Approximate Spin-Orbit Eigenstates with Static and Dynamical Correlations: X2CSO-DSRG-MRPT2 Prescription

Evaluations of spin-orbit coupling (SOC), along with accurate potential energies, are the most important procedures in describing intersystem crossing computationally. Here, we suggest a simple prescription for computing spin-orbit eigenstates and/or SOC matrix elements within the framework of the second-order driven similarity renormalization group multireference perturbation method (DSRG-MRPT2), which describes both static and dynamical correlations to obtain accurate potential energies. In this method, a spin-free state-averaged DSRG-MRPT2 calculation is performed to construct a relaxed Hamiltonian, incorporating scalar-relativistic effects [within the exact two-component framework] and both static and dynamical correlations. Then, the SOC elements are perturbatively included in the Hamiltonian before performing the non-spin-conserving CASCI diagonalization in the determinant basis. The resulting DSRG-MRPT2 states are the spin-orbit states. We present the formalisms and implementations of the method for both energies (eigenstates) and their analytical nuclear gradients. We demonstrate the applicability of this method for evaluating the zero-field splitting parameters of group 3, 11, 13, and 17 element atoms and Co(XPh)₄^2- (X = S, Se).