Thermodynamics of the gas-phase dimerization of formic acid: Fully anharmonic finite temperature calculations at the CCSD(T) and many DFT levels.

A proof-of-concept study is undertaken to demonstrate the utility of the machine learning combined with the thermodynamic perturbation theory (MLPT) to test the accuracy of electronic structure methods in finite-temperature thermodynamic calculations. As a test example, formic acid dimer is chosen, which is one of the systems included in the popular benchmark set S22 [Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985-1993 (2006)]. Starting from the explicit molecular dynamics and thermodynamic integration performed at the PBE + D2 level, the MLPT is used to obtain fully anharmonic dimerization free and internal energies at the reference quality CCSD(T) level and 19 different density functional approximations, including GGA, meta-GGA, non-local, and hybrid functionals with and without dispersion corrections. Our finite-temperature results are shown to be both qualitatively and quantitatively different from those obtained using the conventional benchmarking strategy based on fixed structures. The hybrid functional HSE06 is identified as the best performing approximate method tested, with the errors in free and internal energies of dimerization being 36 and 41 meV, respectively.

Investigating the role of dispersion corrections and anharmonic effects on the phase transition in SrZrS3: A systematic analysis from AIMD free energy calculations.

A thermally driven needle-like (NL) to distorted perovskite (DP) phase transition in SrZrS3 was investigated by means of ab initio free energy calculations accelerated by machine learning. As a first step, a systematic screening of the methods to include long-range interactions in semilocal density functional theory Perdew-Burke-Ernzerhof calculations was performed. Out of the ten correction schemes tested, the Tkatchenko-Scheffler method with iterative Hirshfeld partitioning method was found to yield the best match between calculated and experimental lattice geometries, while predicting the correct order of stability of NL and DP phases at zero temperature. This method was then used in free energy calculations, performed using several approaches, so as to determine the effect of various anharmonicity contributions, such as the anisotropic thermal lattice expansion or the thermally induced internal structure changes, on the phase transition temperature (TNP→DP). Accounting for the full anharmonicity by combining the NPT molecular dynamics data with thermodynamic integration with harmonic reference provided our best estimate of TNL→DP = 867 K. Although this result is ∼150 K lower than the experimental value, it still provides an improvement by nearly 300 K compared to the previous theoretical report by Koocher et al. [Inorg. Chem. 62, 11134-11141 (2023)].

Reference-Quality Free Energy Barriers in Catalysis from Machine Learning Thermodynamic Perturbation Theory.

For the first time, we report calculations of the free energies of activation of cracking and isomerization reactions of alkenes that combine several different electronic structure methods with molecular dynamics simulations. We demonstrate that the use of a high level of theory (here Random Phase Approximation-RPA) is necessary to bridge the gap between experimental and computed values. These transformations, catalyzed by zeolites and proceeding via cationic intermediates and transition states, are building blocks of many chemical transformations for valorization of long chain paraffins originating, e.g., from plastic waste, vegetable oils, Fischer-Tropsch waxes or crude oils. Compared with the free energy barriers computed at the PBE+D2 production level of theory via constrained ab initio molecular dynamics, the barriers computed at the RPA level by the application of Machine Learning thermodynamic Perturbation Theory (MLPT) show a significant decrease for isomerization reaction and an increase of a similar magnitude for cracking, yielding an unprecedented agreement with the results obtained by experiments and kinetic modeling.

How the Temperature and Composition Govern the Structure and Band Gap of Zr-Based Chalcogenide Perovskites: Insights from ML Accelerated AIMD.

The effects of temperature and composition on the structural and electronic properties of chalcogenide perovskite (CP) materials AZrX3 (A = Ba, Sr, Ca; X = S, Se) in the distorted perovskite (DP) phase are investigated using ab initio molecular dynamics (AIMD) accelerated by machine-learned force fields. Long-range van der Waals (vdW) interactions, incorporated into the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional using the DFT-D3 scheme, are found to be crucial for achieving correct predictions of structural parameters. Our calculations show that the distortion of the DP structure with respect to the parent cubic (C) phase, realized in the form of interoctahedral tilting, decreases with the increasing size of the A cations. The tendency for a gradual transformation of the DP-to-C phase with increasing temperature is shown to be strongly composition-dependent. The transformation temperature decreases with the size of cation A and increases with the size of anion X. Thus, within the range of the temperatures considered here (300-1200 K), a complete transformation is observed only for BaZrS3 (∼600 K) and BaZrSe3 (∼900 K). The computed band gap of CPs is shown to monotonically decrease with increasing temperature, and the magnitude of this decrease is found to be proportional to the extent of the thermally induced changes in the internal structure. Diverse factors affecting the magnitude of band gaps of CP materials are analyzed.

