Molecular vibrations in the presence of velocity-dependent forces

• Published in: The Journal of chemical physics Vol. 158; no. 12; pp. 124124 - 124136
• Main Authors: Tellgren, Erik I., Culpitt, Tanner, Peters, Laurens D. M., Helgaker, Trygve
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 28.03.2023
• Subjects: Coupling (molecular); Eigenvalues; Hamiltonian functions; Interatomic forces; Magnetic fields
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/5.0139684

A semiclassical theory of small oscillations is developed for nuclei that are subject to velocity-dependent forces in addition to the usual interatomic forces. When the velocity-dependent forces are due to a strong magnetic field, novel effects arise—for example, the coupling of vibrational, rotational, and translational modes. The theory is first developed using Newtonian mechanics and we provide a simple quantification of the coupling between these types of modes. We also discuss the mathematical structure of the problem, which turns out to be a quadratic eigenvalue problem rather than a standard eigenvalue problem. The theory is then re-derived using the Hamiltonian formalism, which brings additional insight, including a close analogy to the quantum-mechanical treatment of the problem. Finally, we provide numerical examples for the H2, HT, and HCN molecules in a strong magnetic field.