Relativistic effects on molecular hyperfine interactions: Application to XeF and CsO

Hyperion: A New Computational Tool for Relativistic Ab Initio Hyperfine Coupling

Herein we describe Hyperion, a new program for computing relativistic picture-change-corrected magnetic resonance parameters from scalar relativistic active space wave functions, with or without spin–orbit coupling (SOC) included a posteriori. Hyperion also includes a new orbital decomposition method for assisting active space selection for calculations of hyperfine coupling. For benchmarking purposes, we determine hyperfine coupling constants of selected alkali metal, transition metal, and lanthanide atoms, based on complete active space self-consistent field spin–orbit calculations in OpenMolcas. Our results are in excellent agreement with experimental data from atomic spectroscopy as well as theoretical predictions from four-component relativistic calculations.

Structural, IR, and EPR studies of the bis(methoxyacetato)diaquo-copper(II) complex

The structure, stability, and the IR, and EPR spectroscopic properties of bis(methoxyacetato)diaquo-copper(II) were studied both experimentally using FT-IR and theoretically using B3LYP/6-31G**, B3LYP/6-311G, BWP91/6-31G** methods. The same approaches were used to calculate the harmonic frequencies and to compare them to the experimental solid state values. The g-tensors are calculated using the NMR/GIAO computational method.

Computational studies of EPR parameters for paramagnetic molybdenum complexes. II. Larger MoV systems relevant to molybdenum enzymes

The careful validation of modern density functional methods for the computation of electron paramagnetic resonance (EPR) parameters in molybdenum complexes has been extended to a number of low-symmetry MoV systems that model molybdoenzyme active sites. Both g and hyperfine tensors tend to be reproduced best by hybrid density functionals with about 30-40% exact-exchange admixture, with no particular spin contamination problems encountered. Spin-orbit corrections to hyperfine tensors are mandatory for quantitative and, in some cases, even for qualitative agreement. The g11 (g||) component of the g tensor tends to come out too positive when spin-orbit coupling is included only to leading order in perturbation theory. Compared to single-crystal experiments, the calculations reproduce both g- and hyperfine-tensor orientations well, both relative to each other and to the molecular framework. This is significant, as simulations of the EPR spectra of natural-abundance frozen-solution samples frequently do not allow a reliable determination of the hyperfine tensors. These may now be extracted based on the quantum-chemically calculated parameters. In a number of cases, revised simulations of the experimental spectra have brought theory and experiment into substantially improved agreement. Systems with two terminal oxo ligands, and to some extent with an oxo and a sulfido ligand, have been confirmed to exhibit particularly large negative Deltag33 shifts and thus large g anisotropies. This is discussed in the context of the experimental data for xanthine oxidase.

Computational Studies of Electron Paramagnetic Resonance Parameters for Paramagnetic Molybdenum Complexes. 1. Method Validation on Small and Medium-Sized Systems

A variety of density functional methods have been evaluated in the computation of electronic g-tensors and molybdenum hyperfine couplings for systems ranging from the Mo atom through MoIIIN, [MoVOCl4]-, and [MoVOF5]2- to two larger MoV complexes MoXLCl2 (X=O, S; L=tris(3,5-dimethylpyrazolyl)hydroborate anion). In particular, the influence of the molybdenum basis set and of various exchange-correlation functionals with variable admixtures of Hartree-Fock exchange on the computed EPR parameters have been evaluated in detail. Careful basis-set studies have provided a moderate-sized 12s6p5d all-electron basis on molybdenum that gives hyperfine tensors in excellent agreement with much larger basis sets and that will be useful for calculations on larger systems. The best agreement with experimental data for both hyperfine and g-tensors is obtained with hybrid functionals containing approximately 30-40% Hartree-Fock exchange. Only for MoSLCl2 does increasing spin contamination with increasing exact-exchange admixture restrict the achievable computational accuracy. In all cases, spin-orbit corrections to the hyperfine tensors are sizable and have to be included in accurate calculations. Scalar relativistic effects enhance the isotropic Mo hyperfine coupling by approximately 15-20%. Two-component g-tensor calculations with variational inclusion of spin-orbit coupling show that the Deltag parallel components in [MoVOCl4]- and [MoVOF5]2- depend on higher-order spin-orbit contributions and are thus described insufficiently by the usual second-order perturbation approaches. Computed orientations of g- and hyperfine tensors relative to each other and to the molecular framework for the MoXLCl2 complexes provide good agreement between theory and single-crystal electron paramagnetic resonance experiments. In these cases, the hyperfine tensor orientations are influenced only slightly by spin-orbit effects.

