Vibronic mean-field and perturbation theory for Jahn-Teller and pseudo-Jahn-Teller molecules

Abstract

A generalisation of vibrational mean-field theory is developed for non-adiabatic Jahn-Teller and pseudo-Jahn-Teller molecules with coupled vibrational and electronic degrees of freedom treated within a quasi-diabatic framework. Solutions to the vibronic self-consistent field equations of motion generate qualitatively correct zeroth-order vibronic wavefunctions even in the strong coupling limit. These serve as an efficient basis for further perturbative or variational corrections. Particular attention is paid to complications arising in multi-mode Jahn-Teller systems, where the degenerate ground state exhibits artificial symmetry-breaking in the mean-field approximation. This effect is shown to behave like a second-order phase transition, with the symmetry of finite-temperature mean-field solutions restored above a critical temperature.

GRAPHICAL ABSTRACT

Keywords:

• Vibrational self-consistent field theory
• non-adiabatic interactions
• Jahn-Teller effect
• symmetry breaking

Acknowledgments

The author congratulates Prof. John F. Stanton on the happy occasion of his 60th birthday. Prof. Stanton's work has provided much of the motivation for this paper. Its author is grateful for not only his many contributions to molecular spectroscopy, but his valued mentorship, collaboration, and friendship.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The ‘exact’ energies are computed using a sinc discrete-variable representation (DVR) basis of 100 points spanning q = −15 to $+15$ with the usual diagonal-DVR approximation [56].

2 See note 16 of Ref. [55] for details. The harmonic frequencies defining the kinetic energy scaling of the dimensionless normal coordinates is not specified in this reference. Here, we use values of ${\omega }_s=1125.0{\mathrm{cm}}^{-1}$ and ${\omega }_a=1783.9{\mathrm{cm}}^{-1}$.

Additional information

Funding

The author is supported by National Science Foundation (NSF) award no. AST-1908576.