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# LCHIMAG

**LCHIMAG** = .TRUE. | .FALSE.

Default: **LCHIMAG** = .FALSE.

Description: calculate the chemical shifts by means of linear response.

For **LCHIMAG**=.TRUE., VASP calculates the chemical shift tensors by means of linear response.

The chemical shift tensor is defined as:

Here **R** denotes the atomic nuclear site, *i* and *j* denote cartesian indices, *B*^{ext} an applied DC external magnetic field and *B*^{ind}(**R**) the induced magnetic field at the nucleus.
NMR experiments yield information on the symmetric part of the tensor.
VASP can calculate chemical shifts for non-metallic crystalline systems using the linear response method of Yates, Pickard and Mauri.^{[1]}^{[2]}

A typical INCAR could look like this:

PREC = A # nice ENCUT = 600.0 # typically higher cutoffs than usual are needed EDIFF = 1E-8 # you need much smaller EDIFFs than normal. ISMEAR = 0; SIGMA= 0.1 # no fancy smearings, SIGMA sufficiently small LREAL = A # helps for speed for large systems, not necessary per se LCHIMAG = .TRUE. # to switch on linear response for chemical shifts DQ = 0.001 # often the default is sufficient ICHIBARE = 1 # often the default is sufficient LNMR_SYM_RED = .TRUE. # be on the safe side NSLPLINE = .TRUE. # only needed if LREAL is NOT set.

The first block of tags in the INCAR above expresses the fact that the calculations of chemical shifts by means of linear response often require a high accuracy (PREC=A, EDIFF≤1E-8, high ENCUT).

The chemical shifts are calculated from the orbital magnetic response under the assumption that the system is an insulator. It makes no sense to use smearing schemes intended for metals, indeed, doing so can generate nonsense. It is safe to use ISMEAR=0 and make SIGMA so small that states have no fractional occupancies.

The seçond block of tags switches on the calculation of the chemical shifts (**LCHIMAG**=.TRUE.), and controls several aspects of the finite difference *k*-space derivatives (Eqs. 38, 40, and 47 in the work of Yates *et al.*^{[2]}):

- DQ is the step size for the finite difference
*k*-space derivative. Typical values are in the range [0.001 - 0.003]. The default (DQ=0.001) is often sufficient.

- ICHIBARE is the order of the finite difference stencil used to calculate the magnetic susceptibility (second order derivative in Eq. 47 of Yates
*et al.*^{[2]}). ICHIBARE may be set to 1, 2, or 3. Often the default (ICHIBARE=1) is sufficient. A higher ICHIBARE results in a substantial increase of the computational load.

- For NLSPLINE=.TRUE., the PAW projectors in reciprocal space (LREAL=.FALSE.) are set up using a spline interpolation so that they are
*k*-differentiable. This only slightly affects the chemical shifts themselves, but can have impact on the susceptibility contribution (the aforementioned Eq. 47). It is advised to set NLSPLINE=.TRUE., but only in case of calculation of chemical shift. As this option also gives slightly different total energies, it is advised to use the default NLSPLINE=.FALSE. for compatibility in all other calculations. Real space projectors are*k*-differentiable by construction.

- The star on which the
*k*-space derivative is calculated is oriented along the cartesian directions in*k*-space. If the symmetry operations in*k*-space do not map this star onto itself, erroneous results can be obtained. To have VASP check for such operations, set LNMR_SYM_RED=.TRUE., and such operations will be discarded, resulting in a larger IBZ. In case of any doubt set LNMR_SYM_RED=.TRUE. Beware: It matters how the real space lattice vectors are set up relative to the cartesian coordinates in POSCAR. It determines the orientation of the*k*-space star and hence can affect the efficiency via the number of*k*-points in the IBZ.

No special POTCAR files are necessary. The GIPAW is applied using the projectors functions and partial waves that are stored in the regular POTCAR files. A few remarks, however, on accuracy in relation to the different POTCAR flavours:

- Results sensitively depend on the quality,
*i.e.*, completeness of the partial wave/projector function set in the energy range needed for good chemical transferability. Result obtained with different POTCAR flavours can be differ a few ppm for first and second row*sp*-bonded elements are possible (except for H).

- Use POTCAR files generated with a consistent exchange-correlation functional. The PAW reconstruction with AE partial waves is crucial as the field on the nucleus needs to be calculated. So avoid, if possible, overriding
`LEXCH`from POTCAR with an explicit GGA-tag in the INCAR.

What to do in case of insufficient memory? VASP trades off memory savings against speed, opting for the latter.
The response calculation is inherently parallel over *k*-points. This can be used to economize on memory:
First do a regular self-consistent calculation at high accuracy for the full *k*-point mesh. Save the CHGCAR file.
Next do a chemical shift calculation for each *k*-point in the IBZ separately, starting from CHGCAR, *i.e.*, using ICHARG=11.
Finally calculate the shifts as a *k*-point weighted average of the symmetrized shifts of the individual *k*-points.

At the end of OUTCAR file, VASP prints the chemical shift tensors both before and after symmetrization. These are the absolute tensors for the infinite lattice, excluding core contributions. Next lines `Q=0 CONTRIBUTION TO CHEMICAL SHIFT` are printed.
This is a shift tensor arising solely from the **G**=0 component of the induced field. This component is related to the shape of the sample and depends only on the induced macroscopic surface currents (via the orbital magnetic susceptibility).
It is printed for a spherical sample (for which is it nucleus independent), and calculated according to Eqs. 46-48 of Yates * et al.*^{[2]}, *i.e.*, using the so-called *pGv*-approximation to the magnetic susceptibility.
To obtain the full absolute tensor the contribution for **G**=0 has to be added to the nuclear shifts.
The approximate susceptibility itself is also printed.
Finally the isotropic chemical shift δ, span Ω and skew κ are printed.^{[3]} Note that κ is ill-defined if Ω=0.

The response calculation yields the shift due to the valence electrons to
which the rigid core contributions are added.^{[4]}

The chemical shift is calculated via the induced current.^{[1]}^{[2]}
It has contributions from the plane wave grid and one-center contributions (the induced field
at the center of a PAW sphere due to the augmentation current inside that sphere). Two-center contributions (induced fields due to augmentation currents in
other PAW spheres) are standard neglected. These contributions can be switched on using LBONE.

For very high accuracy calculations use LASPH.

**Beware**: the treatment of the orbital magnetism is non-relativistic. This is fine for light nuclei.
The standard POTCARs are scalar-relativistic and account partially for relativistic effects.
The accuracy can be improved using LLRAUG, that restores the small B-component of the wave function inside the PAW spheres.
Spin-orbit coupling is not implemented for chemical shift calculations.

## Related Tags and Sections

DQ, ICHIBARE, LNMR_SYM_RED, NLSPLINE, LLRAUG, LBONE

## References

- ↑
^{a}^{b}C. J. Pickard, F. Mauri, Phys. Rev. B 63, 245101 (2001). - ↑
^{a}^{b}^{c}^{d}^{e}J. R. Yates, C. J. Pickard, F. Mauri, Phys. Rev. B 76, 024401 (2007). - ↑ J. Mason, Solid State Nucl. Magn. Reson. 2, 285 (1993).
- ↑ T. Gregor, F. Mauri, R. Car, J. Chem. Phys. 111, 1815 (1999).