Theoretical determination of spin Hamiltonians with isotropic and anisotropic magnetic interactions in transition metal and lanthanide complexes

Abstract

The determination of anisotropic magnetic parameters is a task of both experimental and theoretical interest. The added value of theoretical calculations can be crucial for analyzing experimental data by (i) allowing assessment of the validity of the phenomenological spin Hamiltonians, (ii) allowing discussion of the values of parameters extracted from experiments, and (iii) proposing rationalizations and magneto-structural correlations to better understand the relations between geometry, electronic structure, and properties. In this review, we discuss the model Hamiltonians that are used to describe magnetic properties, the computational approaches that can be used to compute magnetic parameters, and review their applications to transition metal and (to a lesser extent) lanthanide based complexes. Perspectives concerning current methodological challenges will then be presented, and finally the need for further joint experimental/theoretical efforts will be underlined.

The Role of Anisotropic Exchange in Single Molecule Magnets: A CASSCF/NEVPT2 Study of the Fe4 SMM Building Block [Fe2(OCH3)2(dbm)4] Dimer

“…The sextuplet, all triplets and all doublets CI solutions have been calculated in a state-average fashion and used for the subsequent NEVPT2 step. While this strategy for extracting transition metal single ion anisotropy has already been widely validated [22], calculations on multi-ion transition metals are limited to a few papers [23][24][25][26][27][28]. So far, only active spaces extended over the d-like MOs, i.e., (10,10) in this case, have been considered in this kind of calculations and the same approach will be followed here in order to limit the already large computational demand.…”

Analysis of the Magnetic Exchange Interactions in Yttrium(III) Complexes Containing Nitronyl Nitroxide Radicals

“…49 From the computational point of view, as for magnetic anisotropy or ligand-field effects, [50][51][52][53][54] procedures to investigate magnetic exchange rely on the use of a model Hamiltonian which is derived either from chemical intuition or using the effective Hamiltonian theory. 55,56 In the simplest case, i.e. two half spins interacting isotropically, magnetic exchange can then be effectively described using the Heisenberg-Dirac-Van Vleck Hamiltonian.…”

Basics of the spin Hamiltonian formalism

“…Hence, all matrix elements of the EH can be calculated numerically (e.g., using the ab initio energies and wavefunctions) [46] from this expression. Comparing this numerical matrix with the analytical matrix of the MH enables one to assign each interaction in the proposed model and to check its validity through the information which can be extracted from the projections' norms.…”

“…Also, MHs are usually propounded by assuming that there is a sufficiently large gap between the electronic ground state and the excited states. [45,46] Therefore, working on the smaller space of basis functions or determinants, MHs must mimic the low-energy solutions of the exact electronic Hamiltonian [i.e., energies and wavefunctions in Eq. (1)] as precisely as possible.…”

“…Comparing this numerical matrix with the analytical matrix of the MH enables one to assign each interaction in the proposed model and to check its validity through the information which can be extracted from the projections' norms. [45,46] The derivation of Effective Hamiltonians using perturbation theory (PT)…”