Diagonal Born–Oppenheimer correction for coupled-cluster wave-functions

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.

KEYWORDS:

• Adiabatic approximation
• diagonal Born–Oppenheimer correction
• non-adiabatic coupling
• coupled-cluster
• sum-over-states
• adiabatic-to-diabatic transformations

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.

Additional information

Funding

The research has been supported by generous funding of Science and Engineering Research Board (SERB) of the Department of Science and Technology (DST), India [grant number EMR/2016/000684].