Thermal Rate Constants for Polyatomic Reactions: First Principles Quantum Theory

Eigenstate calculation in the state-averaged (multi-layer) multi-configurational time-dependent Hartree approach

A new approach for the calculation of eigenstates with the state-averaged (multi-layer) multi-configurational time-dependent Hartree (MCTDH) approach is presented. The approach is inspired by the recent work of Larsson [J. Chem. Phys. 151, 204102 (2019)]. It employs local optimization of the basis sets at each node of the multi-layer MCTDH tree and successive downward and upward sweeps to obtain a globally converged result. At the top node, the Hamiltonian represented in the basis of the single-particle functions (SPFs) of the first layer is diagonalized. Here p wavefunctions corresponding to the p lowest eigenvalues are computed by a block Lanczos approach. At all other nodes, a non-linear operator consisting of the respective mean-field Hamiltonian matrix and a projector onto the space spanned by the respective SPFs is considered. Here, the eigenstate corresponding to the lowest eigenvalue is computed using a short iterative Lanczos scheme. Two different examples are studied to illustrate the new approach: the calculation of the vibrational states of methyl and acetonitrile. The calculations for methyl employ the single-layer MCTDH approach, a general potential energy surface, and the correlation discrete variable representation. A five-layer MCTDH representation and a sum of product-type Hamiltonian are used in the acetonitrile calculations. Very fast convergence and order of magnitude reductions in the numerical effort compared to the previously used block relaxation scheme are found. Furthermore, a detailed comparison with the results of Avila and Carrington [J. Chem. Phys. 134, 054126 (2011)] for acetonitrile highlights the potential problems of convergence tests for high-dimensional systems.

First-Principles Theory for the Reaction of Chlorine with Methane

A full-dimensional quantum dynamics simulation of the Cl + CH₄ → HCl + CH₃ reaction based on first-principles theory is reported. Accurate thermal rate constants are calculated, and perfect agreement with experiment is obtained. Despite the heavy atoms present in both reactants, the passage of the reaction barrier is found to occur within only a few tens of femtoseconds. This surprisingly short time scale results from correlated motion of the transferring hydrogen atom and the hydrogen atoms in the methyl fragment which facilitates irreversible barrier passage without relevant participation of heavy atoms. Resonance effects resulting from the heavy-light-heavy characteristics of the reaction system, which were observed in reactive scattering studies, do not affect the thermal rate constant.

Symmetries in the multi-configurational time-dependent Hartree wavefunction representation and propagation

In multi-configurational time-dependent Hartree (MCTDH) approaches, different multi-layered wavefunction representations can be used to represent the same physical wavefunction. Transformations between different equivalent representations of a physical wavefunction that alter the tree structure used in the multi-layer MCTDH wavefunction representation interchange the role of single-particle functions (SPFs) and single-hole functions (SHFs) in the MCTDH formalism. While the physical wavefunction is invariant under these transformations, this invariance does not hold for the standard multi-layer MCTDH equations of motion. Introducing transformed SPFs, which obey normalization conditions typically associated with SHFs, revised equations of motion are derived. These equations do not show the singularities resulting from the inverse single-particle density matrix and are invariant under tree transformations. Based on the revised equations of motion, a new integration scheme is introduced. The scheme combines the advantages of the constant mean-field approach of Beck and Meyer [Z. Phys. D 42, 113 (1997)] and the singularity-free integrator suggested by Lubich [Appl. Math. Res. Express 2015, 311]. Numerical calculations studying the spin boson model in high dimensionality confirm the favorable properties of the new integration scheme.

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Thermal rate constants for Mu + CH₄, Mu + C₂H₆ and Mu + C₃H₈ and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C₃H₈ at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH₄ using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.

Kinetic isotope effects in the water forming reaction H2/D2 + OH from rigorous close-coupling quantum dynamics simulations

Rigorous quantum dynamics simulations of thermal rate constants and kinetic isotope effects for the water-forming H₂/D₂ + OH reaction are presented, which show increased tunneling below 300 K and can serve as benchmarks for approximate methods.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

Bimolecular reaction rates from ring polymer molecular dynamics: application to H + CH4 → H2 + CH3

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH(4) → H(2) + CH(3). The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases.

Thermochemistry and kinetics of acetonylperoxy radical isomerisation and decomposition: a quantum chemistry and CVT/SCT approach

CBS-QB3 calculations have been used to determine thermochemical and kinetic parameters of the isomerisation and decomposition reactions of the acetonylperoxy radical, CH3C(O)CH2OO* , which has been formed via the reaction of acetonyl radical with O2 leading to the formation of an energised peroxy adduct with a calculated well depth of near 111 kJ mol(-1). This species can undergo subsequent 1,5 and 1,3 H-shifts to give the primary and secondary radicals: C*H2C(O)CH2OOH and CH3C(O)C*HOOH, respectively, or rearrange to give a 3-methyl-1,2-dioxetan-3-yloxy radical. Rate constants for isomerisation and subsequent decomposition have been estimated using canonical variational transition state theory with small curvature tunneling cvt/sct. The variational effect for the isomerisation channels is only moderate but the tunneling correction is significant at temperatures up to 1000 K; the formation of a primary radical by a 1,5-shift is the main reaction channel and the competition with the secondary one starts only at around 1500 K. The fate of the primary acetonylhydroperoxy radical is predominantly to form oxetan-3-one while the ketene and 1-oxy-3-hydroxyacetonyl radical channels only compete with the formation of oxetan-3-one at temperatures >1200 K. In addition, consistent and reliable enthalpies of formation have been computed for the molecules acetonylhydroperoxide, 1,3-dihydroxyacetone, methylglyoxal and cyclobutanone, and for some related radicals.