Quantum Transition State Concept Research Articles

Counter-propagating wave packets in the quantum transition state approach to reactive scattering.

The quantum transition state concept provides an intuitive and numerically efficient framework for the description of quantum state-resolved reactive scattering and thermal reaction processes. Combining multiconfigurational time-dependent Hartree wave packet dynamics calculations with a flux correlation function based analysis, rigorous full-dimensional calculations of initial state-selected and state-to-state reaction probabilities for six atom reactions are feasible. In these calculations, a set of wave packets is generated in the transition state region, propagated into the asymptotic area, and analyzed. In the present work, an alternative approach which employs counter-propagating sets of wave packets is introduced. Outgoing wave packets started in the transition state region are matched with incoming wave packets generated in the reactant (or product) asymptotic area. Studying the H + CH4 → H2 + CH3 reaction as a prototypical example, one finds that the incoming wave packets can be propagated closely up to the transition state region with minor numerical effort. Employing cross correlation functions of incoming and outgoing wavefunctions, the propagation times required for the outgoing wave packet and thus the numerical costs of the entire calculation can be reduced significantly. Detailed full-dimensional calculations studying initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction are presented to illustrate the new approach. It is found that converged results can be obtained using shorter propagation times of the outgoing wave packets and less single-particle functions.

Full-dimensional quantum dynamics calculations for H + CHD3 → H2 + CD3: The effect of multiple vibrational excitations

Initial state-selected reaction probabilities for the H + CHD3 → H2 + CD3 reaction starting from various different ro-vibrational states of CHD3 are studied by accurate full-dimensional (12D) quantum dynamics calculation for vanishing total angular momentum (J = 0). The calculations employ the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach. First results focusing on fundamental excitations and the reactivity borrowing effect were communicated recently [R. Ellerbrock and U. Manthe, J. Chem. Phys. 147, 241104 (2017)]. In the present work, all vibrational states of the methane reactant are considered. It is found that energy deposited in overtones and combination bands is less efficient in promoting reactivity than expected from separable or sudden models. Furthermore, the effects of rotational excitation on the reactivity are studied in detail.

Communication: Reactivity borrowing in the mode selective chemistry of H + CHD3 → H2 + CD3.

Quantum state-resolved reaction probabilities for the H + CHD3 → H2 + CD3 reaction are calculated by accurate full-dimensional quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree approach and the quantum transition state concept. Reaction probabilities of various ro-vibrational states of the CHD3 reactant are investigated for vanishing total angular momentum. While the reactivity of the different vibrational states of CHD3 mostly follows intuitive patterns, an unusually large reaction probability is found for CHD3 molecules triply excited in the CD3 umbrella-bending vibration. This surprising reactivity can be explained by a Fermi resonance-type mixing of the single CH-stretch excited and the triple CD3 umbrella-bend excited vibrational states of CHD3. These findings show that resonant energy transfer can significantly affect the mode-selective chemistry of CHD3 and result in counter-intuitive reactivity patterns.

H+CH4 → H2 + CH3 initial state-selected reaction probabilities on different potential energy surfaces

Initial state-selected reaction probabilities for the H+CH4→H2+CH3 reaction on a recently developed potential energy surface which employs neutral network fitting based on permutational invariant polynomials are reported. The quantum dynamics calculations use the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach and study the reaction process in full-dimensionality for vanishing total angular momentum. A detailed comparison with previous results obtained on other high-level potential energy surfaces is given. The connection between the level of quantum state resolution and the sensitivity of the results on differences in the potential energy surfaces is highlighted. Employing a decomposition of the total reactivity into contributions of the different vibrational states of the activated complex, it is found that differences between the potential energy surfaces are mainly related to the umbrella motion of the methyl group.

Full-dimensional and reduced-dimensional calculations of initial state-selected reaction probabilities studying the H + CH4 → H2 + CH3 reaction on a neural network PES.

