Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

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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“…The evaluation of the FC and SD contribution in scalar-relativistic X2C and analytical derivative theory is described in Refs. 46. See also Refs.…”

Section: Hyperne Coupling Tensormentioning

confidence: 99%

“…The isotropic HFC constant A iso is given in MHz and the pNMR shielding constant σ in ppm. For SO X2C/DLU-X2C,48 the orbital contribution is taken from Ref 46,. where we used the scalar-relativistic Hamiltonian.…”

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confidence: 99%

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

2022

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“…indicates convergence in the CPKS equations. 70,74,91,92,112,126,148,149 We use the finite nucleus model for the scalar potential and the vector potential, 145 and the mSNSO approximation. [141][142][143][144] All compounds feature one metal center.…”

Section: Methodsmentioning

confidence: 99%

“…91. The mSNSO-DLU-X2C Hamiltonian 70,74,91,112,126,148,149 in the finite nucleus model 145 is applied together with the x2c-TZVPPall-2c basis set for Tb 127 and the x2c-SVPall-2c basis set for the other elements. 127 This basis set was shown to be sufficient for the Tb HFC constant.…”

Section: Methodsmentioning

confidence: 99%

Current density functional framework for spin–orbit coupling

Holzer

Franzke

Pausch

2022

Preprint

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Relativistic two-component and four-component density functional calculations are carried out in a non-collinear formalism to describe spin-orbit interaction. The exchange-correlation functional itself is constructed as a straightforward generalization of the non-relativistic density functional approximation. However, spin-orbit coupling is a form of magnetic induction and generally leads to a non-vanishing paramagnetic current density. This means that functionals depending on the kinetic energy density such as meta-generalized gradient approximations and local hybrid functionals should be constructed in the framework of current density functional theory (CDFT), which is (almost) exclusively used in the regime of strong magnetic fields. Herein, we present a CDFT approach for spin-orbit coupling, which leads to current-dependent terms in the potential and its derivatives. The ansatz is implemented for the exchange-correlation potential and the exchange-correlation kernel, making it applicable to a wide range of molecular properties. We assess the importance of the current density terms for ground-state energies, excitation energies, nuclear magnetic resonance (NMR) shielding and spin-spin coupling constants, as well as hyperfine coupling constants and ∆g-shifts in electron paramagnetic resonance (EPR) spectroscopy. The most notable changes are found for EPR properties. The impact of the current-dependent terms rises with the number of unpaired electrons and consequently EPR properties are more sensitive towards CDFT. Considerable changes in the results are observed for the strongly constrained and appropriately normed (SCAN) functionals, as well as the B97M family and TASK. The current density terms are less important when exact exchange is incorporated. Consequently, the results with (local) hybrid functionals are not substantially affected. At the same time, the current density does not notably increase the computational costs for hybrid functionals, but the current-dependent kernel ensures the stability of response calculations in all cases. We therefore strongly recommend to use the framework of CDFT for self-consistent spin-orbit calculations.

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“…111,112 We use the X2C Hamiltonian in the diagonal local approximation to the unitary transformation (DLU). 30,92,106,107,[113][114][115][116] The restricted kinetic balance (RKB) condition 117 is employed for the HFC, whereas both RKB and the restricted magnetic balance (RMB) condition 118 are employed for the g-tensor. An SCF threshold of 10 −9 Hartree is applied.…”

Section: Epr Calculationsmentioning

confidence: 99%

A Local Hybrid Exchange Functional Approximation from First Principles

Holzer

Franzke

2022

Preprint

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Local hybrid functionals are a more flexible class of density functional approximations allowing for a position-dependent admixture of exact exchange. This additional flexibility, however, comes with a more involved mathematical form and a more complicated design. A common denominator for previously constructed local hybrid funtionals is usage of thermochemical benchmark data to construct these functionals. Herein, we design a local hybrid functional without relying on benchmark data. Instead, we construct it in a more ab initio manner, following the principles of modern meta-generalized gradient approximations and considering theoretical constrains. To achieve this, we make use of the density matrix expansion and a local mixing function based on an approximate correlation length. The accuracy of the developed density functional approximation is assessed for thermochemistry, excitation energies, polarizabilities, magnetizabilities, NMR spin–spin coupling constants, NMR shieldings and shifts, as well as EPR g-tensors and hyperfine coupling constants. Here, the new exchange functional shows a robust performance and is especially well suited for atomization energies, barrier heights, excitation energies, NMR coupling constants, and EPR properties, whereas it looses some ground for the NMR shifts. Therefore, the designed functional is a major step forwards for functionals that have been designed from first principles.

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Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

Cited by 31 publications

References 212 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

Current density functional framework for spin–orbit coupling

A Local Hybrid Exchange Functional Approximation from First Principles

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