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)42– (X = S, Se).