption structures. The bonds to the surface are generally longer in the case of the dimers compared to the monomers. The dimer of 2-Cl has a 0.07 Å longer bond to the surface than the monomer. The difference is considerably greater with 1-Me and 4. The dimers of 1-Me and 4 are more than 3 Å above the surface, whereas the monomers have a bond length of around 2.0 Å to the surface. A decomposition of (1-Me)₂ and (4)₂ did not take place. In the case of (2-Cl)₂, one bond of the dimer breaks due to the adsorption to the surface.

The comparison of bond lengths, structures, and adsorption energies (E_ads) shows that (2-Cl)₂ binds differently than the other dimers. From the dispersion contribution that is more than the actual bonding energy and the distance above 3 Å to the surface atoms, it can be seen that (1-Me)₂ and (4)₂ are only slightly physisorbed by dispersion. (2-Cl)₂, however, is partially opened and has a bond length below 2 Å, and the dispersion contribution is responsible for only part of the total adsorption energy. We conclude that the dimer (2-Cl)₂ must be covalently bound to the surface. The same applies to the monomers. Dispersion makes only part of their total adsorption energies, and with bond lengths around or below 2 Å, we conclude that electrostatics and orbital overlap are involved, forming a covalent bond to the surface oxygen. The comparison shows that the chlorinated precursors might adsorb even as dimers as well to the surface as other precursors in their monomeric form, and their dimerization might therefore not prevent undesired reactions with surfaces. This is because precursor adsorption to the non-growth area plays a key role in the loss of selectivity in AS-ALD and is therefore to be prevented. (17) That 2-Cl adsorbs to the surface so strongly might be explained by the high Lewis acidity of the Al atom and the possibility to break the dimer bond with a reasonable amount of energy. In contrast to that, the alkyl-substituted precursors of group 1 are less Lewis acidic because they have no strong electron-withdrawing groups whereas 3 and 4 might have such groups but form more stable dimers than the chlorinated precursors of class 2. In case of 4 and 1-Me, the dimers show little interaction with the surface, and due to the high stability, no high chemical reactivity is expected for (4)₂. The monomers, in contrast, can bind to the surface, which shows the chemical difference and therefore the relevance of the dimerization question for the precursor chemistry. The reactivity comparison between monomers and dimers is an interesting avenue for future computational explorations of precursor–surface interactions.

In AS-ALD, not only the interaction between Al precursors with the surface but also with SMIs can be relevant. Here, trimethoxypropylsilane (TMPS) was chosen as an inhibitor for the SiO₂ surface, which has been investigated experimentally and theoretically in previous studies. (16) Figure 8 shows the adsorption of the three molecules as dimers and monomers to a methoxy group of the TMPS inhibitor bound to the SiO₂ surface.

Figure 8. Adsorption of dimers (a) (2-Cl)₂, (b) (4)₂, and (c) (1-Me)₂ and monomers (d) 2-Cl, (e) 4, and (f) 1-Me on the methoxy group of the small-molecule inhibitor TMPS. Bond lengths are shown in Å and adsorption energies in kJ·mol^–1. The dispersion contribution to the adsorption energy is shown in brackets. Color code: (soft) pink─Al, green─Cl, black─C, red─O, white─H. All hydrogens attached to carbon are omitted for clarity.

Again, the monomers adsorb with a higher absolute value of E_ads than the dimers. 2-Cl adsorbs the strongest of all three precursors with E_ads of −139 kJ·mol^–1, whereas its dimer (2-Cl)₂ is only bound by −91 kJ·mol^–1. The monomers of 1-Me and 4 are more weakly bound to the surface than 2-Cl with −98 kJ·mol^–1 (4) and −77 kJ·mol^–1 (1-Me). The dimers (1-Me)₂ and (4)₂ are again only slightly adsorbed by dispersion interactions with adsorption energies of −45 kJ·mol^–1 in the case of (4)₂ and −52 kJ·mol^–1 for (1-Me)₂. The bond lengths are longest with dimers (1-Me)₂ and (4)₂ with 3.83 Å in the case of (1-Me)₂ and 4.14 Å in the case of (4)₂. Their monomers are again adsorbed with a bond length of around 2 Å (1-Me: 2.05 Å, 4: 2.02 Å). Different from these two precursors, 2-Cl binds with approximately the same length as the monomer and dimer with only a 0.04 Å difference. The distance of the Al atom to the methoxy group measures 1.92 Å in the case of the monomer of 2-Cl and is even a bit shorter with 1.88 Å for the dimer.

The comparison of the adsorption structures and energies again shows the difference between monomers and dimers. Like with the pristine surface, (1-Me)₂ and (4)₂ are only slightly adsorbed by dispersion, which can be seen from the relative dispersion contribution and the bond lengths above 3 Å. Because of the partial opening of (2-Cl)₂, the bond length below 2 Å, and an adsorption energy that exceeds the dispersion contribution, we conclude that (2-Cl)₂ forms a chemical bond to the methoxy group. The same argument applies to the monomers regarding bond length and adsorption energies, and we conclude that these bind covalently, too.

The adsorption tests on SiO₂ and on TMPS as inhibitor on SiO₂ both confirm the expectation that monomers behave chemically different to dimers and that dimers have less chemical interaction with inhibitors and the surface. However, it depends on the type of precursor to which degree dimers interact. While (2-Cl)₂ can open and form chemical bonds, the dimers of 1-Me and 4 have been shown to be rather inert in this small test series. The differences in adsorption behavior indicate that dimerization can play a key role for the precursor selectivity in AS-ALD if a compound is dimerized under ALD conditions and dimers are less reactive. It could be subject of further studies to check whether the possibility of interaction with surfaces exists for the nonchlorinated precursors.

3.8. Dimer Opening

Finally, we tested the possibility of dimer opening reactions on the surface of the (3)₂ dimer on SiO₂. Figure 9 shows the energy profile of the adsorption, dimer opening, and subsequent dissociation of (3)₂.

Figure 9. Reaction path of adsorption and dissociation of (3)₂ on SiO₂. (a) Physisorbed dimer (PS). (b) First intermediary minimum (IM1). (c) Second intermediary minimum (IM2). (d) First partially dissociated structure (DISS1). (e) Transition state for the second dissociation step (TS). (f) Fully dissociated dimer (DISS2).

The reaction starts with the physisorbed state (PS) of the dimer and passes two intermediate minima (IM1 and IM2) where a proton is transferred to the dimethylamino group until the dimer is opened and a chemical bond to the surface of 1.993 Å is formed (partially dissociated DISS1). The energy barriers of the proton transfer and that before the partially dissociated intermediary structure DISS1 are comparably small or negligible, as it can be seen from the NEB profile (see Figure S14). Only the second dissociation step has a significant barrier and leads via the transition state (TS) to the final structure of the dissociated dimer (DISS2). The first dimer opening reaction and the second dissociation step are endothermic at 69 kJ·mol^–1. As a reference point for the reaction energy, the PS structure was used. It also served as a reference point for the activation energy of 92 kJ·mol^–1 for the final dissociation because it can be assumed that the intermediary minima are passed quickly during the reaction.

The barrier height for the whole reaction is 92 kJ·mol^–1 slightly below 1 eV (96 kJ·mol^–1). This is important because it is generally assumed that barriers above 1 eV are not overcome at ALD temperatures. (90−93) The barrier is also much lower compared to the dissociation energy of 206 kJ·mol^–1 for (3)₂ (see Table 2). This can in part be explained in chemical terms due to the transfer of a proton to the dimethylamino group in the first step. The protonation withdraws electrons from the nitrogen, and this electron-withdrawing effect leads to an increased Lewis acidity on the neighboring aluminum, which makes the formation of a chemical bond to the surface oxygen with a free electron pair easier. The electron-withdrawing effect furthermore polarizes the bond between N and Al in (d), which could also explain the relatively low barrier of 23 kJ·mol^–1 between (d) and (e) for the breaking of the second bond.

For the (4)₂ dimer, Kim et al. (85) calculated and discussed different reaction paths of dimer opening and decomposition reactions on the chemically similar Al₂O₃ surface in the study discussed before in Section 3.5, using the MLP. Different to the reaction scheme in Figure 9 where the dimer is opened and dissociates without further decomposition, they studied condensation reactions with the surface following the first breaking of the dimer bond. According to their result, the chemisorption and breaking of the first dimer bond (compare DISS1) is possible with a barrier below 1 eV with 71 kJ·mol^–1 (0.74 eV), and the subsequent reactions with the surface have higher activation energies with 131 kJ·mol^–1 (1.36 eV) and 145 kJ·mol^–1 (1.50 eV) depending on the condensation product. The energies to desorb the second fragment of 4 are even higher with 210 kJ·mol^–1 (2.18 eV) and 214 kJ·mol^–1 (2.22 eV), respectively. They also calculated similar condensation reactions of the monomer with the surface, which had much lower barriers than those of the dimer. For one reaction pathway, the activation barriers were even below 1 eV. Therefore, the results by Kim et al. (85) indicate that only the monomer can undergo condensation reactions with the surface under ALD conditions. Consequently, a pathway of dimer opening and dissociation like that in Figure 9 followed by condensation reactions of these monomers with the surface would be a realistic way of how the (4)₂ dimer could react at the surface.

To further demonstrate the lower reactivity of the dimer, Kim et al. (85) have furthermore tested the adsorption of (4)₂ to Al₂O₃ between AlCH₃ fragments doubly bonded to the surface as SMIs and obtained a remarkably less stable structure compared to the free surface. Due to the higher effective size, dimers would have it more difficult to reach reactive groups between SMIs. Moreover, as the adsorption structures in 3.7 have shown, the dimers would not easily adsorb to the surface or the inhibitor layer like monomers. The possibility of dimer opening on the surface does therefore by no means imply that dimerization has no effect on the reactivity of precursors and especially achieved selectivity in AS-ALD. It does, however, highlight the necessity to protect reactive surface groups during AS-ALD.

Conclusions

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In this study the dimerization of a set of Al precursors for ALD was calculated in dependence of pressure and temperature, including conditions that are common for ALD. For the thermochemistry, an improved approach including conformer search and DLPNO-CCSD(T) energies has been applied to obtain more accurate values than by DFT calculations alone. A comparison with typical DFT approaches has shown that the improved protocol gives results that can differ even qualitatively from the DFT results when it comes to predictions of dimer dissociation. The calculated dimerization of the tested set of Al precursors can be summarized as follows: TDMAA and DMAI are predicted to be present as dimers under all typical ALD conditions (pressures from 10^–6 to 1 bar and temperatures from −50 to 400 °C). In contrast, no relevant degree of dimerization is predicted for the aluminum alkyls at the specific set of ALD conditions, and the monomeric form remains preferred under variation of pressure or temperature. The precursors with branched alkyl chains show even a tendency to dimerization that is lower than that of the molecules with linear chains. The chlorinated precursors were at the transition between monomer and dimer, which means they are present in both forms under the abovementioned conditions of 1.73 × 10^–4 bar (130 mTorr) and 200 °C. This finding could open the possibility to influence the present form in ALD processes by choosing the right pressures and temperatures. To better understand the dimerization of precursors, bonding analyses of the bridging dimer bonds were performed. EDA on the dimer bond shows that the preparation energy and Pauli repulsion are responsible for the weaker dimer bond of the aluminum alkyls than those of the chlorinated precursors. The relatively strong bond between TDMAA and DMAI is mainly explained by the electrostatic interaction.

Finally, the possible implications of dimerization for ALD chemistry were discussed. The adsorption of monomers compared to dimers on SiO₂ was tested and a weaker interaction of dimers with the surface was found, although the result depends on the precursor class. The possibility of dimer opening reactions on the surface exists, however, as the example of the TDMAA dimer has shown. If precursors such as TDMAA and DMAI are completely dimeric under ALD conditions, the dimer rather than the monomer needs to be considered when the precursor chemistry is discussed or investigated. In contrast, when the alkyl-substituted Al precursors are completely dissociated under ALD pressures and temperatures, dimerization does not play a role for any explanation of precursor reactivity. A field where the question of dimerization can be especially relevant is area-selective ALD applications. Here, the results on dimerization found in our study can help to explain the different reactivities of precursors like better performance of DMAI in AS-ALD processes than that of TMA. In understanding the impact of dimerization, calculations on dimer and monomer reactions and adsorption to the surface can be helpful in future studies.

Data Availability

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All computational data are available in the open access database Zenodo via DOI: 10.5281/zenodo.14500658.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.4c02557.

Further information on the accuracy of the computational approach, calculation of DDFs from thermodynamic considerations, more information on the EDA results, and the NEB profile (PDF)

cm4c02557_si_001.pdf (1.08 MB)

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Author Information

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Corresponding Author
- Ralf Tonner-Zech - Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany; https://orcid.org/0000-0002-6759-8559; Email: [email protected]
Authors
- Patrick Maue - Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany
- Émilie Chantraine - Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany
- Fabian Pieck - Fakultät für Chemie und Mineralogie, Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstr. 2, Leipzig 04103, Germany; https://orcid.org/0000-0001-6912-2725
Notes
The authors declare no competing financial interest.

Acknowledgments

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This work was supported by Merck KGaA via the 350th Anniversary Grant. We thank Prof. Stacey Bent and Alex Shearer for intense discussions and scientific exchange. We specifically thank Alex for the suggestion to include TiBA in this study. Computational resources were provided by ZIH Dresden, CSC-GOETHE Frankfurt, HLR Stuttgart, and PC² Paderborn.

References

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This article references 93 other publications.

