High-Multiplicity Natural Orbitals in Multireference Configuration Interaction for Excited States

Multireference configuration interaction (MRCI) is a very useful tool in studying excited states, dissociation of molecules, and chemical systems with multireference character. In many cases however, poor computational scaling limits its use to small systems. In the past, several different approaches have been taken in order to make MRCI and other multireference methods more accessible when dealing with larger systems. Here we propose the use of high-multiplicity natural orbitals (HMNO) in order to improve several aspects of the MRCI calculation. Natural orbitals, derived from a configuration interaction with single and double excitations calculation on a high-multiplicity reference state, were used in lieu of the standard complete active space self-consistent field (CASSCF) canonical molecular orbitals. This work examines the ability of the MRCI/HMNO approach to reliably reproduce vertical excitation energies for singlet states as well as energies for conical intersections. It is found that the MRCI/HMNO approach reliably reproduces vertical excitation energies obtained from a standard MRCI using CASSCF orbitals, with an average deviation of 0.12 and 0.15 eV for the uncorrected and Davidson corrected energies, respectively. We also explore some of the computational savings that the new method affords via systematic truncation of the virtual space. Overall, it is found that the HMNO approach is a reliable method for computing MRCI excited-state energies in a fraction of the time it would take to run a standard MRCI calculation.