LCHIMAG: Difference between revisions

Latest revision as of 11:02, 11 March 2025

LCHIMAG = .TRUE. | .FALSE.
Default: LCHIMAG = .FALSE.

Description: Calculate the chemical shifts and magnetic susceptibility within linear response theory.

For LCHIMAG = True, the chemical shift tensors and magnetic susceptibility is computed. The implementation^[1] is based on linear response theory using the gauge-invariant PAW method of Yates, Pickard, and Mauri ^[2]^[3], that is an extension to the standard PAW method to account for the effects of a vector gauge field $A$ . The NMR response currents are computed and the induced B field is calculated based on the Biot-Savart law.

See also WRT_NMRCUR to write the currents and NUCIND to compute the nuclear-independent chemical shielding.

Warning: This method only works for non-metallic systems, i.e., that have a finite bandgap.

Definitions

The chemical shielding tensor is defined as:

{\displaystyle \sigma_{ij}(\mathbf{R}) = - \frac{ \partial B^{\mathrm{in}}_i(\mathbf{R})}{ \partial B^{\mathrm{ext}}_j} }

Here $\mathbf{R}$ denotes the atomic nuclear site, $i$ and $j$ denote Cartesian indices, $\mathbf{B}^{\mathrm{ext}}$ an applied DC external magnetic field and $\mathbf{B}^{\mathrm{in}}(\mathbf{R})$ the induced magnetic field at the nucleus.

NMR experiments yield information on the shielding relative to a reference compound:

{\displaystyle \delta_{ij}(\mathbf{R}) = \sigma_{ij}^{\mathrm{ref}} - \sigma_{ij}(\mathbf{R}) }

Here, $\sigma_{ij}^{\mathrm{ref}}$ is the isotropic shielding of the nucleus in the reference compound. $\delta_{ij}(\mathbf{R})$ is the chemical shift tensor. In order to compare numerical results with the experimental data, one usually considers a series of compounds and references that to the experimental series.

Mind: If VASP reports the chemical shift (LNMRSHIELD = False) it is simply the negative shielding,

\delta_{ij}(\mathbf{R})= - \sigma_{ij}(\mathbf{R})

. The reference must still be added in the postprocessing to analyze the data.

VASP calculates chemical "shifts" for non-metallic crystalline systems using the linear response method of Yates, Pickard, and Mauri ^[2]^[3].

The isotropic chemical "shift" $\sigma_{iso}$ , span $\Omega$ , and skew $\kappa$ are also reported, according to the following Herzfeld-Berger convention ^[4]:

{\displaystyle \sigma_{iso} = (\sigma_{11} + \sigma_{22} + \sigma_{33})/3 }

{\displaystyle \Omega = \sigma_{33} - \sigma_{11} }

{\displaystyle \kappa = 3(\sigma_{iso} - \sigma_{22})/\Omega. }

The orbital magnetic susceptibility $\chi$ is calculated according to a finite-differences approach:

{\displaystyle \chi_{\textrm{bare}} = \lim_{q\to0} \frac{F(q) 2F(q) + F(-q)}{q^2} }

where $F_{ij}(q)=(2-\delta_{ij})Q_{ij}(q)$ .

Q_ij is approximated in two ways. The so-called pGv-approximation is used by default ^[3], where p is momentum, v is velocity, and G is a Green's function. An alternative approach, the vGv-approximation is also used to calculate an alternative susceptibility since VASP 6.4.0 ^[5]. Q is defined for the pGv-approximation as:

{\displaystyle Q(q) = - \frac{1}{c^2 N_k V_c} \sum_{i=x,y,z} \sum_{o,\textbf{k}} \textrm{Re}[\langle \bar{u}^{(0)}_{o,\textbf{k}} | \hat{\textbf{u}}_i \times (-i \nabla + \textbf{k}) \times \mathcal{G}_{\textbf{k} + \textbf{q}_i}(\epsilon_{o,\textbf{k}}) \hat{\textbf{u}}_i \times \textbf{v}_{\textbf{k} + \textbf{q}_i, \textbf{k}}(\epsilon_{o,\textbf{k}}) | \bar{u}^{(0)}_{o,\textbf{k}} \rangle] }

and for the vGv-approximation as:

