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 V_ii and asymmetry parameter η are printed for each atom. Following convention the principal components V_ii are ordered such that:

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

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

Mind: 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 V_zz values into the C_q often encountered in NMR literature, one has to specify the nuclear quadrupole moment by means of the QUAD_EFG-tag.

Recommendations and advice

Tight settings are required for calculating the electric field gradient.

Input parameters

A larger ENCUT value than usual, generally much higher than the value given by ENMAX in the POTCAR file, e.g. 800 eV for C in diamond, rather than the standard 400 eV.
A small EDIFF is required to provide converged chemical shifts, e.g. 1E-8 eV.
Tighter precision, e.g. PREC = Accurate.
Non-spherical contributions to the gradient of the density inside PAW spheres, i.e. LASPH = .TRUE.

Structure

The structure is extremely important, so using the experimental structure can improve results.

PAW pseudopotentials

The use of PAW potentials has a strong influence, GW POTCAR files often improve values.
Semi-core electrons can be important (check the POSCAR files with *_pv or *_sv) as well as explicit inclusion of augmentation channels with $d$ -projectors.

Important: Several definitions of

C_q

are used in the NMR community, ensure that you are comparing between the same definitions in calculation and experiment.

Mind: For heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.

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).

[petrilli:prb:1998-1] 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).

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