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A Combined Use of Perturbation Theory and Diagonalization:
Application to Bound Energy Levels and Semiclassical Rate Theory

Rigoberto Hernandez

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.