{\displaystyle Q(q) = - \frac{1}{c^2 N_k V_c} \sum_{i=x,y,z} \sum_{o,\textbf{k}} \textrm{Re}[\langle \bar{u}^{(0)}_{o,\textbf{k}} | \hat{\textbf{u}}_i \times \textbf{v}_{\textbf{k} + \textbf{q}_i, \textbf{k}}(\epsilon_{o,\textbf{k}}) \times \mathcal{G}_{\textbf{k} + \textbf{q}_i}(\epsilon_{o,\textbf{k}}) \hat{\textbf{u}}_i \times \textbf{v}_{\textbf{k} + \textbf{q}_i, \textbf{k}}(\epsilon_{o,\textbf{k}}) | \bar{u}^{(0)}_{o,\textbf{k}} \rangle] }

.

Output

The isotropic chemical shieldings are printed towards the end of the OUTCAR file, after the self-consistent calculation has finished. The chemical shift tensors both before and after space group symmetrization. These are the absolute tensors for the infinite lattice, excluding core contributions. They can be searched for under the UNSYMMETRIZED TENSORS and SYMMETRIZED TENSORS after Absolute Chemical Shift tensors. Additionally, the magnetic susceptibility is printed shortly after and found under ORBITAL MAGNETIC SUSCEPTIBILITY.

Magnetic susceptibility

The magnetic susceptibility is found at the start of the ORBITAL MAGNETIC SUSCEPTIBILITY, excluding core contribution. The magnetic susceptibility is split into that obtained by the pGv-approximation and obtained by the vGv-approximation:

-------------------------------------------------------------
  ORBITAL MAGNETIC SUSCEPTIBILITY, excluding core contribution
 -------------------------------------------------------------
  Approximate magnetic susceptibility, pGv (10^-6 cm^3/mole)
     1        -70.928534         -0.000000          0.000000
     2         -0.000000        -70.928534          0.000000
     3          0.000000          0.000000        -70.928534
 -------------------------------------------------------------
  Approximate magnetic susceptibility, vGv (10^-6 cm^3/mole)
     1        -63.412095         -0.000000          0.000000
     2         -0.000000        -63.412095          0.000000
     3          0.000000          0.000000        -63.412095

         principal value                      axis
       (10^-6 cm^3/mole)           x,          y,          z
      --------------------------------------------------------
              -63.412095      0.1652     -0.9863      0.0000
              -63.412095     -0.9863     -0.1652      0.0000
              -63.412095      0.0000      0.0000      1.0000
 -------------------------------------------------------------

Chemical shielding

To obtain the full absolute tensors requires adding both the $\mathbf{G=0}$ contribution (cf. G=0 CONTRIBUTION TO CHEMICAL SHIFT) and the contributions due to the core electrons. The latter consists of contributions for each chemical species separately (depending on POTCAR) and a global $\mathbf{G=0}$ susceptibility contribution.

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
 --------------------------------------------------------------------------

Important: The isotropic chemical shift

\delta_{\mathrm{iso}}\mathrm{[VASP]}

(ISO_SHIFT) is the negative of the isotropic shielding. To make it a real shift one should add the reference shielding.

