Gauge invariance of the spin-other-orbit contribution to the g-tensors of electron paramagnetic resonance

Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory

The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi₆O₃(OiPr)₉(salicylate)₆].

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

The Zeeman effect in the (0,0) band of the A 7Pi-X 7Sigma(+) transition of manganese monohydride, MnH

The Zeeman tuning of the P(1)(0) line (nu=17 568.35 cm(-1)) of the A (7)Pi-X (7)Sigma(+) (0,0) band of manganese monohydride, MnH, has been investigated. The laser induced fluorescence spectrum of a supersonic molecular beam sample was recorded at a resolution of approximately 40 MHz and with field strengths of up to 362.0 mT. The observed spectrum was successfully fitted using a traditional effective Zeeman Hamiltonian to determine an effective magnetic g-factor for the J=2 level of the F(1)-spin component of the A (7)Pi(v=0) state. Spectral predictions of the P(1)(0) line at field strengths used in magnetic trapping experiments are presented.

Understanding the electon paramagnetic resonance parameters of protein-bound glycyl radicals

The number of enzymes that require a glycyl-based radical for their function is growing. Here, we provide systematic quantum-chemical studies of spin-density distributions, electronic g-tensors, and hyperfine couplings of various models of protein-bound glycyl radicals. Similarly to what is found in a companion paper on N-acetylglycyl, the small g-anisotropy for this delocalized, unsymmetrical system presents appreciable challenges to state-of-the-art computational methodology. This pertains to the quality of structure optimization, as well as to the choice of the spin-orbit Hamiltonian and the gauge origin of the magnetic vector potential. Environmental effects due to hydrogen bonding are complicated and depend in a subtle fashion on the different intramolecular hydrogen bonding for different conformations of the radical. Indeed, the conformation has the largest overall effect on the computed g-tensors (less so on the hyperfine tensors). This is discussed in the context of different g-tensors obtained by recent high-field electron paramagnetic resonance (EPR) measurements for three different enzymes. On the basis of results of a parallel calibration study for N-acetylglycyl, it is suggested that the glycyl radical observed for E. coli anaerobic RNR may have a fully extended conformation, which differs from those of the corresponding radicals in pyruvate formate-lyase or benzylsuccinate synthase.

Understanding the EPR Parameters of Glycine-Derived Radicals: The Case of N-Acetylglycyl in the N-Acetylglycine Single-Crystal Environment

As a step toward an in-depth understanding of the electron paramagnetic resonance parameters of glycyl radicals in proteins, the hyperfine tensors and, particularly, the g-tensor of N-acetylglcyl in the environment of a single crystal of N-acetylglycine have been studied by systematic state-of-the-art quantum chemical calculations on various suitable model systems. The quantitative computation of the g-tensors for such glycyl-derived radicals is a veritable challenge, mainly because of the very small g-anisotropy combined with a nonsymmetrical, delocalized spin-density distribution and several atoms with comparable spin-orbit contributions to the g-tensors. The choice of gauge origin of the magnetic vector potential, and of approximate spin-orbit operators, both turn out to be more critical than found in previous studies of g-tensors for organic radicals. Environmental effects, included by supermolecular hydrogen-bonded models, were found to be moderate, because of a partial compensation between the influences from intramolecular and intermolecular hydrogen bonds. The largest effects on the g-tensor are caused by the conformation of the radical. The density functional theory methods employed systematically overestimate both the Delta gx and Delta gy components of the g-tensor. This is important for parallel investigations on the protein-glycyl radicals. The 1H alpha and 13C alpha hyperfine couplings depend only slightly on the supermolecular model chosen and appear less sensitive probes of detailed structure and environment.