Restricted active space spin-flip configuration interaction approach: theory, implementation and examples

A new formulation of the spin-flip (SF) method is presented. The electronic wave function is specified by the definition of an active space and through α-to-β excitations from a Hartree–Fock reference. The method belongs to the restricted active space (RAS) family, where the CI expansion is restricted by classifying the molecular orbitals in three subspaces. Properties such as spin completeness, variationality, size consistency, size intensivity, and orbital invariance are discussed. The implementation and applications use a particular truncation of the wave function, with the inclusion of hole and particle contributions such that for fixed active space size, the number of amplitudes is linear in molecular size. This approach is used to investigate single and double bond-breaking, the singlet–triplet gap of linear acenes, electronic transitions in three Ni(II) octahedral complexes, the low-lying states of the 2,5-didehydrometaxylylene (DDMX) tetraradical and the ground state multiplicity of 28 non-Kekulé structures. The results suggest that this approach can provide a quite well balanced description of nearly degenerate electronic states at moderate computational cost.