Anharmonic Correction to Free Energy Barriers from DFT-Based Molecular Dynamics Using Constrained Thermodynamic Integration.

For the calculation of anharmonic contributions to free energy barriers, constrained thermodynamic λ-path integration (λ-TI) from a harmonic reference force field to density functional theory is presented as an alternative to the established Blue Moon ensemble method (ξ-TI), in which free energy gradients along the reaction coordinate ξ are integrated. With good agreement in all cases, the λ-TI method is benchmarked against the ξ-TI method for several reactions, including the internal CH3 group rotation in ethane, a nucleophilic substitution of CH3Cl, a retro-Diels-Alder reaction, and a proton transfer in zeolite H-SSZ-13. An advantage of λ-TI is that one can use virtually any reference state to compute anharmonic contributions to reaction free energies or free energy barriers. This is particularly relevant for catalysis, where it is now possible to compute anharmonic corrections to the free energy of a transition state relative to any reference, for example, the most stable state of the active site and the reactants in the gas phase. This is in contrast to ξ-TI, where free energy barriers can only be computed relative to an initial state with all reactants coadsorbed. Finally, the Bennett acceptance ratio method combined with λ-TI is demonstrated to reduce the number of required integration grid points with tolerable accuracy, favoring thus λ-TI over ξ-TI in terms of computational efficiency.

Assessing the Accuracy of Machine Learning Thermodynamic Perturbation Theory: Density Functional Theory and Beyond.

Machine learning thermodynamic perturbation theory (MLPT) is a promising approach to compute finite temperature properties when the goal is to compare several different levels of ab initio theory and/or to apply highly expensive computational methods. Indeed, starting from a production molecular dynamics trajectory, this method can estimate properties at one or more target levels of theory from only a small number of additional fixed-geometry calculations, which are used to train a machine learning model. However, as MLPT is based on thermodynamic perturbation theory (TPT), inaccuracies might arise when the starting point trajectory samples a configurational space which has a small overlap with that of the target approximations of interest. By considering case studies of molecules adsorbed in zeolites and several different density functional theory approximations, in this work we assess the accuracy of MLPT for ensemble total energies and enthalpies of adsorption. It is shown that problematic cases can be detected even without knowing reference results and that even in these situations it is possible to recover target level results within chemical accuracy by applying a machine-learning-based Monte Carlo (MLMC) resampling. Finally, on the basis of the ideas developed in this work, we assess and confirm the accuracy of recently published MLPT-based enthalpies of adsorption at the random phase approximation level, whose high computational cost would completely hinder a direct molecular dynamics simulation.

Understanding the Fundamentals of Microporosity Upgrading in Zeolites: Increasing Diffusion and Catalytic Performances.

Hierarchical zeolites are regarded as promising catalysts due to their well-developed porosity, increased accessible surface area, and minimal diffusion constraints. Thus far, the focus has been on the creation of mesopores in zeolites, however, little is known about a microporosity upgrading and its effect on the diffusion and catalytic performance. Here the authors show that the "birth" of mesopore formation in faujasite (FAU) type zeolite starts by removing framework T atoms from the sodalite (SOD) cages followed by propagation throughout the crystals. This is evidenced by following the diffusion of xenon (Xe) in the mesoporous FAU zeolite prepared by unbiased leaching with NH4 F in comparison to the pristine FAU zeolite. A new diffusion pathway for the Xe in the mesoporous zeolite is proposed. Xenon first penetrates through the opened SOD cages and then diffuses to supercages of the mesoporous zeolite. Density functional theory (DFT) calculations indicate that Xe diffusion between SOD cage and supercage occurs only in hierarchical FAU structure with defect-contained six-member-ring separating these two types of cages. The catalytic performance of the mesoporous FAU zeolite further indicates that the upgraded microporosity facilitates the intracrystalline molecular traffic and increases the catalytic performance.

Hybrid localized graph kernel for machine learning energy-related properties of molecules and solids.

Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large number of representations for molecules and solids for machine learning applications has been developed. In this work we propose a novel descriptor based on the notion of molecular graph. While graphs are largely employed in classification problems in cheminformatics or bioinformatics, they are not often used in regression problem, especially of energy-related properties. Our method is based on a local decomposition of atomic environments and on the hybridization of two kernel functions: a graph kernel contribution that describes the chemical pattern and a Coulomb label contribution that encodes finer details of the local geometry. The accuracy of this new kernel method in energy predictions of molecular and condensed phase systems is demonstrated by considering the popular QM7 and BA10 datasets. These examples show that the hybrid localized graph kernel outperforms traditional approaches such as, for example, the smooth overlap of atomic positions and the Coulomb matrices.

