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

Abstract

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.

Calculation of state-to-state differential and integral cross sections for atom-diatom reactions with transition-state wave packets

“…Very recently, a new method for computing the reactive S-matrix elements has been proposed by Manthe and coworkers. 19 This method is based on the quantum transitionstate theory (QTST) of Miller,20,21 which was first introduced for the direct calculation of cumulative reaction probability (CRP) N(E) and thermal rate coefficient k(T) using a correlation based expression associated with the flux operator. When both dividing surfaces are placed at an identical position at or near the saddle point, the direct computation of the CRP or rate coefficient can be achieved by several numerical ways, [22][23][24][25][26] including an efficient approach based on a Fourier transform of the flux-flux autocorrelation functions obtained from a few transition-state wave packets (TSWPs).…”

“…The price to pay is that the initial TSWPs need be transformed into the appropriate Jacobi coordinates, but this transformation is performed only once. To this end, we follow Welsch et al 19 and use the thermal flux operator in defining the initial TSWPs, which are thus compact and smooth. Second, unlike the ISSWP approach, the entire S-matrix is obtained for all energies.…”

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

“…41,72,[74][75][76][77][78][79][80][81][82][83][84][85] a) Electronic mail: rwelsch@uni-bielefeld.de b) Electronic mail: uwe.manthe@uni-bielefeld. de Recently the quantum transition state concept was extended to facilitate the calculation of state-to-state reaction probabilities 86,87 hopefully enabling detailed state-to-state calculations for H + CH 4 → H 2 + CH 3 . These calculations would require a global potential energy surface (PES).…”

Communication: State-to-state dynamics of the Cl + H2O → HCl + OH reaction: Energy flow into reaction coordinate and transition-state control of product energy disposal

“…Very recently, we have reported quasi-classical trajectory (QCT) and initial state specific quantum dynamical (QD) calculations of the title reaction and its reverse using a recently developed global PES based on ab initio calculations. [24][25][26][27][28] The state-to-state quantum dynamical calculations reported here are made possible using a transition-state wave packet (TSWP) method recently proposed by Manthe and coworkers, [29][30][31] which is an extension of Miller's quantum transition-state theory. 32,33 Our implementation of this method has been discussed in detail elsewhere, 16,34 so only a brief outline is given here.…”