Transition state optimization of periodic systems using delocalized internal coordinates

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)].

Exploring the Stability and Disorder in the Polymorphs of L-Cysteine through Density Functional Theory and Vibrational Spectroscopy

Static and dynamic density functional calculations are reported for the four known polymorphs of l-cysteine. Static calculations are used to explore the relative free energies (within the harmonic approximation) of the polymorphs as a function of pressure. An important feature of the structural differences between the polymorphs is shown to be the dihedral angle of the C-C-S-H bond. It is shown that, by varying this angle, it is possible to move between hydrogen bonding motifs S-H···S and S-H···O in all four polymorphs. The energetics for dihedral angle rotation are explored, and the barriers for rotation between the hydrogen bonding motifs have been calculated for each polymorph. Two possible models for the experimental disorder observed in Form I at room temperature are explored using both static and dynamic methods; a domain disorder model, where the disorder is localized, and a dispersed disorder model, where the disorder is randomly distributed throughout the crystal. Molecular dynamics calculations show transitions between the two hydrogen bonding motifs occurring in the dispersed disorder model at 300 and 350 K. In addition, molecular dynamics calculations of Form IV also showed the onset of hydrogen bond disorder at 300 K. Calculations of the predicted infrared and terahertz absorption are performed for both the static and dynamic simulations, and the results are compared with experimental results to understand the influence of disorder on the observed spectra.

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.

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.

Perspective on computational reaction prediction using machine learning methods in heterogeneous catalysis

Heterogeneous catalysis plays a significant role in the modern chemical industry. Towards the rational design of novel catalysts, understanding reactions over surfaces is the most essential aspect. Typical industrial catalytic processes such as syngas conversion and methane utilisation can generate a large reaction network comprising thousands of intermediates and reaction pairs. This complexity not only arises from the permutation of transformations between species but also from the extra reaction channels offered by distinct surface sites. Despite the success in investigating surface reactions at the atomic scale, the huge computational expense of ab initio methods hinders the exploration of such complicated reaction networks. With the proliferation of catalysis studies, machine learning as an emerging tool can take advantage of the accumulated reaction data to emulate the output of ab initio methods towards swift reaction prediction. Here, we briefly summarise the conventional workflow of reaction prediction, including reaction network generation, ab initio thermodynamics and microkinetic modelling. An overview of the frequently used regression models in machine learning is presented. As a promising alternative to full ab initio calculations, machine learning interatomic potentials are highlighted. Furthermore, we survey applications assisted by these methods for accelerating reaction prediction, exploring reaction networks, and computational catalyst design. Finally, we envisage future directions in computationally investigating reactions and implementing machine learning algorithms in heterogeneous catalysis.

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).