Gauge-origin dependence in electronic g-tensor calculations

Glasbrenner, Michael; Vogler, Sigurd; Ochsenfeld, Christian

doi:10.1063/1.5028454

Cited by 17 publications

(22 citation statements)

References 74 publications

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“…The gauge dependence of the g tensor is less pronounced than that for the NMR orbital contribution. However, it still leads to comparably large deviations for systems with a spatially extended spin-density distribution. , Therefore, the spin–orbit perturbation term with GIAOs and the X2C picture-change correction needs to be used and becomes As shown for the PSOSO term, the extension for the mSNSO/SNSO approximation is trivial and we list the equations without this approximation in this subsection for brevity.…”

Section: Theorymentioning

confidence: 99%

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

2022

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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 spinorbit perturbation theory including the screened nuclear spinorbit correction for the EPR hyperne coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spinorbit twocomponent and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is suciently 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 [CeTi 6 O 3 (OiPr) 9 (salicylate) 6 ].

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Section: Theorymentioning

confidence: 99%

“…However, it still leads to comparably large deviations for systems with a spatially extended spin-density distribution. 52,140 Therefore, the spin− orbit perturbation term with GIAOs and the X2C picturechange correction needs to be used and becomes…”

Section: The Journal Of Physical Chemistrymentioning

confidence: 99%

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

2022

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“…For a single local paramagnetic center, it has been demonstrated that choosing a gauge origin close to the paramagnetic center usually yields good results. 47 The gauge-origin dependence can be removed by employing gaugeincluding AOs (GIAOs). 48,49 However, this makes the theory significantly more complicated at not much added conceptual insight.…”

Section: Please Cite This Article As Doi:101063/50088162mentioning

confidence: 99%

Theoretical analysis of the long-distance limit of NMR chemical shieldings

Lang

Ravera

Parigi

et al. 2022

The Journal of Chemical Physics

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After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland–McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel–Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree–Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin–orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland–McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.

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“…However, the RKB condition is generally sufficient to recover the nonrelativistic limit for first-order derivatives. The g tensor is commonly obtained with spin–orbit perturbation theory in one-component approaches. ,,− Here, inclusion of the vector potential in the Pauli spin–orbit operator leads to the relativistic mass or Pauli kinetic energy correction and the diamagnetic or gauge correction. , Therefore, using RMB ensures that the two-component approach is directly comparable to the perturbative ansatz. Whereas the use of RMB leads to problematic integrals for the HFC constant and the related nuclear magnetic resonance (NMR) coupling constants in X2C, the integrals can be evaluated straightforwardly for magnetic field derivatives. − , Thus, RMB can be used for EPR g tensors similar to NMR shieldings − , and magnetic circular dichroism …”

Section: Introductionmentioning

confidence: 99%

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

Franzke

2022

J. Chem. Theory Comput.

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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 ansaẗze 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 quasirelativistic 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 [(C 5 Me 5 ) 2 Y(μ-S) 2 Mo(μ-S) 2 Y(C 5 Me 5 ) 2 ] − . Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C 6 Cl 5 ) 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.

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Gauge-origin dependence in electronic g-tensor calculations

Cited by 17 publications

References 74 publications

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

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

Theoretical analysis of the long-distance limit of NMR chemical shieldings

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

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