Quantum trajectory method calculation of collinear collisions in the hydrogen exchange reaction H + ClH′ → HCl + H′

Abstract

The quantum trajectory method was used to study the collinear reaction H + ClH¢ ® HCl + H¢. The potential energy surface was calculated on the QCISD(T)/6-311++G(3df,3pd) level. The reaction probabilities are in good accord with the results obtained by solving the Schroedinger equation using the finite difference method.Collision theory has been used for calculating the rate constant of a chemical reaction. An important step in this approach is calculation of the reaction probability by studying the dynamics of the colliding particles under different initial conditions. Such an investigation in the framework of classical mechanics makes the calculation relatively inexpensive relative to computer time and resources. However, in reactions of light atoms, the wave properties of these atoms cannot be neglected since tunneling may distort the rate constant by an order of magnitude at low temperatures. A rigorous quantum mechanical approach is possible only for reaction systems encompassing not more than five atoms since computer resources increase exponentially with increasing degrees of freedom. The present record is for the study of the reaction H 2 + C 2 H ® H + C 2 H 2 , in which there are nine degrees of freedom. A calculation for the probability for one initial state using a computer cluster consisting of 64 processors took 168 h [1]. Thus, there is an obvious need for alternative quantum methods permitting us to economize on computer resources. One such approach is the quantum trajectory method (QTM) [2,3]. This method has recently been used to calculate reaction probabilities for a model system consisting of 200 degrees of freedom [4]. Attempts to use QTM for actual systems have not yet been very successful due to singularities arising at nodes of the wave functions arising due to interferences of parts of the reflected and incident wave packet. For example, for the simplest system in the hydrogen exchange reaction H + H¢H ® H¢ + H 2 , strong interference makes the use of QTM impossible. On the other hand, we have already noted the possibility of using QTM for collinear light atom-heavy atom-light atom collisions. Thus, in the present work, we selected the reaction H + ClH¢ ® HCl + H¢ and the probability of this reaction was calculated using QTM.The initial step in collision theory is the Born-Oppenheimer principle and calculation of the potential energy surface. Electron correlation plays an important role in the system studied and many previous semiempirical methods have given different values of the potential barrier. Thus, the quantum-chemical calculations should be carried out on a high level. We selected QCISD/6-311++G(3df,3pd). The energy of the collinear ClH 2 system was calculated at 648 points using the GAUSSIAN03 package [5]. The potential energy surface (PES) obtained was virtually identical quantitatively with the PES calculated using a higher level ab initio method [6]. The height of the potential barrier on the calculated surface is 18.42 kcal/mol for r HCl = 2.79 Å. The surface has van der Waals...

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) $

“…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 investigated space was restricted to values of the linear coordinates R and r between 1.5 and 7.5 [R 0 and R k in Eq. (6)]. Artificial interference resulting from edge effects was prevented by the use of the absorption potential by analogy with [11].…”