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Yarbrough, Josiah; Pieck, Fabian; Grigjanis, Daniel; Oh, Il-Kwon; Maue, Patrick; Tonner-Zech, Ralf; Bent, Stacey F.
Chemistry of Materials (2022), 34 (10), 4646-4659CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
Using both expt. and d. functional theory (DFT), we study a group of small mol. inhibitors (SMIs) and aluminum precursors to det. how the interplay between the inhibitor and precursor can affect the selectivity of at. layer deposition (ALD) on different materials. We compare several polyfunctional alkoxysilanes as the SMIs and trimethylaluminum and triethylaluminum as the ALD precursors. Spectroscopic ellipsometry shows a direct correlation between blocking performance and the no. of hydrolysable alkoxy groups on the SMI. DFT results suggest that SMI polymn. at the surface may play an important role in producing a satd. passivation layer, while also indicating that defects in this layer develop primarily due to interactions with the co-reactant rather than with the aluminum ALD precursors. XPS and Auger electron spectroscopy reveal that alkoxysilane SMIs can support the selective growth of up to 4 nm of Al2O3 on copper substrates when the optimal ALD precursor/SMI pair is selected: triethylaluminum as the ALD precursor, water as the co-reactant, and trimethoxypropylsilane as the inhibitor for SiO2 substrates. The blocking performance is much poorer with trimethylaluminum as the precursor, an effect further confirmed by in situ Fourier transform IR spectroscopy. These differences suggest a strong effect of precursor ligand size in achieving AS-ALD with SMIs. In addn., we show that tuning both inhibitor and precursor functionality for the system of interest is required to optimize selective growth.
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Merkx, M. J. M.; Angelidis, A.; Mameli, A.; Li, J.; Lemaire, P. C.; Sharma, K.; Hausmann, D. M.; Kessels, W. M. M.; Sandoval, T. E.; Mackus, A. J. M. Relation between Reactive Surface Sites and Precursor Choice for Area-Selective Atomic Layer Deposition Using Small Molecule Inhibitors. J. Phys. Chem. C 2022, 126 (10), 4845– 4853, DOI: 10.1021/acs.jpcc.1c10816
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Kim, H.; Kim, M.; Kim, B.; Shong, B. Adsorption Mechanism of Dimeric Ga Precursors in Metalorganic Chemical Vapor Deposition of Gallium Nitride. J. Vac. Sci. Technol. A 2023, 41 (6), 063409 DOI: 10.1116/6.0002966
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Baev, A. K.; Shishko, M. A.; Korneev, N. N. Thermodynamics and Thermochemistry of Organoaluminum Compounds. Russ. J. Gen. Chem. 2002, 72 (9), 1389– 1395, DOI: 10.1023/A:1021669611400
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Laubengayer, A. W.; Gilliam, W. F. The Alkyls of the Third Group Elements. I. Vapor Phase Studies of the Alkyls of Aluminum, Gallium and Indium. J. Am. Chem. Soc. 1941, 63 (2), 477– 479, DOI: 10.1021/ja01847a031
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The alkyls of the third-group elements. I. Vapor-phase studies of the alkyls of aluminum, gallium and indium
Laubengayer, A. W.; Gilliam, W. F.
Journal of the American Chemical Society (1941), 63 (), 477-9CODEN: JACSAT; ISSN:0002-7863.
The following data were obtained for Al(CH3)3, Al(C2H5)3, Ga(C2H5)3, and for solid and liquid In(CH3)3: b. p., m. p., consts. for the formula log p = -A/T + B, molar heat of vaporization, molar heat of fusion and Trouton's const. The data indicate that Al(CH3)3 exists as the dimer at 70°. It dissociates with increase in temp., the heat of dissocn. from 100 to 155° being 20.2 kg.-cal. Al(C2H5)3 is 12% assocd. to the dimer at 150°. Ga(C2H5)3 and In(CH3)3 are monomeric in the vapor state.
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Smith, M. B. The Monomer–dimer Equilibria of Liquid Aluminum Alkyls. J. Organomet. Chem. 1972, 46 (1), 31– 49, DOI: 10.1016/S0022-328X(00)90473-X
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Almenningen, A.; Halvorsen, S.; Haaland, A.; Pihlaja, K.; Schaumburg, K.; Ehrenberg, L. A Gas Phase Electron Diffraction Investigation of the Molecular Structures of Trimethylaluminium Monomer and Dimer. Acta Chem. Scand. 1971, 25, 1937– 1945, DOI: 10.3891/acta.chem.scand.25-1937
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Gas phase electron diffraction investigation of the molecular structures of trimethylaluminum monomer and dimer
Almenningen, A.; Halvorsen, S.; Haaland, A.
Acta Chemica Scandinavica (1947-1973) (1971), 25 (6), 1937-45CODEN: ACSAA4; ISSN:0001-5393.
The mol. structures of Me3Al and (Me3Al)2 were detd. by gas phase electron diffraction. The monomer has D3h symmetry with freely rotating methyl groups. The 3 independent structure parameters are R(C-H) = 1.113(3) Å, R(Al-C) = 1.957(3) Å, and ∠Al-C-II = 111.7° (0.5°). The electron scattering pattern for the dimer is consistent with a model with D2h symmetry. The main mol. parameters are R(C-H) mean = 1.117(2) Å, R(Al-C) terminal = 1.957(3) Å, R(Al-C) bridge = 2.140(4) Å, R(Al-Al) = 2.619(5) Å, ∠Cterm-Al-Cterm = 117.3° (1.5°), and ∠Cbr-Al-Cbr = 104.5° (0.1°).
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Lee, S. Y.; Luo, B.; Sun, Y.; White, J. M.; Kim, Y. Thermal Decomposition of Dimethylaluminum Isopropoxide on Si(100). Appl. Surf. Sci. 2004, 222 (1–4), 234– 242, DOI: 10.1016/j.apsusc.2003.08.016
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Champagne, B.; Mosley, D. H.; Fripiat, J. G.; André, J.-M.; Bernard, A.; Bettonville, S.; François, P.; Momtaz, A. Dimerization versus Complexation of Triethylaluminum and Diethylaluminum Chloride: An Ab Initio Determination of Structures, Energies of Formation, and Vibrational Spectra. J. Mol. Struct. Theochem. 1998, 454 (2–3), 149– 159, DOI: 10.1016/S0166-1280(98)00285-1
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Hay, J. N.; Hooper, P. G.; Robb, J. C. Monomer-Dimer Equilibria of Triethylaluminium. J. Organomet. Chem. 1971, 28 (2), 193– 204, DOI: 10.1016/S0022-328X(00)84567-2
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Monomer-dimer equilibriums of triethylaluminum
Hay, James N.; Hooper, P. G.; Robb, James C.
Journal of Organometallic Chemistry (1971), 28 (2), 193-204CODEN: JORCAI; ISSN:0022-328X.
The assocn.-dissocn. equil. for trimethyl- and triethylaluminum are discussed in order to resolve the apparently anomalous range of values quoted in the literature. Thermodynamic liq.-vapor equil. data, the temp. dependence of the NMR spectra, and the range of Arrhenius parameters listed for the addn. reactions of the tri-n-alkylaluminums to n-alkenes are considered.
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Hiraoka, Y. S.; Mashita, M. Ab Initio Study on the Dimer Structures of Trimethylaluminum and Dimethylaluminumhydride. J. Cryst. Growth 1994, 145 (1–4), 473– 477, DOI: 10.1016/0022-0248(94)91094-4
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Ab initio study on the dimer structures of trimethylaluminum and dimethylaluminum hydride
Hiraoka, Yoshiko Someya; Mashita, Masao
Journal of Crystal Growth (1994), 145 (1-4), 473-7CODEN: JCRGAE; ISSN:0022-0248. (Elsevier)
The dimer structures of trimethylaluminum (AlMe3, TMA) and dimethylaluminum hydride (AlHMe2, DMAH) were studied using ab initio MO calcns. The structure of the TMA dimer is C2h; however, that of the DMAH dimer is D2h. The dissocn. energy of the TMA dimer was only 4.2 kcal/mol, while that of the DMAH dimer was 32.3 kcal/mol, which is considerably larger than the TMA dimer. The dimer contributes directly to surface reactions when DMAH is used as the source material for ALE.
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Wang, N. X.; Venkatesh, K.; Wilson, A. K. Behavior of Density Functionals with Respect to Basis Set. 3. Basis Set Superposition Error. J. Phys. Chem. A 2006, 110 (2), 779– 784, DOI: 10.1021/jp0541664
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Behavior of Density Functionals with Respect to Basis Set. 3. Basis Set Superposition Error
Wang, Nick X.; Venkatesh, Krishna; Wilson, Angela K.
Journal of Physical Chemistry A (2006), 110 (2), 779-784CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
The impact of basis set superposition error (BSSE) upon mol. properties detd. using the d. functionals B3LYP, B3PW91, B3P86, BLYP, BPW91, and BP86 in combination with the correlation consistent basis sets [cc-pVnZ, where n = D(2), T(3), Q(4), and 5] for a set of first-row closed-shell mols. has been examd. Correcting for BSSE enables the irregular convergence behavior in mol. properties such as dissocn. energies with respect to increasing basis set size, noted in earlier studies, to be improved. However, for some mols. and functional combinations, BSSE correction alone does not improve the irregular convergence behavior.
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Davidson, E. R.; Chakravorty, S. J. A Possible Definition of Basis Set Superposition Error. Chem. Phys. Lett. 1994, 217 (1–2), 48– 54, DOI: 10.1016/0009-2614(93)E1356-L
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Atkins, P. Physikalische Chemie, 2. Auflage.; VCH Verlagsgesellschaft GmbH: Weinheim, 1996.
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Marques, E. A.; De Gendt, S.; Pourtois, G.; Van Setten, M. J. Benchmarking First-Principles Reaction Equilibrium Composition Prediction. Molecules 2023, 28 (9), 3649, DOI: 10.3390/molecules28093649
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Ritala, M.; Leskelä, M.; Dekker, J.-P.; Mutsaers, C.; Soininen, P. J.; Skarp, J. Perfectly Conformal TiN and Al₂O₃ Films Deposited by Atomic Layer Deposition. Chem. Vap. Depos. 1999, 5 (1), 7– 9, DOI: 10.1002/(SICI)1521-3862(199901)5:1<7::AID-CVDE7>3.0.CO;2-J
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Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition
Ritala, Mikko; Leskela, Markku; Dekker, Jan-Pieter; Mutsaers, Cees; Soininen, Pekka J.; Skarp, Jarmo
Chemical Vapor Deposition (1999), 5 (1), 7-9CODEN: CVDEFX; ISSN:0948-1907. (Wiley-VCH Verlag GmbH)
TiN films were made with a small scale research reactor where the inlets of the sep. precursor flow channels are close to the substrates and the Al2O3 films were deposited using a reactor where the substrates are much further away from the precursor inlets and thus the secondary processes have no effect on the film uniformity. The surface-controlled, self-limiting film growth mechanism of at. layer deposition made it possible to deposit TiN and Al2O3 films uniformly into deep trenches, and the trenches were filled completely without keyhole formation.
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Cremers, V.; Puurunen, R. L.; Dendooven, J. Conformality in Atomic Layer Deposition: Current Status Overview of Analysis and Modelling. Appl. Phys. Rev. 2019, 6 (2), 021302 DOI: 10.1063/1.5060967
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Conformality in atomic layer deposition: Current status overview of analysis and modelling
Cremers, Veronique; Puurunen, Riikka L.; Dendooven, Jolien
Applied Physics Reviews (2019), 6 (2), 021302/1-021302/43CODEN: APRPG5; ISSN:1931-9401. (American Institute of Physics)
A review. Atomic layer deposition (ALD) relies on alternated, self-limiting reactions between gaseous reactants and an exposed solid surface to deposit highly conformal coatings with a thickness controlled at the submonolayer level. In this work, we aim to review the current status of knowledge about the conformality of ALD processes. We describe the basic concepts related to the conformality of ALD, including an overview of relevant gas transport regimes, definitions of exposure and sticking probability, and a distinction between different ALD growth types obsd. in high aspect ratio structures. The different types of high aspect ratio structures and characterization approaches that have been used for quantifying the conformality of ALD processes are reviewed. The different classes of models are discussed with special attention for the key assumptions typically used in the different modeling approaches. The influence of certain assumptions on simulated deposition thickness profiles is illustrated and discussed with the aim of shedding light on how deposition thickness profiles can provide insights into factors governing the surface chem. of ALD processes. We hope that this review can serve as a starting point and ref. work for new and expert researchers interested in the conformality of ALD and, at the same time, will trigger new research to further improve our understanding of this famous characteristic of ALD processes. (c) 2019 American Institute of Physics.
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Buttera, S. C.; Mandia, D. J.; Barry, S. T. Tris(Dimethylamido)Aluminum(III): An Overlooked Atomic Layer Deposition Precursor. J. Vac. Sci. Technol. Vac. Surf. Films 2017, 35 (1), 01B128 DOI: 10.1116/1.4972469
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Gladfelter, W. L. Selective Metalization by Chemical Vapor Deposition. Chem. Mater. 1993, 5 (10), 1372– 1388, DOI: 10.1021/cm00034a004
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Selective metalization by chemical vapor deposition
Gladfelter, Wayne L.
Chemistry of Materials (1993), 5 (10), 1372-88CODEN: CMATEX; ISSN:0897-4756.
The selective growth of metal films by chem. vapor deposition processes is reviewed with 139 refs. A working definition of selectivity, based on the relative rates of nucleation on the growth and nongrowth surfaces, is proposed. After consideration of the factors that effect nucleation and a brief description of the methods used to measure selectivity, a review of the selective depositions of tungsten, copper, and aluminum is presented.
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Neese, F. The ORCA Program System. WIREs Comput. Mol. Sci. 2012, 2 (1), 73– 78, DOI: 10.1002/wcms.81
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The ORCA program system
Neese, Frank
Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (1), 73-78CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
A review. ORCA is a general-purpose quantum chem. program package that features virtually all modern electronic structure methods (d. functional theory, many-body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger mols., transition metal complexes, and their spectroscopic properties. ORCA uses std. Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.
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Neese, F. Software Update: The ORCA Program System, Version 4.0. WIREs Comput. Mol. Sci. 2018, 8 (1), e1327 DOI: 10.1002/wcms.1327
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Neese, F.; Wennmohs, F.; Becker, U.; Riplinger, C. The ORCA Quantum Chemistry Program Package. J. Chem. Phys. 2020, 152 (22), 224108, DOI: 10.1063/5.0004608
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The ORCA quantum chemistry program package
Neese, Frank; Wennmohs, Frank; Becker, Ute; Riplinger, Christoph
Journal of Chemical Physics (2020), 152 (22), 224108CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
In this contribution to the special software-centered issue, the ORCA program package is described. We start with a short historical perspective of how the project began and go on to discuss its current feature set. ORCA has grown into a rather comprehensive general-purpose package for theor. research in all areas of chem. and many neighboring disciplines such as materials sciences and biochem. ORCA features d. functional theory, a range of wavefunction based correlation methods, semi-empirical methods, and even force-field methods. A range of solvation and embedding models is featured as well as a complete intrinsic to ORCA quantum mechanics/mol. mechanics engine. A specialty of ORCA always has been a focus on transition metals and spectroscopy as well as a focus on applicability of the implemented methods to "real-life" chem. applications involving systems with a few hundred atoms. In addn. to being efficient, user friendly, and, to the largest extent possible, platform independent, ORCA features a no. of methods that are either unique to ORCA or have been first implemented in the course of the ORCA development. Next to a range of spectroscopic and magnetic properties, the linear- or low-order single- and multi-ref. local correlation methods based on pair natural orbitals (domain based local pair natural orbital methods) should be mentioned here. Consequently, ORCA is a widely used program in various areas of chem. and spectroscopy with a current user base of over 22 000 registered users in academic research and in industry. (c) 2020 American Institute of Physics.
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Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132 (15), 154104, DOI: 10.1063/1.3382344
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A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32 (7), 1456– 1465, DOI: 10.1002/jcc.21759
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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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Grimme, S. Accurate Description of van Der Waals Complexes by Density Functional Theory Including Empirical Corrections. J. Comput. Chem. 2004, 25 (12), 1463– 1473, DOI: 10.1002/jcc.20078
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Accurate description of van der Waals complexes by density functional theory including empirical corrections
Grimme, Stefan
Journal of Computational Chemistry (2004), 25 (12), 1463-1473CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
An empirical method to account for van der Waals interactions in practical calcns. in the framework of the d. functional theory (termed DFT-D) was tested for a wide variety of mol. complexes. As in previous schemes, the dispersive energy was described by damped interat. potentials of the form C6R-6. The use of pure, gradient-cor. d. functionals (BLYP and PBE), together with the resoln.-of-the-identity (RI) approxn. for the Coulomb operator, allows very efficient computations for large systems. In contrast to the previous work, extended AO basis sets of polarized TZV or QZV quality were employed, which reduced the basis set superposition error to a negligible extend. By using a global scaling factor for the at. C6 coeffs., the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes was found to be insignificant if steep damping functions were employed. The method was applied to a total of 29 complexes of atoms and small mols. (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene·H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theor. or exptl. results for binding energies and intermol. distances is obtained. For stacked arom. systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to std. MP2 treatments that systematically over-bind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chem. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calcns. of the interaction energies.
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Bykov, D.; Petrenko, T.; Izsák, R.; Kossmann, S.; Becker, U.; Valeev, E.; Neese, F. Efficient Implementation of the Analytic Second Derivatives of Hartree–Fock and Hybrid DFT Energies: A Detailed Analysis of Different Approximations. Mol. Phys. 2015, 113 (13–14), 1961– 1977, DOI: 10.1080/00268976.2015.1025114
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Riplinger, C.; Neese, F. An Efficient and near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138 (3), 034106 DOI: 10.1063/1.4773581
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An efficient and near linear scaling pair natural orbital based local coupled cluster method
Riplinger, Christoph; Neese, Frank
Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
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Pracht, P.; Bohle, F.; Grimme, S. Automated Exploration of the Low-Energy Chemical Space with Fast Quantum Chemical Methods. Phys. Chem. Chem. Phys. 2020, 22 (14), 7169– 7192, DOI: 10.1039/C9CP06869D
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Automated exploration of the low-energy chemical space with fast quantum chemical methods
Pracht, Philipp; Bohle, Fabian; Grimme, Stefan
Physical Chemistry Chemical Physics (2020), 22 (14), 7169-7192CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
