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

Importance sampling within configuration space integration for adsorbate thermophysical properties: a case study for CH3/Ni(111)

A new strategy is presented for computing anharmonic partition functions for the motion of adsorbates relative to a catalytic surface. Importance sampling is compared with conventional Monte Carlo. The importance sampling is significantly more efficient. This new approach is applied to CH3* on Ni(111) as a test case. The motion of methyl relative to the nickel surface is found to be anharmonic, with significantly higher entropy compared to the standard harmonic oscillator model. The new method is freely available as part of the Minima-Preserving Neural Network within the ADTHERM package.

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)].

Design Strategies for Hydroxyapatite-Based Materials to Enhance Their Catalytic Performance and Applicability

Hydroxyapatite (HAP) is a green catalyst that has a wide range of applications in catalysis due to its high flexibility and multifunctionality. These properties allow HAP to accommodate a large number of catalyst modifications that can selectively improve the catalytic performance in target reactions. To date, many studies have been conducted to elucidate the effect of HAP modification on the catalytic activities for various reactions. However, systematic design strategies for HAP catalysts are not established yet due to an incomplete understanding of underlying structure-activity relationships. In this review, tuning methods of HAP for improving the catalytic performance are discussed: 1) ionic composition change, 2) morphology control, 3) incorporation of other metal species, and 4) catalytic support engineering. Detailed mechanisms and effects of structural modulations on the catalytic performances for attaining the design insights of HAP catalysts are investigated. In addition, computational studies to understand catalytic reactions on HAP materials are also introduced. Finally, important areas for future research are highlighted.

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.

Rapid Synthesis of Si-Rich SSZ-13 Zeolite under Fluoride-Free Conditions

Rapid synthesis of Si-rich (SiO₂/Al₂O₃ > 100) SSZ-13 zeolite under fluoride-free conditions is highly desirable but still challenging. Herein, we for the first time report a rapid synthesis of all silica and aluminosilicate (SiO₂/Al₂O₃ > 100) SSZ-13 zeolite without the addition of fluoride species. The crystallization could be fully completed at 160 °C for 4 h when the aging of the starting gel is 3 h at room temperature after the addition of a zeolite seed. The key to success is the formation of more basic building units (4- and 6-membered rings) in the initial gel with the aging time of 3 h after the addition of a zeolite seed, leading to the successful rapid synthesis of Si-rich SSZ-13 zeolite. The obtained Si-rich SSZ-13 zeolite displays high crystallinity, uniform cubic morphology with a nanoparticle feature, and a large surface area. More importantly, the obtained Si-rich SSZ-13 zeolite displays excellent performance in the adsorption of ethanol and methanol-to-olefin reaction.

Comparative Analysis of Uncoupled Mode Approximations for Molecular Thermochemistry and Kinetics

The accurate prediction of thermochemistry and kinetic parameters is an important task for reaction modeling. Unfortunately, the commonly used harmonic oscillator model is often not accurate enough due to the absence of anharmonic effects. In this work, we improve the representation of an anharmonic potential energy surface (PES) using uncoupled mode (UM) approximations, which model the full-dimensional PES as a sum of one-dimensional potentials of each mode. We systematically analyze different PES sampling schemes and coordinate systems for constructing the one-dimensional potentials, and benchmark the performance of UM methods on data sets of molecular thermochemistry and kinetic properties. The results show that the accuracy of the UM approach strongly depends on how the one-dimensional potentials are defined. If one-dimensional potentials are constructed by sampling along normal mode directions (UM-N) or along the directions that minimize intermode coupling (E- and E'-optimized), the accuracies of the predicted properties are not significantly improved compared to the harmonic oscillator model. However, significant improvements can be achieved by sampling the torsional modes separately from the vibrational modes (UM-T and UM-VT). In this work, three types of coordinate systems are examined, including redundant internal coordinates (RIC), hybrid internal coordinates (HIC), and translation-rotation-internal coordinates (TRIC). The HIC and TRIC coordinate systems can outperform RIC since transition state species may contain large-amplitude interfragmentary motions that regular internal coordinates can not describe adequately. Among all the methods we examined, the activation energies and pre-exponential factors calculated using UM-VT with either TRIC or HIC best agree with the reference values. Since UM-VT requires only a number of additional single point energy calculations for each independent mode, the scaling of computational costs of UM-VT is the same as that of the standard harmonic oscillator model, making UM-VT an appealing way of calculating the thermochemistry and kinetic properties for large-size systems.

Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5

Herein, we propose a novel computational protocol that enables calculating free energies with improved accuracy by combining the best available techniques for enthalpy and entropy calculation. While the entropy is described by enhanced sampling molecular dynamics techniques, the energy is calculated using ab initio methods. We apply the method to assess the stability of isobutene adsorption intermediates in the zeolite H-SSZ-13, a prototypical problem that is computationally extremely challenging in terms of calculating enthalpy and entropy. We find that at typical operating conditions for zeolite catalysis (400 °C), the physisorbed π-complex, and not the tertiary carbenium ion as often reported, is the most stable intermediate. This method paves the way for sampling-based techniques to calculate the accurate free energies in a broad range of chemistry-related disciplines, thus presenting a big step forward toward predictive modeling.

