Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

Abstract

The self-consistent and complex spin–orbit exact two-component (X2C) formalism for NMR spin–spin coupling constants [J. Chem. Theory Comput.20211738743994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin–dipole (SD) interactions as well as the paramagnetic spin–orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8–24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods

“…Here, the SCF part amounts to about 2 h, while the NMR part requires almost 4.5 h. Therefore, LHFs are clearly computationally more demanding than conventional global or range-separated hybrids using seminumerical integration techniques, as previously discussed in ref . For magnetic response properties, a multigrid approach can be used for the conventional hybrids without loss of accuracy, ,,,, i.e., a large grid is used for the semilocal exchange–correlation parts and a small grid is used for the HF exchange terms. As LHF evaluate both the semilocal and HF exchange parts simultaneously, such a multigrid approach is not straightforward and simply using a small grid for the left-hand side of the response equations results in serious convergence issues for the spin-flip part of the ZFS tensor.…”

“…First, we demonstrate the applicability of the X2C framework for pNMR shifts. Second, we will consider modern density functional approximations up to the rung of local hybrid functionals (LHFs) and mGGAs incorporating the paramagnetic current density. – The latter is needed to properly generalize the kinetic-energy density τ of mGGAs and LHFs for EPR and NMR properties. ,,,– In the absence of magnetic perturbations, τ is defined as τ σ = 1 2 ∑ i | p⃗̂ φ i σ | 2 = 1 2 ∑ i false( p⃗̂ φ i σ false) † · false( p⃗̂ φ i σ false) with the momentum operator p⃗̂ and the Kohn–Sham spin orbitals φ i σ . This variable is formally used to identify inhomogeneities in the electron density and is a key ingredient of modern functionals with accurate thermochemical properties. – For magnetic properties, τ needs to be generalized to τ̃ σ = τ σ − | j⃗ p σ | 2 2 ρ σ with the paramagnetic current density …”

TURBOMOLE: Today and Tomorrow

“…Formally, the coupling tensor is obtained as the mixed derivative of the energy with respect to the corresponding nuclear magnetic moments, which are introduced via the principle of minimal coupling. NMR couplings are available within a nonrelativistic scalar X2C and the spin–orbit X2C framework . All functional classes up to local hybrids are supported and include the current density for gauge invariance. ,, …”

“…Systems containing heavy elements such as Sn, Pb, Pd, and Pt require the inclusion of relativistic effects, ,,,− i.e. , methods based on the Dirac equation are introduced.…”

Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures

“…As a substantial fraction of the atoms in the periodic table is NMR-active, the technique can very often be used to provide critical information about their chemical environment − in a nondestructive way. Regarding computational analysis, apart from the fact that theoretical calculations are extremely useful to interpret experimental signals, it has been demonstrated that it is essential to account for relativistic effects already for elements around the third row of the periodic table. − Magnetic properties are often challenging to calculate due to the dependence of the results on the gauge origin of an external magnetic field for incomplete bases sets. However, the indirect spin–spin coupling is expressed as the second derivative of the electronic energy with respect to the internal magnetic fields caused by nuclear spins, so the gauge-origin issue does not arise.…”