Calculating the chemical shieldings
Considerations for NMR calculations.
There are several different options available to calculate NMR properties. It is possible to calculate the chemical shielding, the two-center contributions, the electric field gradient, and the hyperfine coupling constant. The theory is already covered in NMR category page and corresponding pages, so it will not be reiterated here.
For all of the tags used here, tighter convergence settings than is typical for a structure relaxation are required. No additional files are required beyond the four standard POSCAR, POTCAR, INCAR, and KPOINTS, unless specifically mentioned. It is important to have a well-converged structure. All of these calculations described below can be very sensitive to structure. For each of the following calculations, the NMR property is calculated post-SCF.
Chemical shielding
The chemical shielding tensor σ is calculated by linear response using LCHIMAG.
Two additional tags are unique to NMR calculations:
- LNMR_SYM_RED which ensures that all symmetry operations for the k-space derivatives are consistent when calculating chemical shifts.
- NLSPLINE which constructs PAW projectors in reciprocal space to ensure that they are k-deriviable.
An example 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 LCHIMAG = .TRUE. # Turns on linear response for chemical shifts LNMR_SYM_RED = .TRUE. # Consistent symmetry with star and k-space derivatives NLSPLINE = .TRUE. # Differentiable projectors in reciprocal space
Output
The isotropic chemical shieldings are printed to the OUTCAR file. The shift experienced by the core is first printed, followed by the isotropic chemical shielding for each atom excluding and including G=0 contributions. The span and skew are also included. Finally, core contributions are taken into account.
Core NMR properties
typ El Core shift (ppm)
----------------------------
1 C -200.5098801
----------------------------
Core contribution to magnetic susceptibility: -0.31 10^-6 cm^3/mole
--------------------------------------------------------------------------
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CSA tensor (J. Mason, Solid State Nucl. Magn. Reson. 2, 285 (1993))
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EXCLUDING G=0 CONTRIBUTION INCLUDING G=0 CONTRIBUTION
----------------------------------- -----------------------------------
ATOM ISO_SHIFT SPAN SKEW ISO_SHIFT SPAN SKEW
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(absolute, valence only)
1 77.7746 0.0000 0.0000 66.5779 0.0000 0.0000
2 77.7746 0.0000 0.0000 66.5779 0.0000 0.0000
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(absolute, valence and core)
1 -122.7353 0.0000 0.0000 -134.3162 0.0000 0.0000
2 -122.7353 0.0000 0.0000 -134.3162 0.0000 0.0000
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IF SPAN.EQ.0, THEN SKEW IS ILL-DEFINED
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The chemical shielding tensor itself is found earlier in the OUTCAR file. The UNSYMMETRIZED TENSORS and SYMMETRIZED TENSORS can be found underneath Absolute Chemical Shift tensors. Additionally, the magnetic susceptibility is printed shortly after and can be found by searching for ORBITAL MAGNETIC SUSCEPTIBILITY.
Recommendations and advice
A typical INCAR file requires a few specific settings:
- A larger ENCUT value than is usually required, generally much higher than the value given by ENMAX in the POTCAR file.
- A small EDIFF is typically 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.
- Occasionally, e.g. for molecules containing H or first-row elements and short bonds, the two-center contributions are important. In this case, LLRAUG = .TRUE. should be used .
For each system, it is important to test that the chemical shieldings calculated are converged with respect to ENCUT, EDIFF, and KPOINTS mesh. Convergence is typically to within 0.1 ppm.
Electric field gradient
The electric field gradient is calculated using LEFG.
There is one additional keyword that must be defined:
- QUAD_EFG defines the isotope-specific quadrupole moment for each species in your POSCAR file, taken from an online database, e.g. here.
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
Output
The EFG is listed atom-wise after the SCF cycle has been completed. First, as calculated:
Electric field gradients (V/A^2)
---------------------------------------------------------------------
ion V_xx V_yy V_zz V_xy V_xz V_yz
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1 - - - - - -
And then afterwards following diagonalization:
Electric field gradients after diagonalization (V/A^2)
(convention: |V_zz| > |V_xx| > |V_yy|)
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ion V_xx V_yy V_zz asymmetry (V_yy - V_xx)/ V_zz
----------------------------------------------------------------------
1 - - - -
The corresponding eigenvectors are then printed. Finally, the quadrupolar parameters are presented, which, unlike the EFG, may be measured in 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)
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ion Cq(MHz) eta Q (mb)
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1 - - -
Recommendations and advice
The same tight settings for chemical shielding are required, alongside a stronger dependence on the structure and the chosen POTCAR used:
- The structure is extremely important, so the experimental structure may sometimes be preferable to be used.
- The use of PAW potentials has a strong influence. GW POTCAR files often improve.
Hyperfine coupling
The hyperfine coupling constants are calculated using LHYPERFINE.
There is one additional keyword that must be defined:
- NGYROMAG defines the nuclear gyromagnetic ratios for each element in your POSCAR file. The defaults are set to 1, which will return meaningless results. Reasonable values may be found here.
An example INCAR file is given here:
ENCUT = 500 # 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 LHYPERFINE = .TRUE. # Turns on calculating the hyperfine coupling tensor NGYROMAG = 10.7084 42.577478461 # Specifies the nuclear gyromagnetic ratios for the ions - C and H in this case ISPIN = 2 # Turns on spin-polarization - noncollinear can also be used
Output
You can find the output for the hyperfine calculation in the OUTCAR file after the SCF cycle finishes. The total magnetic moment is listed, then the Fermi contact term, the dipolar hyperfine coupling parameter, and finally the total hyperfine coupling parameter:
Total magnetic moment S= 1.0000000 Fermi contact (isotropic) hyperfine coupling parameter (MHz) ------------------------------------------------------------- ion A_pw A_1PS A_1AE A_1c A_tot ------------------------------------------------------------- 1 - - - - - 2 - - - - - ------------------------------------------------------------- Dipolar hyperfine coupling parameters (MHz) --------------------------------------------------------------------- ion A_xx A_yy A_zz A_xy A_xz A_yz --------------------------------------------------------------------- 1 - - - - - - 2 - - - - - - --------------------------------------------------------------------- Total hyperfine coupling parameters after diagonalization (MHz) (convention: |A_zz| > |A_xx| > |A_yy|) ---------------------------------------------------------------------- ion A_xx A_yy A_zz asymmetry (A_yy - A_xx)/ A_zz ---------------------------------------------------------------------- 1 - - - - 2 - - - - ---------------------------------------------------------------------
Recommendations and advice
Distinct from the chemical shielding and EFG, the hyperfine constant is less dependent on EDIFF and ENCUT, generally converging relatively quickly with respect to both. However, it is extremely strongly influenced by the method used. HSE06 was found to give values close to experimental values for molecular systems [1].