We propose and discuss an efficient scheme for the in silico sampling for parts of the mol. chem. space by semiempirical tight-binding methods combined with a meta-dynamics driven search algorithm. The focus of this work is set on the generation of proper thermodn. ensembles at a quantum chem. level for conformers, but similar procedures for protonation states, tautomerism and non-covalent complex geometries are also discussed. The conformational ensembles consisting of all significantly populated min. energy structures normally form the basis of further, mostly DFT computational work, such as the calcn. of spectra or macroscopic properties. By using basic quantum chem. methods, electronic effects or possible bond breaking/formation are accounted for and a very reasonable initial energetic ranking of the candidate structures is obtained. Due to the huge computational speedup gained by the fast low-cost quantum chem. methods, overall short computation times even for systems with hundreds of atoms (typically drug-sized mols.) are achieved. Furthermore, specialized applications, such as sampling with implicit solvation models or constrained conformational sampling for transition-states, metal-, surface-, or noncovalently bound complexes are discussed, opening many possible applications in modern computational chem. and drug discovery. The procedures have been implemented in a freely available computer code called CREST, that makes use of the fast and reliable GFNn-xTB methods.
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Grimme, S. Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations. J. Chem. Theory Comput. 2019, 15 (5), 2847– 2862, DOI: 10.1021/acs.jctc.9b00143
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Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations
Grimme, Stefan
Journal of Chemical Theory and Computation (2019), 15 (5), 2847-2862CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The semiempirical tight-binding based quantum chem. method GFN2-xTB is used in the framework of meta-dynamics (MTD) to globally explore chem. compd., conformer, and reaction space. The biasing potential given as a sum of Gaussian functions is expressed with the root-mean-square-deviation (RMSD) in Cartesian space as a metric for the collective variables. This choice makes the approach robust and generally applicable to three common problems (i.e., conformer search, chem. reaction space exploration in a virtual nanoreactor, and for guessing reaction paths). Because of the inherent locality of the at. RMSD, functional group or fragment selective treatments are possible facilitating the investigation of catalytic processes where, for example, only the substrate is thermally activated. Due to the approx. character of the GFN2-xTB method, the resulting structure ensembles require further refinement with more sophisticated, for example, d. functional or wave function theory methods. However, the approach is extremely efficient running routinely on common laptop computers in minutes to hours of computation time even for realistically sized mols. with a few hundred atoms. Furthermore, the underlying potential energy surface for mols. contg. almost all elements (Z = 1-86) is globally consistent including the covalent dissocn. process and electronically complicated situations in, for example, transition metal systems. As examples, thermal decompn., ethyne oligomerization, the oxidn. of hydrocarbons (by oxygen and a P 450 enzyme model), a Miller-Urey model system, a thermally forbidden dimerization, and a multistep intramol. cyclization reaction are shown. For typical conformational search problems of org. drug mols., the new MTD(RMSD) algorithm yields lower energy structures and more complete conformer ensembles at reduced computational effort compared with its already well performing predecessor.
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Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38 (6), 3098– 3100, DOI: 10.1103/PhysRevA.38.3098
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Density-functional exchange-energy approximation with correct asymptotic behavior
Becke, A. D.
Physical Review A: Atomic, Molecular, and Optical Physics (1988), 38 (6), 3098-100CODEN: PLRAAN; ISSN:0556-2791.
Current gradient-cor. d.-functional approxns. for the exchange energies of at. and mol. systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy d. A gradient-cor. exchange-energy functional is given with the proper asymptotic limit. This functional, contg. only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of at. systems with remarkable accuracy, surpassing the performance of previous functionals contg. two parameters or more.
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Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98 (7), 5648– 5652, DOI: 10.1063/1.464913
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Density-functional thermochemistry. III. The role of exact exchange
Becke, Axel D.
Journal of Chemical Physics (1993), 98 (7), 5648-52CODEN: JCPSA6; ISSN:0021-9606.
Despite the remarkable thermochem. accuracy of Kohn-Sham d.-functional theories with gradient corrections for exchange-correlation, the author believes that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional (contg. local-spin-d., gradient, and exact-exchange terms) is tested for 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total at. energies of first- and second-row systems. This functional performs better than previous functionals with gradient corrections only, and fits expt. atomization energies with an impressively small av. abs. deviation of 2.4 kcal/mol.
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Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37 (2), 785– 789, DOI: 10.1103/PhysRevB.37.785
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Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
Lee, Chengteh; Yang, Weitao; Parr, Robert G.
Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.
A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
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Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7 (18), 3297, DOI: 10.1039/b508541a
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Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
Weigend, Florian; Ahlrichs, Reinhart
Physical Chemistry Chemical Physics (2005), 7 (18), 3297-3305CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 mols. representing (nearly) all elements-except lanthanides-in their common oxidn. states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, d. functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.
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Weigend, F. Accurate Coulomb-Fitting Basis Sets for H to Rn. Phys. Chem. Chem. Phys. 2006, 8 (9), 1057, DOI: 10.1039/b515623h
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Accurate Coulomb-fitting basis sets for H to Rn
Weigend, Florian
Physical Chemistry Chemical Physics (2006), 8 (9), 1057-1065CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approx. Coulomb energies in conjunction with orbital basis sets of split valence, triple zeta valence and quadruple zeta valence quality with errors of typically below ca. 0.15 kJ mol-1 per atom; this was demonstrated in conjunction with the recently developed orbital basis sets of types def2-SV(P), def2-TZVP and def2-QZVPP for a large set of small mols. representing (nearly) each element in all of its common oxidn. states. These auxiliary bases are slightly more than three times larger than orbital bases of split valence quality. Compared to non-approximated treatments, computation times for the Coulomb part are reduced by a factor of ca. 8 for def2-SV(P) orbital bases, ca. 25 for def2-TZVP and ca. 100 for def2-QZVPP orbital bases.
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Becke, A. D. A Multicenter Numerical Integration Scheme for Polyatomic Molecules. J. Chem. Phys. 1988, 88 (4), 2547– 2553, DOI: 10.1063/1.454033
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A multicenter numerical integration scheme for polyatomic molecules
Becke, A. D.
Journal of Chemical Physics (1988), 88 (4), 2547-53CODEN: JCPSA6; ISSN:0021-9606.
A simple scheme is proposed for decompn. of mol. functions into single-center components. The problem of three-dimensional integration in mol. systems thus reduces to a sum of one-center, at.-like integrations which are treated using std. numerical techniques in spherical polar coordinates. The resulting method is tested on representative diat. and polyat. systems for which we obtain five- or six-figure accuracy using a few thousand integration points per atom.
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Liakos, D. G.; Neese, F. Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory. J. Chem. Theory Comput. 2015, 11 (9), 4054– 4063, DOI: 10.1021/acs.jctc.5b00359
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Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory
Liakos, Dimitrios G.; Neese, Frank
Journal of Chemical Theory and Computation (2015), 11 (9), 4054-4063CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calcns. with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calcns., even for small and medium sized mols. where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calcn., it is useful to compare the method against modern d. functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid d. functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals cor. counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean abs. deviation of less than 1 kcal/mol to the ref. values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.
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Truhlar, D. G. Basis-Set Extrapolation. Chem. Phys. Lett. 1998, 294 (1–3), 45– 48, DOI: 10.1016/S0009-2614(98)00866-5
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Basis-set extrapolation
Truhlar, Donald G.
Chemical Physics Letters (1998), 294 (1,2,3), 45-48CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
A proposal for extrapolation of correlated electronic structure calcns. based on correlation-consistent polarized double- and triple-zeta basis sets is evaluated. Optimum exponents are presented for sep. extrapolating the Hartree-Fock and correlation energies, and the method yields energies that are more accurate than those from straight correlation-consistent polarized sextuple-zeta calcns. at less than 1% of the cost. For the test problems, the root-mean-square deviations from the complete basis limit are 1.3-2.4 kcal/mol for the extrapolated calcns. and 3.0-4.4 kcal/mol for the polarized sextuple-zeta calcns.
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Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90 (2), 1007– 1023, DOI: 10.1063/1.456153
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Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
Dunning, Thom H., Jr.
Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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Wedler, G.; Freund, H.-J. Lehrbuch Der Physikalischen Chemie, 6. Auflage.; WILEY-VCH: Weinheim, 2012.
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Jensen, F. Introduction to Computational Chemistry, 1 ed.; JOHN WILEY & SONS: Chichester, 1999.
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AMS. http://www.scm.com/ Accessed 3 July 2024.
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Van Lenthe, E.; Baerends, E. J. Optimized Slater-type Basis Sets for the Elements 1–118. J. Comput. Chem. 2003, 24 (9), 1142– 1156, DOI: 10.1002/jcc.10255
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Optimized Slater-type basis sets for the elements 1-118
Van Lenthe, E.; Baerends, E. J.
Journal of Computational Chemistry (2003), 24 (9), 1142-1156CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral at. and diat. oxide calcns. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. At. tests reveal that, on av., the abs. basis set error of 0.03 kcal/mol in the d. functional calcn. of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the av. abs. difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This av. abs. basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approx. 4 kcal/mol for the all electron basis sets of double zeta quality. The mol. tests reveal that, on av., the calcd. atomization energies of 118 neutral diat. oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approx. 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calcn. of the atomization energies of the group 2 and group 14 diat. oxides. The basis sets that are optimized for calcns. using the frozen core approxn. (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On av., the use of these frozen core basis sets give at. basis set errors that are approx. twice as large as the corresponding all electron basis set errors and mol. atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calcns. larger errors are found, esp. for the heavier elements, due to the addnl. approxn. that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.
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Chong, D. P.; Van Lenthe, E.; Van Gisbergen, S.; Baerends, E. J. Even-tempered Slater-type Orbitals Revisited: From Hydrogen to Krypton. J. Comput. Chem. 2004, 25 (8), 1030– 1036, DOI: 10.1002/jcc.20030
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Even-tempered Slater-type orbitals revisited: from hydrogen to krypton
Chong, Delano P.; Van Lenthe, Erik; Van Gisbergen, Stan; Baerends, Evert Jan
Journal of Computational Chemistry (2004), 25 (8), 1030-1036CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
Even-tempered STO basis sets were developed in 1973, based on total at. energy optimization. Here, we revisit ET STOs and propose new sets based on past experience and recent computational studies. From preliminary at. and mol. tests, these sets are shown to be very well balanced and to perform, at lower cost, almost as well as a very large (close to complete) basis set.
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Kitaura, K.; Morokuma, K. A New Energy Decomposition Scheme for Molecular Interactions within the Hartree-Fock Approximation. Int. J. Quantum Chem. 1976, 10 (2), 325– 340, DOI: 10.1002/qua.560100211
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A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation
Kitaura, Kazuo; Morokuma, Keiji
International Journal of Quantum Chemistry (1976), 10 (2), 325-40CODEN: IJQCB2; ISSN:0020-7608.
In an extension of previous work (M., et al., 1974; M., 1971; S. Iwata and M., 1975; S. Yamabe and M., 1975), a new method was developed for calcg. sep. the components of mol. interaction energy within the Hartree-Fock approxn. The Hartree-Fock MO's of the isolated mols. are used as the basis set for construction of the Fock matrix for the supermol. Then certain blocks of this matrix are set to zero, subject to specific boundary conditions for the supermol. MO's; the resultant matrix is diagonalized iteratively to obtain the desired energy components. This method has an advantage over the previous method in the explicit definition of the charge-transfer energy, placing it on an equal status with the exchange and polarization terms. The new method is compared with existing perturbation methods, and was also applied to decomp. the energy and electron d. of (H2O)2.
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Ziegler, T.; Rauk, A. Carbon Monoxide, Carbon Monosulfide, Molecular Nitrogen, Phosphorus Trifluoride, and Methyl Isocyanide as σ Donors and π Acceptors. A Theoretical Study by the Hartree-Fock-Slater Transition-State Method. Inorg. Chem. 1979, 18 (7), 1755– 1759, DOI: 10.1021/ic50197a006
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Carbon monoxide, carbon monosulfide, molecular nitrogen, phosphorus trifluoride, and methyl isocyanide as σ donors and π acceptors. A theoretical study by the Hartree-Fock-Slater transition-state method
Ziegler, Tom; Rauk, Arvi
Inorganic Chemistry (1979), 18 (7), 1755-9CODEN: INOCAJ; ISSN:0020-1669.
Hartree-Fock-Slater calcns. were carried out on Ni(CO)3L for a no. of different ligands (L) in order to investigate the abilities of the ligands to act as σ donors and π acceptors. The order, based on extent of electron transfer, for σ donation is CS ≃ CO > CNCH3 > N2 ∼ PF3 and for π back-bonding is CNCH3 > CS > CO > PF3 > N2. The contributions to the total bonding energy between Ni(CO)3 and L from σ donation and π back-donation were evaluated by the Hartree-Fock-Slater transition-state method, and the same method was used to optimize the Ni-L bond distances. Calcns. on the stretching frequency νCO of carbon monoxide complexed to Ni(CO)3 showed that νCO is decreased by the π back-donation but is increased by the steric interaction energy between Ni(CO)3 and CO. Thus the decrease in νCO is not a reliable measure of the extent of π back-bonding in the metal-ligand bond. The calcd. influence on νCO from σ donation was negligible.
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Ziegler, T.; Rauk, A. A Theoretical Study of the Ethylene-Metal Bond in Complexes between Cu⁺, Ag⁺, Au⁺, Pt⁰, or Pt²⁺ and Ethylene, Based on the Hartree-Fock-Slater Transition-State Method. Inorg. Chem. 1979, 18 (6), 1558– 1565, DOI: 10.1021/ic50196a034
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A theoretical study of the ethylene-metal bond in complexes between copper(1+), silver(1+), gold(1+), platinum(0) or platinum(2+) and ethylene, based on the Hartree-Fock-Slater transition-state method
Ziegler, Tom; Rauk, Arvi
Inorganic Chemistry (1979), 18 (6), 1558-65CODEN: INOCAJ; ISSN:0020-1669.
An anal. based on the Hartree-Fock-Slater (HFS) transition-state method is given of the metal-ethylene bond in the ion-ethylene complexes Cu+-C2H4, Ag+-C2H4, and Au+-C2H4 as well as in complexes with PtCl3- and Pt(PH3)2. The contribution from σ-donation to the bonding energy was equally important for all three complexes with the ions, whereas the contribution from the π back-donation was important only for the Cu complex. A similar anal. of Pt(Cl)3--C2H4 and Pt(PH3)2-C2H4 showed that the position of ethylene perpendicular to the coordination plane of Pt(Cl)3- in Zeise's salt is caused by steric factors, whereas the position of ethylene in Pt(PH3)2-C2H4 is due to electronic factors, specifically π back-donations.
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Bickelhaupt, F. M.; Nibbering, N. M. M.; Van Wezenbeek, E. M.; Baerends, E. J. Central Bond in the Three CṄ Dimers NC-CN, CN-CN and CN-NC: Electron Pair Bonding and Pauli Repulsion Effects. J. Phys. Chem. 1992, 96 (12), 4864– 4873, DOI: 10.1021/j100191a027
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63
Tonner, R.; Frenking, G. Divalent Carbon(0) Chemistry, Part 1: Parent Compounds. Chem. – Eur. J. 2008, 14 (11), 3260– 3272, DOI: 10.1002/chem.200701390
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Divalent carbon(0) chemistry, part 1: parent compounds
Tonner, Ralf; Frenking, Gernot
Chemistry - A European Journal (2008), 14 (11), 3260-3272CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
Quantum-chem. calcns. with DFT (BP86) and ab initio methods [MP2, SCS-MP2, CCSD(T)] have been carried out for the mols. C(PH3)2 (1), C(PMe3)2 (2), C-(PPh3)2 (3), C(PPh3)(CO) (4), C(CO)2 (5), C(NHCH)2 (6), C(NHCMe)2 (7) (Me2N)2C=C=C(NMe2)2 (8), and NHC (9), where NHC=N-heterocyclic carbene and NHCMe=N-methyl-substituted NHC. The electronic structure in 1-9 was analyzed with charge- and energy-partitioning methods. The results show that the bonding situations in L2C compds. 1-8 can be interpreted in terms of donor-acceptor interactions between closed-shell ligands L and a carbon atom which has two lone-pair orbitals L→C←L. This holds particularly for the carbodiphosphoranes 1-3 where L=PR3, which therefore are classified as divalent carbon(0) compds. The NBO anal. suggests that the best Lewis structures for the carbodicarbenes 6 and 7 where L is a NHC ligand have C=C=C double bonds as in the tetraaminoallene 8. However, the Lewis structures of 6-8, in which two lone-pair orbitals at the central carbon atom are enforced, have only a slightly higher residual d. Visual inspection of the frontier orbitals of the latter species reveals their pronounced lone-pair character, which suggests that even the quasi-linear tetraaminoallene 8 is a "masked" divalent carbon(0) compd. This explains the very shallow bending potential of 8. The same conclusion is drawn for phosphoranylketene 4 and for carbon sub-oxide (5), which according to the bonding anal. have hidden double-lone-pair character. The AIM anal. and the EDA calcns. support the assignment of carbodiphosphoranes as divalent carbon(0) compds., while NHC 9 is characterized as a divalent carbon(II) compd. The L→C(1D) donor-acceptor bonds are roughly twice as strong as the resp. L→BH3 bond.
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Pecher, L.; Tonner, R. Deriving Bonding Concepts for Molecules, Surfaces, and Solids with Energy Decomposition Analysis for Extended Systems. WIREs Comput. Mol. Sci. 2019, 9 (4), e1401 DOI: 10.1002/wcms.1401
