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.}}
-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.
+==Output==
+The EFG is listed atom-wise after the SCF cycle has been completed. First, the full 3x3 tensor is printed:
-<math>C_q = \frac{e Q V_{zz}}{h}</math>
+<pre>
+  Electric field gradients (V/A^2)
+ ---------------------------------------------------------------------
+  ion       V_xx      V_yy      V_zz      V_xy      V_xz      V_yz
+ ---------------------------------------------------------------------
+        -         -         -         -         -         -
+</pre>
-Suppose a solid contains Al, C, and Si, then the {{TAG|QUAD_EFG}} tag could read:
+The tensor is then diagonalized and reprinted:
-  QUAD_EFG = 146.6 33.27 0.0
+<pre>
+  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>
-<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.
+The corresponding eigenvectors are printed atom-wise. Finally, the quadrupolar parameters are presented, which are commonly reported in NMR experiments.
-{{NB|Important|for heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.}}
+<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>
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