Calculating the chemical shieldings: Difference between revisions
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==Chemical shielding== | ==Chemical shielding== | ||
The chemical shielding tensor ''σ'' is the relation between the induced and external magnetic fields and describes how much electrons shield the nuclei from an external field. The absolute chemical shielding is calculated by linear response using {{TAG|LCHIMAG}} {{Cite|pickard:prb:2001}}{{Cite|yates:prb:2007}}. This is directly related to the chemical shift ''δ'' (cf. [[:Category:NMR|NMR category page]] and {{TAG|LCHIMAG}} page for details) and, indirectly, to the resonance frequency. | 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 {{TAG|LCHIMAG}} {{Cite|pickard:prb:2001}}{{Cite|yates:prb:2007}}. This is directly related to the chemical shift ''δ'' (cf. [[:Category:NMR|NMR category page]] and {{TAG|LCHIMAG}} page for details) and, indirectly, to the resonance frequency. | ||
Two additional tags are unique to NMR calculations: | Two additional tags are unique to NMR calculations: | ||
Revision as of 15:59, 25 February 2025
Performing 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 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]. This 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.
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 first printed.
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. Finally, core contributions are taken into account for each of these.
---------------------------------------------------------------------------------
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 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 systems 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
Nuclei with a spin > ± ½ are called quadrupolar nuclei. They have a non-spherical shape and therefore a non-zero electric field gradient (EFG). The EFG is calculated using LEFG [3]. By including the quadrupole moment of the isotopes, the nuclear quadrupole moments may be calculated. 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 [4][5].
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
---------------------------------------------------------------------
1 - - - - - -
And then afterwards following diagonalization:
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 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)
----------------------------------------------------------------------
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:
- 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, i.e. the hyperfine splitting [6]. Specifically, the coupling between the nuclear magnetic dipole moment and the magnetic field generated by the electrons (or nuclear spin-electron spin coupling) is referred to. For the interaction between the nuclear quadrupole moment and the electric field gradient, see LEFG and the description in insert link back to efg above when hyperfine made into its own how-to page.
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:
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 - - - - - -------------------------------------------------------------
Note the A_tot does not include the core contribution term A_1c [7]. The dipolar hyperfine coupling parameter comes next and finally the total hyperfine coupling parameter
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 [6].
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).
- ↑ 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).
- ↑ a b K. Szasz, T. Hornos, M. Marsman, and A. Gali, Hyperfine coupling of point defects in semiconductors by hybrid density functional calculations: The role of core spin polarization, Phys. Rev. B, 88, 075202 (2013).
- ↑ O. V. Yazyev, I. Tavernelli, L. Helm, and U. R. Roethlisberger, Core spin-polarization correction in pseudopotential-based electronic structure calculations, Phys. Rev. B 71, 115110 (2006).