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Electric Field Gradients

Electric field gradients at the positions of the atomic nuclei can be calculated by VASP using the method of Ref. [150].

The following flags control the behaviour of VASP:

• LEFG-tag (default: .FALSE.)

  LEFG = .TRUE. | .FALSE.
  

  LEFG switches on the calculation of the electric field gradient tensors. The EFG tensors are symmetric. The principal components $V_{ii}$ and asymmetry parameter $\eta$ are printed for each atom. Following convention the principal components $V_{ii}$ are ordered such that:
  $$\vert V_{zz}\vert > \vert V_{xx}\vert > \vert V_{yy}\vert$$
  The asymmetry parameter $\eta = {(V_{yy} - V_{xx})}/ V_{zz}$. For so-called ``quadrupolar nuclei'', i.e. nuclei with nuclear spin $I > 1/2$, NMR experiments can access $V_{zz}$ and $\eta$.

  Beware: Attaining convergence can require somewhat smaller EDIFF than the default of 1.e-4 and somewhat larger cutoff ENCUT than default with PREC=A. Moreover, the calculation of EFGs typically requires high quality PAW data sets. Semi-core electrons can be important (check with *_pv or *_sv POTCARs) as well as explicit inclusion of augmentation channel(s) with $d$-projectors.

• QUAD_EFG-tag (default: 1.) This tag allows the conversion by VASP of the $V_{zz}$ values into the $C_q$ often encountered in NMR literature. The conversion formula ($Q$ is the element and isotope specific quadrupole moment):
  $$C_q = \frac{e Q V_{zz}}{h}$$
  The QUAD_EFG-tag consists of the nuclear quadrupole moment in millibarns for each atomic species, in the same order as in the POTCAR file. The output $C_q$ is in MHz. See Ref. [151] for a compilation of nuclear quadrupole moments.

  Suppose a solid contains Al, C and Si, than the QUAD_EFG-tag could read:

  QUAD_EFG = 146.6 33.27 0
  

  $^{27}$Al is the stable isotope of Al with a natural abundance of 100 % and $Q = 146.6$. The stable isotopes $^{12}$C and $^{13}$C are not quadrupolar nuclei, however, the radioactive $^{11}$C is. It has $Q = 33.27$. For Si it is pointless to calculate a $C_q$: Again all stable isotopes have $I \le 1/2$. No moments are known for the other isotopes.

  Beware: several definitions of $C_q$ are used in the NMR community.

Beware: for heavy nuclei inaccuracies are to be expected because of an incomplete treatement of relativistic effects.