Rapid Characterization of Point Defects in Solid-State Ion Conductors Using Raman Spectroscopy, Machine-Learning Force Fields, and Atomic Raman Tensors.

The successful design of solid-state photo- and electrochemical devices depends on the careful engineering of point defects in solid-state ion conductors. Characterization of point defects is critical to these efforts, but the best-developed techniques are difficult and time-consuming. Raman spectroscopy─with its exceptional speed, flexibility, and accessibility─is a promising alternative. Raman signatures arise from point defects due to local symmetry breaking and structural distortions. Unfortunately, the assignment of these signatures is often hampered by a shortage of reference compounds and corresponding reference spectra. This issue can be circumvented by calculation of defect-induced Raman signatures from first principles, but this is computationally demanding. Here, we introduce an efficient computational procedure for the prediction of point defect Raman signatures in solid-state ion conductors. Our method leverages machine-learning force fields and "atomic Raman tensors", i.e., polarizability fluctuations due to motions of individual atoms. We find that our procedure reduces computational cost by up to 80% compared to existing first-principles frozen-phonon approaches. These efficiency gains enable synergistic computational-experimental investigations, in our case allowing us to precisely interpret the Raman spectra of Sr(Ti0.94Ni0.06)O3-δ, a model oxygen ion conductor. By predicting Raman signatures of specific point defects, we determine the nature of dominant defects and unravel impacts of temperature and quenching on in situ and ex situ Raman spectra. Specifically, our findings reveal the temperature-dependent distribution and association behavior of oxygen vacancies and nickel substitutional defects. Overall, our approach enables rapid Raman-based characterization of point defects to support defect engineering in novel solid-state ion conductors.

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.

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.

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.

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.

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).

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.

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.

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.

Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning.

Recently we have demonstrated that the applicability of the Tkatchenko-Scheffler (TS) method for calculating dispersion corrections to density-functional theory can be extended to ionic systems if the Hirshfeld method for estimating effective volumes and charges of atoms in molecules or solids (AIM's) is replaced by its iterative variant [T. Bucko, S. Lebègue, J. Hafner, and J. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)]. The standard Hirshfeld method uses neutral atoms as a reference, whereas in the iterative Hirshfeld (HI) scheme the fractionally charged atomic reference states are determined self-consistently. We show that the HI method predicts more realistic AIM charges and that the TS/HI approach leads to polarizabilities and C6 dispersion coefficients in ionic or partially ionic systems which are, as expected, larger for anions than for cations (in contrast to the conventional TS method). For crystalline materials, the new algorithm predicts polarizabilities per unit cell in better agreement with the values derived from the Clausius-Mosotti equation. The applicability of the TS/HI method has been tested for a wide variety of molecular and solid-state systems. It is demonstrated that for systems dominated by covalent interactions and/or dispersion forces the TS/HI method leads to the same results as the conventional TS approach. The difference between the TS/HI and TS approaches increases with increasing ionicity. A detailed comparison is presented for isoelectronic series of octet compounds, layered crystals, complex intermetallic compounds, and hydrides, and for crystals built of molecules or containing molecular anions. It is demonstrated that only the TS/HI method leads to accurate results for systems where both electrostatic and dispersion interactions are important, as illustrated for Li-intercalated graphite and for molecular adsorption on the surfaces in ionic solids and in the cavities of zeolites.

Understanding the adsorption of CuPc and ZnPc on noble metal surfaces by combining quantum-mechanical modelling and photoelectron spectroscopy.

Phthalocyanines are an important class of organic semiconductors and, thus, their interfaces with metals are both of fundamental and practical relevance. In the present contribution we provide a combined theoretical and experimental study, in which we show that state-of-the-art quantum-mechanical simulations are nowadays capable of treating most properties of such interfaces in a quantitatively reliable manner. This is shown for Cu-phthalocyanine (CuPc) and Zn-phthalocyanine (ZnPc) on Au(111) and Ag(111) surfaces. Using a recently developed approach for efficiently treating van der Waals (vdW) interactions at metal/organic interfaces, we calculate adsorption geometries in excellent agreement with experiments. With these geometries available, we are then able to accurately describe the interfacial electronic structure arising from molecular adsorption. We find that bonding is dominated by vdW forces for all studied interfaces. Concomitantly, charge rearrangements on Au(111) are exclusively due to Pauli pushback. On Ag(111), we additionally observe charge transfer from the metal to one of the spin-channels associated with the lowest unoccupied π-states of the molecules. Comparing the interfacial density of states with our ultraviolet photoelectron spectroscopy (UPS) experiments, we find that the use of a hybrid functionals is necessary to obtain the correct order of the electronic states.

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.

Spin crossover transition of Fe(phen)2(NCS)2: periodic dispersion-corrected density-functional study.

