Ab initio calculations of zero-field splitting parameters

We present calculations of electron spin-spin (SS) coupling strengths evaluated as expectation values over multi-configuration and restricted high-spin self-consistent field wave functions. Together with the spin-orbit (SO) configuration interaction methodology, this enables us to analyze the full spin Hamiltonian including the zero-field splitting (ZFS) parameters of the triplet state. The calculated ZFS parameters include both the SS coupling to first order and SO coupling to second order of perturbation theory. The relative importance of these two contributions is strongly system dependent. In the lowest triplet state of the benzene molecule, the main ZFS parameter - the D parameter - is determined entirely by the SS coupling, with D calculated to be 0.1583 cm^-1. In contrast, the calculated D parameter in the X³Σ_g^- ground state of the oxygen molecule (3.77 cm^-1) includes a large one-center SS contribution (Dss = 1.455 cm^-1) but an even larger SO coupling contribution (Dso = 2.315 cm^-1). ZFS parameters for molecular oxygen excited states, A³Σ_u⁺ and B³Σ_u^-, which belong to Hund's case (b), are also calculated. A large negative D value (-10.2 cm^-1) for the A³Σ_u⁺ state is to 90% determined by the Dso contribution, while the Schumann-Runge state spin splitting is mainly determined by SS coupling. The calculated values for benzene and oxygen are in good agreement with data from EPR and rotational fine-structure spectra. The applicability of response theory is with this contribution expanded to include the calculation of the SS coupling of the spin Hamiltonian, complementing the previous implementations of hyperfine A- and g-tensors.