Ralph Welsch

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.

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.

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.

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.

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.

Thermal flux based analysis of state-to-state reaction probabilities

Flux correlation functions facilitate rigorous quantum mechanical calculations of reaction rates and initial state-selected reaction probabilities. Combined with an efficient multi-dimensional wave packet propagation employing the multi-configurational time-dependent Hartree scheme, polyatomic reactions can be accurately studied. Very recently, the approach has been generalized to the treatment of fully resolved state-to-state reaction probabilities. The generalized flux correlation function employed utilizes two flux operators corresponding to a dividing surface located in the transition state region and two additional dividing surfaces located in the reactant and product asymptotic areas. The present work provides further analysis of this generalized flux correlation function. It studies state-to-state reaction probabilities of the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0 and investigates the contributions of the different thermal flux eigenstate pairs, which correspond to vibrational states of the activated complex.

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.

A new method to generate spin-orbit coupled potential energy surfaces: Effective relativistic coupling by asymptotic representation

A new method has been developed to generate fully coupled potential energy surfaces including derivative and spin-orbit coupling. The method is based on an asymptotic (atomic) representation of the molecular fine structure states and a corresponding diabatization. The effective relativistic coupling is described by a constant spin-orbit coupling matrix and the geometry dependence of the coupling is accounted for by the diabatization. This approach is very efficient, particularly for certain systems containing a very heavy atom, and yields consistent results throughout nuclear configuration space. A first application to a diatomic system is presented as proof of principle and is compared to accurate ab initio calculations. However, the method is widely applicable to general polyatomic systems in full dimensionality, containing several relativistic atoms and treating higher order relativistic couplings as well.

Rigorous close-coupling quantum dynamics calculation of thermal rate constants for the water formation reaction of H2 + OH on a high-level PES

Thermal rate constants for the prototypical H2 + OH → H + H2O reaction are calculated using quantum dynamics simulations including all degrees of freedom and accurately accounting for overall rotation via close-coupling. Results are reported for a recent, highly accurate neural network potential [J. Chen et al., J. Chem. Phys. 138, 154301 (2013)] and compared to results obtained on a previous, semi-empirical potential. Thermal rate constants between 300 K and 1000 K are reported and very good agreement with experimental work is found. Additionally, reasonable agreement for the close-coupling simulations on both potentials is found. In contrast to previous work, we find that the J-shifting approximation works well for the title reaction given that a high-level PES is used for the dynamics calculation. Moreover, the importance of treating the spin-orbit coupling in the reactant partition function is discussed. The highly accurate results reported here will provide a benchmark for the development of approximate methods.