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. [1].
The EFG tensors are symmetric. The principal components Vii and asymmetry parameter η are printed for each atom. Following convention the principal components Vii are ordered such that:
The asymmetry parameter is defined as . For so-called "quadrupolar nuclei", i.e., nuclei with nuclear spin I>1/2, NMR experiments can access Vzz and η.
To convert the Vzz values into the Cq 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-8eV. - 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 [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 -projectors.
| Mind: Several definitions of 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. |