Anharmonic Correction to Adsorption Free Energy from DFT-Based MD Using Thermodynamic Integration.

Adsorption processes are often governed by weak interactions for which the estimation of entropy contributions by means of the harmonic approximation is prone to be inaccurate. Thermodynamic integration (TI) from the harmonic to the fully interacting system (λ-path integration) can be used to compute anharmonic corrections. Here, we combine TI with (curvilinear) internal coordinates in periodic systems to make the formalism available in computational studies. Our implementation of ab initio molecular dynamics in VASP is independent of the reaction path and can be thus applied to study adsorption processes relative to the gas phase and does hence provide a useful tool for computational catalysis. We discuss the application of the approach on three model systems for which exact semianalytical solutions exist and illustrate and quantify the importance of anharmonic vibrations, hindered rotations, and hindered translations (dissociation). Eventually, we apply the method to study the adsorption of small adsorbates in a zeolite (H-SSZ-13).

Ab Initio Calculations of Free Energy of Activation at Multiple Electronic Structure Levels Made Affordable: An Effective Combination of Perturbation Theory and Machine Learning.

While free energies are fundamental thermodynamic quantities to characterize chemical reactions, their calculation based on ab initio theory is usually limited by the high computational cost. This is particularly true if multiple levels of theory have to be tested to establish their relative accuracy, if highly expensive quantum mechanical approximations are of interest, and also if several different temperatures have to be considered. We present an ab initio approach that effectively couples perturbation theory and machine learning to make ab initio free energy calculations more affordable. Starting from results based on a certain production ab initio theory, perturbation theory is applied to obtain free energies. The large number of single point calculations required by a brute force application of this approach are here significantly decreased by applying machine learning techniques. Importantly, the training of the machine learning model requires only a small amount of data and does not need to be performed again when the temperature is decreased. The accuracy and efficiency of this method is demonstrated by computing the free energy of activation of the proton exchange reaction in the zeolite chabazite. Starting from an ab initio calculation based on a semilocal approximation of density functional theory, free energies based on significantly more expensive nonlocal van der Waals and hybrid functionals are obtained with only a few tens of additional single point calculations. In this way this work paves the route to quick free energy calculations using different levels of theory or approximations that would be too computationally expensive to be directly employed in molecular dynamics or Monte Carlo simulations.

Dynamic Features of Transition States for ß-Scission Reactions of Alkenes over Acid Zeolites Revealed by AIMD Simulations.

Zeolite-catalyzed alkene cracking is key to optimize the size of hydrocarbons. The nature and stability of intermediates and transition states (TS) are, however, still debated. We combine transition path sampling and blue moon ensemble density functional theory simulations to unravel the behavior of C7 alkenes in CHA zeolite. Free energy profiles are determined, linking π-complexes, alkoxides and carbenium ions, for B1 (secondary to tertiary) and B2 (tertiary to secondary) ß-scissions. B1 is found to be easier than B2 . The TS for B1 occurs at the breaking of the C-C bond, while for B2 it is the proton transfer from propenium to the zeolite. We highlight the dynamic behaviors of the various intermediates along both pathways, which reduce activation energies with respect to those previously evaluated by static approaches. We finally revisit the ranking of isomerization and cracking rate constants, which are crucial for future kinetic studies.

Computing RPA Adsorption Enthalpies by Machine Learning Thermodynamic Perturbation Theory.

Correlated quantum-chemical methods for condensed matter systems, such as the random phase approximation (RPA), hold the promise of reaching a level of accuracy much higher than that of conventional density functional theory approaches. However, the high computational cost of such methods hinders their broad applicability, in particular for finite-temperature molecular dynamics simulations. We propose a method that couples machine learning techniques with thermodynamic perturbation theory to estimate finite-temperature properties using correlated approximations. We apply this approach to compute the enthalpies of adsorption in zeolites and show that reliable estimates can be obtained by training a machine learning model with as few as 10 RPA energies. This approach paves the way to the broader use of computationally expensive quantum-chemical methods to predict the finite-temperature properties of condensed matter systems.

Carbon dioxide capture in 2,2'-iminodiethanol aqueous solution from ab initio molecular dynamics simulations.