Next, the tensor is processed and its chemical shielding anisotropy (CSA) characteristics are printed in the OUTCAR. The tensor is symmetrized ( $\sigma_{ij} = \sigma_{ji}$ is enforced) and diagonalized. From the three diagonal values the isotropic chemical "shift" $\delta_{\mathrm{iso}}\mathrm{[VASP]}$ , span $\Omega$ , and skew $\kappa$ are calculated and printed see Ref. ^[4] for unambiguous definitions. Note that $\kappa$ is ill-defined if $\Omega = 0$ . Units are ppm, except for the skew. A typical output is given below:

                                                                                                          
   ---------------------------------------------------------------------------------
    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    4598.8125      0.0000      0.0000     4589.9696      0.0000      0.0000
       2     291.5486      0.0000      0.0000      282.7058      0.0000      0.0000
       3     736.5979    344.8803      1.0000      727.7550    344.8803      1.0000
       4     736.5979    344.8803      1.0000      727.7550    344.8803      1.0000
       5     736.5979    344.8803      1.0000      727.7550    344.8803      1.0000
   ---------------------------------------------------------------------------------
    (absolute, valence and core)
       1   -6536.1417      0.0000      0.0000    -6547.9848      0.0000      0.0000
       2   -5706.3864      0.0000      0.0000    -5718.2296      0.0000      0.0000
       3   -2369.4015    344.8803      1.0000    -2381.2446    344.8803      1.0000
       4   -2369.4015    344.8803      1.0000    -2381.2446    344.8803      1.0000
       5   -2369.4015    344.8803      1.0000    -2381.2446    344.8803      1.0000
   ---------------------------------------------------------------------------------
    IF SPAN.EQ.0, THEN SKEW IS ILL-DEFINED
   ---------------------------------------------------------------------------------

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.

Important:

The columns excluding the $\mathbf{G=0}$ contribution are useful for supercell calculations on molecules.
The columns including the $\mathbf{G=0}$ contribution are for crystals.
The upper block gives the shielding due to only the electrons included in the SCF calculation.
The lower block has the contributions due to the frozen PAW cores added. These core contributions are rigid ^[6]. They depend on POTCAR and are isotropic, i.e. affect neither SPAN nor SKEW.

References

[dewijs:laskowski:jcp:2017-1] G. A. de Wijs, R. Laskowski, P. Blaha, R. W. A. Havenith, G. Kresse, and M. Marsman, NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations, J. Chem. Phys. 146, 064115 (2017).

[pickard:prb:2001-2] C. J. Pickard and F. Mauri, All-electron magnetic response with pseudopotentials: NMR chemical shifts, Phys. Rev. B 63, 245101 (2001).

[yates:prb:2007-3] 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).

[mason:ssn:1993-4] J. Mason, Conventions for the reporting of nuclear magnetic shielding (or shift) tensors suggested by participants in the NATO ARW on NMR shielding constants at the University of Maryland, College Park, July 1992, Solid State Nucl. Magn. Reson. 2, 285 (1993).

[avezac:prb:2007-5] M. d'Avezac, N. Marzari, and F. Mauri, Spin and orbital magnetic response in metals: Susceptibility and NMR shifts, Phys. Rev. B 76, 165122 (2007).

[gregor:jcp:1999-6] T. Gregor, F. Mauri, and R. Car, A comparison of methods for the calculation of NMR chemical shifts, J. Chem. Phys. 111, 1815 (1999).

[1]

[2]

[3]

[4]

[5]

[6]