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Bickelhaupt, F. M.; Baerends, E. J. Kohn-Sham Density Functional Theory: Predicting and Understanding Chemistry. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; Wiley, 2000; Vol. 15, pp 1– 86. DOI: 10.1002/9780470125922.ch1 .
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Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22 (9), 931– 967, DOI: 10.1002/jcc.1056
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Chemistry with ADF
Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T.
Journal of Computational Chemistry (2001), 22 (9), 931-967CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
A review with 241 refs. We present the theor. and tech. foundations of the Amsterdam D. Functional (ADF) program with a survey of the characteristics of the code (numerical integration, d. fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chem. shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, at. VDD charges). In the Applications section we discuss the phys. model of the electronic structure and the chem. bond, i.e., the Kohn-Sham MO (MO) theory, and illustrate the power of the Kohn-Sham MO model in conjunction with the ADF-typical fragment approach to quant. understand and predict chem. phenomena. We review the "Activation-strain TS interaction" (ATS) model of chem. reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in org. chem. or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochem. (structure and bonding of DNA) and of time-dependent d. functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the anal. of chem. phenomena.
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Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47 (1), 558– 561, DOI: 10.1103/PhysRevB.47.558
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Ab initio molecular dynamics of liquid metals
Kresse, G.; Hafner, J.
Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.
The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal–Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49 (20), 14251– 14269, DOI: 10.1103/PhysRevB.49.14251
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Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium
Kresse, G.; Hafner, J.
Physical Review B: Condensed Matter and Materials Physics (1994), 49 (20), 14251-69CODEN: PRBMDO; ISSN:0163-1829.
The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.
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Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6 (1), 15– 50, DOI: 10.1016/0927-0256(96)00008-0
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Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
Kresse, G.; Furthmuller, J.
Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)
The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
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Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54 (16), 11169– 11186, DOI: 10.1103/PhysRevB.54.11169
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70
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
Kresse, G.; Furthmueller, J.
Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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Kresse, G.; Hafner, J. Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition Elements. J. Phys.: Condens. Matter 1994, 6 (40), 8245– 8257, DOI: 10.1088/0953-8984/6/40/015
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Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements
Kresse, G.; Hafner, J.
Journal of Physics: Condensed Matter (1994), 6 (40), 8245-57CODEN: JCOMEL; ISSN:0953-8984.
The construction of accurate pseudopotentials with good convergence properties for the first-row and transition elements is discussed. By combining an improved description of the pseudo-wavefunction inside the cut-off radius with the concept of ultrasoft pseudopotentials introduced by Vanderbilt optimal compromise between transferability and plane-wave convergence can be achieved. With the new pseudopotentials, basis sets with no more than 75-100 plane waves per atom are sufficient to reproduce the results obtained with the most accurate norm-conserving pseudopotentials.
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Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865– 3868, DOI: 10.1103/PhysRevLett.77.3865
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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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Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59 (3), 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
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From ultrasoft pseudopotentials to the projector augmented-wave method
Kresse, G.; Joubert, D.
Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13 (12), 5188– 5192, DOI: 10.1103/PhysRevB.13.5188
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Pack, J. D.; Monkhorst, H. J. Special Points for Brillouin-Zone Integrations”─a Reply. Phys. Rev. B 1977, 16 (4), 1748– 1749, DOI: 10.1103/PhysRevB.16.1748
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Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44 (6), 1272– 1276, DOI: 10.1107/S0021889811038970
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VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
Momma, Koichi; Izumi, Fujio
Journal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.
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Gražulis, S.; Chateigner, D.; Downs, R. T.; Yokochi, A. F. T.; Quirós, M.; Lutterotti, L.; Manakova, E.; Butkus, J.; Moeck, P.; Le Bail, A. Crystallography Open Database – an Open-Access Collection of Crystal Structures. J. Appl. Crystallogr. 2009, 42 (4), 726– 729, DOI: 10.1107/S0021889809016690
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Crystallography Open Database - an open-access collection of crystal structures
Grazulis, Saulius; Chateigner, Daniel; Downs, Robert T.; Yokochi, A. F. T.; Quiros, Miguel; Lutterotti, Luca; Manakova, Elena; Butkus, Justas; Moeck, Peter; Le Bail, Armel
Journal of Applied Crystallography (2009), 42 (4), 726-729CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
The Crystallog. Open Database (COD), which is a project that aims to gather all available inorg., metal-org. and small org. mol. structural data in one database, is described. The database adopts an open-access model. The COD currently contains ∼80,000 entries in crystallog. information file format, with nearly full coverage of the International Union of Crystallog. publications, and is growing in size and quality.
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Kroll, P.; Milko, M. Theoretical Investigation of the Solid State Reaction of Silicon Nitride and Silicon Dioxide Forming Silicon Oxynitride (Si₂N₂O) under Pressure. Z. Für Anorg. Allg. Chem. 2003, 629 (10), 1737– 1750, DOI: 10.1002/zaac.200300122
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Henkelman, G.; Jónsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113 (22), 9978– 9985, DOI: 10.1063/1.1323224
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Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
Henkelman, Graeme; Jonsson, Hannes
Journal of Chemical Physics (2000), 113 (22), 9978-9985CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
An improved way of estg. the local tangent in the nudged elastic band method for finding min. energy paths is presented. In systems where the force along the min. energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the min. energy path. We show how the kinks arise and present an improved way of estg. the local tangent which solves the problem. The task of finding an accurate energy and configuration for the saddle point is also discussed and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point. Both methods only require the first deriv. of the energy and can, therefore, easily be applied in plane wave based d.-functional theory calcns. Examples are given from studies of the exchange diffusion mechanism in a Si crystal, Al addimer formation on the Al(100) surface, and dissociative adsorption of CH4 on an Ir(111) surface.
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Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113 (22), 9901– 9904, DOI: 10.1063/1.1329672
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A climbing image nudged elastic band method for finding saddle points and minimum energy paths
Henkelman, Graeme; Uberuaga, Blas P.; Jonsson, Hannes
Journal of Chemical Physics (2000), 113 (22), 9901-9904CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A modification of the nudged elastic band method for finding min. energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring consts. are used to increase the d. of images near the top of the energy barrier to get an improved est. of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir(111) and H2 on Si(100) using plane wave based d. functional theory are presented.
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Sheppard, D.; Terrell, R.; Henkelman, G. Optimization Methods for Finding Minimum Energy Paths. J. Chem. Phys. 2008, 128 (13), 134106, DOI: 10.1063/1.2841941
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Optimization methods for finding minimum energy paths
Sheppard, Daniel; Terrell, Rye; Henkelman, Graeme
Journal of Chemical Physics (2008), 128 (13), 134106/1-134106/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A comparison of chain-of-states based methods for finding min. energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local min. is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equiv. and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approx. inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the min. than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based d. functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111). (c) 2008 American Institute of Physics.
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Smidstrup, S.; Pedersen, A.; Stokbro, K.; Jónsson, H. Improved Initial Guess for Minimum Energy Path Calculations. J. Chem. Phys. 2014, 140 (21), 214106, DOI: 10.1063/1.4878664
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Improved initial guess for minimum energy path calculations
Smidstrup, Soeren; Pedersen, Andreas; Stokbro, Kurt; Jonsson, Hannes
Journal of Chemical Physics (2014), 140 (21), 214106/1-214106/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A method is presented for generating a good initial guess of a transition path between given initial and final states of a system without evaluation of the energy. An objective function surface is constructed using an interpolation of pairwise distances at each discretization point along the path and the nudged elastic band method then used to find an optimal path on this image dependent pair potential (IDPP) surface. This provides an initial path for the more computationally intensive calcns. of a min. energy path on an energy surface obtained, for example, by ab initio or d. functional theory. The optimal path on the IDPP surface is significantly closer to a min. energy path than a linear interpolation of the Cartesian coordinates and, therefore, reduces the no. of iterations needed to reach convergence and averts divergence in the electronic structure calcns. when atoms are brought too close to each other in the initial path. The method is illustrated with three examples: (1) rotation of a Me group in an ethane mol., (2) an exchange of atoms in an island on a crystal surface, and (3) an exchange of two Si-atoms in amorphous silicon. In all three cases, the computational effort in finding the min. energy path with DFT was reduced by a factor ranging from 50% to an order of magnitude by using an IDPP path as the initial path. The time required for parallel computations was reduced even more because of load imbalance when linear interpolation of Cartesian coordinates was used. (c) 2014 American Institute of Physics.
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Hackler, R. A.; McAnally, M. O.; Schatz, G. C.; Stair, P. C.; Van Duyne, R. P. Identification of Dimeric Methylalumina Surface Species during Atomic Layer Deposition Using Operando Surface-Enhanced Raman Spectroscopy. J. Am. Chem. Soc. 2017, 139 (6), 2456– 2463, DOI: 10.1021/jacs.6b12709
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Identification of Dimeric Methylalumina Surface Species during Atomic Layer Deposition Using Operando Surface-Enhanced Raman Spectroscopy
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Journal of the American Chemical Society (2017), 139 (6), 2456-2463CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Operando surface-enhanced Raman spectroscopy (SERS) was used to successfully identify hitherto unknown dimeric methylalumina surface species during at. layer deposition (ALD) on a silver surface. Vibrational modes assocd. with the bridging moieties of both trimethylaluminum (TMA) and dimethylaluminum chloride (DMACl) surface species were found during ALD. The appropriate monomer vibrational modes were found to be absent as a result of the selective nature of SERS. D. functional theory (DFT) calcns. were also performed to locate and identify the expected vibrational modes. An operando localized surface plasmon resonance (LSPR) spectrometer was utilized to account for changes in SER signal as a function of the no. of ALD cycles. DMACl surface species were unable to be measured after multiple ALD cycles as a result of a loss in SERS enhancement and shift in LSPR. This work highlights how operando optical spectroscopy by SERS and LSPR scattering are useful for probing the identity and structure of the surface species involved in ALD and, ultimately, catalytic reactions on these support materials.
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Kim, M.; Kim, S.; Shong, B. Adsorption of Dimethylaluminum Isopropoxide (DMAI) on the Al₂O₃ Surface: A Machine-Learning Potential Study. J. Sci. Adv. Mater. Devices 2024, 9, 100754 DOI: 10.1016/j.jsamd.2024.100754
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Xu, W.; Haeve, M. G. N.; Lemaire, P. C.; Sharma, K.; Hausmann, D. M.; Agarwal, S. Functionalization of the SiO₂ Surface with Aminosilanes to Enable Area-Selective Atomic Layer Deposition of Al₂O₃. Langmuir 2022, 38 (2), 652– 660, DOI: 10.1021/acs.langmuir.1c02216
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Functionalization of the SiO2 Surface with Aminosilanes to Enable Area-Selective Atomic Layer Deposition of Al2O3
Xu, Wanxing; Haeve, Mitchel G. N.; Lemaire, Paul C.; Sharma, Kashish; Hausmann, Dennis M.; Agarwal, Sumit
Langmuir (2022), 38 (2), 652-660CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
Small-mol. inhibitors are promising for achieving area-selective at. layer deposition (ALD) due to their excellent compatibility with industrial processes. In this work, we report on growth inhibition during ALD of Al2O3 on a SiO2 surface functionalized with small-mol. aminosilane inhibitors. The SiO2 surface was prefunctionalized with bis(dimethylamino)dimethylsilane (BDMADMS) and (N,N-dimethylamino)trimethylsilane (DMATMS) through soln. and the vapor phase. ALD of Al2O3 using dimethylaluminum isopropoxide (DMAI) and H2O was performed on these functionalized SiO2 surfaces. Our in situ four-wavelength ellipsometry measurements show superior growth inhibition when using BDMADMS and DMATMS in sequence over just using BDMADMS or DMATMS. Vapor phase functionalization provided a growth delay of ∼30 ALD cycles, which was similar to soln.-based functionalization. Using in situ attenuated total reflection Fourier transmission IR spectroscopy, we show that the interaction of DMAI with SiO2 surfaces leads to pronounced changes in absorbance for the Si-O-Si phonon mode without any detectable DMAI absorbed on the SiO2 surface. Detailed anal. of the IR spectra revealed that the decrease in absorbance was likely caused by the coordination of Al in DMAI to O atoms in surface Si-O-Si bonds without the breaking the Si-O-Si bonds. Finally, we postulate that a minimal amt. of DMAI remains adsorbed on surface Si-O-Si bonds even after purging, which can initiate ALD of Al2O3 on functionalized SiO2: this highlights the need for higher surface coverage for enhanced steric blocking.
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89
Seo, S.; Yeo, B. C.; Han, S. S.; Yoon, C. M.; Yang, J. Y.; Yoon, J.; Yoo, C.; Kim, H.; Lee, Y.; Lee, S. J.; Myoung, J.-M.; Lee, H.-B.-R.; Kim, W.-H.; Oh, I.-K.; Kim, H. Reaction Mechanism of Area-Selective Atomic Layer Deposition for Al₂O₃ Nanopatterns. ACS Appl. Mater. Interfaces 2017, 9 (47), 41607– 41617, DOI: 10.1021/acsami.7b13365
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Reaction mechanism of area-selective atomic layer deposition for Al2O3 nanopatterns
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ACS Applied Materials & Interfaces (2017), 9 (47), 41607-41617CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
The reaction mechanism of area-selective at. layer deposition (AS-ALD) of Al2O3 thin films using self-assembled monolayers (SAMs) was systematically investigated by theor. and exptl. studies. Trimethylaluminum (TMA) and H2O were used as the precursor and oxidant, resp., with octadecylphosphonic acid (ODPA) as an SAM to block Al2O3 film formation. However, Al2O3 layers began to form on the ODPA SAMs after several cycles, despite reports that CH3-terminated SAMs cannot react with TMA. We showed that TMA does not react chem. with the SAM but is phys. adsorbed, acting as a nucleation site for Al2O3 film growth. Moreover, the amt. of physisorbed TMA was affected by the partial pressure. By controlling it, we developed a new AS-ALD Al2O3 process with high selectivity, which produces films of ∼60 nm thickness over 370 cycles. The successful deposition of Al2O3 thin film patterns using this process is a breakthrough technique in the field of nanotechnol.
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90
Yu, P.; Merkx, M. J. M.; Tezsevin, I.; Lemaire, P. C.; Hausmann, D. M.; Sandoval, T. E.; Kessels, W. M. M.; Mackus, A. J. M. Blocking Mechanisms in Area-Selective ALD by Small Molecule Inhibitors of Different Sizes: Steric Shielding versus Chemical Passivation. Appl. Surf. Sci. 2024, 665, 160141 DOI: 10.1016/j.apsusc.2024.160141
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Ande, C. K.; Elliott, S. D.; Kessels, W. M. M. First-Principles Investigation of C–H Bond Scission and Formation Reactions in Ethane, Ethene, and Ethyne Adsorbed on Ru(0001). J. Phys. Chem. C 2014, 118 (46), 26683– 26694, DOI: 10.1021/jp5069363
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First-Principles Investigation of C-H Bond Scission and Formation Reactions in Ethane, Ethene, and Ethyne Adsorbed on Ru(0001)
Ande, Chaitanya Krishna; Elliott, Simon D.; Kessels, Wilhelmus M. M.
Journal of Physical Chemistry C (2014), 118 (46), 26683-26694CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
We have studied all possible elementary reactions (including isomerization reactions) involved in the interaction of CH4 (methane), CH3CH3 (ethane), CH2CH2 (ethene), and CHCH (ethyne) with the Ru(0001) surface using d. functional theory based first-principles calcns. Site preference and adsorption energies for all the reaction intermediates and activation energies for the elementary reactions are calcd. From the calcd. adsorption and activation energies, we find that dehydrogenation of the adsorbates is thermodynamically favored in agreement with expts. Dehydrogenation of CH (methylidyne) is the most difficult in the dehydrogenation of CH4 (methane). CH3CH3 (ethane), CH2CH2 (ethene), and CHCH (ethyne) dehydrogenate through the CH3C (ethylidyne) intermediate. Of the five possible pathways for the prodn. of CH3C (ethylidyne), the CH2CH (ethenyl)-CH2C (ethenylidene) pathway is the most dominant. In the case of ethene, the ethynyl-ethenylidene pathway is also the dominant pathway on Pt(111). Comparison of α and β-C-H bond scission reactions, important for the Fischer-Tropsch process, shows that alkenes should be the major products compared to the formation of alkynes. Dehydrogenation becomes slightly favorable at lower coverages of the hydrocarbon fragments while hydrogenation becomes slightly unfavorable. In addn. to resolving the dominant pathways during decompn. of the above hydrocarbons, the activation energies calcd. in this paper can also be used in the modeling of processes that involve the considered elementary reactions at longer length and time scales.
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Shirazi, M.; Elliott, S. D. Cooperation between Adsorbates Accounts for the Activation of Atomic Layer Deposition Reactions. Nanoscale 2015, 7 (14), 6311– 6318, DOI: 10.1039/C5NR00900F
