Four-Component Relativistic Density Functional Theory Calculations of NMR Shielding Tensors for Paramagnetic Systems

Abstract

A four-component relativistic method for the calculation of NMR shielding constants of paramagnetic doublet systems has been developed and implemented in the ReSpect program package. The method uses a Kramer unrestricted noncollinear formulation of density functional theory (DFT), providing the best DFT framework for property calculations of open-shell species. The evaluation of paramagnetic nuclear magnetic resonance (pNMR) tensors reduces to the calculation of electronic g tensors, hyperfine coupling tensors, and NMR shielding tensors. For all properties, modern four-component formulations were adopted. The use of both restricted kinetically and magnetically balanced basis sets along with gauge-including atomic orbitals ensures rapid basis-set convergence. These approaches are exact in the framework of the Dirac-Coulomb Hamiltonian, thus providing useful reference data for more approximate methods. Benchmark calculations on Ru(III) complexes demonstrate good performance of the method in reproducing experimental data and also its applicability to chemically relevant medium-sized systems. Decomposition of the temperature-dependent part of the pNMR tensor into the traditional contact and pseudocontact terms is proposed.

Four-component relativistic density functional theory with the polarisable continuum model: application to EPR parameters and paramagnetic NMR shifts

“…(29) it follows that accurate measurements of the paramagnetic shift provide us with an indirect link to the EPR parameters. This connection has already been examined in the framework of relativistic four-component DFT theory [45].…”

Paramagnetic Enhancement of Nuclear Spin–Spin Coupling

“…However, significant scalar relativistic effects have been pointed out in studies of pNMR shielding tensors for transition element systems. 18,19 In this article, the perturbational description of SO effects in HFC is contrasted with a fully relativistic 4-component method, 20 …”

Two-dimensional NMR measurement and point dipole model prediction of paramagnetic shift tensors in solids

“…Recently, a general formalism has been introduced by Moon and Patchkovskii [92] and expanded upon by Vaara and others [93,94] for calculating the NMR paramagnetic shift tensor from EPR tensors. Accurately calculating g-and hyperfine coupling tensors from first principles is far from trivial, however, and the development of computational tools for calculating NMR properties from these tensors, particularly for transition metal systems, remains active [95][96][97][98]. Moreover, this formalism has been devoted almost exclusively to determining the open-shell contribution to isotropic shifts for molecular systems in solution, being only concerned with the anisotropic components of the g-and hyperfine coupling tensors insofar as they contribute to the contact and pseudo-contact shifts.…”