Point Charge Nuclear Quadrupole Moment Model

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

M. Pempointner, M. Seth, P. Schwerdt-feger. A point-charge model for the nuclear quadrupole moment Coupled-cluster, Dirac-Fock, Douglas-KroU, and nonrelativistic Hartree-Eock calculations for the Cu and F electric field gradients in CuF. /. Chem. Phys., 108(16) (1998) 6722-6738. 

The relaxation of the quadrupolar Xe nucleus is predominantly due to the interaction between the nuclear electric quadrupole moment and the fluctuating EFG at the nuclear site. The origin of the EFG contributing in a solution is, however, still partly an open question. Various models, both electrostatic and electronic, have been developed. The electrostatic models assume the EFG to be due to solvent molecules represented by point charges, point dipoles or quadrupoles, or a dielectric continuum. In the electronic approach, EFG is considered to be a consequence of the deformation of the spherical electron distribution of Xe. The deformation arises from the collisions between xenon and solvent molecules. It is obvious (evidence is provided, for example, by i Xe NMR experiments in liquid-crystal solutions, and by first principles calculations) that neither of these approaches alone is sufficient. In typical isotropic solvents, the Xe ranges from 4 ms to -40 ms. 

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