Relativistic Density Functional Calculations of Hyperfine Coupling with Variational versus Perturbational Treatment of Spin–Orbit Coupling

Abstract

Different approaches are compared for relativistic density functional theory (DFT) and Hartree-Fock (HF) calculations of electron-nucleus hyperfine coupling (HFC) in molecules with light atoms, in transition metal complexes, and in selected actinide halide complexes with a formal metal 5f(1) configuration. The comparison includes hybrid density functionals with range-separated exchange. Within the variationally stable zeroth-order regular approximation (ZORA) relativistic framework, the HFC is obtained (i) with a linear response (LR) method where spin-orbit (SO) coupling is treated as a linear perturbation, (ii) with a spin-polarized approach closely related to a DFT method for calculating magnetic anisotropy (MA) previously devised by van Wüllen et al. where SO coupling is included variationally, (iii) with a quasi-restricted variational SO method previously devised by van Lenthe, van der Avoird, and Wormer (LWA). The MA and LWA approaches for HFC calculations were implemented in the open-source NWChem quantum chemistry package as part of this study. The methodology extends recent implementations for calculations of electronic g-factors (J. Chem. Theor. Comput.2013, 9, 1052). The impact of electron correlation (DFT vs HF) and DFT delocalization errors, the effects of spin-polarization, the importance of treating spin-orbit coupling beyond first-order, and the magnitude of finite-nucleus effects, are investigated. Similar to calculations of g-factors, the MA approach in conjunction with hybrid functionals performs reasonably well for theoretical predictions of HFC in a wide range of scenarios.

Relativistic DFT Calculations of Hyperfine Coupling Constants in 5d Hexafluorido Complexes: [ReF6]2− and [IrF6]2−

“…This behaviour was previously observed for actinide systems,13 but not to this extent. Notably, this transition can only cause such an overestimation if the corresponding matrix elements over the perturbation operators are non‐vanishing.…”

“…In the DFT‐based EV ZORA implementation in the ADF program,18 the hyperfine coupling tensor was calculated in a restricted fashion on the basis of a Kramer's pair of the singly occupied molecular orbital ( φ 1 and φ 2 ) 13, 14. Consequently, this method applies only to doublet systems and the elements of the hyperfine coupling tensor of nucleus N , A N , are calculated as described in Equations (3), (4), (5):$true{A}_{N,ux}=2g_N{\mu }_N\mathrm{Re}⟨{\phi }_1|{\widehat{h}}_{N,u}^{\mathrm{SO}-\mathrm{ZORA}}|{\phi }_2⟩$ $true{A}_{N,uy}=-2g_N{\mu }_N\mathrm{Im}⟨{\phi }_1|{\widehat{h}}_{N,u}^{\mathrm{SO}-\mathrm{ZORA}}|{\phi }_2⟩$ $true{A}_{N,uz}=2g_N{\mu }_N\mathrm{Re}⟨{\phi }_1|{\widehat{h}}_{N,u}^{\mathrm{SO}-\mathrm{ZORA}}|{\phi }_1⟩$ …”

A Nonorthogonal State-Interaction Approach for Matrix Product State Wave Functions

“…Similarly, calculating magnetic properties 6 such as molecular g-factors and electron-nucleus hyperfine coupling, which are central parameters in electron paramagnetic resonance (EPR) spectroscopy, requires spin-orbit coupled wave functions 7,8 . To this end, correlated two-and four-component ab initio wave function [9][10][11][12] , and density functional theory approaches [13][14][15] . In the present study we focus on EPR g-tensors for testing purposes, but it should be noted that the underlying novel method of gaining access to wave functions that include the effects from SOC has a vast range of applications.…”

“…9,16-23 and literature citations in these works and in Refs. [8][9][10][11][13][14][15]. In these schemes, the calculation of a number of non-or scalar-relativistic many-particle spin-free states that are eigenfunctions of the spin-squared operator S 2 , is decoupled from a subsequent perturbative or variational mixing of the latter through the SO coupling operator to obtain SO coupled many-electron wave functions (e.g.…”

Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

“…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). Though the work by Lan et al 27,28 has clearly shown that the DMRG-CASSCF method provides benchmark accuracy for small systems, the use of such large active spaces severely limits the scope of applications; the necessity of such large active spaces originates from the fact that the DMRG-CASSCF model is not designed to efficiently capture dynamical electron correlation, the importance of which has been emphasized in the previous studies based on the coupled cluster theory.…”