Calculation of Spin–orbit Couplings Using RASCI Spinless One-Particle Density Matrices: Theory and Applications

This work presents the formalism and implementation for calculations of spin–orbit couplings (SOCs) within the Breit–Pauli (BP) Hamiltonian using zero-order (non- relativistic) wave-functions described by the restricted active space configuration in- teraction (RASCI) method with general excitation operators: excitation energies, spin- flip, ionization potential, and electron attachment. The implementation is based on the application of Wigner–Eckart’s theorem within the spin space, which allows the computation of the entire SOC matrix based on the explicit calculation of just one tran- sition between the two spin-multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of balanced treatment of correlation and adequate basis sets, and illustrate overall robust performance of RASCI SOCs. The new imple- mentation is a useful addition to a methodological toolkit for studying spin-forbidden processes.