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Lagrangian approach for geometrical derivatives and nonadiabatic coupling terms in MRCISD

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.