SEMICLASSICAL STUDY ON MULTIDIMENSIONAL EFFECTS IN TUNNELING CHEMICAL-REACTIONS - TUNNELING PATHS AND TUNNELING TUBES

The effects of multidimensionality in the quantum mechanical tunneling of chemical reactions are investigated. The aim of the present report is twofold. In the first place, we construct a new semiclassical theo ry to describe the tunneling by incorporating nonclassical solutions o f the time-dependent Hamilton-Jacobi equation into the Feynman kernel. A systematic class of complex-valued (nonclassical) solutions for the time-independent Hamilton-Jacobi equation has been found that are gen erated along non-Newtonian paths in real-valued configuration space [K . Takatsuka and H. Ushiyama, Phys. Rev. A 51, 4353 (1995)]. In the pre sent paper, the straightforward extension is applied to the time-depen dent Hamilton-Jacobi equation, the solutions of which describe the tun neling in chemical reactions. It is shown that no damping factor due t o the tunneling arises from the preexponential factor in the thus obta ined nonclassical kernel, since it is still real valued, aside from th e complex phase due to the Maslov index, and moreover its functional f orm is essentially the same as in the nontunneling case. Thus only the imaginary part of the action integral is responsible for the damping. A quasiclassical treatment of the semiclassical mechanics is develope d to characterize the real-valued tunneling paths. In the second-half of this paper, some typical tunneling reactions in collinear three ato mic systems on the LEPS (London-Eyring-Polanyi-Sato) potential surface are investigated in terms of our semiclassical theory. The effect of the initial energy distribution among the vibrational and translationa l modes is investigated asking which is preferable for tunneling and w hat is the resultant distribution of the energy in the product molecul es. The following two factors to control the tunneling reactions are m ainly examined as our first case study: (a) the mass effects featuring heavy-light-heavy and light-heavy-light patterns and (b) the anisotro py of the potential surface, namely, the early or late barrier. Tunnel ing paths of the types of Marcus-Coltrin and Miller-George ate both ge nerated spontaneously. A path of Marcus-Coltrin type takes a major rol e when the translational energy dominates in tunneling, while that of Miller-George type is dominant in a case where the vibrational excitat ion is important. As a distinguished feature of the multidimensionalit y in tunneling, we have identified what we call a tunneling tube, in w hich a;bunch of the tunneling paths are involved emanating from the so -called caustic line. It turns out that the width of the tunneling tub e determines in part the final energy distribution among the product v ibrational modes. (C) 1997 American Institute of Physics.