Classical versus Quantum Vibrational Spectra of Isolated and Coupled Morse Oscillators

Abstract

Classical molecular dynamics provides a computationally economical approach to finite-temperature vibrational spectroscopy; but, its reliability is limited by the absence of vibrational quantization, zero-point energy, and discrete quantum state mixing. This study examines the validity of the classical description by direct comparisons with quantum calculations for controlled anharmonic model systems. Isolated Morse oscillators with nominal frequencies of 300 and 3800 cm⁻¹ were investigated using linear, quadratic, and cubic dipole moment functions to distinguish the effects of mechanical and electrical anharmonicities. A two-dimensional system of coupled Morse oscillators with frequencies of 1900 and 3800 cm⁻¹ was subsequently employed to examine the temperature dependence and the Fermi resonance. Identical potential energy and dipole moment functions were used in classical and quantum calculations. Classical molecular dynamics reproduced the principal band and overall spectral profile of the low-frequency oscillators. However, for the high-frequency oscillator, the classical fundamental was blue-shifted relative to the quantum transition, and the disagreement increased substantially for the higher-order spectral features. The nonlinear dipole functions generated overtone-like features in both descriptions, although their positions and relative intensities showed an increasing classical–quantum divergence. Increasing the temperature produced greater fragmentation of the classical spectra through sampling of more anharmonic regions of the potential energy surface, whereas the quantum transition frequencies remained comparatively stable. Both approaches qualitatively reproduced the coupling-induced splitting associated with the Fermi resonance; however, the strong coupling generated considerably greater spectral congestion in classical results. Classical molecular dynamics is therefore the most reliable method for low-frequency motion, qualitative trends, and overall spectral envelopes, whereas quantum treatment remains necessary for high-frequency stretching vibrations, higher-order transitions, and detailed resonance assignments.