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Cooperation between adsorbates accounts for the activation of atomic layer deposition reactions
Shirazi, Mahdi; Elliott, Simon D.
Nanoscale (2015), 7 (14), 6311-6318CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
Atomic layer deposition (ALD) is a technique for producing conformal layers of nanometer-scale thickness, used com. in non-planar electronics and increasingly in other high-tech industries. ALD depends on self-limiting surface chem. but the mechanistic reasons for this are not understood in detail. Here we demonstrate, by first-principle calcns. of growth of HfO2 from Hf(N(CH3)2)4-H2O and HfCl4-H2O and growth of Al2O3 from Al(CH3)3-H2O, that, for all these precursors, co-adsorption plays an important role in ALD. By this we mean that previously-inert adsorbed fragments can become reactive once sufficient nos. of mols. adsorb in their neighborhood during either precursor pulse. Through the calcd. activation energies, this 'cooperative' mechanism is shown to have a profound influence on proton transfer and ligand desorption, which are crucial steps in the ALD cycle. Depletion of reactive species and increasing coordination cause these reactions to self-limit during one precursor pulse, but to be re-activated via the cooperative effect in the next pulse. This explains the self-limiting nature of ALD.
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Shirazi, M.; Elliott, S. D. Multiple Proton Diffusion and Film Densification in Atomic Layer Deposition Modeled by Density Functional Theory. Chem. Mater. 2013, 25 (6), 878– 889, DOI: 10.1021/cm303630e
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Abstract
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Figure 1
Figure 1. Dimerization reaction of Al precursors shown at the example of TMA with the equilibrium constant K_diss for the dissociation defined via the partial pressures p_monomer and p_dimer and standard pressure p₀.
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Figure 2
Figure 2. Set of aluminum precursors investigated in this study grouped in substance classes 1–4. Abbreviations used in the ALD literature are shown in parentheses where available.
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Figure 3
Figure 3. Dimer structures with one example of each substance class.
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Figure 4
Figure 4. Dissociated dimer fraction (DDF) as a function of total pressure of the system at 200 °C for the tested set of Al precursors. Common ALD pressures from 10^–4 to 10^–2 bar are highlighted in gray.
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Figure 5
Figure 5. Dissociated dimer fraction (DDF) versus temperature at total pressure of the system of 1.73 × 10^–4 bar (130 mTorr) for the tested set of Al precursors. A common temperature range for ALD is highlighted in gray.
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Figure 6
Figure 6. EDA on the dimer bond of the Al precursors. All energy terms are given in kJ·mol^–1.
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Figure 7
Figure 7. Adsorption of dimers (a) (2-Cl)₂, (b) (4)₂, and (c) (1-Me)₂ and monomers (d) 2-Cl, (e) 4, and (f) 1-Me on SiO₂. Bond lengths are shown in Å, and adsorption energies in kJ·mol^–1. The dispersion contribution to the adsorption energy is shown in brackets. Color code: (soft) pink─Al, green─Cl, black─C, red─O, and white─H. All hydrogens attached to carbon are omitted for clarity.
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Figure 8
Figure 8. Adsorption of dimers (a) (2-Cl)₂, (b) (4)₂, and (c) (1-Me)₂ and monomers (d) 2-Cl, (e) 4, and (f) 1-Me on the methoxy group of the small-molecule inhibitor TMPS. Bond lengths are shown in Å and adsorption energies in kJ·mol^–1. The dispersion contribution to the adsorption energy is shown in brackets. Color code: (soft) pink─Al, green─Cl, black─C, red─O, white─H. All hydrogens attached to carbon are omitted for clarity.
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Figure 9
Figure 9. Reaction path of adsorption and dissociation of (3)₂ on SiO₂. (a) Physisorbed dimer (PS). (b) First intermediary minimum (IM1). (c) Second intermediary minimum (IM2). (d) First partially dissociated structure (DISS1). (e) Transition state for the second dissociation step (TS). (f) Fully dissociated dimer (DISS2).
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References
This article references 93 other publications.
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  A review. The concept of the transformation of mols. to materials has been well established in the field of chem. vapor deposition (CVD) and at. layer deposition (ALD). However, materials scientists are always on the lookout for new materials with enhanced functionalities for eventual application in devices. New materials have become an integral part of modern day technol. esp. in the field of microelectronics and optoelectronics. The importance of CVD and ALD processes for high throughput and coating on complex device geometries is well recognized for these applications. Since the underlying precursor chem. is one of the main parameters that dictate these processes, there is still scope for further exploratory research, in terms of precursor design and development that suits the demands of advanced technologies. A wide range of precursors can be used to realize specific class of materials but the trend recently has been driven by the reduced thermal budget needed esp. for components employed in microelectronics and optoelectronics. The chronol. developments in precursors for CVD/ALD point out that, designer precursors are set to play a major role in the field of materials engineering. The desirable growth conditions could be achieved with a proper selection of compds. which may stem from the available class of metal complexes or even engineered compds. In this review article, the concept of utilizing 'old chemistries' for new CVD and ALD applications will be highlighted focussing on some representative functional materials namely group IV and rare earth oxides. Some of the very recent results on precursor development carried out in the Inorg. Materials Chem. research group at Bochum, Germany are summarized.
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8. 8
  Hatanpää, T.; Ritala, M.; Leskelä, M. Precursors as Enablers of ALD Technology: Contributions from University of Helsinki. Coord. Chem. Rev. 2013, 257 (23–24), 3297– 3322, DOI: 10.1016/j.ccr.2013.07.002
  There is no corresponding record for this reference.
9. 9
  Oh, I.-K.; Sandoval, T. E.; Liu, T.-L.; Richey, N. E.; Nguyen, C. T.; Gu, B.; Lee, H.-B.-R.; Tonner-Zech, R.; Bent, S. F. Elucidating the Reaction Mechanism of Atomic Layer Deposition of Al₂O₃ with a Series of Al(CH₃)_xCl_3–x and Al(C_yH_2y+1)₃ Precursors. J. Am. Chem. Soc. 2022, 144 (26), 11757– 11766, DOI: 10.1021/jacs.2c03752
  9
  Elucidating reaction mechanism of atomic layer deposition of alumina with series of aluminum based precursors
  Oh, Il-Kwon; Sandoval, Tania E.; Liu, Tzu-Ling; Richey, Nathaniel E.; Nguyen, Chi Thang; Gu, Bonwook; Lee, Han-Bo-Ram; Tonner-Zech, Ralf; Bent, Stacey F.
  Journal of the American Chemical Society (2022), 144 (26), 11757-11766CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The adsorption of metalorg. and metal halide precursors on the SiO2 surface plays an essential role in thin-film deposition processes such as at. layer deposition (ALD). In the case of aluminum oxide (Al2O3) films, the growth characteristics are influenced by the precursor structure, which controls both chem. reactivity and the geometrical constraints during deposition. In this work, a systematic study using a series of Al(CH3)xCl3-x (x = 0, 1, 2, and 3) and Al(CyH2y+1)3 (y = 1, 2, and 3) precursors is carried out using a combination of exptl. spectroscopic techniques together with d. functional theory calcns. and Monte Carlo simulations to analyze differences across precursor mols. Results show that reactivity and steric hindrance mutually influence the ALD surface reaction. The increase in the no. of chlorine ligands in the precursor shifts the deposition temp. higher, an effect attributed to more favorable binding of the intermediate species due to higher Lewis acidity, while differences between precursors in film growth per cycle are shown to originate from variations in adsorption activation barriers and size-dependent satn. coverage. Comparison between the theor. and exptl. results indicates that the Al(CyH2y+1)3 precursors are favored to undergo two ligand exchange reactions upon adsorption at the surface, whereas only a single Cl-ligand exchange reaction is energetically favorable upon adsorption by the AlCl3 precursor. By pursuing the first-principles design of ALD precursors combined with exptl. anal. of thin-film growth, this work enables a robust understanding of the effect of precursor chem. on ALD processes.
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10. 10
  Potts, S. E.; Kessels, W. M. M. Energy-Enhanced Atomic Layer Deposition for More Process and Precursor Versatility. Coord. Chem. Rev. 2013, 257 (23–24), 3254– 3270, DOI: 10.1016/j.ccr.2013.06.015
  There is no corresponding record for this reference.
11. 11
  Leskelä, M.; Ritala, M. Atomic Layer Deposition (ALD): From Precursors to Thin Film Structures. Thin Solid Films 2002, 409 (1), 138– 146, DOI: 10.1016/S0040-6090(02)00117-7
  11
  Atomic layer deposition (ALD): from precursors to thin film structures
  Leskela, Markku; Ritala, Mikko
  Thin Solid Films (2002), 409 (1), 138-146CODEN: THSFAP; ISSN:0040-6090. (Elsevier Science B.V.)
  A review. The principles of the at. layer deposition (ALD) method are presented emphasizing the importance of precursor and surface chem. With a proper adjustment of the exptl. conditions, i.e., temps. and pulsing times, the growth proceeds via saturative steps. Selected recent ALD processes developed for films used in microelectronics are described as examples. These include deposition of oxide films for dielecs., and nitride and metal films for metalizations. The use of a plasma source to form radicals is expanding the selection of ALD films to metals. Plasma-enhanced ALD also facilitates the deposition of nitride films at low temps.
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12. 12
  Parsons, G. N.; Clark, R. D. Area-Selective Deposition: Fundamentals, Applications, and Future Outlook. Chem. Mater. 2020, 32 (12), 4920– 4953, DOI: 10.1021/acs.chemmater.0c00722
  12
  Area-Selective Deposition: Fundamentals, Applications, and Future Outlook
  Parsons, Gregory N.; Clark, Robert D.
  Chemistry of Materials (2020), 32 (12), 4920-4953CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
  A review. This review provides an overview of area-selective thin film deposition (ASD) with a primary focus on vapor-phase thin film formation via chem. vapor deposition (CVD) and at. layer deposition (ALD). Area-selective deposition has been successfully implemented in microelectronic processes, but most approaches to date rely on high-temp. reactions to achieve the desired substrate sensitivity. Continued size and performance scaling of microelectronics, as well as new materials, patterning methods, and device fabrication schemes are seeking solns. for new low-temp. ( < 400°C) ASD methods for dielecs., metals, and org. thin films. To provide an overview of the ASD field, this article critically reviews key challenges that must be overcome for ASD to be successful in microelectronics and other fields, including descriptions of current process application needs. We provide an overview of basic mechanisms in film nucleation during CVD and ALD and summarize current known ASD approaches for semiconductors, metals, dielecs., and org. materials. For a few key materials, selectivity is quant. compared for different reaction precursors, giving important insight into needs for favorable reactant and reaction design. We summarize current limitations of ASD and future opportunities that could be achieved using advanced bottom-up at. scale processes.
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13. 13
  Bonvalot, M.; Vallée, C.; Mannequin, C.; Jaffal, M.; Gassilloud, R.; Possémé, N.; Chevolleau, T. Area Selective Deposition Using Alternate Deposition and Etch Super-Cycle Strategies. Dalton Trans. 2022, 51, 442– 450, DOI: 10.1039/D1DT03456A
  There is no corresponding record for this reference.
14. 14
  Oh, I.-K.; Sandoval, T. E.; Liu, T.-L.; Richey, N. E.; Bent, S. F. Role of Precursor Choice on Area-Selective Atomic Layer Deposition. Chem. Mater. 2021, 33 (11), 3926– 3935, DOI: 10.1021/acs.chemmater.0c04718
  14
  Role of Precursor Choice on Area-Selective Atomic Layer Deposition
  Oh, Il-Kwon; Sandoval, Tania E.; Liu, Tzu-Ling; Richey, Nathaniel E.; Bent, Stacey F.
  Chemistry of Materials (2021), 33 (11), 3926-3935CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
  Area-selective at. layer deposition (AS-ALD) is a highly sought-after strategy for the fabrication of next-generation electronics. This work reveals how key precursor design parameters strongly influence the efficacy of AS-ALD by comparing a series of precursors possessing the same metal center but different ligands. When the no. of Me and chloride groups in Al(CH3)xCl3-x (x = 0, 2, and 3) and the chain length of alkyl ligands in AlCyH2y+1 (y = 1 and 2) are changed, the effect of precursor chem. (reactivity and mol. size) on the selectivity is elucidated. The results show that optimized parameters for the Al2O3 ALD processes on a self-assembled monolayer (SAM)-terminated substrate, which serves as the nongrowth surface, differ significantly from those on a Si substrate. Chlorine-contg. precursors need a much longer purging time on the SAMs because of a stronger Lewis acidity compared to that of alkyl precursors. With reoptimized conditions, the ALD of Al2O3 using the Al(C2H5)3 precursor is blocked most effectively by SAM inhibitors, whereas the widely employed Al(CH3)3 precursor is blocked least effectively among the precursors tested. Finally, we show that a selectivity exceeding 0.98 is achieved for up to 75 ALD cycles with Al(C2H5)3, for which 6 nm of Al2O3 film grows selectively on SiO2-covered Si. Quantum chem. calcns. show significant differences in the energetics of dimer formation across the Al precursors, with only ∼ 1% of AlCl3 and Al(CH3)2Cl precursors but 99% of the alkyl precursors, Al(CH3)3 and Al(C2H5)3, existing as monomers at 200°C. We propose that a combination of precursor reactivity and effective mol. size affects the blocking of the different precursors, explaining why Al(C2H5)3, with weaker Lewis acidity and relatively large size, exhibits the best blocking results.
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15. 15
  Kim, H. G.; Kim, M.; Gu, B.; Khan, M. R.; Ko, B. G.; Yasmeen, S.; Kim, C. S.; Kwon, S.-H.; Kim, J.; Kwon, J.; Jin, K.; Cho, B.; Chun, J.-S.; Shong, B.; Lee, H.-B.-R. Effects of Al Precursors on Deposition Selectivity of Atomic Layer Deposition of Al₂O₃ Using Ethanethiol Inhibitor. Chem. Mater. 2020, 32 (20), 8921– 8929, DOI: 10.1021/acs.chemmater.0c02798
  15
  Effects of Al Precursors on Deposition Selectivity of Atomic Layer Deposition of Al2O3 Using Ethanethiol Inhibitor
  Kim, Hyun Gu; Kim, Miso; Gu, Bonwook; Khan, Mohammad Rizwan; Ko, Byeong Guk; Yasmeen, Sumaira; Kim, Chang Su; Kwon, Se-Hun; Kim, Jiyong; Kwon, Junhyuck; Jin, Kwangseon; Cho, Byungchul; Chun, J. -S.; Shong, Bonggeun; Lee, Han-Bo-Ram
  Chemistry of Materials (2020), 32 (20), 8921-8929CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
  Area-selective at. layer deposition (AS-ALD) is a promising bottom-up patterning approach for fabricating conformal thin films. One of the current challenges with respect to AS-ALD is the deficiency of the surface inhibitor used for fabricating nanoscale three-dimensional structures. In this study, a vapor-deliverable small inhibitor called ethanethiol (ET) that thermally adsorbs on surfaces was used for the AS-ALD of Al2O3. The inhibitor selectively adsorbed on Co and Cu substrates but not on the SiO2 substrate, allowing for the selective deactivation of Co and Cu substrates in Al2O3 ALD. The use of dimethylaluminum isopropoxide (DMAI) as the Al precursor resulted in better inhibition than the use of trimethylaluminum (TMA). Various exptl. and theor. methods, including water contact angle measurements, spectroscopic ellipsometry, XPS, d. functional theory calcns., and Monte Carlo simulations, were used to elucidate the process of AS-ALD using ET. Dimerization of the DMAI precursor is considered to be a governing factor for its high deposition selectivity, while the probability of this phenomenon is very low for the TMA precursor. The current study provides insight into the selectivity of AS-ALD from the perspective of the chem. reaction and an opportunity to improve selectivity via precursor selection.
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16. 16
  Yarbrough, J.; Pieck, F.; Grigjanis, D.; Oh, I.-K.; Maue, P.; Tonner-Zech, R.; Bent, S. F. Tuning Molecular Inhibitors and Aluminum Precursors for the Area-Selective Atomic Layer Deposition of Al₂O₃. Chem. Mater. 2022, 34 (10), 4646– 4659, DOI: 10.1021/acs.chemmater.2c00513
  16
  Tuning Molecular Inhibitors and Aluminum Precursors for the Area-Selective Atomic Layer Deposition of Al2O3
  Yarbrough, Josiah; Pieck, Fabian; Grigjanis, Daniel; Oh, Il-Kwon; Maue, Patrick; Tonner-Zech, Ralf; Bent, Stacey F.
  Chemistry of Materials (2022), 34 (10), 4646-4659CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
  Using both expt. and d. functional theory (DFT), we study a group of small mol. inhibitors (SMIs) and aluminum precursors to det. how the interplay between the inhibitor and precursor can affect the selectivity of at. layer deposition (ALD) on different materials. We compare several polyfunctional alkoxysilanes as the SMIs and trimethylaluminum and triethylaluminum as the ALD precursors. Spectroscopic ellipsometry shows a direct correlation between blocking performance and the no. of hydrolysable alkoxy groups on the SMI. DFT results suggest that SMI polymn. at the surface may play an important role in producing a satd. passivation layer, while also indicating that defects in this layer develop primarily due to interactions with the co-reactant rather than with the aluminum ALD precursors. XPS and Auger electron spectroscopy reveal that alkoxysilane SMIs can support the selective growth of up to 4 nm of Al2O3 on copper substrates when the optimal ALD precursor/SMI pair is selected: triethylaluminum as the ALD precursor, water as the co-reactant, and trimethoxypropylsilane as the inhibitor for SiO2 substrates. The blocking performance is much poorer with trimethylaluminum as the precursor, an effect further confirmed by in situ Fourier transform IR spectroscopy. These differences suggest a strong effect of precursor ligand size in achieving AS-ALD with SMIs. In addn., we show that tuning both inhibitor and precursor functionality for the system of interest is required to optimize selective growth.
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17. 17
  Merkx, M. J. M.; Angelidis, A.; Mameli, A.; Li, J.; Lemaire, P. C.; Sharma, K.; Hausmann, D. M.; Kessels, W. M. M.; Sandoval, T. E.; Mackus, A. J. M. Relation between Reactive Surface Sites and Precursor Choice for Area-Selective Atomic Layer Deposition Using Small Molecule Inhibitors. J. Phys. Chem. C 2022, 126 (10), 4845– 4853, DOI: 10.1021/acs.jpcc.1c10816
  There is no corresponding record for this reference.
18. 18
  Kim, H.; Kim, M.; Kim, B.; Shong, B. Adsorption Mechanism of Dimeric Ga Precursors in Metalorganic Chemical Vapor Deposition of Gallium Nitride. J. Vac. Sci. Technol. A 2023, 41 (6), 063409 DOI: 10.1116/6.0002966
  There is no corresponding record for this reference.
19. 19
  Baev, A. K.; Shishko, M. A.; Korneev, N. N. Thermodynamics and Thermochemistry of Organoaluminum Compounds. Russ. J. Gen. Chem. 2002, 72 (9), 1389– 1395, DOI: 10.1023/A:1021669611400
  There is no corresponding record for this reference.
20. 20
  Laubengayer, A. W.; Gilliam, W. F. The Alkyls of the Third Group Elements. I. Vapor Phase Studies of the Alkyls of Aluminum, Gallium and Indium. J. Am. Chem. Soc. 1941, 63 (2), 477– 479, DOI: 10.1021/ja01847a031
  20
  The alkyls of the third-group elements. I. Vapor-phase studies of the alkyls of aluminum, gallium and indium
  Laubengayer, A. W.; Gilliam, W. F.
  Journal of the American Chemical Society (1941), 63 (), 477-9CODEN: JACSAT; ISSN:0002-7863.
  The following data were obtained for Al(CH3)3, Al(C2H5)3, Ga(C2H5)3, and for solid and liquid In(CH3)3: b. p., m. p., consts. for the formula log p = -A/T + B, molar heat of vaporization, molar heat of fusion and Trouton's const. The data indicate that Al(CH3)3 exists as the dimer at 70°. It dissociates with increase in temp., the heat of dissocn. from 100 to 155° being 20.2 kg.-cal. Al(C2H5)3 is 12% assocd. to the dimer at 150°. Ga(C2H5)3 and In(CH3)3 are monomeric in the vapor state.
