Calculating the chemical shieldings: Difference between revisions
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* A small {{TAG|EDIFF}} is typically required to provide converged chemical shifts, e.g. <code>1E-8</code> eV. | * A small {{TAG|EDIFF}} is typically required to provide converged chemical shifts, e.g. <code>1E-8</code> eV. | ||
* Tighter precision, e.g. {{TAG|PREC}} = Accurate. | * Tighter precision, e.g. {{TAG|PREC}} = Accurate. | ||
* The structure is '''extremely important''' so using the experimental structure can improve results. EFG is very sensitive to structure so differences of 25 mÅ can make differences of 40 % to | * The structure is '''extremely important''' so using the experimental structure can improve results. EFG is very sensitive to structure so differences of 25 mÅ can make differences of 40 % to <math>V_{zz}</math> {{Cite|petrilli:prb:1998}}. | ||
* The use of PAW potentials has a strong influence, GW {{FILE|POTCAR}} files often improve values. | * 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. | * 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. | ||
Revision as of 09:16, 3 March 2025
There are several different options available to calculate NMR properties. It is possible to calculate the chemical shielding, the two-center contributions, and the electric field gradient. The theory is already covered in the NMR category page and corresponding pages, so it will not be reiterated here.
For all calculations, tighter convergence settings than typical are required, e.g. for a structure relaxation. No additional files are required besides the four standard POSCAR, POTCAR, INCAR, and KPOINTS, unless specifically mentioned. It is important to have a well-converged structure, as all of these calculations described below can be very sensitive to it. For each of the following calculations, the NMR property is calculated post-SCF.
Chemical shielding
The chemical shielding tensor σ is the relation between the induced and external magnetic fields and describes how much the electrons shield the nuclei from an external field. The absolute chemical shielding is calculated by linear response using LCHIMAG [1][2]. The chemical shielding is directly related to the chemical shift δ (cf. NMR category page and LCHIMAG page for details) and, indirectly, to the resonance frequency.
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-derivable.
Input
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 reference shift experienced by the core is given first:
Core NMR properties
typ El Core shift (ppm)
----------------------------
1 C -200.5098801
----------------------------
Core contribution to magnetic susceptibility: -0.31 10^-6 cm^3/mole
--------------------------------------------------------------------------
The isotropic chemical shielding for each atom excluding and including G=0 contributions, as well as the span and skew (descriptions of asymmetry), follow. Finally, core contributions are taken into account for the ISO_SHIFT, SPAN, and SKEW:
---------------------------------------------------------------------------------
CSA tensor (J. Mason, Solid State Nucl. Magn. Reson. 2, 285 (1993))
---------------------------------------------------------------------------------
EXCLUDING G=0 CONTRIBUTION INCLUDING G=0 CONTRIBUTION
----------------------------------- -----------------------------------
ATOM ISO_SHIFT SPAN SKEW ISO_SHIFT SPAN SKEW
---------------------------------------------------------------------------------
(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
---------------------------------------------------------------------------------
(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
---------------------------------------------------------------------------------
IF SPAN.EQ.0, THEN SKEW IS ILL-DEFINED
---------------------------------------------------------------------------------
The chemical shielding tensor is found earlier in the OUTCAR file, with the UNSYMMETRIZED TENSORS and SYMMETRIZED TENSORS found underneath Absolute Chemical Shift tensors. Additionally, the magnetic susceptibility is printed shortly after and is found by searching for ORBITAL MAGNETIC SUSCEPTIBILITY.
Recommendations and advice
A typical INCAR file requires a few specific settings:
- 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.
- A small EDIFF is typically required to provide converged chemical shifts, e.g.
1E-8eV. - Tighter precision, e.g. PREC = Accurate.
Two additional terms may make a difference depending on your system, which should be tested with and without to determine their importance:
- Non-spherical contributions to the gradient of the density inside PAW spheres, i.e. LASPH = .TRUE.
- Occasionally, e.g. for systems containing H or first-row elements, and short bonds, the two-center contributions are important. In this case, LLRAUG = .TRUE. should be used [3][4].
For each system, make sure to test that the chemical shieldings calculated are converged with respect to ENCUT, EDIFF, and KPOINTS mesh. Convergence is considered to be typically within 0.1 ppm.
Electric field gradient
Nuclei with a spin > ± ½ are called quadrupolar nuclei. They have a non-spherical shape and therefore a non-zero electric field gradient (EFG) at the nucleus. The EFG is calculated using LEFG [5]. By including the quadrupole moment of the isotopes, the quadrupole coupling constants Cq can be calculated (multiple definitions exist in the literature, ensure that you are correctly comparing). These are measured using nuclear quadrupole resonance (NQR) spectroscopy, a type of zero- to ultralow-field (ZULF) NMR.
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 [6][7].
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
The same tight settings for chemical shielding are required, alongside a stronger dependence on the structure and the chosen POTCAR used:
- 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.
- A small EDIFF is typically required to provide converged chemical shifts, e.g.
1E-8eV. - Tighter precision, e.g. PREC = Accurate.
- The structure is extremely important so using the experimental structure can improve results. EFG is very sensitive to structure so differences of 25 mÅ can make differences of 40 % to [5].
- 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.
In addition, test whether non-spherical contributions are important for your system:
- Non-spherical contributions to the gradient of the density inside PAW spheres, i.e. LASPH = .TRUE.
Be aware of some specifics relevant to the implementation used:
- Several definitions of are used in the NMR community, ensure that you are comparing between the same definitions in calculation and experiment.
- For heavy nuclei inaccuracies are to be expected because of an incomplete treatment of relativistic effects.
For each system, make sure to test that the chemical shieldings calculated are converged with respect to ENCUT, EDIFF, and KPOINTS mesh. Convergence is considered to be typically within 3 significant figures for the EFG in the z-direction (though this may be infeasible for heavier elements).
References
- ↑ C. J. Pickard and F. Mauri, All-electron magnetic response with pseudopotentials: NMR chemical shifts, Phys. Rev. B 63, 245101 (2001).
- ↑ J. R. Yates, C. J. Pickard, and F. Mauri, Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials, Phys. Rev. B 76, 024401 (2007).
- ↑ F. Vasconcelos, G.A. de Wijs, R. W. A. Havenith, M. Marsman, and G. Kresse, Finite-field implementation of NMR chemical shieldings for molecules: Direct and converse gauge-including projector-augmented-wave methods, J. Chem. Phys. 139, 014109 (2013).
- ↑ G.A. de Wijs, G. Kresse, R. W. A. Havenith, and M. Marsman, Comparing GIPAW with numerically exact chemical shieldings: The role of two-center contributions to the induced current, J. Chem. Phys. 155, 234101 (2021).
- ↑ a b 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).
- ↑ P. Pyykkö, Year-2008 nuclear quadrupole moments, Mol. Phys. 106, 1965-1974 (2008).
- ↑ P. Pyykkö, Year-2017 nuclear quadrupole moments, Mol. Phys. 116, 1328-1338 (2018).