The reaction of carbon dioxide (CO2) with aqueous 2,2'-iminodiethanol (trivial name is diethanolamine: DEA) has been investigated using both blue moon ensemble and metadynamics approaches combined with ab initio molecular dynamics (AIMD) simulations. A spontaneous direct proton transfer from DEA zwitterion (DEAZW) to DEA but not to H2O has been observed in straightforward AIMD simulation in the time scale of ps. The ab initio free-energy calculations reproduced the overall free-energy difference, predicting the ionic products DEA carbamate ion (DEAC) and the protonated DEA (DEAH). The computed free-energy barrier for the first reaction step, which is the CO2 binding (48 kJ mol-1), is found to agree reasonably well with the available experimental data (52-56 kJ mol-1). By contrast, the barriers for the next step, the deprotonation of zwitterion realized either via reaction with DEA or H2O, are underestimated by 25-35 kJ mol-1 compared to the experimental reference. A part of this error is attributed to the neglected reversible work needed to bring two reactants together, which might significantly contribute to the free-energy of activation of bimolecular reactions in a dilute solution. The computed free-energy profile is compared with our results [Y. Kubota et al., J. Chem. Phys. 146, 094303 (2017)] for the same reaction in 2-aminoethanol (trivial name is monoethanolamine: MEA).

On the work function of the surface Mo(0 0 1) and its temperature dependence: an ab initio molecular dynamics study.

Ab initio molecular dynamics simulations in NVT ensemble have been performed to investigate the finite temperature structure of the Mo(0 0 1) surface and its effect on work function (ϕ). In accord with previous experimental and theoretical work, our simulations predict that a termination with a stable reconstruction pattern is formed at T = 123 K. This pattern vanishes when temperature is increased to 423 K or 623 K and a disordered surface phase is formed whose time average corresponds to a bulk-like termination. Our results demonstrate that the surface relaxation is an important factor contributing to thermal variation of ϕ. At the lowest temperature, at which a stable reconstruction pattern is formed, the work function is found to increase by ∼0.23 eV compared to relaxed unreconstructed surface. The disappearance of stable reconstruction pattern at elevated temperatures leads to a decrease of ϕ by ∼0.07 eV. In contrast, the values computed for a non-reconstructing surface Mo(1 1 0) at T = 123 K, 423 K and 623 K are found to be nearly identical to the zero temperature value, which is a consequence of restricted atomic motion due to high packing density in this surface.

Effect of alkaline metal cations on the ionic structure of cryolite melts: Ab-initio NpT MD study.

Ab initio molecular dynamics simulations in an NpT ensemble have been performed to study the role of alkaline metal cations (Me = Li, Na, K, Rb) on the structure and vibrational properties of melts of Me-cryolites (Me3AlF6) at T = 1300 K. In all melts examined in this work, the species AlF52- has been found to be formed at the highest abundance [from 58% (Li) to 70% (Na)] among the Al-containing anionic clusters. The concentration of clusters AlF4- increases with the size of cations while that of anions AlF63- follows the opposite trend and it becomes negligible in the melts of the K- and Rb-cryolites. The computed percentage of the Al atoms participating in the formation of dimers Al2Fm6-m bridged via common F atoms is significant only in the case of Li- and Na-cryolites (16% and 10%, respectively) and the formation of even larger aggregates is found to be unlikely in all four melts. The percentage of the F atoms that are not bound to Al is ∼20% in all four melts and the ions formed by Me+ and F- are found to be only short-lived. Vibrational analysis has been performed using the velocity autocorrelation functions computed for the Cartesian and selected internal coordinates describing Raman-active symmetric stretching vibrations of different AlFn species. The results of vibrational analysis allowed us to identify trends in the variation of positions and shapes of peaks corresponding to the anionic fragments AlF4-, AlF52-, and AlF63- with the size of cations, and these trends are found to be consistent with those deduced from the available Raman spectroscopy experiments. Our findings represent a new insight into the properties of cryolite melts, which will be useful for the interpretation of experimental data.

Dissociative iodomethane adsorption on Ag-MOR and the formation of AgI clusters: an ab initio molecular dynamics study.

Radioactive iodine species belong to the most dangerous components of nuclear effluents and waste produced by nuclear facilities. In this work, we use computer simulations at the periodic DFT level to investigate dissociative adsorption of iodomethane on silver-exchanged mordenite, which is among the most effective sorbents of iodine species available today. The structure, energetics, and mobility of complexes Ag-(CH3I) and Ag-(CH3I)2 formed upon adsorption of iodomethane on Ag+ sites are investigated using the ab initio MD approach. The free-energy profiles for the reaction CH3I + Ag-MOR → AgI + CH3-MOR are determined using the blue moon ensemble technique. The AgI species formed as a product of dissociative adsorption are shown to combine spontaneously into small clusters (AgI)n with the dimensions restricted by the size and geometry of confining voids. The structure and energetics of the (AgI)n species are analysed in detail and compared with the available experimental and theoretical data. The internal energy of formation of clusters in mordenite is shown to contribute significantly to the shift of equilibrium from the undissociated to dissociated form of adsorbed CH3I.

