NMR J-couplings
NMR J-coupling or nuclear spin-spin coupling is an indirect interaction of the nuclear magnetic moments mediated by the bonding electrons. It is manifested as the fine structure in NMR spectra, providing a direct measure of bond strength and a map of the connectivities of the system.
The J-coupling mechanism is an essential component of many NMR experiments. Joyce et al. (2007) developed a method to calculate J-coupling constants from first-principles in extended systems in a planewave-pseudopotential density functional theory framework, using the projected augmented wave method (PAW) to reconstruct the all-electron properties of the system. This method has been validated for a small number of systems containing light atoms against quantum chemical calculations and against experimental data (see for example, Joyce et al., 2008). This technique has been further developed by Green and Yates (2014) to incorporate scalar relativistic effects in the ZORA (zeroth-order regular approximation) approach and hence to provide a highly efficient method for predicting J-coupling in extended systems containing heavy ions at negligible extra computational cost compared to the non-relativistic method.
A general review of the formalism is given by Yates (2010), this discusses various aspects of the calculations which should be taken into account when comparing results with solid-state NMR experiments including anisotropy and orientation of the J tensors, the reduced coupling constant, and the relationship between the J-coupling and crystal structure.
J-coupling interactions can be decomposed into four mechanisms:
- two due to interactions of the electron spins with the nuclear moments
- two due to electron currents induced by the nuclear moments
When spin-orbit coupling is neglected these can be treated separately.
The spin term can be decomposed into an analog of a spin-dipole interaction plus a Fermi-contact term, which is due to the finite probability of the presence of an electron at the nucleus.
Induced current operators can be decomposed into diamagnetic and paramagnetic current operators.
Joyce et al. (2007) found that the Fermi-contact contribution to be consistently the largest component, while the diamagnetic and spin-dipolar contributions were very small for all the cases studied.
Experimental interest is focused primarily on the isotropic coupling constant which is obtained from the trace of the J-coupling tensor and is measured in Hertz. Recent extensive validation studies (for example, by Green and Yates 2014) demonstrate that the pseudopotential PAW approach for J-coupling calculations gives results in good qualitative and quantitative agreement with experiment both for light and heavy elements.
It is important to note that solid state calculations of J-couplings using CASTEP correctly account for long-range effects in the periodic systems and reproduce the differences between solution and solid-state values (Joyce et al., 2008).
Induced magnetization density and current density are expected to be short-ranged. This forms the basis of using J-coupling as a tool for probing the strength of interatomic bonds. However, in a periodic calculation the perturbing nucleus can be viewed as similar to a defect in a defect calculation. Hence, sometimes it might be necessary to construct a supercell which is large enough to inhibit the interaction between the periodic defects or perturbations. Convergence with respect to the cell size should represent an important test in establishing accuracy of J-coupling calculations in either periodic systems or in molecule in a box calculations.