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# Electric Field Gradient

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Electric field gradients at the positions of the atomic nuclei can be calculated by VASP using the method described in reference [1].

The following flags control the behaviour of VASP (the given value is the default value):

• LEFG=.FALSE. This tag switches on the calculation of the electric field gradient tensors (LEFG=.TRUE.). The EFG tensors are symmetric. The principal components ${\displaystyle V_{{ii}}}$ and asymmetry parameter ${\displaystyle \eta }$ are printed out for each atom. Following convention is made for the principal components ${\displaystyle V_{{ii}}}$ :

${\displaystyle |V_{{zz}}|>|V_{{xx}}|>|V_{{yy}}|}$

The asymmetry parameter ${\displaystyle \eta ={(V_{{yy}}-V_{{xx}})}/V_{{zz}}}$ . For so-called "quadrupolar nuclei", i.e. nuclei with nuclear spin ${\displaystyle I>1/2}$ , NMR experiments can access ${\displaystyle V_{{zz}}}$ and ${\displaystyle \eta }$ .

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

• QUAD_EFG=1 This tag allows the conversion by VASP of the ${\displaystyle V_{{zz}}}$ values into the ${\displaystyle C_{q}}$ often encountered in NMR literature. The conversion formula is given as follows(${\displaystyle Q}$ is the element and isotope specific quadrupole moment):

${\displaystyle C_{q}={\frac {eQV_{{zz}}}{h}}}$

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 of ${\displaystyle C_{q}}$ is in MHz. See reference [2] 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


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

Beware:

• Several definitions of ${\displaystyle C_{q}}$ are used in the NMR community.
• For heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.