LEFG
LEFG = .TRUE. | .FALSE.
Default: LEFG = .FALSE.
Description: The LEFG computes the Electric Field Gradient at positions of the atomic nuclei.
For LEFG=.TRUE., the electric field gradient tensors at the positions of the atomic nuclei are calculated using the method of Petrilli et al. [1].
The EFG tensors are symmetric. The principal components Vii and asymmetry parameter η are printed for each atom. Following convention the principal components Vii are ordered such that:
- [math]\displaystyle{ |V_{zz}| \gt |V_{xx}| \gt |V_{yy}|. }[/math]
The asymmetry parameter is defined as [math]\displaystyle{ \eta = {(V_{yy} - V_{xx})}/ V_{zz} }[/math]. For so-called "quadrupolar nuclei", i.e., nuclei with nuclear spin I>1/2, NMR experiments can access Vzz and η.
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.
To convert the Vzz values into the Cq often encountered in NMR literature, one has to specify the nuclear quadrupole moment by means of the QUAD_EFG-tag. The output of [math]\displaystyle{ C_q }[/math] is in MHz. See references [2] and Ref. [3] for a compilation of nuclear quadrupole moments.
Suppose a solid contains Al, C, and Si, then the QUAD_EFG tag could read:
QUAD_EFG = 146.6 33.27 0.0
[math]\displaystyle{ ^{27}\mathrm{Al} }[/math] is the stable isotope of Al with a natural abundance of 100% and [math]\displaystyle{ Q = 146.6 }[/math]. The stable isotopes [math]\displaystyle{ ^{12}\mathrm{C} }[/math] and [math]\displaystyle{ ^{13}\mathrm{C} }[/math] are not quadrupolar nuclei, however, the radioactive [math]\displaystyle{ ^{11}\mathrm{C} }[/math] is. It has [math]\displaystyle{ Q = 33.27 }[/math]. For Si it is pointless to calculate a [math]\displaystyle{ C_q }[/math] since all stable isotopes have [math]\displaystyle{ I \le 1/2 }[/math]. No moments are known for the other isotopes.
Beware: for heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.
Related tags and articles
References
- ↑ H. M. Petrilli, P. E. Blöchl, P. Blaha, and K. Schwarz, Electric-field-gradient calculations using the projector augmented wave method, Phys. Rev. B 57, 14690 (1998).
- ↑ P. Pyykkö, Year-2008 nuclear quadrupole moments, Mol. Phys. 106, 1965-1974 (2008).
- ↑ P. Pyykkö, Year-2017 nuclear quadrupole moments, Mol. Phys. 116, 1328-1338 (2018).