Initial state-selected reaction probabilities of the H + CH4 → H2 + CH3 reaction are calculated in full and reduced dimensionality on a recent neural network potential [X. Xu, J. Chen, and D. H. Zhang, Chin. J. Chem. Phys. 27, 373 (2014)]. The quantum dynamics calculation employs the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach and rigorously studies the reaction for vanishing total angular momentum (J = 0). The calculations investigate the accuracy of the neutral network potential and study the effect resulting from a reduced-dimensional treatment. Very good agreement is found between the present results obtained on the neural network potential and previous results obtained on a Shepard interpolated potential energy surface. The reduced-dimensional calculations only consider motion in eight degrees of freedom and retain the C3v symmetry of the methyl fragment. Considering reaction starting from the vibrational ground state of methane, the reaction probabilities calculated in reduced dimensionality are moderately shifted in energy compared to the full-dimensional ones but otherwise agree rather well. Similar agreement is also found if reaction probabilities averaged over similar types of vibrational excitation of the methane reactant are considered. In contrast, significant differences between reduced and full-dimensional results are found for reaction probabilities starting specifically from symmetric stretching, asymmetric (f2-symmetric) stretching, or e-symmetric bending excited states of methane.

Loss of Memory in H + CH4 → H2 + CH3 State-to-State Reactive Scattering.

State-to-state reaction probabilities for the H + CH4→ H2 + CH3 reaction are calculated by accurate full-dimensional quantum dynamics calculations employing the multilayer multiconfigurational time-dependent Hartree approach and the quantum transition-state concept. Reactions starting from different vibrational and rotational states of the methane reactant are investigated for vanishing total angular momentum. The vibrational state distributions of the products are found to be essentially independent of the initial rovibrational state of the reactants. The reaction products only show vibrational excitation in the methyl umbrella mode. No excitation in H2 vibration or another CH3 vibration is observed. Analyzing the results, the observed loss of vibrational memory can be explained by a transition-state-based view of the reaction process.

The role of the transition state in polyatomic reactions: initial state-selected reaction probabilities of the H + CH₄ → H₂ + CH₃ reaction.

Full-dimensional calculations of initial state-selected reaction probabilities on an accurate ab initio potential energy surface (PES) have been communicated recently [R. Welsch and U. Manthe, J. Chem. Phys. 141, 051102 (2014)]. These calculations use the quantum transition state concept, the multi-layer multi-configurational time-dependent Hartree approach, and graphics processing units to speed up the potential evaluation. Here further results of these calculations and an extended analysis are presented. State-selected reaction probabilities are given for many initial ro-vibrational states. The role of the vibrational states of the activated complex is analyzed in detail. It is found that rotationally cold methane mainly reacts via the ground state of the activated complex while rotationally excited methane mostly reacts via H-H-CH3-bending excited states of the activated complex. Analyzing the different contributions to the reactivity of the vibrationally states of methane, a complex pattern is found. Comparison with initial state-selected reaction probabilities computed on the semi-empirical Jordan-Gilbert PES reveals the dependence of the results on the specific PES.

Communication: Ro-vibrational control of chemical reactivity in H+CH₄→ H₂+CH₃: full-dimensional quantum dynamics calculations and a sudden model.

The mode-selective chemistry of the title reaction is studied by full-dimensional quantum dynamics simulation on an accurate ab initio potential energy surface for vanishing total angular momentum. Using a rigorous transition state based approach and multi-configurational time-dependent Hartree wave packet propagation, initial state-selected reaction probabilities for many ro-vibrational states of methane are calculated. The theoretical results are compared with experimental trends seen in reactions of methane. An intuitive interpretation of the ro-vibrational control of the chemical reactivity provided by a sudden model based on the quantum transition state concept is discussed.

Correlation functions for fully or partially state-resolved reactive scattering calculations.

