Study of the most relevant spin-orbit coupling descriptions of magnetic excitations in a series of lanthanide complexes

We present a number of computationally cost-effective approaches to calculate magnetic excitations (i.e. crystal field energies and magnetic anisotropies in the lowest spin-orbit multiplet) in lanthanide complexes. In particular, we focus on the representation of the spin-orbit coupling term of the molecular Hamiltonian, which has been implemented within the quantum chemistry package CERES using various approximations to the Breit-Pauli Hamiltonian. The approximations include the (i) bare one-electron approximation, (ii) atomic mean field and molecular mean field approximations of the two-electron term, (iii) full representation of the Breit-Pauli Hamiltonian. Within the framework of the CERES implementation, the spin-orbit Hamiltonian is always fully diagonalized together with the electron repulsion Hamiltonian (CASCI-SO) on the full basis of Slater determinants arising within the 4f ligand field space. For the first time, we make full use of the Cholesky decomposition of two-electron spin-orbit integrals to speed up the calculation of the two-electron spin-orbit operator. We perform an extensive comparison of the different approximations on a set of lanthanide complexes varying both the lanthanide ion and the ligands. Surprisingly, while our results confirm the need of at least a mean field approach to accurately describe the spin-orbit coupling interaction within the ground Russell-Saunders term, we find that the simple bare one-electron spin-orbit Hamiltonian performs reasonably well to describe the crystal field split energies and g tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.