Field gradient
In atomic, molecular, and solid-state physics, the electric field gradient (EFG) measures the rate of change of the electric field at an atomic nucleus generated by the electronic charge distribution and the other nuclei. The EFG couples with the nuclear electric quadrupole moment of quadrupolar nuclei (those with spin quantum number greater than one-half) to generate an effect which can be measured using several spectroscopic methods, such as nuclear magnetic resonance (NMR), microwave spectroscopy, electron paramagnetic resonance (EPR, ESR), nuclear quadrupole resonance (NQR), Mössbauer spectroscopy or perturbed angular correlation (PAC). The EFG is non-zero only if the charges surrounding the nucleus violate cubic symmetry and therefore generate an inhomogeneous electric field at the position of the nucleus.
EFGs are highly sensitive to the electronic density in the immediate vicinity of a nucleus. This is because the EFG operator scales as r−3, where r is the distance from a nucleus. This sensitivity has been used to study effects on charge distribution resulting from substitution, weak interactions, and charge transfer.
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:
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