Flux correlation functions and the quantum transition state concept are important tools for the accurate description of polyatomic reaction processes. Combined with the multi-configurational time-dependent Hartree approach, they facilitate rigorous full-dimensional calculations of cumulative and initial-state selected reaction probabilities for six atom reactions. In recent work [R. Welsch, F. Huarte-Larrañaga, and U. Manthe, J. Chem. Phys. 136, 064117 (2012)], an approach which allows one to calculate also state-to-state reaction probabilities within the quantum transition state concept has been introduced. This article presents further developments. Alternative generalized flux correlation functions are introduced and discussed. Equations for the calculation of fully state-resolved differential cross section using arbitrary definitions of the body fixed frame are derived. An approach for the efficient calculation of partially state-resolved observables as a function of the collision energy is introduced. Finally, numerical test studying the D + H2 reaction illustrate important aspects of the formalism.

Fast Shepard interpolation on graphics processing units: Potential energy surfaces and dynamics for H + CH4 → H2 + CH3

A strategy for the fast evaluation of Shepard interpolated potential energy surfaces (PESs) utilizing graphics processing units (GPUs) is presented. Speed ups of several orders of magnitude are gained for the title reaction on the ZFWCZ PES [Y. Zhou, B. Fu, C. Wang, M. A. Collins, and D. H. Zhang, J. Chem. Phys. 134, 064323 (2011)]. Thermal rate constants are calculated employing the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach. Results for the ZFWCZ PES are compared to rate constants obtained for other ab initio PESs and problems are discussed. A revised PES is presented. Thermal rate constants obtained for the revised PES indicate that an accurate description of the anharmonicity around the transition state is crucial.

Reaction dynamics with the multi-layer multi-configurational time-dependent Hartree approach: H + CH4 → H2 + CH3 rate constants for different potentials

The multi-layer extension of the multi-configurational time-dependent Hartree (MCTDH) approach is applied to the investigation of elementary bimolecular chemical reactions. Cumulative reaction probabilities and thermal rate constants of the H + CH(4) → H(2) + CH(3) reaction are calculated using flux correlation functions and the quantum transition state concept. Different coordinate systems and potential energy surfaces (PESs) are studied. The convergence properties of different layerings are investigated and the efficiency of multi-layer MCTDH approach is compared to the standard MCTDH approach. It is found that the multi-layer approach can decrease the numerical effort by more than an order of magnitude. The increased efficiency resulting from the multi-layer MCTDH approach is crucial for quantum dynamical calculations on recent global H + CH(4) → H(2) + CH(3) PESs, e.g., the ZBB3-PES [Z. Xie, J. M. Bowman, and X. Zhang, J. Chem. Phys. 125, 133120 (2006)] based on permutational invariant polynomials, which are numerically more demanding than earlier PESs. The results indicate that an accurate description of all transition state frequencies is important to obtain accurate thermal rate constants.

ChemInform Abstract: Accurate Calculations of Reaction Rates: Predictive Theory Based on a Rigorous Quantum Transition State Concept

AbstractReview: 135 refs.

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H(2)(ν, j) → HD(ν', j') + H reaction for J = 0.

Thermal Rate Constants for Polyatomic Reactions: First Principles Quantum Theory

The truly accurate knowledge of molecular dynamics phenomena is generally achieved through a combination of detailed experiments and first principle theory. The complexity of such a level of description had until recently restricted accurate studies to rather small systems. However, the sophistication of theoretical methods and massive technological developments have provided remarkable progress in the detailed knowledge of reactive events during the past three decades. Moreover, significant progress towards the detailed understanding of polyatomic reaction has been made in recent years. Detailed experimental and accurate theoretical studies of reactions involving more than only three or four atoms are becoming increasingly available. In this work, aspects of the theoretical work aiming at the accurate description of polyatomic reactions are reviewed. The present article focuses on the development of the first principle theory of reaction rates. It reviews theoretical developments and benchmark applications to reactions as CH4 + H → CH3 + H2 and CH4 + O → CH3 + OH. The importance of quantum effects for the thermal rate constants in different temperature regimes is discussed in detail. The accuracy of the classical transition state theory and of different approximate quantum theories is investigated in detail. A quantum transition state concept which facilitates accurate reaction rate calculations for polyatomic reaction is described. Benchmark results for the CH4 + H → CH3 + H2 reaction are shown which demonstrate that the accuracy of thermal rate constants calculated by first principle theory can rival the accuracy of available experimental data. The perspectives offered by these developments are discussed.