Relativistic molecular orbital study of the optical and magnetic properties of hexachloro protactinate (IV): PaCl62−

Our ab initio all-electron Dirac-Fock and the corresponding nonrelativistic limit calculations performed at four Pa-Cl bond distances yield for octahedral PaCl(6) (2-) the optimized Pa-Cl bond distances of 2.758 and 2.771 Angstroms, respectively. Dirac scattered wave and its nonrelativistic limit calculations are performed at the optimized Pa-Cl bond distances using a first-order perturbation procedure to obtain the molecular g and hyperfine tensors for the octahedral anion PaCl(6) (2-). The calculated Zeeman and (231)Pa hyperfine interactions are in fairly good agreement with the electron paramagnetic resonance and electron nuclear double resonance values of the Pa(4+) impurity site in the octahedral Cs(2)ZrCl(6) lattice. The calculated relativistic transition energies of the 5f-->5f and 5f-->6d absorption bands are also in good agreement with the experimental results.

Comparative Density-Functional Study of the Electron Paramagnetic Resonance Parameters of Amavadin

Electronic g tensors and hyperfine coupling tensors have been calculated for amavadin, an unusual eight-coordinate vanadium(IV) complex isolated from Amanita muscaria mushrooms. Different density-functional methods have been compared, ranging from local via gradient-corrected to hybrid functionals with a variable Hartree-Fock exchange admixture. For both electron paramagnetic resonance (EPR) properties, hybrid functionals with an appreciable exact-exchange admixture provide the closest agreement with experimental data. Second-order spin-orbit corrections provide non-negligible contributions to the 51V hyperfine tensor. The orientation of g and A tensors relative to each other also depends on spin-orbit corrections to the A tensor. A rationalization for the close resemblance of the EPR parameters of amavadin to those of the structurally rather different vanadyl complexes is provided, based on the nature of the relevant frontier orbitals.

Relativistically corrected hyperfine structure constants calculated with the regular approximation applied to correlation corrected ab initio theory

The infinite-order regular approximation (IORA) and IORA with modified metric (IORAmm) is used to develop an algorithm for calculating relativistically corrected isotropic hyperfine structure (HFS) constants. The new method is applied to the calculation of alkali atoms Li-Fr, coinage metal atoms Cu, Ag, and Au, the Hg(+) radical ion, and the mercury containing radicals HgH, HgCH(3), HgCN, and HgF. By stepwise improvement of the level of theory from Hartree-Fock to second-order Møller-Plesset theory and to quadratic configuration interaction theory with single and double excitations, isotropic HFS constants of high accuracy were obtained for atoms and for molecular radicals. The importance of relativistic corrections is demonstrated.

Calculated optical and magnetic properties of hexafluorouranate (V) anion: UF[sub 6][sup −]

Our ab initio all-electron Dirac-Fock and the corresponding nonrelativistic limit calculations performed at four U-F bond distances yield for octahedral UF(6) (-) the optimized U-F bond distance of 2.091 and 2.088 A, respectively. We have also performed Dirac scattered wave calculations at the optimized U-F bond distances using the first-order pertubational procedure to obtain the Zeeman and hyperfine magnetic tensors for the octahedral anion UF(6) (-). The calculated isotropic Zeeman tensor of Deltag=-2.87 is in fairly good agreement with the value of Deltag=-2.78+/-0.10 obtained in electron spin resonance experiments on the H(3)O(+)UF(6) (-) adduct and the unpaired electron-spin spends approximately 2.5% of its time on the fluorine 2p(3/2) spinors. The calculated relativistic transition energies of the near-IR and visible absorption bands are also in good agreement with the experimental results. The octahedral uranium hexafluoride anion has a simple crystal field f(1) configuration; however, relativistic four-component wave functions are necessary to interpret correctly the available magnetic data, while a relativistic treatment taking into account double group symmetrized basis functions should suffice for the interpretation of the optical data.