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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 and asymmetry parameter are printed out for each atom. Following convention is made for the principal components :

The asymmetry parameter . For so-called "quadrupolar nuclei", i.e. nuclei with nuclear spin , NMR experiments can access and .

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 -projectors.

  • QUAD_EFG=1 This tag allows the conversion by VASP of the values into the often encountered in NMR literature. The conversion formula is given as follows( is the element and isotope specific quadrupole moment):

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 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

is the stable isotope of Al with a natural abundance of 100% and . The stable isotopes and are not quadrupolar nuclei, however, the radioactive is. It has . For Si it is pointless to calculate a since all stable isotopes have . No moments are known for the other isotopes.

Beware:

  • Several definitions of are used in the NMR community.
  • For heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.

Related Tags and Sections

LEFG

Examples that use this tag

References

  1. H. M. Petrilli, P. E. Blöchl, P. Blaha, and K. Schwarz, Phys. Rev. B 57, 14690 (1998).
  2. P. Pyykkö, Mol. Phys. 106, 1965-1974 (2008), online compilation: http://www.chem.helsinki.fi/pyykko/Q2008.pdf.