Periodic dispersion corrected DFT calculations have been performed to study the spin-crossover transition of Fe(phen)(2)(NCS)(2) in the molecular and in the crystalline state. We show that London dispersion interactions play a crucial role in the cohesion of the crystals. Based on calculations of vibrational eigenstates of the isolated molecule and of the crystalline phase in both the low- and high-spin states, the transition entropies and enthalpies have been calculated. We demonstrate that, due to the stabilization of the low-spin state by intermolecular dispersion forces, the transition enthalpy at the transition temperature is larger for the crystalline phase in comparison with an isolated molecule. The effective coordination number of the nitrogen atoms of the ligands around the iron atom has been identified as the order parameter driving the quasi-reversible low-spin to high-spin transition in the crystal. Finally, using constrained geometry relaxations at fixed values of the coordination number, we computed the energy barrier of the LS to HS transition and found it to be in a reasonable agreement with the experimental value.

Assessment of ten DFT methods in predicting structures of sheet silicates: importance of dispersion corrections.

The performance of ten density functional theory (DFT) methods in a prediction of the structure of four clay minerals, in which non-bonding interactions dominate in the layer stacking (dispersive forces in talc and pyrophyllite, and hydrogen bonds in lizardite and kaolinite), is reported. In a set of DFT methods following functionals were included: standard local and semi-local (LDA, PW91, PBE, and RPBE), dispersion corrected (PW91-D2, PBE-D2, RPBE-D2, and vdW-TS), and functionals developed specifically for solids and solid surfaces (PBEsol and AM05). We have shown that the standard DFT functionals fail in the correct prediction of the structural parameters, for which non-bonding interactions are important. The remarkable improvement leading to very good agreement with experimental structures is achieved if the dispersion corrections are included in the DFT calculations. In such cases the relative error for the most sensitive lattice vector c dropped below 1%. Very good performance was also observed for both DFT functionals developed for solids. Especially, the results achieved with the PBEsol are qualitatively similar to those with DFT-D2.

Van der Waals interactions between hydrocarbon molecules and zeolites: periodic calculations at different levels of theory, from density functional theory to the random phase approximation and Møller-Plesset perturbation theory.

The adsorption of small alkane molecules in purely siliceous and protonated chabazite has been investigated at different levels of theory: (i) density-functional (DFT) calculations with a gradient-corrected exchange-correlation functional; DFT calculations using the Perdew-Burke-Ernzerhof (PBE) functional with corrections for the missing dispersion forces in the form of C(6)∕R(6) pair potentials with (ii) C(6) parameters and vdW radii determined by fitting accurate energies for a large molecular data base (PBE-d) or (iii) derived from "atoms in a solid" calculations; (iv) DFT calculations using a non-local correlation functional constructed such as to account for dispersion forces (vdW-DF); (v) calculations based on the random phase approximation (RPA) combined with the adiabatic-coupling fluctuation-dissipation theorem; and (vi) using Hartree-Fock (HF) calculations together with correlation energies calculated using second-order Møller-Plesset (MP2) perturbation theory. All calculations have been performed for periodic models of the zeolite and using a plane-wave basis and the projector-augmented wave method. The simpler and computationally less demanding approaches (i)-(iv) permit a calculation of the forces acting on the atoms using the Hellmann-Feynman theorem and further a structural optimization of the adsorbate-zeolite complex, while RPA and MP2 calculations can be performed only for a fixed geometry optimized at a lower level of theory. The influence of elevated temperature has been taken into account by averaging the adsorption energies calculated for purely siliceous and protonated chabazite, with weighting factors determined by molecular dynamics calculations with dispersion-corrected forces from DFT. Compared to experiment, the RPA underestimates the adsorption energies by about 5 kJ/mol while MP2 leads to an overestimation by about 6 kJ/Mol (averaged over methane, ethane, and propane). The most accurate results have been found for the "hybrid" RPA-HF method with an average error of less than 2 kJ/mol only, while RPA underestimates the adsorption energies by about 8 kJ/mol on average. MP2 overestimates the adsorption energies slightly, with an average error of 5 kJ/mol. The more approximate and computationally less demanding methods such as the vdW-DF density functional or the C(6)∕R(6) pair potentials with C(6) parameters from "atoms in a solid" calculations overestimate the adsorption energies quite strongly. Relatively good agreement with experiment is achieved with the empirical PBE+d method with an average error of about 5 kJ/mol.

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.

Ab initio study of structure and interconversion of native cellulose phases.

Dispersion-interaction corrected DFT simulations are performed to study the structure of two allomorphs of native cellulose I. Good agreement between theoretical and experimental data is achieved. Two H-bond patterns, previously identified experimentally, are examined for both allomorphs. The transition mechanism for the conversion between the phase I(α) and I(ß) is studied by means of constrained relaxations. New metastable intermediate phase occurring on the I(α) → I(ß) route is identified, and the corresponding structural data are reported.