Field gradient tensor element

Table 5.7 Breakdown of the contributions to the largest field gradient tensor element in a.u. from spin-polarized B3LYP DPT calculations (from [60])...

When inserting into (4.5), the term ZeR will be multiplied with the elements of the electric field gradient tensor V. Fortunately, the procedure can be restricted to diagonal elements Vu, because V is symmetric and, consequently, a principal axes system exists in which the nondiagonal elements vanish, = 0. The diagonal elements can be determined by using Poisson s differential equation for the electronic potential at point r = 0 with charge density (0), AV = Anp, which yields... 

The remaining matrix element in (8.382) leads to definitions of the q = 0, 2 components of the electric field gradient tensor (actually, its negative), which are... 

Letting Vhe the potential at the nucleus in question due to all other charges, matrix elements taken of the electric field gradient tensor U are given by matrix elements of the second derivative of V directed along the space-fixed Z axis (= axis of quantization) ... 

For asymmetric top molecules, the principal axis system of the inertia tensor and the field gradient tensor do not coincide in general. In the case of a completely non-symmetric position of the quadmpolar nucleus in the molecule, none of the components Xgg- of the field gradient tensor eqnals zero. If a nucleus lies on a plane which contains the principal inertial axes g and g and which is a symmetry plane of the molecule, then the off-diagonal elements Zgg and Xg g" vanish. 

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