Definition
A given charge distribution of electrons and nuclei, ρ(r), generates an electrostatic potential V(r). The derivative of this potential is the negative of the electric field generated. The first derivatives of the field, or the second derivatives of the potential, is the electric field gradient. The nine components of the EFG are thus defined as the second spatial derivatives of the electrostatic potential, evaluated at the position of a nucleus:
For each nucleus, the components Vij are combined as a symmetric 3 × 3 matrix. Under the assumption that the charge distribution generating the electrostatic potential is external to the nucleus, the matrix is traceless, for in that situation Laplace's equation, ∇2V(r) = 0, holds. Relaxing this assumption, a more general form of the EFG tensor which retains the symmetry and traceless character is
where ∇2V(r) is evaluated at a given nucleus.
As V (and φ) is symmetric it can be diagonalized. The principal tensor components are usually denoted Vzz, Vyy and Vxx in order of decreasing modulus. Given the traceless character, only two of the principal components are independent. Typically these are described by Vzz and the asymmetry parameter, η, defined as
Read more about this topic: Electric Field Gradient
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