H. Ushiyama et K. Takatsuka, SEMICLASSICAL STUDY ON MULTIDIMENSIONAL EFFECTS IN TUNNELING CHEMICAL-REACTIONS - TUNNELING PATHS AND TUNNELING TUBES, The Journal of chemical physics, 106(17), 1997, pp. 7023-7035
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.