Chemical Shifts

The following five INCAR tags are relevant to linear response calculations of chemical shifts:
`LCHIMAG`

, `DQ`

, `ICHIBARE`

, `LNMR_SYM_RED`

, and `NLSPLINE`

.
The defaults are:

LCHIMAG=.FALSE. DQ=0.001 ICHIBARE=1 LNMR_SYM_RED=.FALSE. NLSPLINE=.FALSE.To switch linear response chemical shifts on, set:

`LCHIMAG=.TRUE.`

The other tags are related to the finite difference k-space derivatives (Eqs. 38, 40 and 47 of Ref. [155]).
`DQ`

is the step size for the finite difference k-space derivative. Typical values are in the range . The default is often sufficient.`ICHIBARE`

can have the values 1, 2 and 3.`ICHIBARE`

sets the order of the stencils used to calculate the magnetic susceptibility (second order derivative in Eq. 47 of Ref. [155]). Often the default is sufficient. A higher`ICHIBARE`

results in a substantial increase of the computational load.- 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. `NLSPLINE=.TRUE.`

makes that the reciprocal space projectors 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.

`ISMEAR=0`

and make `SIGMA`

so small
that no states have fractional occupancies.
The linear response calculation requires a high accuracy. Use `EDIFF = 1E-10`

or similar.

No special POTCARs are used. The GIPAW is applied using the projectors functions and partial waves that are in the regular POTCARs. A few remarks on accuracy in relation to POTCARs:

- 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 POTCARs can be differ a few ppm for first and second row sp-bonded elements are possible (except for H).
- Use POTCARs 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 do not override
`LEXCH`

from POTCAR with an explicit`GGA`

-tag in INCAR. - Cutoffs
`ENCUT`

needed are typically higher than usual for`PREC=A`

(it is advised to set`PREC=A`

).

LCHIMAG = .TRUE. # to switch on linear response for chemical shifts ENCUT = 600.0 # typically higher cutoffs than usual are needed EDIFF = 1E-10 # you'd need much smaller EDIFFs. ISMEAR = 0; SIGMA= 0.1 # no fancy smearings, SIGMA sufficiently small PREC = A # nice 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. LREAL = A # helps for speed for large systems, not needed NBANDS = ??? # to safe memory, ??? = NELECT/2What 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`

output.
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 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
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 nucleous independent), and calculated according to Eqs. 46-48 of Ref. [155],
i.e. using the so-called -approximation to the magnetic susceptibility. To obtain the full absolute tensor the
contribution for has to be added to the nuclear shifts. The approximate susceptibility itself is also printed.
Finally the isotropic chemical shift , span and skew are printed [156]. Note that
is ill-defined if
.

All shifts are calculated from the only the valence electrons. Core contributions are rigid [157].

Beware: the treatment of the orbital magnetism is non-relativistic. This is fine for light nuclei.