@@ Line 1: / Line 1: @@
 {{TAGDEF|LCHIMAG|.TRUE. {{!}} .FALSE. | .FALSE.}}
-Description: calculate the chemical shifts by means of linear response.
+Description: Calculate the chemical shifts and magnetic susceptibility within linear response theory.
 ----
-For {{TAG|LCHIMAG}}=.TRUE., VASP calculates the chemical shift tensors.
+For {{TAGO|LCHIMAG|True}}, the chemical shift tensors and magnetic susceptibility is computed. The implementation{{Cite|dewijs:laskowski:jcp:2017}} is based on linear response theory using the gauge-invariant PAW method of Yates, Pickard, and Mauri {{Cite|pickard:prb:2001}}{{Cite|yates:prb:2007}}, that is an extension to the standard [[PAW method]] to account for the effects of a vector gauge field <math>A</math>. The NMR response currents are computed and the induced B field is calculated based on the Biot-Savart law.
+See also {{TAG|WRT_NMRCUR}} to write the currents and {{TAG|NUCIND}} to compute the nuclear-independent chemical shielding.
+{{NB|warning|This method only works for non-metallic systems, i.e., that have a finite bandgap.}}
+== Definitions ==
 The chemical shielding tensor is defined as:
 :<math>
-\sigma_{ij}(\mathbf{R}) = - \frac{ \partial B^{\mathrm{ind}}_i(\mathbf{R})}{ \partial B^{\mathrm{ext}}_j}
+\sigma_{ij}(\mathbf{R}) = - \frac{ \partial B^{\mathrm{in}}_i(\mathbf{R})}{ \partial B^{\mathrm{ext}}_j}
 </math>
-Here <math>\mathbf{R}</math> denotes the atomic nuclear site, <math>i</math> and <math>j</math> denote cartesian indices, <math>B^{\mathrm{ext}}</math> an applied DC external magnetic field and <math>B^{\mathrm{ind}}(\mathbf{R})</math> the induced magnetic field at the nucleus.
+Here <math>\mathbf{R}</math> denotes the atomic nuclear site, <math>i</math> and <math>j</math> denote Cartesian indices, <math>\mathbf{B}^{\mathrm{ext}}</math> an applied DC external magnetic field and <math>\mathbf{B}^{\mathrm{in}}(\mathbf{R})</math> the induced magnetic field at the nucleus.
-NMR experiments yield information on the symmetric part of the tensor. Typical NMR experiments yield information on the shielding relative to that of a reference compound:
+NMR experiments yield information on the shielding relative to a reference compound:
 :<math>
 \delta_{ij}(\mathbf{R}) = \sigma_{ij}^{\mathrm{ref}} - \sigma_{ij}(\mathbf{R})
 </math>
-In this (approximate) formula <math>\sigma_{ij}^{\mathrm{ref}}</math> is the isotropic shielding of the nucleus in the reference compound.  <math>\delta_{ij}(\mathbf{R})</math> is the chemical shift tensor.
+Here, <math>\sigma_{ij}^{\mathrm{ref}}</math> is the isotropic shielding of the nucleus in the reference compound.  <math>\delta_{ij}(\mathbf{R})</math> is the chemical shift tensor. In order to compare numerical results with the experimental data, one usually considers a series of compounds and references that to the experimental series.
+{{NB|mind|If VASP reports the chemical shift ({{TAGO|LNMRSHIELD|False}}) it is simply the negative shielding, <math>\delta_{ij}(\mathbf{R})= - \sigma_{ij}(\mathbf{R})</math>. The reference must still be added in the postprocessing to analyze the data.}}
+VASP calculates chemical "shifts" for non-metallic crystalline systems using the linear response method of Yates, Pickard, and Mauri {{Cite|pickard:prb:2001}}{{Cite|yates:prb:2007}}.
+The isotropic chemical "shift" <math>\sigma_{iso}</math>, span <math>\Omega</math>, and skew <math>\kappa</math> are also reported, according to the following  Herzfeld-Berger convention {{Cite|mason:ssn:1993}}:
-In VASP the chemical "shift" tensor is calculated as:
 :<math>
-\delta_{ij}(\mathbf{R})\mathrm{[VASP]} = \frac{ \partial B^{\mathrm{ind}}_i(\mathbf{R})}{ \partial B^{\mathrm{ext}}_j}
+\sigma_{iso} = (\sigma_{11} + \sigma_{22} + \sigma_{33})/3
 </math>
