Configuration-averaged 4f orbitals in ab initio calculations of low-lying crystal field levels in lanthanide(iii) complexes

Abstract

A successful and commonly used ab initio method for the calculation of crystal field levels and magnetic anisotropy of lanthanide complexes consists of spin-adapted state-averaged CASSCF calculations followed by state interaction with spin-orbit coupling (SI-SO). Based on two observations valid for Ln(III) complexes, namely: (i) CASSCF 4f orbitals are expected to change very little when optimized for different states belonging to the 4f electronic configuration, (ii) due to strong spin-orbit coupling the total spin is not a good quantum number, we show here via a straightforward analysis and direct calculation that the CASSCF/SI-SO method can be simplified to a single configuration-averaged HF calculation and one complete active space CI diagonalization, including spin-orbit coupling, on determinant basis. Besides its conceptual simplicity, this approach has the advantage that all spin states of the 4f n configuration are automatically included in the SO coupling, thereby overcoming one of the computational limitations of the existing CASSCF/SI-SO approach.As an example, we consider three isostructural complexes [Ln(acac) 3 (H 2 O) 2 ], Ln = Dy 3+ , Ho 3+ , Er 3+ , and find that the proposed simplified method yields crystal field levels and magnetic g-tensors that are in very good agreement with those obtained with CASSCF/SI-SO.

Ab Initio Non-Covalent Crystal Field Theory for Lanthanide Complexes: A Multiconfigurational Non-Orthogonal Group Functions Approach

“…Calculations were carried out on a set of Ln(III) complexes to analyze how the FAIMP and NOGF approximations to the molecular wave function affect the energy gaps within the lowest energy spin-orbit multiplet and the magnetic properties. The results were compared with the energies obtained at the CAHF/CASCI-SO level 30,41 . In the CAHF/CASCI-SO strategy, the set of molecular orbitals are generated at CAHF level minimizing the average-energy functional represented on the basis of all possible Slater determinants, of any M S quantum number, built up allowing N act active electrons to be distributed in all the possible ways in M act active orbitals.…”

CERES: Anab initiocode dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes

“…Note also that while in a general SA‐CASSCF calculation orbital rotations are coupled to the CI coefficients optimization problem, when averaging is carried out over all possible multiconfigurational eigenstates within a given active space carrying a specific irreducible representation (irrep) of a given symmetry group (e.g., having a given total spin), the average energy becomes the trace of the electrostatic Hamiltonian matrix within a given irrep of the symmetry group, which, being invariant under a unitary transformation, becomes independent of the eigenstates of the problem. In other words, the orbital optimization problem becomes exactly decoupled from the CI problem in typical applications of SA‐CASSCF to complexes, and could in principle be solved as a single CAHF problem …”

“…and into the average energy expression eq. gives the CAHF energy expression: …”

“…In a recent work, we have discussed the limits of the CASSCF/RASSI–SO approach for lanthanide SMMs and proposed an alternative computational strategy, called CAHF/CASCI–SO (Configurational Average Hartree–Fock/Complete Active Space Configuration Interaction with Spin–Orbit Coupling), which allows the calculation of magnetic properties of complexes where all spin states are included. In the preliminary calculations shown there, the new method did not introduce any significant deviation from CASSCF/RASSI–SO crystal field levels and magnetic properties.…”

BonnMag: Computer program for ligand‐field analysis of f n systems within the angular overlap model

“…Prediction of physical properties of f n systems is of interest due to their various technical applications (white‐light‐diodes, 1a single molecule magnets, 1b SmCo 5 , 1c Nd 2 Fe 14 B 1d ). For their investigation, highly accurate first‐principles methods have been applied, complete active space self‐consistent field (CASSCF), CASSCF combined with perturbation theory (CAS‐PT2 or NEV‐PT2), and the discrete‐variational multi‐electron method (DV‐ME), DV‐Xα . The f→d transitions in lanthanoide ions have also been studied with ligand field density functional theory (LF‐DFT) .…”