The aim of this work is twofold. In the first part, a detailed description is given of a specific vibrational model, designed for calculations on the vibrational energy levels in benzene and benzene isotopic species of D 6h symmetry. For the description of the C-H stretch system in benzene, a local mode (LM) formalism was applied, while, for the remaining non-C-H stretch vibrations, a symmetrized mode (SM) treatment was applied: this was called the combined LM/SM model. The model is based on a set of complex symmetrized curvilinear vibrational coordinates, which can be expressed as simple linear combinations of Whiffen's coordinates. The description in terms of complex symmetrized coordinates and wave functions allows for the construction of a separable symmetrized infinite-dimensional vibrational basis set, which is of crucial importance for large-scale calculations. In the second part of this work, using the described complex symmetrized LM/ SM vibrational model, calculations have been carried out on a large number of vibrational energy levels of four benzene D 6h isotopomers. The aim of the calculations was to redetermine a reliable set of harmonic force constants for benzene. Some of the force constant values obtained in the present work are substantially different from previous determinations by other authors. Using the presently determined set of harmonic force constant values in the calculations, a very good fit has been obtained to a large number of experimentally measured vibrational (both fundamental and overtone) energy levels of various symmetries, belonging to all four D 6h benzene isotopomers: C

In this work a fully symmetrized quantum mechanical description of vibrational motion in terms of complex vibrational coordinates and complex basis wavefunctions is outlined, designed for studying vibrational level mixing and intramolecular vibrational energy redistribution (IVR) around CH stretch overtone states in benzene. Symmetrized local mode (LM) formalism has been applied to the CH stretch system, while the remaining benzene vibrations (including out-of-plane modes) were treated as normal modes (NM). Using the outlined approach a model calculation of the absorption spectrum of the first overtone state CH (n=2) at ∼6000 cm−1 has been carried out.

ABSTRACT:The aim of this work is to introduce specific complex coordinates and wave functions (Hamiltonian eigenfunctions) for the description of vibrational motion in benzene. When suitably chosen, these complex functions are shown to possess interesting transformation behavior under the symmetry operations of the molecular symmetrical top point group D 6 . This behavior is analyzed and classified as "complex symmetry types" (CSTs). CSTs can be defined for all symmetrical top point groups. The description in terms of complex symmeterized coordinates and wave functions allows for the construction of a separable symmeterized vibrational basis set for benzene. New results from calculations on vibrational energies and redeterminations of harmonic force constants in benzene, obtained using the CST description, are presented.