NMR Spin–Spin Coupling Constants Derived from Relativistic Four-Component DFT Theory—Analysis and Visualization

Abstract

An unambiguous assignment of coupling pathways plays an important role in the description and rationalization of NMR indirect spin–spin coupling constants (SSCCs). Unfortunately, the SSCC analysis and visualization tools currently available to quantum chemists are restricted to nonrelativistic theory. Here, we present the theoretical foundation for novel relativistic SSCC visualization techniques based on analysis of the SSCC densities and the first-order current densities induced by the nuclear magnetic dipole moments. Details of the implementation of these techniques in the ReSpect program package are discussed. Numerical assessments are performed on through-space SSCCs, and we choose as our examples the heavy-atom Se–Se, Se–Te, and Te–Te coupling constants in three similar molecules for which experimental data are available. SSCCs were calculated at the nonrelativistic, scalar relativistic, and four-component relativistic density functional levels of theory. Furthermore, with the aid of different visualization methods, we discuss the interpretation of the relativistic effects, which are sizable for Se–Se, very significant for Se–Te, and cannot be neglected for Te–Te couplings. A substantial improvement of the theoretical SSCC values is obtained by also considering the molecular properties of a second conformation.

Quantum chemical calculations of 77Se and 125Te nuclear magnetic resonance spectral parameters and their structural applications

“…Therefore, that basis scheme has been chosen for all their calculations. Moreover, considering a failure of Nakanishi et al in prediction of the Se–Se distance in 50c, [ 341 ] Komorovsky et al [ 388 ] were very meticulous about the geometry optimization methodology. They calculated equilibrium geometries at the quasi‐relativistic ZORA/QZ4P level using PBE0 and BP86 functionals as well as at the corresponding nonrelativistic levels, and obtained a noticeably shorter Se–Se distances at the relativistic levels of DFT theory.…”

“…Overall, the geometric parameters obtained at the relativistic DFT level occurred much closer to the experimental values than that obtained at the nonrelativistic DFT level. Another important issue of Komorovsky et al, [ 388 ] that has not been considered by Nakanishi and Hayashi, [ 341 ] is the potential energy surface. Komorovsky et al have found two main conformers resulting in a huge difference in corresponding Se–Se SSCCs, while Nakanishi and Hayashi considered only one structure.…”

“…Komorovsky et al have found two main conformers resulting in a huge difference in corresponding Se–Se SSCCs, while Nakanishi and Hayashi considered only one structure. The Boltzmann averaged DKS/PBE0‐50 Se–Se SSCC in 50c were reported as 153.0–163.8 Hz in Komorovsky et al, [ 388 ] depending on the method used for optimizations. Apparently, these are much closer to the experimental value of 199.5 Hz than that of 80.3 Hz, reported by Nakanishi et al [ 341 ]…”

“…Komorovsky et al have found two main conformers resulting in a huge difference in corresponding Se-Se SSCCs, while Nakanishi and Hayashi considered only one structure. The Boltzmann averaged DKS/PBE0-50 Se-Se SSCC in 50c were reported as 153.0-163.8 Hz in Komorovsky et al, [388] depending on the method used for optimizations. Apparently, these are much closer to the experimental value of 199.5 Hz than that of 80.3 Hz, reported by Nakanishi et al [341] 3 | THE QC COMPUTATIONS OF TELLURIUM NMR SPECTRUM 125 Te NMR chemical shifts of a number of organic, inorganic, and organometallic tellurium-containing complexes were reported by Ruiz-Morales et al [389] The authors tested the performance of newly developed frozen core GIAO-DFT method, extended by the inclusion of the scalar relativity within the two-component Pauli-type Hamiltonian, [207] on the example of 125 Te chemical shifts.…”

“…Based on these data and the rest of the statistical analysis made in that work, the authors made a conclusion that, for selenium-phosphorus SSCCs in phosphine selenides, the "pure" relativistic 4-DFT scheme performs better than the combined one does. Theory and the computer implementation of novel relativistic SSCC visualization techniques based on the analysis of the SSCC densities and the first-order current densities induced by the nuclear magnetic dipole moments were presented by Komorovsky et al [388] The authors analyzed the through-space SSCCs between selenium nuclei in methyl(8-(methylseleninyl)naph thalen-1-yl)selane, 50c (see Chart 8), and focused their attention on the role of the relativistic effects. The SSCCs were calculated at the nonrelativistic, scalar relativistic, and four-component relativistic density functional levels of theory.…”