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21. 21
  Smith, M. B. The Monomer–dimer Equilibria of Liquid Aluminum Alkyls. J. Organomet. Chem. 1972, 46 (1), 31– 49, DOI: 10.1016/S0022-328X(00)90473-X
  There is no corresponding record for this reference.
22. 22
  Almenningen, A.; Halvorsen, S.; Haaland, A.; Pihlaja, K.; Schaumburg, K.; Ehrenberg, L. A Gas Phase Electron Diffraction Investigation of the Molecular Structures of Trimethylaluminium Monomer and Dimer. Acta Chem. Scand. 1971, 25, 1937– 1945, DOI: 10.3891/acta.chem.scand.25-1937
  22
  Gas phase electron diffraction investigation of the molecular structures of trimethylaluminum monomer and dimer
  Almenningen, A.; Halvorsen, S.; Haaland, A.
  Acta Chemica Scandinavica (1947-1973) (1971), 25 (6), 1937-45CODEN: ACSAA4; ISSN:0001-5393.
  The mol. structures of Me3Al and (Me3Al)2 were detd. by gas phase electron diffraction. The monomer has D3h symmetry with freely rotating methyl groups. The 3 independent structure parameters are R(C-H) = 1.113(3) Å, R(Al-C) = 1.957(3) Å, and ∠Al-C-II = 111.7° (0.5°). The electron scattering pattern for the dimer is consistent with a model with D2h symmetry. The main mol. parameters are R(C-H) mean = 1.117(2) Å, R(Al-C) terminal = 1.957(3) Å, R(Al-C) bridge = 2.140(4) Å, R(Al-Al) = 2.619(5) Å, ∠Cterm-Al-Cterm = 117.3° (1.5°), and ∠Cbr-Al-Cbr = 104.5° (0.1°).
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23. 23
  Lee, S. Y.; Luo, B.; Sun, Y.; White, J. M.; Kim, Y. Thermal Decomposition of Dimethylaluminum Isopropoxide on Si(100). Appl. Surf. Sci. 2004, 222 (1–4), 234– 242, DOI: 10.1016/j.apsusc.2003.08.016
  There is no corresponding record for this reference.
24. 24
  Champagne, B.; Mosley, D. H.; Fripiat, J. G.; André, J.-M.; Bernard, A.; Bettonville, S.; François, P.; Momtaz, A. Dimerization versus Complexation of Triethylaluminum and Diethylaluminum Chloride: An Ab Initio Determination of Structures, Energies of Formation, and Vibrational Spectra. J. Mol. Struct. Theochem. 1998, 454 (2–3), 149– 159, DOI: 10.1016/S0166-1280(98)00285-1
  There is no corresponding record for this reference.
25. 25
  Hay, J. N.; Hooper, P. G.; Robb, J. C. Monomer-Dimer Equilibria of Triethylaluminium. J. Organomet. Chem. 1971, 28 (2), 193– 204, DOI: 10.1016/S0022-328X(00)84567-2
  25
  Monomer-dimer equilibriums of triethylaluminum
  Hay, James N.; Hooper, P. G.; Robb, James C.
  Journal of Organometallic Chemistry (1971), 28 (2), 193-204CODEN: JORCAI; ISSN:0022-328X.
  The assocn.-dissocn. equil. for trimethyl- and triethylaluminum are discussed in order to resolve the apparently anomalous range of values quoted in the literature. Thermodynamic liq.-vapor equil. data, the temp. dependence of the NMR spectra, and the range of Arrhenius parameters listed for the addn. reactions of the tri-n-alkylaluminums to n-alkenes are considered.
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26. 26
  Hiraoka, Y. S.; Mashita, M. Ab Initio Study on the Dimer Structures of Trimethylaluminum and Dimethylaluminumhydride. J. Cryst. Growth 1994, 145 (1–4), 473– 477, DOI: 10.1016/0022-0248(94)91094-4
  26
  Ab initio study on the dimer structures of trimethylaluminum and dimethylaluminum hydride
  Hiraoka, Yoshiko Someya; Mashita, Masao
  Journal of Crystal Growth (1994), 145 (1-4), 473-7CODEN: JCRGAE; ISSN:0022-0248. (Elsevier)
  The dimer structures of trimethylaluminum (AlMe3, TMA) and dimethylaluminum hydride (AlHMe2, DMAH) were studied using ab initio MO calcns. The structure of the TMA dimer is C2h; however, that of the DMAH dimer is D2h. The dissocn. energy of the TMA dimer was only 4.2 kcal/mol, while that of the DMAH dimer was 32.3 kcal/mol, which is considerably larger than the TMA dimer. The dimer contributes directly to surface reactions when DMAH is used as the source material for ALE.
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27. 27
  Wang, N. X.; Venkatesh, K.; Wilson, A. K. Behavior of Density Functionals with Respect to Basis Set. 3. Basis Set Superposition Error. J. Phys. Chem. A 2006, 110 (2), 779– 784, DOI: 10.1021/jp0541664
  27
  Behavior of Density Functionals with Respect to Basis Set. 3. Basis Set Superposition Error
  Wang, Nick X.; Venkatesh, Krishna; Wilson, Angela K.
  Journal of Physical Chemistry A (2006), 110 (2), 779-784CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  The impact of basis set superposition error (BSSE) upon mol. properties detd. using the d. functionals B3LYP, B3PW91, B3P86, BLYP, BPW91, and BP86 in combination with the correlation consistent basis sets [cc-pVnZ, where n = D(2), T(3), Q(4), and 5] for a set of first-row closed-shell mols. has been examd. Correcting for BSSE enables the irregular convergence behavior in mol. properties such as dissocn. energies with respect to increasing basis set size, noted in earlier studies, to be improved. However, for some mols. and functional combinations, BSSE correction alone does not improve the irregular convergence behavior.
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28. 28
  Davidson, E. R.; Chakravorty, S. J. A Possible Definition of Basis Set Superposition Error. Chem. Phys. Lett. 1994, 217 (1–2), 48– 54, DOI: 10.1016/0009-2614(93)E1356-L
  There is no corresponding record for this reference.
29. 29
  Atkins, P. Physikalische Chemie, 2. Auflage.; VCH Verlagsgesellschaft GmbH: Weinheim, 1996.
  There is no corresponding record for this reference.
30. 30
  Marques, E. A.; De Gendt, S.; Pourtois, G.; Van Setten, M. J. Benchmarking First-Principles Reaction Equilibrium Composition Prediction. Molecules 2023, 28 (9), 3649, DOI: 10.3390/molecules28093649
  There is no corresponding record for this reference.
31. 31
  Ritala, M.; Leskelä, M.; Dekker, J.-P.; Mutsaers, C.; Soininen, P. J.; Skarp, J. Perfectly Conformal TiN and Al₂O₃ Films Deposited by Atomic Layer Deposition. Chem. Vap. Depos. 1999, 5 (1), 7– 9, DOI: 10.1002/(SICI)1521-3862(199901)5:1<7::AID-CVDE7>3.0.CO;2-J
  31
  Perfectly conformal TiN and Al2O3 films deposited by atomic layer deposition
  Ritala, Mikko; Leskela, Markku; Dekker, Jan-Pieter; Mutsaers, Cees; Soininen, Pekka J.; Skarp, Jarmo
  Chemical Vapor Deposition (1999), 5 (1), 7-9CODEN: CVDEFX; ISSN:0948-1907. (Wiley-VCH Verlag GmbH)
  TiN films were made with a small scale research reactor where the inlets of the sep. precursor flow channels are close to the substrates and the Al2O3 films were deposited using a reactor where the substrates are much further away from the precursor inlets and thus the secondary processes have no effect on the film uniformity. The surface-controlled, self-limiting film growth mechanism of at. layer deposition made it possible to deposit TiN and Al2O3 films uniformly into deep trenches, and the trenches were filled completely without keyhole formation.
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32. 32
  Cremers, V.; Puurunen, R. L.; Dendooven, J. Conformality in Atomic Layer Deposition: Current Status Overview of Analysis and Modelling. Appl. Phys. Rev. 2019, 6 (2), 021302 DOI: 10.1063/1.5060967
  32
  Conformality in atomic layer deposition: Current status overview of analysis and modelling
  Cremers, Veronique; Puurunen, Riikka L.; Dendooven, Jolien
  Applied Physics Reviews (2019), 6 (2), 021302/1-021302/43CODEN: APRPG5; ISSN:1931-9401. (American Institute of Physics)
  A review. Atomic layer deposition (ALD) relies on alternated, self-limiting reactions between gaseous reactants and an exposed solid surface to deposit highly conformal coatings with a thickness controlled at the submonolayer level. In this work, we aim to review the current status of knowledge about the conformality of ALD processes. We describe the basic concepts related to the conformality of ALD, including an overview of relevant gas transport regimes, definitions of exposure and sticking probability, and a distinction between different ALD growth types obsd. in high aspect ratio structures. The different types of high aspect ratio structures and characterization approaches that have been used for quantifying the conformality of ALD processes are reviewed. The different classes of models are discussed with special attention for the key assumptions typically used in the different modeling approaches. The influence of certain assumptions on simulated deposition thickness profiles is illustrated and discussed with the aim of shedding light on how deposition thickness profiles can provide insights into factors governing the surface chem. of ALD processes. We hope that this review can serve as a starting point and ref. work for new and expert researchers interested in the conformality of ALD and, at the same time, will trigger new research to further improve our understanding of this famous characteristic of ALD processes. (c) 2019 American Institute of Physics.
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33. 33
  Buttera, S. C.; Mandia, D. J.; Barry, S. T. Tris(Dimethylamido)Aluminum(III): An Overlooked Atomic Layer Deposition Precursor. J. Vac. Sci. Technol. Vac. Surf. Films 2017, 35 (1), 01B128 DOI: 10.1116/1.4972469
  There is no corresponding record for this reference.
34. 34
  Gladfelter, W. L. Selective Metalization by Chemical Vapor Deposition. Chem. Mater. 1993, 5 (10), 1372– 1388, DOI: 10.1021/cm00034a004
  34
  Selective metalization by chemical vapor deposition
  Gladfelter, Wayne L.
  Chemistry of Materials (1993), 5 (10), 1372-88CODEN: CMATEX; ISSN:0897-4756.
  The selective growth of metal films by chem. vapor deposition processes is reviewed with 139 refs. A working definition of selectivity, based on the relative rates of nucleation on the growth and nongrowth surfaces, is proposed. After consideration of the factors that effect nucleation and a brief description of the methods used to measure selectivity, a review of the selective depositions of tungsten, copper, and aluminum is presented.
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35. 35
  Neese, F. The ORCA Program System. WIREs Comput. Mol. Sci. 2012, 2 (1), 73– 78, DOI: 10.1002/wcms.81
  35
  The ORCA program system
  Neese, Frank
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (1), 73-78CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  A review. ORCA is a general-purpose quantum chem. program package that features virtually all modern electronic structure methods (d. functional theory, many-body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger mols., transition metal complexes, and their spectroscopic properties. ORCA uses std. Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.
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36. 36
  Neese, F. Software Update: The ORCA Program System, Version 4.0. WIREs Comput. Mol. Sci. 2018, 8 (1), e1327 DOI: 10.1002/wcms.1327
  There is no corresponding record for this reference.
37. 37
  Neese, F.; Wennmohs, F.; Becker, U.; Riplinger, C. The ORCA Quantum Chemistry Program Package. J. Chem. Phys. 2020, 152 (22), 224108, DOI: 10.1063/5.0004608
  37
  The ORCA quantum chemistry program package
  Neese, Frank; Wennmohs, Frank; Becker, Ute; Riplinger, Christoph
  Journal of Chemical Physics (2020), 152 (22), 224108CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  In this contribution to the special software-centered issue, the ORCA program package is described. We start with a short historical perspective of how the project began and go on to discuss its current feature set. ORCA has grown into a rather comprehensive general-purpose package for theor. research in all areas of chem. and many neighboring disciplines such as materials sciences and biochem. ORCA features d. functional theory, a range of wavefunction based correlation methods, semi-empirical methods, and even force-field methods. A range of solvation and embedding models is featured as well as a complete intrinsic to ORCA quantum mechanics/mol. mechanics engine. A specialty of ORCA always has been a focus on transition metals and spectroscopy as well as a focus on applicability of the implemented methods to "real-life" chem. applications involving systems with a few hundred atoms. In addn. to being efficient, user friendly, and, to the largest extent possible, platform independent, ORCA features a no. of methods that are either unique to ORCA or have been first implemented in the course of the ORCA development. Next to a range of spectroscopic and magnetic properties, the linear- or low-order single- and multi-ref. local correlation methods based on pair natural orbitals (domain based local pair natural orbital methods) should be mentioned here. Consequently, ORCA is a widely used program in various areas of chem. and spectroscopy with a current user base of over 22 000 registered users in academic research and in industry. (c) 2020 American Institute of Physics.
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38. 38
  Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132 (15), 154104, DOI: 10.1063/1.3382344
  38
  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
  Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
  Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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39. 39
  Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32 (7), 1456– 1465, DOI: 10.1002/jcc.21759
  39
  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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40. 40
  Grimme, S. Accurate Description of van Der Waals Complexes by Density Functional Theory Including Empirical Corrections. J. Comput. Chem. 2004, 25 (12), 1463– 1473, DOI: 10.1002/jcc.20078
  40
  Accurate description of van der Waals complexes by density functional theory including empirical corrections
  Grimme, Stefan
  Journal of Computational Chemistry (2004), 25 (12), 1463-1473CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  An empirical method to account for van der Waals interactions in practical calcns. in the framework of the d. functional theory (termed DFT-D) was tested for a wide variety of mol. complexes. As in previous schemes, the dispersive energy was described by damped interat. potentials of the form C6R-6. The use of pure, gradient-cor. d. functionals (BLYP and PBE), together with the resoln.-of-the-identity (RI) approxn. for the Coulomb operator, allows very efficient computations for large systems. In contrast to the previous work, extended AO basis sets of polarized TZV or QZV quality were employed, which reduced the basis set superposition error to a negligible extend. By using a global scaling factor for the at. C6 coeffs., the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes was found to be insignificant if steep damping functions were employed. The method was applied to a total of 29 complexes of atoms and small mols. (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene·H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theor. or exptl. results for binding energies and intermol. distances is obtained. For stacked arom. systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to std. MP2 treatments that systematically over-bind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chem. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calcns. of the interaction energies.
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41. 41
  Bykov, D.; Petrenko, T.; Izsák, R.; Kossmann, S.; Becker, U.; Valeev, E.; Neese, F. Efficient Implementation of the Analytic Second Derivatives of Hartree–Fock and Hybrid DFT Energies: A Detailed Analysis of Different Approximations. Mol. Phys. 2015, 113 (13–14), 1961– 1977, DOI: 10.1080/00268976.2015.1025114
  There is no corresponding record for this reference.
42. 42
  Riplinger, C.; Neese, F. An Efficient and near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138 (3), 034106 DOI: 10.1063/1.4773581
  42
  An efficient and near linear scaling pair natural orbital based local coupled cluster method
  Riplinger, Christoph; Neese, Frank
  Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
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43. 43
  Pracht, P.; Bohle, F.; Grimme, S. Automated Exploration of the Low-Energy Chemical Space with Fast Quantum Chemical Methods. Phys. Chem. Chem. Phys. 2020, 22 (14), 7169– 7192, DOI: 10.1039/C9CP06869D
  43
  Automated exploration of the low-energy chemical space with fast quantum chemical methods
  Pracht, Philipp; Bohle, Fabian; Grimme, Stefan
  Physical Chemistry Chemical Physics (2020), 22 (14), 7169-7192CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  We propose and discuss an efficient scheme for the in silico sampling for parts of the mol. chem. space by semiempirical tight-binding methods combined with a meta-dynamics driven search algorithm. The focus of this work is set on the generation of proper thermodn. ensembles at a quantum chem. level for conformers, but similar procedures for protonation states, tautomerism and non-covalent complex geometries are also discussed. The conformational ensembles consisting of all significantly populated min. energy structures normally form the basis of further, mostly DFT computational work, such as the calcn. of spectra or macroscopic properties. By using basic quantum chem. methods, electronic effects or possible bond breaking/formation are accounted for and a very reasonable initial energetic ranking of the candidate structures is obtained. Due to the huge computational speedup gained by the fast low-cost quantum chem. methods, overall short computation times even for systems with hundreds of atoms (typically drug-sized mols.) are achieved. Furthermore, specialized applications, such as sampling with implicit solvation models or constrained conformational sampling for transition-states, metal-, surface-, or noncovalently bound complexes are discussed, opening many possible applications in modern computational chem. and drug discovery. The procedures have been implemented in a freely available computer code called CREST, that makes use of the fast and reliable GFNn-xTB methods.
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44. 44
  Grimme, S. Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations. J. Chem. Theory Comput. 2019, 15 (5), 2847– 2862, DOI: 10.1021/acs.jctc.9b00143
  44
  Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations
  Grimme, Stefan
  Journal of Chemical Theory and Computation (2019), 15 (5), 2847-2862CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The semiempirical tight-binding based quantum chem. method GFN2-xTB is used in the framework of meta-dynamics (MTD) to globally explore chem. compd., conformer, and reaction space. The biasing potential given as a sum of Gaussian functions is expressed with the root-mean-square-deviation (RMSD) in Cartesian space as a metric for the collective variables. This choice makes the approach robust and generally applicable to three common problems (i.e., conformer search, chem. reaction space exploration in a virtual nanoreactor, and for guessing reaction paths). Because of the inherent locality of the at. RMSD, functional group or fragment selective treatments are possible facilitating the investigation of catalytic processes where, for example, only the substrate is thermally activated. Due to the approx. character of the GFN2-xTB method, the resulting structure ensembles require further refinement with more sophisticated, for example, d. functional or wave function theory methods. However, the approach is extremely efficient running routinely on common laptop computers in minutes to hours of computation time even for realistically sized mols. with a few hundred atoms. Furthermore, the underlying potential energy surface for mols. contg. almost all elements (Z = 1-86) is globally consistent including the covalent dissocn. process and electronically complicated situations in, for example, transition metal systems. As examples, thermal decompn., ethyne oligomerization, the oxidn. of hydrocarbons (by oxygen and a P 450 enzyme model), a Miller-Urey model system, a thermally forbidden dimerization, and a multistep intramol. cyclization reaction are shown. For typical conformational search problems of org. drug mols., the new MTD(RMSD) algorithm yields lower energy structures and more complete conformer ensembles at reduced computational effort compared with its already well performing predecessor.
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45. 45
  Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38 (6), 3098– 3100, DOI: 10.1103/PhysRevA.38.3098
  45
  Density-functional exchange-energy approximation with correct asymptotic behavior
  Becke, A. D.
