Towards an exact factorization of the molecular wave function

Abstract

An exact single-product factorisation of the molecular wave function for the timedependent Schrödinger equation is investigated by using an ansatz involving a phase factor. By using the Frenkel variational method, we obtain the Schrödinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter ω in the phase factor is chosen such that the equations of motion retain the physically appealing Born– Oppenheimer-like form, and is therefore unique.

Keywords:

• molecular wave function
• exact factorisation
• Born–Oppenheimer approximation

Acknowledgements

This paper is dedicated to our colleague and friend Sourav Pal on his 60th birthday. S.K. Ghosh would like to thank DAE for Raja Ramanna fellowship. S. Parashar acknowledges HBCSE for visiting fellowship under the NIUS programme of DAE.

Disclosure statement

No potential conflict of interest was reported by the authors.