Prediction of electron paramagnetic resonance g values using coupled perturbed Hartree–Fock and Kohn–Sham theory

Abstract

A method for calculating the EPR g-tensor based on coupled perturbed Hartree-Fock ͑HF͒ and density functional theory ͑DFT͒ is presented. The one-electron molecular orbitals of a spinunrestricted Slater determinant are calculated up to first order in the applied magnetic field. The g-tensor is evaluated as a mixed second derivative property with respect to the applied field and the electron magnetic moment. Thus, spin-polarization and spin-orbit coupling are simultaneously included in the calculation. The treatment focuses on orbitally nondegenerate molecules but is valid for a general ground state spin S and, for the first time, it is possible to include hybrid density functionals in the treatment. The relativistic mass and diamagnetic gauge corrections are also considered. An implementation of the theory is described. Extensive numerical calculations for a series of small molecules are reported with the Hartree-Fock ͑HF͒ method, the local density approximation ͑LSD͒, the generalized gradient approximation ͑GGA͒ and hybrid density functionals such as B3LYP and PBE0 and large Gaussian basis sets. Detailed comparison with available ab initio and DFT calculations are made. The results indicate that the hybrid functionals offer little or no improvement over the GGA functionals for small radicals made of light atoms. For transition metal complexes the situation is different. The hybrid functionals give, on average, better results than the GGA functionals but significant disagreement between theoretical and experimental g-shifts still remain. Overall, the results indicate that the present method is among the most accurate so far developed models for the prediction of g values.

Insights into the Electronic Structure of CuIIBound to an Imidazole Analogue of Westiellamide

“…The general overestimation of the g shift (especially g z ) has been attributed to a combination of too much covalent bonding and the over prediction of the d-orbital splitting and consequently hybrid functionals like B3LYP (usually with at least 20% Hartree Fock exchange) are certainly to be preferred. 76 However, elevated levels of HF exchange are problematic since they also lead to strong spin contamination.…”

DFT insight into o-semiquinone radicals and Ca2+ ion interaction: structure, g tensor, and stability

“…The conductor-like screening model (COSMO) [72,73] was the continuum solvation model used in the computations. The g tensors were computed using Neese's CPKS method [74] combined with an accurate mean field approximation [RI-SOMF(1X)] [75] to the Breit-Pauli spin-orbit coupling operator [76,77]. In this work, all the computed components of the g tensors are given as g-shifts (Dg ij ) in parts per million (ppm):…”

Four-Component Relativistic Density Functional Theory Calculations of EPRg- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin–Orbit Effects

“…While such approaches may in the future become more important for EPR parameter calculations, computations for larger systems, for example the transition metal complexes we focus on in this work, will have to rely on density functional theory (DFT) methods for some time to come. Initial DFT implementations of g-tensors and HFCs either included SO effects by leading-order perturbation theory [28][29][30][31][32][33][34] or variationally in two-component quasirelativistic spin-restricted zero-order regular approximation (ZORA) or Douglas-Kroll-Hess calculations. [35][36][37][38] Subsequently, the Kramers-unrestricted two-component DKH, [39][40] resolution of identity Dirac-Kohn-Sham (DKS-RI) method 41 and, more recently, four-component DFT calculations of EPR parameters became available, allowing both spin polarization and higher-order SO effects to be included simultaneously.…”