Analytic MRCI gradient for excited states:: formalism and application to the n-π* valence- and n-(3s,3p) Rydberg states of formaldehyde

The previously developed formalism for the calculation of the analytic multireference (MR) CI energy gradient with respect to nuclear coordinates based on a single-state MCSCF calculation was extended to the case of state-averaged MCSCF. This extension is of particular importance for calculations of electronically excited states and enables automatic high-level geometry optimizations and saddle point searches on excited-state energy surfaces. Beyond MR-CI, the present analytic gradient method is also available for the MR-ACPF/AQCC methods including size-extensivity corrections for the multireference case. Full geometry optimizations for six electronic states of formaldehyde (valence and Rydberg states) are reported.