-This is minus the shielding tensor. It is not the true chemical shift tensor. To convert it to the real shift tensor one should add the
-reference shielding:
 :<math>
-\delta_{ij}(\mathbf{R}) = \sigma_{ij}^{\mathrm{ref}} + \delta_{ij}(\mathbf{R})\mathrm{[VASP]}
+\Omega = \sigma_{33} - \sigma_{11}
 </math>
-VASP calculates chemical "shifts" for non-metallic crystalline systems using the linear response method of Yates, Pickard and Mauri.<ref name="pickard:prb:01"/><ref name="yates:prb:07"/>
+:<math>
+\kappa = 3(\sigma_{iso} - \sigma_{22})/\Omega.
+</math>
-== Input ==
+The orbital magnetic susceptibility <math>\chi</math> is calculated according to a finite-differences approach:
-A typical {{FILE|INCAR}} could look like this:
+:<math>
+\chi_{\textrm{bare}} = \lim_{q\to0} \frac{F(q) 2F(q) + F(-q)}{q^2}
+</math>
- {{TAGBL|PREC}} = A               # nice
+where <math>F_{ij}(q)=(2-\delta_{ij})Q_{ij}(q)</math>.
- {{TAGBL|ENCUT}} = 600.0          # typically higher cutoffs than usual are needed
- {{TAGBL|EDIFF}} = 1E-8           # you need much smaller EDIFFs than normal.
- {{TAGBL|ISMEAR}} = 0; {{TAGBL|SIGMA}} = 0.1 # no fancy smearings, SIGMA sufficiently small
- {{TAGBL|LREAL}} = A              # helps for speed for large systems, not necessary per se
- LCHIMAG = .TRUE.       # to switch on linear response for chemical shifts
- {{TAGBL|DQ}} = 0.001             # often the default is sufficient
- {{TAGBL|ICHIBARE}} = 1           # often the default is sufficient
- {{TAGBL|LNMR_SYM_RED}} = .TRUE.  # be on the safe side
- {{TAGBL|NLSPLINE}} = .TRUE.      # only needed if LREAL is NOT set.
-The first block of tags in the {{FILE|INCAR}} above expresses the fact that the calculations of chemical shifts by means of linear response often require a high accuracy ({{TAG|PREC}}=A, {{TAG|EDIFF}}&le;1E-8, high {{TAG|ENCUT}}).
+''Q<sub>ij</sub>'' is approximated in two ways. The so-called ''pGv''-approximation is used by default {{Cite|yates:prb:2007}}, where ''p'' is momentum, ''v'' is velocity, and ''G'' is a Green's function. An alternative approach, the ''vGv''-approximation is also used to calculate an alternative susceptibility since VASP 6.4.0 {{Cite|avezac:prb:2007}}. ''Q'' is defined for the ''pGv''-approximation as:
-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 {{TAG|ISMEAR}}=0 and make {{TAG|SIGMA}} so small that states have no fractional occupancies.
+:<math>
+Q(q) = - \frac{1}{c^2 N_k V_c} \sum_{i=x,y,z} \sum_{o,\textbf{k}} \textrm{Re}[\langle \bar{u}^{(0)}_{o,\textbf{k}} | \hat{\textbf{u}}_i \times (-i \nabla + \textbf{k})  \times \mathcal{G}_{\textbf{k} + \textbf{q}_i}(\epsilon_{o,\textbf{k}}) \hat{\textbf{u}}_i \times \textbf{v}_{\textbf{k} + \textbf{q}_i, \textbf{k}}(\epsilon_{o,\textbf{k}}) | \bar{u}^{(0)}_{o,\textbf{k}} \rangle]
+</math>
-The second block of tags switches on the calculation of the chemical shifts ({{TAG|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.''<ref name="yates:prb:07"/>):
+and for the ''vGv''-approximation as:
-*{{TAG|DQ}} is the step size for the finite difference ''k''-space derivative. Typical values are in the range [0.001 - 0.003]. The default ({{TAG|DQ}}=0.001) is often sufficient.
+:<math>
+Q(q) = - \frac{1}{c^2 N_k V_c} \sum_{i=x,y,z} \sum_{o,\textbf{k}} \textrm{Re}[\langle \bar{u}^{(0)}_{o,\textbf{k}} | \hat{\textbf{u}}_i \times \textbf{v}_{\textbf{k} + \textbf{q}_i, \textbf{k}}(\epsilon_{o,\textbf{k}})  \times \mathcal{G}_{\textbf{k} + \textbf{q}_i}(\epsilon_{o,\textbf{k}}) \hat{\textbf{u}}_i \times \textbf{v}_{\textbf{k} + \textbf{q}_i, \textbf{k}}(\epsilon_{o,\textbf{k}}) | \bar{u}^{(0)}_{o,\textbf{k}} \rangle]
+</math>.
