Quantum-dynamical study in three-dimensional space of the exchange reaction H+ClH'→HCl+H' with zero total angular momentum $ \left( {\overrightarrow J = 0} \right) $

Abstract

WITH ZERO TOTAL ANGULAR MOMENTUM ( r J = 0) UDC 544.435 D. P. Babyuk and V. V. NechiporukThe 3D quantum dynamics of the exchange reaction H + ClH¢ ® HCl + H¢ with zero angular momentum was studied. The nonstationary Schrödinger equation was solved by expansion into a basis set using discrete variable representation. The probabilities of the reaction were determined in relation to the total energy for the ground and first excited vibrational states.After calculation of the high-precision potential energy surface (PES) for the H 2 Cl system [1] the exchange reaction Cl + H 2 ® ClH + H [2] and its isotopic analog Cl + D 2 ® ClD + D [3] were studied in terms of quantum approaches. However, attention was not paid to the dynamics of the substitution reaction H + ClH¢ ® HCl + H¢, which can also be studied on the basis of the PES and is an example of interaction of the light atom-heavy atom-light atom type. A characteristic feature of such a reaction is the relatively smooth behavior of the wave packet during passage of the reaction band on the PES. In this case it is possible to use the method of quantum trajectories (MQT) without any modifications [4,5]. Indeed this reaction became the first real system for which MQT was used for the case of a collinear reaction [6]. Before using MQT for this reaction with account of the rotational motion and with a number of degrees of freedom greater than two it is expedient to study it in terms of traditional quantum methods. The aim of the present work was therefore to investigate this system with the inclusion of all the independent coordinates. The only restriction was the equality of the total angular momentum of the system to zero.We will consider the collision of the H atom with the HCl molecule, leading to substitution of the hydrogen. Our task was to calculate the probability of the reaction in relation to the energy of the collisions and the initial state of the HCl molecule. The quantum-dynamic approach implies accounting for the wave characteristics of all three nuclei of the interacting particles. The dynamic equation will then be the nonstationary Schrödinger equation: