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.

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes.

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin-orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree-Fock (CAHF) algorithm for the determination of 4f quasi-atomic active orbitals common to all multi-electron spin manifolds contributing to the ground spin-orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi-Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem-specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state-of-the-art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres, represents a more time-efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non-perturbative spin-orbit coupling effects. © 2017 Wiley Periodicals, Inc.