LEFG: Difference between revisions

Latest revision as of 15:25, 7 March 2025

LEFG = .TRUE. | .FALSE.
Default: LEFG = .FALSE.

Description: The LEFG computes the electric field gradient (EFG) 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.

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.

Output

The EFG is listed atom-wise after the SCF cycle has been completed. First, the full 3x3 tensor is printed:

  Electric field gradients (V/A^2)
 ---------------------------------------------------------------------
  ion       V_xx      V_yy      V_zz      V_xy      V_xz      V_yz
 ---------------------------------------------------------------------
    1        -         -         -         -         -         -

The tensor is then diagonalized and reprinted:

  Electric field gradients after diagonalization (V/A^2)
  (convention: |V_zz| > |V_xx| > |V_yy|)
 ----------------------------------------------------------------------
  ion       V_xx      V_yy      V_zz     asymmetry (V_yy - V_xx)/ V_zz
 ----------------------------------------------------------------------
    1       -         -         -             -

The corresponding eigenvectors are printed atom-wise. Finally, the quadrupolar parameters are presented, which are commonly reported in NMR experiments.

            NMR quadrupolar parameters

  Cq : quadrupolar parameter    Cq=e*Q*V_zz/h
  eta: asymmetry parameters     (V_yy - V_xx)/ V_zz
  Q  : nuclear electric quadrupole moment in mb (millibarn)
 ----------------------------------------------------------------------
  ion       Cq(MHz)       eta       Q (mb)
 ----------------------------------------------------------------------
    1        -             -         -

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).

[1]

@@ Line 1: / Line 1: @@
 {{TAGDEF|LEFG|.TRUE. {{!}} .FALSE. | .FALSE.}}
-Description: The {{TAG|LEFG}} computes the {{TAG|Electric Field Gradient}} at positions of the atomic nuclei.
+Description: The {{TAG|LEFG}} computes the electric field gradient (EFG) at positions of the atomic nuclei.
 ----
 For {{TAG|LEFG}}=.TRUE., the electric field gradient tensors at the positions of the atomic nuclei are calculated using the method of Petrilli ''et al.'' {{Cite|petrilli:prb:1998}}.
@@ 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.
-{{NB|mind|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.
+{{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.}}
-==Recommendations and advice==
+==Output==
-Tight settings are required for calculating the electric field gradient.
+The EFG is listed atom-wise after the SCF cycle has been completed. First, the full 3x3 tensor is printed:
-===Input parameters===
+<pre>
-* 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.
+  Electric field gradients (V/A^2)
-* 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.
+  ion       V_xx      V_yy      V_zz      V_xy      V_xz      V_yz
-* 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.
+</pre>
-===PAW pseudopotentials===
-* The use of PAW potentials has a strong influence, GW {{FILE|POTCAR}} files often improve values.
+The tensor is then diagonalized and reprinted:
-* 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|important|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.}}
+<pre>
-{{NB|mind|For heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.}}
+  Electric field gradients after diagonalization (V/A^2)
+  (convention: |V_zz| > |V_xx| > |V_yy|)
+ ----------------------------------------------------------------------
+  ion       V_xx      V_yy      V_zz     asymmetry (V_yy - V_xx)/ V_zz
+ ----------------------------------------------------------------------
+       -         -         -             -
+</pre>
+The corresponding eigenvectors are printed atom-wise. Finally, the quadrupolar parameters are presented, which are commonly reported in NMR experiments.
+<pre>
+            NMR quadrupolar parameters
+  Cq : quadrupolar parameter    Cq=e*Q*V_zz/h
+  eta: asymmetry parameters     (V_yy - V_xx)/ V_zz
+  Q  : nuclear electric quadrupole moment in mb (millibarn)
+ ----------------------------------------------------------------------
+  ion       Cq(MHz)       eta       Q (mb)
+ ----------------------------------------------------------------------
+        -             -         -
+</pre>
 == Related tags and articles ==