-*{{TAG|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.''<ref name="yates:prb:07"/>). {{TAG|ICHIBARE}} may be set to 1, 2, or 3. Often the default ({{TAG|ICHIBARE}}=1) is sufficient. A higher {{TAG|ICHIBARE}} results in a substantial increase of the computational load.
+== Output ==
+The isotropic chemical shieldings are printed towards the end of the {{FILE|OUTCAR}} file, after the self-consistent calculation has finished. The chemical shift tensors both before and after space group symmetrization. These are the absolute tensors for the infinite lattice, excluding core contributions. They can be searched for under the <code>UNSYMMETRIZED TENSORS</code> and <code>SYMMETRIZED TENSORS</code> after <code>Absolute Chemical Shift tensors</code>. Additionally, the magnetic susceptibility is printed shortly after and found under <code>ORBITAL MAGNETIC SUSCEPTIBILITY</code>.
-*For {{TAG|NLSPLINE}}=.TRUE., the PAW projectors in reciprocal space ({{TAG|LREAL}}=.FALSE.) are set up using a spline interpolation so that they are ''k''-differentiable. This improves the susceptibility contribution to the shifts (via the aforementioned Eq. 47). It only slightly affects the other contributions to the shifts (Eqs. 38 and 40). It is advised to set {{TAG|NLSPLINE}}=.TRUE. if PAW projectors are applied in reciprocal space, but only in case of calculation of chemical shifts. As this option also gives slightly different total energies, it is advised to use the default {{TAG|NLSPLINE}}=.FALSE. in all other calculations for reasons of compatibility. Real space projectors are ''k''-differentiable by construction, hence do not require to set {{TAG|NLSPLINE}}=.TRUE.
+===Magnetic susceptibility===
+The magnetic susceptibility is found at the start of the <code>ORBITAL MAGNETIC SUSCEPTIBILITY, excluding core contribution</code>. The magnetic susceptibility is split into that obtained by the ''pGv''-approximation and obtained by the ''vGv''-approximation:
-*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 {{TAG|LNMR_SYM_RED}}=.TRUE., and such operations will be discarded, resulting in a larger IBZ. In case of any doubt set {{TAG|LNMR_SYM_RED}}=.TRUE. Beware: It matters how the real space lattice vectors are set up relative to the cartesian coordinates in {{FILE|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.
+<pre>
+-------------------------------------------------------------
+  ORBITAL MAGNETIC SUSCEPTIBILITY, excluding core contribution
+ -------------------------------------------------------------
+  Approximate magnetic susceptibility, pGv (10^-6 cm^3/mole)
+        -70.928534         -0.000000          0.000000
+         -0.000000        -70.928534          0.000000
+          0.000000          0.000000        -70.928534
+ -------------------------------------------------------------
+  Approximate magnetic susceptibility, vGv (10^-6 cm^3/mole)
+        -63.412095         -0.000000          0.000000
+         -0.000000        -63.412095          0.000000
+          0.000000          0.000000        -63.412095
-The chemical shift is calculated via the induced current (cf. {{TAG|LWRTCUR}}).<ref name="pickard:prb:01"/><ref name="yates:prb:07"/>
+         principal value                      axis
-It has contributions from the plane wave grid and one-center contributions (the induced field
+       (10^-6 cm^3/mole)           x,          y,          z
-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 {{TAG|LLRAUG}}.
+              -63.412095      0.1652     -0.9863      0.0000
+              -63.412095     -0.9863     -0.1652      0.0000
+              -63.412095      0.0000      0.0000      1.0000
+ -------------------------------------------------------------
+</pre>
-For very high accuracy calculations use {{TAG|LASPH}}.
+===Chemical shielding===
