Molecules with Spin and Vibronic Coupling Effects: A Computational Perspective

Abstract While fundamental to molecular quantum mechanics, limitations of the Born-Oppenheimer Approximation (BOA) have long been known. Nonetheless, calculations that include molecular interactions, such as vibronic coupling and electron spin effects, that violate the BOA have remained a challenge due to their large demand on computational resources. The purpose of this paper is to describe two complementary software programs, SOCJT and XSIM, designed for efficient calculations that include these interactions. The programs are sufficiently general and user friendly that they can be readily applied to a variety of molecules of different symmetries, state degeneracies, and interaction strengths. The programs can typically produce spin-vibronic eigenvalues and eigenvectors with sufficient accuracy for the analysis and interpretation of molecular spectra with features attributable to violations of the BOA. The two programs utilize different matrix representations of the molecular Hamiltonian, with XSIM being Cartesian based and SOCJT being cylindrically based, and their advantages/disadvantages are discussed. Several algorithms can be chosen to obtain the Hamiltonian’s eigenvalues and eigenvectors and their speed and memory usage are compared. Examples of application of SOCJT and XSIM to explain spectral observations for particular molecules are briefly reviewed.