Full dimensional quantum calculations of the CH4+H→CH3+H2 reaction rate

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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.

Section: Introductionmentioning

confidence: 99%

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

Welsch

Huarte-Larrañaga

Manthe

2012

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“…Full-dimensional quantum dynamics calculations studying all initial state-selected reaction probabilities of the H + CH 4 → H 2 +CH 3 reaction relevant at total energies below 0.58 eV are presented. The calculations employ a flux correlation function based approach to obtain the initial state-selected reaction probabilities: A complete set of wavepackets is generated at the top of the reaction barrier and propagated into the reactant asymptotic region.…”

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confidence: 99%

“…Rigorous full-dimensional quantum dynamics calculations for X +CH 4 reactions have been restricted to the calculation of thermal rate constants and cumulative reaction probabilities for J =0. [4][5][6][7][8][9][10][11][12] Quantum mechanical studies of state-resolved observables have been restricted to reduced-dimensional calculations. The most elaborate studies could include six to seven degrees of freedom explicitly.…”

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confidence: 99%

“…This reaction has emerged as the prototypical benchmark example of a X +CH 4 reaction studied in theoretical research. [4][5][6]8,9,[13][14][15][17][18][19][20][21][22][23][24][25] Most of this research has been based on the Jordan-Gilbert potential energy surface ͑JG PES͒. 26 To allow comparison with previous theoretical work, the JG PES is used also in the present work despite the fact that meanwhile a more accurate global 25 PES has become available.…”

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confidence: 99%

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Communications: A rigorous transition state based approach to state-specific reaction dynamics: Full-dimensional calculations for H+CH4→H2+CH3

Schiffel

Manthe

2010

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“…However, due to the fact that computational effort grows exponentially with dimensionality, it is impractical at present to study polyatomic dynamical processes exactly in full dimensions although there has been some progress in this direction. 5 Naturally, one has to resort to the reduced dimensionality approach to cut down the number of degrees of freedom included in dynamical studies, or some computational approximate methods to overcome the scaling of effort with dimensionality.…”

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confidence: 99%

Continuous configuration time-dependent self-consistent field method for polyatomic quantum dynamical problems

Zhang

Bao

Yang

et al. 2005

A new continuous configuration time-dependent self-consistent field method has been developed to study polyatomic dynamical problems by using the discrete variable representation for the reaction system, and applied to a reaction system coupled to a bath. The method is very efficient because the equations involved are as simple as those in the traditional single configuration approach, and can account for the correlations between the reaction system and bath modes rather well. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1869496͔The last decade has witnessed significant progress in quantum mechanical studies of dynamical chemical processes at the molecular level. The development of the timedependent wave packet ͑TDWP͒ method has made it possible to perform exact quantum mechanical calculations for four-atom systems. [1][2][3][4] The recent report on the state-to-state integral cross sections for the H + H 2 O reaction suggests that we are close to solving four-atom reactive scattering problems completely. 2 The grand challenge in the field of quantum dynamics now is to develop practical yet accurate methods to study polyatomic dynamical problems involving many atoms. However, due to the fact that computational effort grows exponentially with dimensionality, it is impractical at present to study polyatomic dynamical processes exactly in full dimensions although there has been some progress in this direction. 5 Naturally, one has to resort to the reduced dimensionality approach to cut down the number of degrees of freedom included in dynamical studies, or some computational approximate methods to overcome the scaling of effort with dimensionality.A promising approach is the time-dependent selfconsistent field ͑TDSCF͒ method. [6][7][8][9][10][11][12][13][14][15] In the simplest version, i.e., the single configuration time-dependent self-consistent field ͑SC-TDSCF͒ approach, the wave function of the system is written as a direct product of the wave functions for subsystems. [7][8][9][10]12 A principal drawback of SC-TDSCF is that it replaces exact interaction between subsystems by meanfield coupling, resulting in the lack of correlations between subsystems. One way to account for the important correlations neglected in SC-TDSCF is to add wave functions with different configurations to give more flexibility to the wave function of the system, resulting in the so-called multiconfiguration time-dependent self-consistent field ͑MC-TDSCF͒ method. 6,13-15 Wave functions with different configurations are usually constructed by imposing orthogonal condition explicitly, making it hard to use more than a few configurations in numerical implementation. Furthermore, the resulting equations for MC-TDSCF are very complicated compared to those in SC-TDSCF method. For these reasons, MC-TDSCF has only been applied to some model problems. The closely related multiconfiguration time-dependent Hartree method ͑MCTDH͒ generalizes MC-TDSCF in a systematic way, thus eliminating the need for choices of the TDSCF states. 16,17 It ha...