A Quasidegenerate Second-Order Perturbation Theory Approximation to RAS-nSF for Excited States and Strong Correlations

We present a modification of the recently developed Restricted Active Space with n Spin Flips method (RAS-nSF), which provides significant efficiency advantages. In the RAS-nSF configuration interaction wave function, an arbitrary number of spin-flips are performed within an orbital active space (often simply the singly occupied orbitals), with state-specific orbital relaxation being described by single excitations into and out of the active space (termed hole and particle state, respectively). As the number of hole and particle states dominates the cost of the calculation, we present an attractive simplification in which the orbital relaxation effects (via hole and particle states) are treated perturbatively rather than variationally. The physical justification for this simplification stems from the spin-flip methodology itself, which suggests that the underlying molecular orbitals (high-spin ROHF) are capable of providing a decent description of the target (spin-flipped) electronic states. The current approach termed SF-CAS(h,p)(n) (Spin-Flip Complete Active-Space with perturbative Hole and Particle states) yields spin-pure energies and eigenfunctions due to the spin-free formulation. A description of the theory is presented, and a number of numerical examples are investigated to determine the accuracy of the approximation. Computational speedups of over 100 times were demonstrated on a 254 electron, 358 basis function calculation on a Cu(II) porphyrin derivatized with a verdazyl group.