Application to Bound Energy Levels and Semiclassical Rate Theory

Department of Chemistry,
University of California, and

Chemical Sciences Division,
Lawrence Berkeley Laboratory

Berkeley, California 94720

A new method, *Mixed-Diagonalization*, is introduced in
which an effective Hamiltonian operator acting on a reduced dimensional
space is constructed using the similarity transformations
of canonical Van Vleck perturbation theory (CVPT).
This construction requires the characterization of modes into
two categories: global and local, which in the bound vibrational
problem are tantamount to the large and small amplitude vibrations,
respectively.
The local modes in the Hamiltonian are projected out by
CVPT, and the resulting Hamiltonian operator acts
only on the space of global modes.
The method affords the treatment of energy levels of bound systems
in which some vibrational assignments are possible.
In addition, it
systematically provides a reduced dimensional Hamiltonian
which is more amenable to exact numerical solution than the original
full-dimensional Hamiltonian.
In recent work, a semiclassical transition
state theory (SCTST) rate expression has been written in terms of a
Hamiltonian operator parameterized by the imaginary action along the
local reaction path in the transition state region
[Chem. Phys. Let. **214**, 129 (1993)].
We show that the Hamiltonian constructed by
mixed-diagonalization has this form, and can be used to obtain
more accurate semiclassical rate expressions.

- i Introduction
- ii Standard CVPT for Vibrational Hamiltonians
- iii Mixed-Diagonalization
- iv Application to Bound 2-Dimensional Anharmonic Oscillator
- v Application to Collinear Reaction
- vi Concluding Remarks
- vii Acknowledgments
- A Appendix
- References