A Fractionally Ionic Approach to Polarizability and van der Waals Many-Body Dispersion Calculations.

By explicitly including fractionally ionic contributions to the polarizability of a many-component system, we are able to significantly improve on previous atom-wise many-body van der Waals approaches with essentially no extra numerical cost. For nonionic systems, our method is comparable in accuracy to existing approaches. However, it offers substantial improvements in ionic solids, e.g., producing better polarizabilities by over 65% in some cases. It has particular benefits for two-dimensional transition metal dichalcogenides and interactions of H2 with modified coronenes, ionic systems of nanotechnological interest. It thus offers an efficient improvement on existing approaches, valid for a wide range of systems.

A DFT investigation of the adsorption of iodine compounds and water in H-, Na-, Ag-, and Cu- mordenite.

The potential use of some cation-exchanged mordenite (H(+), Na(+), Cu(+), and Ag(+)) as a selective adsorbent for volatile iodine species (ICH3 and I2), which can be released during a nuclear accident together with a steam carrier gas, is investigated using density functional theory. It is found that in the case of Cu-MOR and Ag-MOR, the absolute values of interaction energies of ICH3 and I2 are higher than that of water which indicates that these forms of zeolite could be suitable for selective adsorption of iodine species. In contrast, the H-MOR and Na-MOR are found to be unsuitable for this purpose. A systematic investigation of all adsorption sites allowed us to analyze the structural effects affecting the adsorption behavior. For the Ag-MOR and Cu-MOR zeolites, the iodine compounds are adsorbed preferentially in the large channel of mordenite (main channel) while water prefers the small channel or the side pocket where it forms stronger hydrogen bonds. The factors governing the interaction energies between the cationic sites and the different molecules are analyzed and the important role of van der Waals interactions in these systems is highlighted.

C6 Coefficients and Dipole Polarizabilities for All Atoms and Many Ions in Rows 1-6 of the Periodic Table.

Using time-dependent density functional theory (TDDFT) with exchange kernels, we calculate and test imaginary frequency-dependent dipole polarizabilities for all atoms and many ions in rows 1-6 of the periodic table. These are then integrated over frequency to produce C6 coefficients. Results are presented under different models: straight TDDFT calculations using two different kernels; "benchmark" TDDFT calculations corrected by more accurate quantum chemical and experimental data; and "benchmark" TDDFT with frozen orbital anions. Parametrizations are presented for 411+ atoms and ions, allowing results to be easily used by other researchers. A curious relationship, C6,XY ∝ [αX(0)αY(0)](0.73), is found between C6 coefficients and static polarizabilities α(0). The relationship C6,XY = 2C6,XC6,Y/[(αX/αY)C6,Y + (αY/αX)C6,X] is tested and found to work well (<5% errors) in ∼80% of the cases, but can break down badly (>30% errors) in a small fraction of cases.

On the structure of crystalline and molten cryolite: Insights from the ab initio molecular dynamics in NpT ensemble.

Ab initio molecular dynamics simulations in isobaric-isothermal ensemble have been performed to study the low- and the high-temperature crystalline and liquid phases of cryolite. The temperature induced transitions from the low-temperature solid (α) to the high-temperature solid phase (ß) and from the phase ß to the liquid phase have been simulated using a series of MD runs performed at gradually increasing temperature. The structure of crystalline and liquid phases is analysed in detail and our computational approach is shown to reliably reproduce the available experimental data for a wide range of temperatures. Relatively frequent reorientations of the AlF6 octahedra observed in our simulation of the phase ß explain the thermal disorder in positions of the F(-) ions observed in X-ray diffraction experiments. The isolated AlF6(3-), AlF5(2-), AlF4(-), as well as the bridged Al2Fm(6-m) ionic entities have been identified as the main constituents of cryolite melt. In accord with the previous high-temperature NMR and Raman spectroscopic experiments, the compound AlF5(2-) has been shown to be the most abundant Al-containing species formed in the melt. The characteristic vibrational frequencies for the AlFn(3-n) species in realistic environment have been determined and the computed values have been found to be in a good agreement with experiment.