Automatic Active Space Selection for Calculating Electronic Excitation Energies Based on High-Spin Unrestricted Hartree–Fock Orbitals

Multireference perturbation theory (MR-PT2, e.g., MS-CASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) use a multiconfigurational wave function as the reference wave function, and this can be generated, for example, by the complete active space self-consistent field (CASSCF) method or restricted active space self-consistent field (RASSCF) method. The MR-PT2 and MC-PDFT methods have proved successful in many previous studies, but their performance depends on the quality of the reference wave function, and the quality of a CASSCF or RASSCF wave function depends on the active space. Even for a given number of active electrons and active orbitals, the orbitals obtained at the end of the self-consistent field iterations of the CASSCF calculation may be different for different sets of initial guess orbitals. Consequently, it is a worthwhile goal to automate active space selection, including the choice of orbitals to start the iterations, and here we examine the question of whether we can devise a broadly applicable automatic scheme for producing guess orbitals that lead to an active space that gives accurate excitation energies. Such a scheme depends on the target number of excitation energies that one is trying to calculate, and here our target is the first two spin-conserving excited electronic states of a closed-shell molecule or a doublet radical. For this target, we propose a scheme called ABC2 to automatically select an active space for MC-PDFT calculations and MS-CASPT2 calculations; the scheme uses high-spin-state unrestricted Hartree-Fock (UHF) natural orbitals as guess orbitals. A novel feature of the ABC2 scheme is that it contains a reliability test that should be passed for the results to be considered reliable. This test requires that the MC-PDFT or CASPT2 excitation energy be within 1.1 eV of the CASSCF excitation energy for the result to be considered reliable. We evaluated the performance of ABC2 for the two lowest excitation energies (or only the lowest when an accurate value of the second lowest state is not available) of 16 singlet systems and 10 doublet systems. We compared the performance of ABC2 to that of our previous ABC scheme, which finds active orbitals through a more expensive (multiconfigurational) excited-state calculation, to the use of ground-state UHF natural orbitals, and to the default scheme in OpenMolcas. We found that the new scheme is more robust than previous methods for a variety of systems.