Vibrational Hamiltonian of Naphthalene (C₁₀H₈) Using Dynamical U(2) Lie Algebras

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 D_2h 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.

Keywords:

• Dynamical U(2) Lie algebras
• molecular vibration spectroscopy
• naphthalene
• polycyclic aromatic hydrocarbons

Acknowledgements

The authors thank the topical editor Prof. Philippe Garrigues and the anonymous reviewers for valuable suggestions. Acknowledgments are due to National Institute of Science and Technology (https://webbook.nist.gov) for providing the experimental reference spectrum database 69.

Disclosure statement

There are no conflicts of interest.