Lagrangian approach for geometrical derivatives and nonadiabatic coupling terms in MRCISD

Abstract

A new formulation for multireference configuration interaction method, with single and double excitations (MRCISD), energy gradients and nonadiabatic coupling terms based on a Lagrangian approach is suggested and the gradients demonstrated to be accurate with calculations on several molecules. Of particular interest, the suggested formalism can straightforwardly use state-averaged-multiconfiguration self-consistent field (SA-MCSCF) descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited ¹Σ⁺ states of LiH, including calculations near an avoided crossing. The formalism can use either complete or incomplete model (i.e. reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. The formalism for nonadiabatic coupling shares many structural features with the energy gradient formalism, with the use of a function that corresponds to the energy for the coupling.

Keywords:

• electronic structure theory
• energy gradients
• multireference CI
• nonadiabatic coupling

Acknowledgements

The authors gratefully acknowledge the DOE Office of Science under Award Number DE-FG02-06ER46292 and NSF Grant Number EPS-0814442 for the financial support for this research.