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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): V_{{ii}} and asymmetry parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \eta are printed out for each atom. Following convention is made for the principal components Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): V_{{ii}} :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): |V_{{zz}}|>|V_{{xx}}|>|V_{{yy}}|

The asymmetry parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \eta ={(V_{{yy}}-V_{{xx}})}/V_{{zz}} . For so-called "quadrupolar nuclei", i.e. nuclei with nuclear spin Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): I>1/2 , NMR experiments can access Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): V_{{zz}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): d -projectors.

  • QUAD_EFG=1 This tag allows the conversion by VASP of the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): V_{{zz}} values into the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): C_{q} often encountered in NMR literature. The conversion formula is given as follows(Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q is the element and isotope specific quadrupole moment):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): ^{{27}}{\mathrm {Al}} is the stable isotope of Al with a natural abundance of 100% and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q=146.6 . The stable isotopes Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): ^{{12}}{\mathrm {C}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): ^{{13}}{\mathrm {C}} are not quadrupolar nuclei, however, the radioactive Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): ^{{11}}{\mathrm {C}} is. It has Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q=33.27 . For Si it is pointless to calculate a Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): C_{q} since all stable isotopes have Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): I\leq 1/2 . No moments are known for the other isotopes.

Beware:

  • Several definitions of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): C_{q} 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.
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