Quantum reaction dynamics of an asymmetric exoergic heavy–light–heavy system : Cl + HBr Ç HCl + Br Gennady V. MilÏnikov,¤ Oleg I. Tolstikhin,” Katsuyuki Nobusada and Hiroki Nakamura* Division of T heoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan Received 15th October 1998, Accepted 8th December 1998 Quantum dynamics calculations for HBr ] Cl ] Br ] HCl are carried out using the hyperspherical elliptic coordinates. The concepts of potential ridge and nonadiabatic transitions at avoided crossings introduced previously for isoergic and symmetric three-dimensional heavyÈlightÈheavy reactions are conÐrmed to be useful to clarify the mechanisms of vibrationally nonadiabatic reactions in this exo-(or endo-)ergic system. The role of important avoided crossings which dominate the reaction dynamics is illustrated. I Introduction In recent years, various methods based on the hyperspherical coordinate approach have been proposed and successfully uti- lized for numerical studies of atomÈdiatom chemical reac- tions.1h7 Although these give an e†ective tool for evaluating an S-matrix for di†erent collision processes in chemical systems, a general qualitative understanding of the reaction mechanisms is still not sufficient. It has not yet been possible to elucidate the e†ects of potential energy surface (PES) topography on the dynamics and to clarify the relative roles of various competitive processes without carrying out time con- suming accurate numerical calculations even in the atomÈ diatom case. Furthermore, in many cases those accurate numerical results are not sufficient enough to qualitatively reveal the e†ects of the topography of the PES and mass com- binations of the reactants. Any new idea which can provide such qualitative insights is strongly desirable. One of the helpful and important characteristics of the PES is, of course, the saddle point which gives the reaction barrier in the classical sense. Obviously, it gives only a minor portion of the information embedded in the PES. In the case of col- linear atomÈdiatom reactions Ohsaki and Nakamura noted the importance of the mountain ridge of the PES (potential ridge line) as its generalization.8 This provides the boundary between fragmentation and condensation9 and represents the area where rearrangement processes occur. Such a qualitative notion was made possible in the case of collinear reactions simply by assuming the approximate adiabatic separability between the hyperradius o and the hyperangle.10,11 As far as the reactive transitions are concerned, this implies that the hyperradial motion can be treated adiabatically except at some small regions where the adiabatic potential curves depict avoided crossings and nonadiabatic transitions become important. The same concept should pertain equally to the 3D case, although at Ðxed hyperradius we are still on the 2D hypersphere and the adiabatic channel functions are much more complicated. Kubach and his coworkers have noted the signiÐcance of avoided crossings in 3D heavyÈlightÈheavy ¤ Permanent address : Institute of Structural Macrokinetics, Russian Academy of Sciences, Chernogolovka, Moscow region, Russia. ” Permanent address : Kurchatov Institute, Russian Academy of Sci- ences, Moscow, Russia. (HLH) reactions using the BornÈOppenheimer separation approximation.12 Recently, Tolstikhin et al. came up with the new hyperspherical elliptic coordinates for studying three- body Coulombic systems.13 Tolstikhin and Nakamura14 implemented this approach for the hydrogen transfer reactions in 3D HLH systems, taking the reaction O(3P) ] HCl ] OH ] Cl as an example.14 Not only its high efficiency has been demonstrated, but also the reaction mecha- nisms have been clariÐed.14,15 The heart of the method con- sists of a new way of parameterizing the hypersphere in terms of the hyperspherical elliptic coordinates m, g which allow us to make a second step of hierarchy in the adiabatic separa- tion.14 Namely, in the HLH chemical reaction systems the adiabatic Hamiltonian at Ðxed hyperradius o permits a further adiabatic separation between two hyperangle variables m and g, and the quantum number of the m-motion corre- n m sponds to the vibrational quantum numbers both for initial and Ðnal arrangements. This not only greatly simpliÐes the solution of the eigenvalue problem on the hypersphere but also enables us to clarify qualitatively the reaction mecha- nisms. The approximate adiabatic separability makes it pos- sible to consider the manifold of a given and thus to reduce n m approximately the dimensionality of the problem. By using this novel formulation, the notion of ridge line and non- adiabatic transitions at avoided crossings was extended to the 3D reactions and applied to O(3P) ] HCl ] OH ] Cl and Cl ] HCl ] HCl ] Cl.15 h17 Such a consideration looks rele- vant mostly for these isoergic and symmetric reactions in which the processes without vibrational excitation of products are dominant, and it is not clear whether this concept is still pertinent to the more general case of vibrationally endoergic or exoergic reactions. Although in ref. 16 and 17 we have con- Ðrmed to some extent that the answer is positive, in this paper we shall directly demonstrate this. As an example we consider the 1, 2) reaction, using HBr(v i \ 0) ] Cl ] Br ] HCl(v f \ 0, the LEPS PES.18 Here the products are mostly produced in the Ðnal vibrational quantum number and 2. v f \ 1 This paper is organized as follows. The next section outlines the implemented numerical scheme of exact quantum calcu- lations for the entitled reactions for the zero total angular momentum quantum number J \ 0. Section III presents the calculated results of cumulative reaction probabilities. Section IV provides the results of state-to-state reaction probabilities and gives a qualitative analysis of the reaction mechanisms based on the concept of nonadiabatic transitions at avoided Phys. Chem. Chem. Phys., 1999, 1, 1159È1163 1159 Published on 01 January 1999. Downloaded on 10/11/2014 07:34:43. View Article Online / Journal Homepage / Table of Contents for this issue