Systematic design of active spaces for multi-reference calculations of singlet–triplet gaps of organic diradicals, with benchmarks against doubly electron-attached coupled-cluster data

Singlet-triplet gaps in diradical organic π-systems are of interest in many applications. In this study, we calculate them in a series of molecules, including cyclobutadiene and its derivatives and cyclopentadienyl cation, by using correlated participating orbitals within the complete active space (CAS) and restricted active space (RAS) self-consistent field frameworks, followed by second-order perturbation theory (CASPT2 and RASPT2). These calculations are evaluated by comparison with the results of doubly electron-attached (DEA) equation-of-motion (EOM) coupled-cluster (CC) calculations with up to 4-particle-2-hole (4p-2h) excitations. We find active spaces that can accurately reproduce the DEA-EOMCC(4p-2h) data while being small enough to be applicable to larger organic diradicals.