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 15: / Line 15: @@
 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.}}
-==Input==
+{{NB|important|For heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.}}
-A typical {{FILE|INCAR}} file is given below:
-<pre>
- ENCUT = 400              # Plane-wave energy cutoff in eV
- ISMEAR = 0; SIGMA = 0.01 # Defines the type of smearing; smearing width in eV
- EDIFF = 1E-8             # Energy cutoff criterion for the SCF loop, in eV
- PREC = Accurate          # Sets the "precision" mode
- LASPH = .TRUE.           # Non-spherical contributions to the gradient of the density in the PAW spheres
- LEFG = .TRUE.            # Electric field gradient calculations
- QUAD_EFG = 0. -696. 20.44 0. 2.860  # Nuclear quadrupolar moments for Pb I N O D
-</pre>
-{{NB|important|Make sure to replace the {{TAGO|QUAD_EFG}} in the {{FILE|INCAR}} with the values for the isotopes in your system.}}
 ==Output==
@@ Line 54: / Line 40: @@
 </pre>
-The corresponding eigenvectors are printed atom-wise. Finally, the quadrupolar parameters are presented, which, unlike the EFG, may be measured by experiment.
+The corresponding eigenvectors are printed atom-wise. Finally, the quadrupolar parameters are presented, which are commonly reported in NMR experiments.
 <pre>
@@ Line 67: / Line 53: @@
         -             -         -
 </pre>
-==Recommendations and advice==
-Tight settings are required for calculating the electric field gradient.
-===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 0.0025 in internal coordinates can make a difference of 50 % to <math>V_{zz}</math> {{Cite|petrilli:prb:1998}}.
-===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.}}
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