Rigid Body Approximation for the Anharmonic Description of Molecule-Surface Vibrations

We present an anharmonic approach for molecule-surface vibrations that employs rigid body coordinates, based on the Rodrigues rotation formula, to describe curvilinear displacements (rotations and translations) of the molecule along normal modes. These displacements are used to calculate energy data points from which one-dimensional polynomial potentials are fitted using cubic splines. In these potentials, for each of the six rigid body modes separately, one-dimensional Schrödinger equations are solved with harmonic oscillator or Fourier functions (for pure rotations) as basis sets. The anharmonic vibrational energies obtained are used to calculate partition functions and from them enthalpies, entropies, and Gibbs free energies of adsorption. Our numerical implementation has been successfully tested for Morse and cosine potentials with known analytical solutions. The methods have been applied to adsorption of CH₄ on the hydroxyl group of the proton form of the chabazite zeolite (H-CHA), as well as to adsorption of CH₄ and CO on the Mg²⁺ ions of the metal-organic framework (MOF) Mg₂(dobdc). To obtain the best estimates for thermodynamic functions, we include the coupling between molecule-surface vibrations and intrasystem vibrations at the harmonic level. The calculated Gibbs free energies show that the coupling is small for CH₄/H-CHA and CO/MOF (between -0.7 and +0.1 kJ/mol) but substantial for CH₄/MOF (-3.4 kJ/mol). The predicted anharmonic effect on the Gibbs free energy of adsorption for CH₄/H-CHA, CH₄/MOF, and CO/MOF is -4.7, 0.3 ± 0.7, and -2.4 ± 0.6 kJ/mol, respectively, which results in +4.2, +0.9 ± 0.7, and -0.4 ± 0.6 kJ/mol, respectively, for the deviation from experiment. This is well within chemical accuracy limits (±4.2 kJ/mol) for the adsorption of CH₄ and CO in the MOF. The larger deviation for CH₄/H-CHA, at the edge of the chemical accuracy range, is most likely due to contributions from soft zeolite modes which are neglected in our approach.

Kinetics of NH3 Desorption and Diffusion on Pt: Implications for the Ostwald Process

We report accurate time-resolved measurements of NH₃ desorption from Pt(111) and Pt(332) and use these results to determine elementary rate constants for desorption from steps, from (111) terrace sites and for diffusion on (111) terraces. Modeling the extracted rate constants with transition state theory, we find that conventional models for partition functions, which rely on uncoupled degrees of freedom (DOFs), are not able to reproduce the experimental observations. The results can be reproduced using a more sophisticated partition function, which couples DOFs that are most sensitive to NH₃ translation parallel to the surface; this approach yields accurate values for the NH₃ binding energy to Pt(111) (1.13 ± 0.02 eV) and the diffusion barrier (0.71 ± 0.04 eV). In addition, we determine NH₃'s binding energy preference for steps over terraces on Pt (0.23 ± 0.03 eV). The ratio of the diffusion barrier to desorption energy is ∼0.65, in violation of the so-called 12% rule. Using our derived diffusion/desorption rates, we explain why established rate models of the Ostwald process incorrectly predict low selectivity and yields of NO under typical reactor operating conditions. Our results suggest that mean-field kinetics models have limited applicability for modeling the Ostwald process.

Chemically Accurate Vibrational Free Energies of Adsorption from Density Functional Theory Molecular Dynamics: Alkanes in Zeolites

We present a methodology to compute, at reduced computational cost, Gibbs free energies, enthalpies, and entropies of adsorption from molecular dynamics. We calculate vibrational partition functions from vibrational energies, which we obtain from the vibrational density of states by projection on the normal modes. The use of a set of well-chosen reference structures along the trajectories accounts for the anharmonicities of the modes. For the adsorption of methane, ethane, and propane in the H-CHA zeolite, we limit our treatment to a set of vibrational modes localized at the adsorption site (zeolitic OH group) and the alkane molecule interacting with it. Only two short trajectories (1–20 ps) are required to reach convergence (<1 kJ/mol) for the thermodynamic functions. The mean absolute deviations from the experimentally measured values are 2.6, 2.8, and 4.7 kJ/mol for the Gibbs free energy, the enthalpy, and the entropy term (−TΔS), respectively. In particular, the entropy terms show a major improvement compared to the harmonic approximation and almost reach the accuracy of the previous use of anharmonic frequencies obtained with curvilinear distortions of individual modes. The thermodynamic functions so obtained follow the trend of the experimental values for methane, ethane, and propane, and the Gibbs free energy of adsorption at experimental conditions is correctly predicted to change from positive for methane (5.9 kJ/mol) to negative for ethane (−4.8 kJ/mol) and propane (−7.1 kJ/mol).

Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction-the dissociation of molecular nitrogen on ruthenium-at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an "on-top" adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. These findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.