  Physical Review A: Atomic, Molecular, and Optical Physics (1988), 38 (6), 3098-100CODEN: PLRAAN; ISSN:0556-2791.
  Current gradient-cor. d.-functional approxns. for the exchange energies of at. and mol. systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy d. A gradient-cor. exchange-energy functional is given with the proper asymptotic limit. This functional, contg. only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of at. systems with remarkable accuracy, surpassing the performance of previous functionals contg. two parameters or more.
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46. 46
  Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98 (7), 5648– 5652, DOI: 10.1063/1.464913
  46
  Density-functional thermochemistry. III. The role of exact exchange
  Becke, Axel D.
  Journal of Chemical Physics (1993), 98 (7), 5648-52CODEN: JCPSA6; ISSN:0021-9606.
  Despite the remarkable thermochem. accuracy of Kohn-Sham d.-functional theories with gradient corrections for exchange-correlation, the author believes that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional (contg. local-spin-d., gradient, and exact-exchange terms) is tested for 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total at. energies of first- and second-row systems. This functional performs better than previous functionals with gradient corrections only, and fits expt. atomization energies with an impressively small av. abs. deviation of 2.4 kcal/mol.
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47. 47
  Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37 (2), 785– 789, DOI: 10.1103/PhysRevB.37.785
  47
  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
  Lee, Chengteh; Yang, Weitao; Parr, Robert G.
  Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.
  A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
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48. 48
  Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7 (18), 3297, DOI: 10.1039/b508541a
  48
  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
  Weigend, Florian; Ahlrichs, Reinhart
  Physical Chemistry Chemical Physics (2005), 7 (18), 3297-3305CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 mols. representing (nearly) all elements-except lanthanides-in their common oxidn. states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, d. functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.
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49. 49
  Weigend, F. Accurate Coulomb-Fitting Basis Sets for H to Rn. Phys. Chem. Chem. Phys. 2006, 8 (9), 1057, DOI: 10.1039/b515623h
  49
  Accurate Coulomb-fitting basis sets for H to Rn
  Weigend, Florian
  Physical Chemistry Chemical Physics (2006), 8 (9), 1057-1065CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approx. Coulomb energies in conjunction with orbital basis sets of split valence, triple zeta valence and quadruple zeta valence quality with errors of typically below ca. 0.15 kJ mol-1 per atom; this was demonstrated in conjunction with the recently developed orbital basis sets of types def2-SV(P), def2-TZVP and def2-QZVPP for a large set of small mols. representing (nearly) each element in all of its common oxidn. states. These auxiliary bases are slightly more than three times larger than orbital bases of split valence quality. Compared to non-approximated treatments, computation times for the Coulomb part are reduced by a factor of ca. 8 for def2-SV(P) orbital bases, ca. 25 for def2-TZVP and ca. 100 for def2-QZVPP orbital bases.
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50. 50
  Becke, A. D. A Multicenter Numerical Integration Scheme for Polyatomic Molecules. J. Chem. Phys. 1988, 88 (4), 2547– 2553, DOI: 10.1063/1.454033
  50
  A multicenter numerical integration scheme for polyatomic molecules
  Becke, A. D.
  Journal of Chemical Physics (1988), 88 (4), 2547-53CODEN: JCPSA6; ISSN:0021-9606.
  A simple scheme is proposed for decompn. of mol. functions into single-center components. The problem of three-dimensional integration in mol. systems thus reduces to a sum of one-center, at.-like integrations which are treated using std. numerical techniques in spherical polar coordinates. The resulting method is tested on representative diat. and polyat. systems for which we obtain five- or six-figure accuracy using a few thousand integration points per atom.
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51. 51
  Liakos, D. G.; Neese, F. Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory. J. Chem. Theory Comput. 2015, 11 (9), 4054– 4063, DOI: 10.1021/acs.jctc.5b00359
  51
  Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory
  Liakos, Dimitrios G.; Neese, Frank
  Journal of Chemical Theory and Computation (2015), 11 (9), 4054-4063CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calcns. with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calcns., even for small and medium sized mols. where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calcn., it is useful to compare the method against modern d. functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid d. functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals cor. counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean abs. deviation of less than 1 kcal/mol to the ref. values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.
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52. 52
  Truhlar, D. G. Basis-Set Extrapolation. Chem. Phys. Lett. 1998, 294 (1–3), 45– 48, DOI: 10.1016/S0009-2614(98)00866-5
  52
  Basis-set extrapolation
  Truhlar, Donald G.
  Chemical Physics Letters (1998), 294 (1,2,3), 45-48CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
  A proposal for extrapolation of correlated electronic structure calcns. based on correlation-consistent polarized double- and triple-zeta basis sets is evaluated. Optimum exponents are presented for sep. extrapolating the Hartree-Fock and correlation energies, and the method yields energies that are more accurate than those from straight correlation-consistent polarized sextuple-zeta calcns. at less than 1% of the cost. For the test problems, the root-mean-square deviations from the complete basis limit are 1.3-2.4 kcal/mol for the extrapolated calcns. and 3.0-4.4 kcal/mol for the polarized sextuple-zeta calcns.
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53. 53
  Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90 (2), 1007– 1023, DOI: 10.1063/1.456153
  53
  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
  Dunning, Thom H., Jr.
  Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
  Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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54. 54
  Wedler, G.; Freund, H.-J. Lehrbuch Der Physikalischen Chemie, 6. Auflage.; WILEY-VCH: Weinheim, 2012.
  There is no corresponding record for this reference.
55. 55
  Jensen, F. Introduction to Computational Chemistry, 1 ed.; JOHN WILEY & SONS: Chichester, 1999.
  There is no corresponding record for this reference.
56. 56
  AMS. http://www.scm.com/ Accessed 3 July 2024.
  There is no corresponding record for this reference.
57. 57
  Van Lenthe, E.; Baerends, E. J. Optimized Slater-type Basis Sets for the Elements 1–118. J. Comput. Chem. 2003, 24 (9), 1142– 1156, DOI: 10.1002/jcc.10255
  57
  Optimized Slater-type basis sets for the elements 1-118
  Van Lenthe, E.; Baerends, E. J.
  Journal of Computational Chemistry (2003), 24 (9), 1142-1156CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral at. and diat. oxide calcns. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. At. tests reveal that, on av., the abs. basis set error of 0.03 kcal/mol in the d. functional calcn. of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the av. abs. difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This av. abs. basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approx. 4 kcal/mol for the all electron basis sets of double zeta quality. The mol. tests reveal that, on av., the calcd. atomization energies of 118 neutral diat. oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approx. 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calcn. of the atomization energies of the group 2 and group 14 diat. oxides. The basis sets that are optimized for calcns. using the frozen core approxn. (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On av., the use of these frozen core basis sets give at. basis set errors that are approx. twice as large as the corresponding all electron basis set errors and mol. atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calcns. larger errors are found, esp. for the heavier elements, due to the addnl. approxn. that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.
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58. 58
  Chong, D. P.; Van Lenthe, E.; Van Gisbergen, S.; Baerends, E. J. Even-tempered Slater-type Orbitals Revisited: From Hydrogen to Krypton. J. Comput. Chem. 2004, 25 (8), 1030– 1036, DOI: 10.1002/jcc.20030
  58
  Even-tempered Slater-type orbitals revisited: from hydrogen to krypton
  Chong, Delano P.; Van Lenthe, Erik; Van Gisbergen, Stan; Baerends, Evert Jan
  Journal of Computational Chemistry (2004), 25 (8), 1030-1036CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  Even-tempered STO basis sets were developed in 1973, based on total at. energy optimization. Here, we revisit ET STOs and propose new sets based on past experience and recent computational studies. From preliminary at. and mol. tests, these sets are shown to be very well balanced and to perform, at lower cost, almost as well as a very large (close to complete) basis set.
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59. 59
  Kitaura, K.; Morokuma, K. A New Energy Decomposition Scheme for Molecular Interactions within the Hartree-Fock Approximation. Int. J. Quantum Chem. 1976, 10 (2), 325– 340, DOI: 10.1002/qua.560100211
  59
  A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation
  Kitaura, Kazuo; Morokuma, Keiji
  International Journal of Quantum Chemistry (1976), 10 (2), 325-40CODEN: IJQCB2; ISSN:0020-7608.
  In an extension of previous work (M., et al., 1974; M., 1971; S. Iwata and M., 1975; S. Yamabe and M., 1975), a new method was developed for calcg. sep. the components of mol. interaction energy within the Hartree-Fock approxn. The Hartree-Fock MO's of the isolated mols. are used as the basis set for construction of the Fock matrix for the supermol. Then certain blocks of this matrix are set to zero, subject to specific boundary conditions for the supermol. MO's; the resultant matrix is diagonalized iteratively to obtain the desired energy components. This method has an advantage over the previous method in the explicit definition of the charge-transfer energy, placing it on an equal status with the exchange and polarization terms. The new method is compared with existing perturbation methods, and was also applied to decomp. the energy and electron d. of (H2O)2.
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60. 60
  Ziegler, T.; Rauk, A. Carbon Monoxide, Carbon Monosulfide, Molecular Nitrogen, Phosphorus Trifluoride, and Methyl Isocyanide as σ Donors and π Acceptors. A Theoretical Study by the Hartree-Fock-Slater Transition-State Method. Inorg. Chem. 1979, 18 (7), 1755– 1759, DOI: 10.1021/ic50197a006
  60
  Carbon monoxide, carbon monosulfide, molecular nitrogen, phosphorus trifluoride, and methyl isocyanide as σ donors and π acceptors. A theoretical study by the Hartree-Fock-Slater transition-state method
  Ziegler, Tom; Rauk, Arvi
  Inorganic Chemistry (1979), 18 (7), 1755-9CODEN: INOCAJ; ISSN:0020-1669.
  Hartree-Fock-Slater calcns. were carried out on Ni(CO)3L for a no. of different ligands (L) in order to investigate the abilities of the ligands to act as σ donors and π acceptors. The order, based on extent of electron transfer, for σ donation is CS ≃ CO > CNCH3 > N2 ∼ PF3 and for π back-bonding is CNCH3 > CS > CO > PF3 > N2. The contributions to the total bonding energy between Ni(CO)3 and L from σ donation and π back-donation were evaluated by the Hartree-Fock-Slater transition-state method, and the same method was used to optimize the Ni-L bond distances. Calcns. on the stretching frequency νCO of carbon monoxide complexed to Ni(CO)3 showed that νCO is decreased by the π back-donation but is increased by the steric interaction energy between Ni(CO)3 and CO. Thus the decrease in νCO is not a reliable measure of the extent of π back-bonding in the metal-ligand bond. The calcd. influence on νCO from σ donation was negligible.
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61. 61
  Ziegler, T.; Rauk, A. A Theoretical Study of the Ethylene-Metal Bond in Complexes between Cu⁺, Ag⁺, Au⁺, Pt⁰, or Pt²⁺ and Ethylene, Based on the Hartree-Fock-Slater Transition-State Method. Inorg. Chem. 1979, 18 (6), 1558– 1565, DOI: 10.1021/ic50196a034
  61
  A theoretical study of the ethylene-metal bond in complexes between copper(1+), silver(1+), gold(1+), platinum(0) or platinum(2+) and ethylene, based on the Hartree-Fock-Slater transition-state method
  Ziegler, Tom; Rauk, Arvi
  Inorganic Chemistry (1979), 18 (6), 1558-65CODEN: INOCAJ; ISSN:0020-1669.
  An anal. based on the Hartree-Fock-Slater (HFS) transition-state method is given of the metal-ethylene bond in the ion-ethylene complexes Cu+-C2H4, Ag+-C2H4, and Au+-C2H4 as well as in complexes with PtCl3- and Pt(PH3)2. The contribution from σ-donation to the bonding energy was equally important for all three complexes with the ions, whereas the contribution from the π back-donation was important only for the Cu complex. A similar anal. of Pt(Cl)3--C2H4 and Pt(PH3)2-C2H4 showed that the position of ethylene perpendicular to the coordination plane of Pt(Cl)3- in Zeise's salt is caused by steric factors, whereas the position of ethylene in Pt(PH3)2-C2H4 is due to electronic factors, specifically π back-donations.
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62. 62
  Bickelhaupt, F. M.; Nibbering, N. M. M.; Van Wezenbeek, E. M.; Baerends, E. J. Central Bond in the Three CṄ Dimers NC-CN, CN-CN and CN-NC: Electron Pair Bonding and Pauli Repulsion Effects. J. Phys. Chem. 1992, 96 (12), 4864– 4873, DOI: 10.1021/j100191a027
  There is no corresponding record for this reference.
63. 63
  Tonner, R.; Frenking, G. Divalent Carbon(0) Chemistry, Part 1: Parent Compounds. Chem. – Eur. J. 2008, 14 (11), 3260– 3272, DOI: 10.1002/chem.200701390
  63
  Divalent carbon(0) chemistry, part 1: parent compounds
  Tonner, Ralf; Frenking, Gernot
  Chemistry - A European Journal (2008), 14 (11), 3260-3272CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
  Quantum-chem. calcns. with DFT (BP86) and ab initio methods [MP2, SCS-MP2, CCSD(T)] have been carried out for the mols. C(PH3)2 (1), C(PMe3)2 (2), C-(PPh3)2 (3), C(PPh3)(CO) (4), C(CO)2 (5), C(NHCH)2 (6), C(NHCMe)2 (7) (Me2N)2C=C=C(NMe2)2 (8), and NHC (9), where NHC=N-heterocyclic carbene and NHCMe=N-methyl-substituted NHC. The electronic structure in 1-9 was analyzed with charge- and energy-partitioning methods. The results show that the bonding situations in L2C compds. 1-8 can be interpreted in terms of donor-acceptor interactions between closed-shell ligands L and a carbon atom which has two lone-pair orbitals L→C←L. This holds particularly for the carbodiphosphoranes 1-3 where L=PR3, which therefore are classified as divalent carbon(0) compds. The NBO anal. suggests that the best Lewis structures for the carbodicarbenes 6 and 7 where L is a NHC ligand have C=C=C double bonds as in the tetraaminoallene 8. However, the Lewis structures of 6-8, in which two lone-pair orbitals at the central carbon atom are enforced, have only a slightly higher residual d. Visual inspection of the frontier orbitals of the latter species reveals their pronounced lone-pair character, which suggests that even the quasi-linear tetraaminoallene 8 is a "masked" divalent carbon(0) compd. This explains the very shallow bending potential of 8. The same conclusion is drawn for phosphoranylketene 4 and for carbon sub-oxide (5), which according to the bonding anal. have hidden double-lone-pair character. The AIM anal. and the EDA calcns. support the assignment of carbodiphosphoranes as divalent carbon(0) compds., while NHC 9 is characterized as a divalent carbon(II) compd. The L→C(1D) donor-acceptor bonds are roughly twice as strong as the resp. L→BH3 bond.
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64. 64
  Pecher, L.; Tonner, R. Deriving Bonding Concepts for Molecules, Surfaces, and Solids with Energy Decomposition Analysis for Extended Systems. WIREs Comput. Mol. Sci. 2019, 9 (4), e1401 DOI: 10.1002/wcms.1401
  There is no corresponding record for this reference.
65. 65
  Bickelhaupt, F. M.; Baerends, E. J. Kohn-Sham Density Functional Theory: Predicting and Understanding Chemistry. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; Wiley, 2000; Vol. 15, pp 1– 86. DOI: 10.1002/9780470125922.ch1 .
  There is no corresponding record for this reference.
66. 66
  Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22 (9), 931– 967, DOI: 10.1002/jcc.1056
  66
  Chemistry with ADF
  Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T.
  Journal of Computational Chemistry (2001), 22 (9), 931-967CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  A review with 241 refs. We present the theor. and tech. foundations of the Amsterdam D. Functional (ADF) program with a survey of the characteristics of the code (numerical integration, d. fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chem. shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, at. VDD charges). In the Applications section we discuss the phys. model of the electronic structure and the chem. bond, i.e., the Kohn-Sham MO (MO) theory, and illustrate the power of the Kohn-Sham MO model in conjunction with the ADF-typical fragment approach to quant. understand and predict chem. phenomena. We review the "Activation-strain TS interaction" (ATS) model of chem. reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in org. chem. or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochem. (structure and bonding of DNA) and of time-dependent d. functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the anal. of chem. phenomena.
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67. 67
  Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47 (1), 558– 561, DOI: 10.1103/PhysRevB.47.558
  67
  Ab initio molecular dynamics of liquid metals
  Kresse, G.; Hafner, J.
  Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.
  The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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68. 68
  Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal–Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49 (20), 14251– 14269, DOI: 10.1103/PhysRevB.49.14251
  68
  Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium
  Kresse, G.; Hafner, J.
  Physical Review B: Condensed Matter and Materials Physics (1994), 49 (20), 14251-69CODEN: PRBMDO; ISSN:0163-1829.
  The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.
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69. 69
  Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6 (1), 15– 50, DOI: 10.1016/0927-0256(96)00008-0
  69
  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
  Kresse, G.; Furthmuller, J.
  Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)
  The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
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70. 70
  Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54 (16), 11169– 11186, DOI: 10.1103/PhysRevB.54.11169
  70
  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
  Kresse, G.; Furthmueller, J.
  Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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71. 71
  Kresse, G.; Hafner, J. Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition Elements. J. Phys.: Condens. Matter 1994, 6 (40), 8245– 8257, DOI: 10.1088/0953-8984/6/40/015
  71
  Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements
  Kresse, G.; Hafner, J.
  Journal of Physics: Condensed Matter (1994), 6 (40), 8245-57CODEN: JCOMEL; ISSN:0953-8984.
  The construction of accurate pseudopotentials with good convergence properties for the first-row and transition elements is discussed. By combining an improved description of the pseudo-wavefunction inside the cut-off radius with the concept of ultrasoft pseudopotentials introduced by Vanderbilt optimal compromise between transferability and plane-wave convergence can be achieved. With the new pseudopotentials, basis sets with no more than 75-100 plane waves per atom are sufficient to reproduce the results obtained with the most accurate norm-conserving pseudopotentials.
