Beyond Born–Oppenheimer theory for spectroscopic and scattering processes

Abstract

We review our development on beyond Born–Oppenheimer (BBO) theory and its implementation on various models and realistic molecular processes as carried out over the last 15 years. The theoretical formulation leading to the BBO equations are thoroughly discussed with ab initio calculations. We have employed first principle based BBO theory not only to formulate single surface extended Born–Oppenheimer equation to understand the nature of nonadiabatic effect but also to construct accurate diabatic potential energy surfaces (PESs) for important spectroscopic systems, namely, NO${}_2$ radical, Na${}_3$ and K${}_3$ clusters, NO${}_3$ radical, benzene and 1,3,5-trifluorobenzene radical cations (${\mathrm{C}}_6{\mathrm{H}}_6^{+}$ and ${\mathrm{C}}_6{\mathrm{H}}_3{\mathrm{F}}_3^{+}$) as well as triatomic reactive scattering systems like ${\mathrm{H}}^{+}+{\mathrm{H}}_2$ and $\mathrm{F}+{\mathrm{H}}_2$. The nonadiabatic phenomena like Jahn–Teller (JT), Renner–Teller, pseudo Jahn–Teller effects and the accidental conical intersections are the key players in dictating spectroscopic and reactive scattering profiles. The nature of diabatic coupling elements derived from ab initio data with BBO theory for molecular processes in Franck-Condon region has been analysed in the context of linearly and bilinearly coupled JT model Hamiltonian. The results obtained from quantum dynamical calculations on BBO based diabatic PESs of the above molecular systems are found to be in accord with available experimental outcomes.

Keywords:

• Adiabatic potential energy surfaces
• nonadiabatic coupling terms
• extended Born–Oppenheimer equation
• adiabatic-to-diabatic transformation
• diabatic Hamiltonian
• nonadiabatic dynamics

Acknowledgments

SA also acknowledges IACS for CRAY supercomputing facility.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Satrajit Adhikari http://orcid.org/0000-0002-2462-4892

Additional information

Funding

BM (file no.: 09/080(0960)/2014-EMR-I), KN (file no.: 09/080(1068)/2018-EMR-I) and SM (file no.: SPM-07/080(0250)/2016-EMR-I) acknowledge Council of Scientific and Industrial Research (CSIR), India for research fellowship, and SG thanks IACS for funding. SA acknowledges Science and Engineering Research Board (DST), India, through project no. File No. EMR/2015/001314 for the research funding.