Transforming the Vibrational Hamiltonian of a Polyatomic Molecule Using Van Vleck Perturbation Theory
Dr. William Polik, Hope College
The goal of analyzing vibrational levels of polyatomic molecules with Van Vleck perturbation theory is to connect experimental and theoretical approaches for determining molecular potential energy surfaces. Chemists model reactivity of molecules along potential energy surfaces, which are functions of the internal coordinates of the molecule. Vibrations move along these coordinates, so measuring vibrations experimentally characterizes the potential energy surface. Vibrational energy levels are calculated from a quartic potential function via Van Vleck perturbation theory, a procedure that approximately diagonalizes the vibrational Hamiltonian. The matrix elements of the transformed Hamiltonian have been derived, and some of the equations are presented. A new computational technique, VPT2+K, will be defined by these results and used to calculate vibrational states.
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