LEFG: Difference between revisions

Latest revision as of 09:19, 3 March 2025

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.

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. Differences of 25 mÅ in structure can make a difference of 40 % to $V_{zz}$ ^[1].

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.

Mind: Several definitions of

C_q

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

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

References

↑ ^a ^b 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).

[1]

@@ Line 13: / Line 13: @@
 For so-called "quadrupolar nuclei", ''i.e.'', nuclei with nuclear spin I>1/2, NMR experiments can
 access ''V''<sub>zz</sub> and η.
-'''Beware''': Attaining convergence can require somewhat smaller {{TAG|EDIFF}} than the default of <tt>1.e-4</tt>
-and somewhat larger cutoff {{TAG|ENCUT}} than default with {{TAG|PREC}}=A. Moreover, the calculation of
-EFGs typically requires high quality PAW data sets. Semi-core electrons can be important (check with
-<tt>*_pv</tt> or <tt>*_sv</tt> POTCARs) as well as explicit inclusion of augmentation channel(s) with ''d''-projectors.
 To convert the ''V''<sub>zz</sub> values into the ''C''<sub>q</sub> often encountered in NMR literature, one has to specify the nuclear quadrupole moment by means of the {{TAG|QUAD_EFG}}-tag.
-The output of <math>C_q</math> is in MHz. See references {{Cite|pyykko:molphys:2008}} and Ref. {{Cite|pyykko:molphys:2017}} for a compilation of nuclear quadrupole moments.
+==Recommendations and advice==
+Tight settings are required for calculating the electric field gradient.
-<math>C_q = \frac{e Q V_{zz}}{h}</math>
-Suppose a solid contains Al, C, and Si, then the {{TAG|QUAD_EFG}} tag could read:
- QUAD_EFG = 146.6 33.27 0.0
-<math>^{27}\mathrm{Al}</math> is the stable isotope of Al with a natural abundance of 100% and <math>Q = 146.6</math>. The stable isotopes <math>^{12}\mathrm{C}</math> and <math>^{13}\mathrm{C}</math> are not quadrupolar nuclei, however, the radioactive <math>^{11}\mathrm{C}</math> is. It has <math>Q = 33.27</math>. For Si it is pointless to calculate a <math>C_q</math> since all stable isotopes have <math>I \le 1/2</math>. No moments are known for the other isotopes.
+===Input parameters===
+* A larger {{TAG|ENCUT}} value than usual, generally much higher than the value given by ENMAX in the {{FILE|POTCAR}} file, e.g. 800 eV for C in diamond, rather than the standard 400 eV.
+* A small {{TAG|EDIFF}} is required to provide converged chemical shifts, e.g. <code>1E-8</code> eV.
+* Tighter precision, e.g. {{TAG|PREC}} = Accurate.
+* Non-spherical contributions to the gradient of the density inside PAW spheres, i.e. {{TAG|LASPH}} = .TRUE.
+===Structure===
+* The structure is extremely important, so using the experimental structure can improve results. Differences of 25 mÅ in structure can make a difference of 40 % to <math>V_{zz}</math> {{Cite|petrilli:prb:1998}}.
-'''Beware''': for heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.
+===PAW pseudopotentials===
+* The use of PAW potentials has a strong influence, GW {{FILE|POTCAR}} files often improve values.
+* Semi-core electrons can be important (check the {{TAG|POSCAR}} files with ''*_pv'' or ''*_sv'') as well as explicit inclusion of augmentation channels with <math>d</math>-projectors.
+{{NB|mind|Several definitions of <math>C_q</math> are used in the NMR community, ensure that you are comparing between the same definitions in calculation and experiment.}}
+{{NB|important|For heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.}}
 == Related tags and articles ==
@@ Line 40: / Line 40: @@
 == References ==
-[[Category:INCAR tag]][[Category:NMR]][[Category:Electric-field gradient]]
+[[Category:INCAR tag]][[Category:NMR]]