VPT2+K Spectroscopic Constants and Matrix Elements of the Transformed Vibrational Hamiltonian of a Polyatomic Molecule with Resonances Using Van Vleck Perturbation Theory
Dr. William Polik
Vibrational levels of polyatomic molecules are analyzed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalizing the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for formaldehyde are included. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.
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