Vibrational Hamiltonian of Naphthalene (C<sub>10</sub>H<sub>8</sub>) Using Dynamical U(2) Lie Algebras
Malleswara Rao Balla, Vijayasekhar Jaliparthi
Abstract
This article is the first to demonstrate the application of dynamical U(2) Lie algebras to model a vibrational Hamiltonian of naphthalene (C10H8), a prototype polycyclic aromatic hydrocarbon molecule containing a fused pair of benzene rings, in the gas phase having considerable astrophysical interest. A vibrational Hamiltonian that preserves the D2h symmetry of naphthalene is modeled using 19 coupled one-dimensional Morse oscillators to describe the eight C-H single bonds, the eleven C-C aromatic bonds, and their dynamic interactions, making use of the Casimir and Majorana operators. Results indicate that the dynamical U(2) Lie algebraic Hamiltonian has successfully reproduced the vibrational frequencies at the 48 fundamental excitations near to the level of spectroscopic accuracy, as well as predicted their first three overtones. The observed degeneracy of the stretching, bending, and combination vibrations at the fundamental and lower overtone excitations are expected to modify the shape of the two major bands (centered at 782 cm−1 and 3065 cm−1), and several minor bands in the infrared absorption spectrum of naphthalene in the gas phase.