ABSTRACT
We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born–Oppenheimer correction (DBOC) to the ground-state Born–Oppenheimer potential energy surface (PES). By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. This is shown to lead to a biorthogonal version of SOS formula with similar properties. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. One of this agrees with the formula used in the current literature. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified.
Acknowledgments
I acknowledge Prof. Michael Baer for his excellent set of lectures on non-adiabatic dynamics at IISER Mohali. The discussions with Prof. Satrajit Adhikari and his group are also acknowledged. I would also like to thank my colleagues Dr Alok Maharana, Dr K. P. Yogendran, Dr Chetan Balwe for several interesting discussions. I would also like specially thank the referee for valuable comments which led to a considerably concise presentation.
Disclosure statement
No potential conflict of interest was reported by the author.