Analytical second derivatives for excited electronic states using the single excitation configuration interaction method: theory and application to benzo[a]pyrene and chalcone

A compact formulation and a semi-direct implementation are described of ana lytical second derivatives of the single excitation configuration interacti on (CIS) energy. CPU time, memory usage and disc storage all scale with the same power of system size as the ground state Hartree-Fock (HF) method, wi th a coefficient only 2 to 3 times larger. Thus usually analytical excited state CIS frequencies are feasible when HF frequencies are feasible. As a c omputational example, analytical CIS/3-21G frequencies for benzo[a]pyrene a re calculated more efficiently than with finite differences. As a chemical application, analytical CIS/6-31G* frequencies are used to investigate non- planarity in the lowest pi --> pi* excited state of trans-chalcone.