LEFG

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. .

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:

$|V_{zz}| > |V_{xx}| > |V_{yy}|.$

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.

Input

A typical INCAR file is given below:

 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

Important: Make sure to replace the QUAD_EFG in the INCAR with the values for the isotopes in your system.

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, unlike the EFG, may be measured by experiment.

            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        -             -         -                      

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 0.0025 in internal coordinates can make a difference of 50 % to $V_{zz}$ .

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.

Related tags and articles

QUAD_EFG

Examples that use this tag