A Critical Validation of Density Functional and Coupled-Cluster Approaches for the Calculation of EPR Hyperfine Coupling Constants in Transition Metal Complexes

Abstract

The performance of various density functional approaches for the calculation of electron paramagnetic resonance (EPR) hyperfine coupling constants in transition metal complexes has been evaluated critically by comparison with experimental data and high-level coupled-cluster results for 21 systems, representing a large variety of different electronic situations. While both gradient-corrected and hybrid functionals allow the calculation of isotropic metal hyperfine coupling constants to within ca. 10-15% for the less critical cases (e.g., ScO, TiN, TiO, VO, MnO, MnF), none of the functionals investigated performs well for all complexes. Gradient-corrected functionals tend to underestimate the important core-shell spin polarization. While this may be improved by exact-exchange mixing in some cases, the accompanying spin contamination may even lead to a deterioration of the results for other complexes. We also identify cases, where essentially none of the functionals performs satisfactorily. In the absence of a "universal functional", the functionals to be applied to the calculation of hyperfine couplings in certain areas of transition metal chemistry have to be carefully selected. Desirable, improved functionals should provide sufficiently large spin polarization for core and valence shells without exaggerating it for the latter (and thus introducing spin contamination). Coupling anisotropies and coupling constants for ligand nuclei are also discussed. The computationally much more demanding coupled cluster (CCSD and CCSD(T)) methods, which have been applied to a subset of complexes, show good performance, even when a UHF reference wave function is moderately spin-contaminated.

An evaluation of the density functional approach in the zero order regular approximation for relativistic effects: Magnetic interactions in small metal compounds

“…However, our calculations suggest that A ʈ and A Ќ are of opposite sign. As in previous studies on TiF 3 , 43 the spin polarization of the inner shells ͑even the lowest occupied 1s shell!͒ on fluorine is very important, both for the anisotropic and the isotropic parts of the hyperfine tensor.…”

“…In particular, a number of density functional theory ͑DFT͒ studies on transition metal hyperfine parameters have appeared, using the local spin density approximation, generalized gradient approximations ͑GGA͒, and several hybrid functionals. [1][2][3] Reasonable agreement between theory and experiment for the ESR parameters (g and A tensors͒ has been found, provided that a sufficiently large basis set is employed. Munzarová and Kaupp 3 systematically studied the hyperfine interaction in a number of small 3d transition metal complexes.…”

DFT investigation of the effect of spin-orbit coupling on the NMR shifts in paramagnetic solids

“…For this, three hybrid exchange-correlation functionals were used: the PBE0 incorporating 25% Hartree-Fock (HF) exchange [54,55], shown to provide satisfactory performances for the electronic and magnetic structures of the class of materials of interest [53], and the related 20% HF hybrid (PBE20) and 35% HF hybrid (PBE35). The choice of studying these systems with a range of hybrid functionals was motivated by the known sensitivity of the electronic delocalisation and spin polarisation on the percent of HF exchange included [12,53,56,57]. Two levels of allelectron atom-centered basis set were used, a smaller set used for structure optimisation and a more extended one used for hyperfine calculations [12].…”

Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

“…5 For instance, the methods based on single-reference manybody perturbation and coupled-cluster theories have been studied in the past few decades. [6][7][8][9][10][11][12] In general, the coupled cluster approaches provide benchmark accuracy when the wave function is well described by a single Slater determinant. The methods based on the complete active space selfconsistent field (CASSCF) and (uncontracted) multiconfiguration interaction (MRCI) methods have been reported as well.…”

“…[13][14][15][16] Yet another approach is based on density functional theory (DFT). 10,[17][18][19][20][21] These approaches have been generalized to relativistic analogues to account for the scalar relativistic and spin-orbit effects. [22][23][24][25][26] Recently, Lan et al 27,28 has used the CASSCF method with the density-matrix renormalization group (DMRG) algorithm to show that it is capable of reproducing experimental results when used with very large active spaces (up to 36 orbitals).…”