Nuclear magnetic resonance spin–spin coupling constants from density functional theory: Problems and results

Our recently developed method for the calculation of indirect nuclear spin-spin coupling constants is studied in more detail. For the couplings between nuclei other than N, O, and F ͑which have lone pairs͒ the method yields very reliable results. The results for 1 J͑Si-H͒ couplings are presented and their dependence on the basis set quality is analyzed. Also, The limitations of the method, which is based on density functional theory, are connected with the inability of the present LDA and GGA exchange-correlation functionals to describe properly the spin-perturbations ͑through the Fermi-contact mechanism͒ on atoms to the right of the periodic table ͑containing lone pairs͒. However, the deviations from experiment of the calculated couplings for such nuclei are systematic, at least for one-bond couplings, and therefore these calculated couplings should still be useful for NMR structure determinations

Calculations of the EPR g-tensor using unrestricted two- and four-component relativistic approaches within the HF and DFT frameworks

Approaches and programs for calculations of the EPR g-tensor in the framework of the two- and four-component methods are still very rare. There are three main reasons for this: the wider community's unawareness of the importance of second- and higher order spin–orbit effects on the g-tensor, the methodological problems associated with performing such calculations and the lack of understanding of these problems. This paper reports on the implementation of a method for calculation of the g-tensor in the framework of the relativistic unrestricted two- and four-component Hartree–Fock and density functional theory approaches based on the Kramers pair formalism. This implementation allows us to analyse problems which arise when the g-tensor is calculated via Kramers pairs in the unrestricted framework

Visualization of Electron Paramagnetic Resonance Hyperfine Structure Coupling Pathways

The close relation between the EPR hyperfine coupling constant and NMR indirect spin–spin coupling constant is well-known. For example, the Karplus-type dependence of hyperfine constants on the dihedral angle, originally proposed for NMR spin–spin coupling, is widely used in pNMR studies. In the present work we propose a new tool for visualization of hyperfine coupling pathways based on our experience with visualization of NMR indirect spin–spin couplings. The plotted 3D-function is the difference between the total electron densities when the magnetic moment of the nucleus of interest changes its sign and as such is an observable from the physical point of view. It has been shown that it is proportional to the linear response of the spin density to the nuclear spin (i.e., magnetic moment). In contrast to the widely used visualization of spin density, our new approach depicts only the part of the electron cloud of a molecule that is affected by the interaction of the unpaired electron(s) with the desired nuclear magnetic moment. Because visualization of NMR spin–spin couplings and hyperfine interaction is based on the same ideas and done using similar techniques, it allows a direct comparison of the corresponding pathways for the two phenomena so as to analyze their resemblance and/or dissimilarity

ReSpect: Relativistic spectroscopy DFT program package

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac–Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin–spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program’s website http://www.respectprogram.org

Transmission of spin-polarization by π-orbitals:an approach to assessing its effect on NMR spin-spin coupling and EPR hyperfine structure

Funding: We acknowledge the support from Slovak-French PHC Stefanik project “Spin Coupling Advanced Level Perception” (SCALP). OM, VM and JRA acknowledge the support from Slovak grant agencies APVV (grants No. SK-FR-19-0001 and APVV-19-0516) and VEGA (grant No. 2/0135/21). This work was also supported by the CNRS, the Université de Bourgogne, the Conseil Régional BFC (CHIMENE project), the PIA-excellence ISITE-BFC program (COMICS project) and the FEDER, which are all sincerely thanked.A new approach to assessing the effect of the transmission of spin-polarization by π-orbitals (π-TSP) is presented. In order to switch off the π-TSP effect, we artificially average the α- and β-densities of the valence π-orbitals when calculating the exchange–correlation contribution to the Fock matrix in the unrestricted Kohn–Sham framework. The π-TSP effect is then evaluated as the difference between the results obtained with switched-on and switched-off options. This approach is applied to estimate the π-TSP effect on the Fermi-contact contribution to spin–spin couplings and EPR hyperfine structure coupling constants. The π-TSP effect on the distribution of spin-density, spin–spin coupling pathways and pathways of EPR hyperfine couplings is demonstrated for benzene, naphthalene, 1,3,5,7,9-decapentaene and the 1,3,5,7,9-decapentaen-1-yl radical. The sign alternation of the spin-polarization transmitted by π-orbitals is explained in a theoretical framework based on perturbation theory. However, the delocalized nature of the π-system can interfere with the sign alternation in certain cases, two of which – the cyclobutadiene dication and the cyclooctatetraene dication – are examined, and an explanation for which is provided.PostprintPeer reviewe

Indirect Nuclear ¹⁵N–¹⁵N Scalar Coupling through a Hydrogen Bond: Dependence on Structural Parameters Studied by Quantum Chemistry Tools

NMR spin–spin couplings through a hydrogen bond in the free-base and protonated forms of the complete series of [¹⁵N₂]-N-methylated 1,8-diaminonaphthalenes have been analyzed using quantum chemistry tools. The dominating role of the overlap of the coupling pathway orbitals has been demonstrated. The correlation of the sum of the ¹³C NMR shifts of the naphthalene ring C­(1,8) carbons directly attached to the interacting nitrogens with the <i>J</i>(N–N) values and the degree of methylation found earlier by G. C. Lloyd-Jones et al. [Chem.Eur. J. 2003, 9, 4523] have been reexamined. It has been found that the correlations of <i>J</i>(N–N) and [Δ∑C_1,8] with the degree of methylation have different reasons. While the former is mostly connected with the structural changes due to the solvent effect, the latter is attributed to the changes in the paramagnetic contributions from the C–N and C–C bonds caused by the replacement of a hydrogen by a methyl group