Electric-field-gradient tensor principal-axis system

The electric field gradient is again a tensor interaction that, in its principal axis system (PAS), is described by the tluee components F Kand V, where indicates that the axes are not necessarily coincident with the laboratory axes defined by the magnetic field. Although the tensor is completely defined by these components it is conventional to recast these into the electric field gradient eq = the largest component,... 

For nuclei with 7 1, the nuclear electric quadrupole moment interacts with the electric field gradient in a nonsymmetric environment of electrons around the nucleus. The electric field gradient is described by a tensor that can be expressed in diagonal form (components Vx, VY, and IQ) in a principal axis system fixed in the molecule. By Laplace s equation the sum of the three components is zero, so there are two independent parameters, usually taken as the largest of the three components, V7 = d2V/dz2, and the asymmetry parameter tj = (Vx — IQ)/ Vz, with the convention that VZ VX. The electrical interaction leads to... 

The electric field gradient is described by the traceless and symmetrical tensor V. V, in turn, is quantified in terms of its largest component, = eQ, and the asymmetry parameter, In the principal axis system, the quadrupolar Hamiltonian is... 

For Zn SSNMR spectroscopy, the observed spectrum is usually dominated by the nuclear electric quadrupolar interaction unless the zinc sits at a site with spherical symmetry (such as tetrahedral, octahedral and cubic sites). This anisotropic interaction originates from the coupfing between the quadrupole moment (eQ) of the nucleus and the electric field gradient (EFG) at the nuclear site. The EFG is described by a second-rank tensor that can be diagonalized in a principal axis system (PAS). In the PAS, the EFG is described by three components, which are ordered in such that I Fxx I kVy I ud they satisfy FxxT TyyT Tzz fi-The quadrupolar interaction is characterized by two parameters one is quadrupolar coupling constant ... 

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