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72. 72
  Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865– 3868, DOI: 10.1103/PhysRevLett.77.3865
  72
  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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73. 73
  Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59 (3), 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
  73
  From ultrasoft pseudopotentials to the projector augmented-wave method
  Kresse, G.; Joubert, D.
  Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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74. 74
  Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13 (12), 5188– 5192, DOI: 10.1103/PhysRevB.13.5188
  There is no corresponding record for this reference.
75. 75
  Pack, J. D.; Monkhorst, H. J. Special Points for Brillouin-Zone Integrations”─a Reply. Phys. Rev. B 1977, 16 (4), 1748– 1749, DOI: 10.1103/PhysRevB.16.1748
  There is no corresponding record for this reference.
76. 76
  Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44 (6), 1272– 1276, DOI: 10.1107/S0021889811038970
  76
  VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
  Momma, Koichi; Izumi, Fujio
  Journal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
  VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.
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77. 77
  Gražulis, S.; Chateigner, D.; Downs, R. T.; Yokochi, A. F. T.; Quirós, M.; Lutterotti, L.; Manakova, E.; Butkus, J.; Moeck, P.; Le Bail, A. Crystallography Open Database – an Open-Access Collection of Crystal Structures. J. Appl. Crystallogr. 2009, 42 (4), 726– 729, DOI: 10.1107/S0021889809016690
  77
  Crystallography Open Database - an open-access collection of crystal structures
  Grazulis, Saulius; Chateigner, Daniel; Downs, Robert T.; Yokochi, A. F. T.; Quiros, Miguel; Lutterotti, Luca; Manakova, Elena; Butkus, Justas; Moeck, Peter; Le Bail, Armel
  Journal of Applied Crystallography (2009), 42 (4), 726-729CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
  The Crystallog. Open Database (COD), which is a project that aims to gather all available inorg., metal-org. and small org. mol. structural data in one database, is described. The database adopts an open-access model. The COD currently contains ∼80,000 entries in crystallog. information file format, with nearly full coverage of the International Union of Crystallog. publications, and is growing in size and quality.
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78. 78
  Kroll, P.; Milko, M. Theoretical Investigation of the Solid State Reaction of Silicon Nitride and Silicon Dioxide Forming Silicon Oxynitride (Si₂N₂O) under Pressure. Z. Für Anorg. Allg. Chem. 2003, 629 (10), 1737– 1750, DOI: 10.1002/zaac.200300122
  There is no corresponding record for this reference.
79. 79
  Henkelman, G.; Jónsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113 (22), 9978– 9985, DOI: 10.1063/1.1323224
  79
  Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
  Henkelman, Graeme; Jonsson, Hannes
  Journal of Chemical Physics (2000), 113 (22), 9978-9985CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  An improved way of estg. the local tangent in the nudged elastic band method for finding min. energy paths is presented. In systems where the force along the min. energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the min. energy path. We show how the kinks arise and present an improved way of estg. the local tangent which solves the problem. The task of finding an accurate energy and configuration for the saddle point is also discussed and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point. Both methods only require the first deriv. of the energy and can, therefore, easily be applied in plane wave based d.-functional theory calcns. Examples are given from studies of the exchange diffusion mechanism in a Si crystal, Al addimer formation on the Al(100) surface, and dissociative adsorption of CH4 on an Ir(111) surface.
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80. 80
  Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113 (22), 9901– 9904, DOI: 10.1063/1.1329672
  80
  A climbing image nudged elastic band method for finding saddle points and minimum energy paths
  Henkelman, Graeme; Uberuaga, Blas P.; Jonsson, Hannes
  Journal of Chemical Physics (2000), 113 (22), 9901-9904CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A modification of the nudged elastic band method for finding min. energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring consts. are used to increase the d. of images near the top of the energy barrier to get an improved est. of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir(111) and H2 on Si(100) using plane wave based d. functional theory are presented.
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81. 81
  Sheppard, D.; Terrell, R.; Henkelman, G. Optimization Methods for Finding Minimum Energy Paths. J. Chem. Phys. 2008, 128 (13), 134106, DOI: 10.1063/1.2841941
  81
  Optimization methods for finding minimum energy paths
  Sheppard, Daniel; Terrell, Rye; Henkelman, Graeme
  Journal of Chemical Physics (2008), 128 (13), 134106/1-134106/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A comparison of chain-of-states based methods for finding min. energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local min. is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equiv. and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approx. inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the min. than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based d. functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111). (c) 2008 American Institute of Physics.
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82. 82
  Smidstrup, S.; Pedersen, A.; Stokbro, K.; Jónsson, H. Improved Initial Guess for Minimum Energy Path Calculations. J. Chem. Phys. 2014, 140 (21), 214106, DOI: 10.1063/1.4878664
  82
  Improved initial guess for minimum energy path calculations
  Smidstrup, Soeren; Pedersen, Andreas; Stokbro, Kurt; Jonsson, Hannes
  Journal of Chemical Physics (2014), 140 (21), 214106/1-214106/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A method is presented for generating a good initial guess of a transition path between given initial and final states of a system without evaluation of the energy. An objective function surface is constructed using an interpolation of pairwise distances at each discretization point along the path and the nudged elastic band method then used to find an optimal path on this image dependent pair potential (IDPP) surface. This provides an initial path for the more computationally intensive calcns. of a min. energy path on an energy surface obtained, for example, by ab initio or d. functional theory. The optimal path on the IDPP surface is significantly closer to a min. energy path than a linear interpolation of the Cartesian coordinates and, therefore, reduces the no. of iterations needed to reach convergence and averts divergence in the electronic structure calcns. when atoms are brought too close to each other in the initial path. The method is illustrated with three examples: (1) rotation of a Me group in an ethane mol., (2) an exchange of atoms in an island on a crystal surface, and (3) an exchange of two Si-atoms in amorphous silicon. In all three cases, the computational effort in finding the min. energy path with DFT was reduced by a factor ranging from 50% to an order of magnitude by using an IDPP path as the initial path. The time required for parallel computations was reduced even more because of load imbalance when linear interpolation of Cartesian coordinates was used. (c) 2014 American Institute of Physics.
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83. 83
  Hackler, R. A.; McAnally, M. O.; Schatz, G. C.; Stair, P. C.; Van Duyne, R. P. Identification of Dimeric Methylalumina Surface Species during Atomic Layer Deposition Using Operando Surface-Enhanced Raman Spectroscopy. J. Am. Chem. Soc. 2017, 139 (6), 2456– 2463, DOI: 10.1021/jacs.6b12709
  83
  Identification of Dimeric Methylalumina Surface Species during Atomic Layer Deposition Using Operando Surface-Enhanced Raman Spectroscopy
  Hackler, Ryan A.; McAnally, Michael O.; Schatz, George C.; Stair, Peter C.; Van Duyne, Richard P.
  Journal of the American Chemical Society (2017), 139 (6), 2456-2463CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Operando surface-enhanced Raman spectroscopy (SERS) was used to successfully identify hitherto unknown dimeric methylalumina surface species during at. layer deposition (ALD) on a silver surface. Vibrational modes assocd. with the bridging moieties of both trimethylaluminum (TMA) and dimethylaluminum chloride (DMACl) surface species were found during ALD. The appropriate monomer vibrational modes were found to be absent as a result of the selective nature of SERS. D. functional theory (DFT) calcns. were also performed to locate and identify the expected vibrational modes. An operando localized surface plasmon resonance (LSPR) spectrometer was utilized to account for changes in SER signal as a function of the no. of ALD cycles. DMACl surface species were unable to be measured after multiple ALD cycles as a result of a loss in SERS enhancement and shift in LSPR. This work highlights how operando optical spectroscopy by SERS and LSPR scattering are useful for probing the identity and structure of the surface species involved in ALD and, ultimately, catalytic reactions on these support materials.
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84. 84
  Kim, M.; Shong, B. Dimerization Equilibrium of Group 13 Precursors for Vapor Deposition of Thin Films. Comput. Theor. Chem. 2024, 1242, 114953 DOI: 10.1016/j.comptc.2024.114953
  There is no corresponding record for this reference.
85. 85
  Kim, M.; Kim, S.; Shong, B. Adsorption of Dimethylaluminum Isopropoxide (DMAI) on the Al₂O₃ Surface: A Machine-Learning Potential Study. J. Sci. Adv. Mater. Devices 2024, 9, 100754 DOI: 10.1016/j.jsamd.2024.100754
  There is no corresponding record for this reference.
86. 86
  Henrickson, C. H.; Eyman, D. P. Lewis Acidity of Alanes. Interactions of Trimethylalane with Sulfides. Inorg. Chem. 1967, 6 (8), 1461– 1465, DOI: 10.1021/ic50054a006
  There is no corresponding record for this reference.
87. 87
  Wellmann, P. P.; Pieck, F.; Tonner-Zech, R. An Atomistic Picture of Buildup and Degradation Reactions in Area-Selective Atomic Layer Deposition with a Small Molecule Inhibitor. Chem. Mater. 2024, 36, 7343, DOI: 10.1021/acs.chemmater.4c01269
  There is no corresponding record for this reference.
88. 88
  Xu, W.; Haeve, M. G. N.; Lemaire, P. C.; Sharma, K.; Hausmann, D. M.; Agarwal, S. Functionalization of the SiO₂ Surface with Aminosilanes to Enable Area-Selective Atomic Layer Deposition of Al₂O₃. Langmuir 2022, 38 (2), 652– 660, DOI: 10.1021/acs.langmuir.1c02216
  88
  Functionalization of the SiO2 Surface with Aminosilanes to Enable Area-Selective Atomic Layer Deposition of Al2O3
  Xu, Wanxing; Haeve, Mitchel G. N.; Lemaire, Paul C.; Sharma, Kashish; Hausmann, Dennis M.; Agarwal, Sumit
  Langmuir (2022), 38 (2), 652-660CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
  Small-mol. inhibitors are promising for achieving area-selective at. layer deposition (ALD) due to their excellent compatibility with industrial processes. In this work, we report on growth inhibition during ALD of Al2O3 on a SiO2 surface functionalized with small-mol. aminosilane inhibitors. The SiO2 surface was prefunctionalized with bis(dimethylamino)dimethylsilane (BDMADMS) and (N,N-dimethylamino)trimethylsilane (DMATMS) through soln. and the vapor phase. ALD of Al2O3 using dimethylaluminum isopropoxide (DMAI) and H2O was performed on these functionalized SiO2 surfaces. Our in situ four-wavelength ellipsometry measurements show superior growth inhibition when using BDMADMS and DMATMS in sequence over just using BDMADMS or DMATMS. Vapor phase functionalization provided a growth delay of ∼30 ALD cycles, which was similar to soln.-based functionalization. Using in situ attenuated total reflection Fourier transmission IR spectroscopy, we show that the interaction of DMAI with SiO2 surfaces leads to pronounced changes in absorbance for the Si-O-Si phonon mode without any detectable DMAI absorbed on the SiO2 surface. Detailed anal. of the IR spectra revealed that the decrease in absorbance was likely caused by the coordination of Al in DMAI to O atoms in surface Si-O-Si bonds without the breaking the Si-O-Si bonds. Finally, we postulate that a minimal amt. of DMAI remains adsorbed on surface Si-O-Si bonds even after purging, which can initiate ALD of Al2O3 on functionalized SiO2: this highlights the need for higher surface coverage for enhanced steric blocking.
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89. 89
  Seo, S.; Yeo, B. C.; Han, S. S.; Yoon, C. M.; Yang, J. Y.; Yoon, J.; Yoo, C.; Kim, H.; Lee, Y.; Lee, S. J.; Myoung, J.-M.; Lee, H.-B.-R.; Kim, W.-H.; Oh, I.-K.; Kim, H. Reaction Mechanism of Area-Selective Atomic Layer Deposition for Al₂O₃ Nanopatterns. ACS Appl. Mater. Interfaces 2017, 9 (47), 41607– 41617, DOI: 10.1021/acsami.7b13365
  89
  Reaction mechanism of area-selective atomic layer deposition for Al2O3 nanopatterns
  Seo, Seunggi; Yeo, Byung Chul; Han, Sang Soo; Yoon, Chang Mo; Yang, Joon Young; Yoon, Jonggeun; Yoo, Choongkeun; Kim, Ho-jin; Lee, Yong-baek; Lee, Su Jeong; Myoung, Jae-Min; Lee, Han-Bo-Ram; Kim, Woo-Hee; Oh, Il-Kwon; Kim, Hyungjun
  ACS Applied Materials & Interfaces (2017), 9 (47), 41607-41617CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
  The reaction mechanism of area-selective at. layer deposition (AS-ALD) of Al2O3 thin films using self-assembled monolayers (SAMs) was systematically investigated by theor. and exptl. studies. Trimethylaluminum (TMA) and H2O were used as the precursor and oxidant, resp., with octadecylphosphonic acid (ODPA) as an SAM to block Al2O3 film formation. However, Al2O3 layers began to form on the ODPA SAMs after several cycles, despite reports that CH3-terminated SAMs cannot react with TMA. We showed that TMA does not react chem. with the SAM but is phys. adsorbed, acting as a nucleation site for Al2O3 film growth. Moreover, the amt. of physisorbed TMA was affected by the partial pressure. By controlling it, we developed a new AS-ALD Al2O3 process with high selectivity, which produces films of ∼60 nm thickness over 370 cycles. The successful deposition of Al2O3 thin film patterns using this process is a breakthrough technique in the field of nanotechnol.
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90. 90
  Yu, P.; Merkx, M. J. M.; Tezsevin, I.; Lemaire, P. C.; Hausmann, D. M.; Sandoval, T. E.; Kessels, W. M. M.; Mackus, A. J. M. Blocking Mechanisms in Area-Selective ALD by Small Molecule Inhibitors of Different Sizes: Steric Shielding versus Chemical Passivation. Appl. Surf. Sci. 2024, 665, 160141 DOI: 10.1016/j.apsusc.2024.160141
  There is no corresponding record for this reference.
91. 91
  Ande, C. K.; Elliott, S. D.; Kessels, W. M. M. First-Principles Investigation of C–H Bond Scission and Formation Reactions in Ethane, Ethene, and Ethyne Adsorbed on Ru(0001). J. Phys. Chem. C 2014, 118 (46), 26683– 26694, DOI: 10.1021/jp5069363
  91
  First-Principles Investigation of C-H Bond Scission and Formation Reactions in Ethane, Ethene, and Ethyne Adsorbed on Ru(0001)
  Ande, Chaitanya Krishna; Elliott, Simon D.; Kessels, Wilhelmus M. M.
  Journal of Physical Chemistry C (2014), 118 (46), 26683-26694CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  We have studied all possible elementary reactions (including isomerization reactions) involved in the interaction of CH4 (methane), CH3CH3 (ethane), CH2CH2 (ethene), and CHCH (ethyne) with the Ru(0001) surface using d. functional theory based first-principles calcns. Site preference and adsorption energies for all the reaction intermediates and activation energies for the elementary reactions are calcd. From the calcd. adsorption and activation energies, we find that dehydrogenation of the adsorbates is thermodynamically favored in agreement with expts. Dehydrogenation of CH (methylidyne) is the most difficult in the dehydrogenation of CH4 (methane). CH3CH3 (ethane), CH2CH2 (ethene), and CHCH (ethyne) dehydrogenate through the CH3C (ethylidyne) intermediate. Of the five possible pathways for the prodn. of CH3C (ethylidyne), the CH2CH (ethenyl)-CH2C (ethenylidene) pathway is the most dominant. In the case of ethene, the ethynyl-ethenylidene pathway is also the dominant pathway on Pt(111). Comparison of α and β-C-H bond scission reactions, important for the Fischer-Tropsch process, shows that alkenes should be the major products compared to the formation of alkynes. Dehydrogenation becomes slightly favorable at lower coverages of the hydrocarbon fragments while hydrogenation becomes slightly unfavorable. In addn. to resolving the dominant pathways during decompn. of the above hydrocarbons, the activation energies calcd. in this paper can also be used in the modeling of processes that involve the considered elementary reactions at longer length and time scales.
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92. 92
  Shirazi, M.; Elliott, S. D. Cooperation between Adsorbates Accounts for the Activation of Atomic Layer Deposition Reactions. Nanoscale 2015, 7 (14), 6311– 6318, DOI: 10.1039/C5NR00900F
  92
  Cooperation between adsorbates accounts for the activation of atomic layer deposition reactions
  Shirazi, Mahdi; Elliott, Simon D.
  Nanoscale (2015), 7 (14), 6311-6318CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
  Atomic layer deposition (ALD) is a technique for producing conformal layers of nanometer-scale thickness, used com. in non-planar electronics and increasingly in other high-tech industries. ALD depends on self-limiting surface chem. but the mechanistic reasons for this are not understood in detail. Here we demonstrate, by first-principle calcns. of growth of HfO2 from Hf(N(CH3)2)4-H2O and HfCl4-H2O and growth of Al2O3 from Al(CH3)3-H2O, that, for all these precursors, co-adsorption plays an important role in ALD. By this we mean that previously-inert adsorbed fragments can become reactive once sufficient nos. of mols. adsorb in their neighborhood during either precursor pulse. Through the calcd. activation energies, this 'cooperative' mechanism is shown to have a profound influence on proton transfer and ligand desorption, which are crucial steps in the ALD cycle. Depletion of reactive species and increasing coordination cause these reactions to self-limit during one precursor pulse, but to be re-activated via the cooperative effect in the next pulse. This explains the self-limiting nature of ALD.
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93. 93
  Shirazi, M.; Elliott, S. D. Multiple Proton Diffusion and Film Densification in Atomic Layer Deposition Modeled by Density Functional Theory. Chem. Mater. 2013, 25 (6), 878– 889, DOI: 10.1021/cm303630e
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Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.4c02557.
- Further information on the accuracy of the computational approach, calculation of DDFs from thermodynamic considerations, more information on the EDA results, and the NEB profile (PDF)
- cm4c02557_si_001.pdf (1.08 MB)
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Accurately Computed Dimerization Trends of ALD Precursors and Their Impact on Surface Reactivity in Area-Selective Atomic Layer DepositionClick to copy article linkArticle link copied!

Chemistry of Materials

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1. Introduction

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2. Computational Details

2.1. Molecular Calculations

2.1.1. Structural Optimizations

2.1.2. Thermochemistry

2.1.3. Energy Decomposition Analysis

2.2. Computations for Extended Systems

3. Results and Discussion

3.1. Structures of Dimerized Precursors

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3.2. Pressure Dependence of Dimer Dissociation

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3.3. Temperature Dependence of Dimer Dissociation

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3.4. Thermochemistry for Typical ALD Conditions

3.5. Comparison with Previous Data on Precursor Dimerization

3.6. EDA on Dimer Bond

Figure 6

3.7. Dimer versus Monomer Adsorption

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3.8. Dimer Opening

Figure 9

Conclusions

Data Availability

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Accurately Computed Dimerization Trends of ALD Precursors and Their Impact on Surface Reactivity in Area-Selective Atomic Layer Deposition
Click to copy article linkArticle link copied!