+To obtain the full absolute tensors requires adding both the <math>\mathbf{G=0}</math> contribution (cf. <code>G=0 CONTRIBUTION TO CHEMICAL SHIFT</code>) and the contributions due to the core electrons. The latter consists of contributions for each chemical species separately (depending on {{TAG|POTCAR}}) and a global <math>\mathbf{G=0}</math> susceptibility contribution.
-No special {{FILE|POTCAR}} files are necessary. The GIPAW is applied using the projectors functions and partial waves that are stored in the regular {{FILE|POTCAR}} files. A few remarks, however, on accuracy in relation to the different {{FILE|POTCAR}} flavours:
+The reference shift experienced by the core is given first:
-*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 {{FILE|POTCAR}} flavours can differ a few ppm for first and second row ''sp''-bonded elements (except for H).
+<pre>
+  Core NMR properties
-*Use {{FILE|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 <tt>LEXCH</tt> from {{FILE|POTCAR}} with an explicit {{TAG|GGA}}-tag in the {{FILE|INCAR}}.
+  typ  El   Core shift (ppm)
+ ----------------------------
+  C     -200.5098801
+ ----------------------------
-== Output ==
+  Core contribution to magnetic susceptibility:     -0.31  10^-6 cm^3/mole
+ --------------------------------------------------------------------------
+</pre>
+{{NB|important|The isotropic chemical shift <math>\delta_{\mathrm{iso}}\mathrm{[VASP]}</math> (ISO_SHIFT) is the negative of the isotropic shielding. To make it a ''real shift'' one should add the reference shielding.}}
-At the end of the {{FILE|OUTCAR}} file, VASP prints the chemical shift tensors both before and after space group symmetrization. These are the absolute tensors for the infinite lattice, excluding core contributions. Next lines "<tt>Q=0 CONTRIBUTION TO CHEMICAL SHIFT</tt>" are printed.
+Next, the tensor is processed and its chemical shielding anisotropy (CSA) characteristics are printed in the {{FILE|OUTCAR}}. The tensor is symmetrized (<math>\sigma_{ij} = \sigma_{ji}</math> is enforced) and diagonalized. From the three diagonal values the isotropic chemical "shift" <math>\delta_{\mathrm{iso}}\mathrm{[VASP]}</math>, span <math>\Omega</math>, and skew <math>\kappa</math> are calculated and printed see Ref. {{Cite|mason:ssn:1993}} for unambiguous definitions. Note that <math>\kappa</math> is ill-defined if <math>\Omega = 0</math>. Units are ppm, except for the skew. A typical output is given below:
-This is a shift tensor arising solely from the <math>\mathbf{G=0}</math> component of the induced field. This component is related to the shape of the sample and depends only on the induced macroscopic surface currents.
-It is printed for a spherical sample (for which is it nucleus independent), and calculated from the orbital magnetic susceptibility (see below), that is also printed.
-To obtain the full absolute tensors requires adding both the <math>\mathbf{G=0}</math> contribution and the contributions due to the core electrons. The latter consist of contributions for each chemical species separately
-(depending on {{TAG|POTCAR}}) and a global <math>\mathbf{G=0}</math> susceptibility contribution.
-Finally the tensor is processed and its (CSA) characteristics are printed on {{FILE|OUTCAR}}. The tensor is symmetrized (<math>\sigma_{ij} = \sigma_{ji}</math> is enforced) and diagonalized. From the three diagonal values the isotropic chemical "shift" <math>\delta_{\mathrm{iso}}\mathrm{[VASP]}</math>, span <math>\Omega</math> and skew <math>\kappa</math> are calculated and printed.<ref name="mason:ssn:93"/> Note that <math>\kappa</math> is ill-defined if <math>\Omega = 0</math>. Note that the isotropic chemical shift <math>\delta_{\mathrm{iso}}\mathrm{[VASP]}</math> (ISO_SHIFT) as printed is actually minus the isotropic shielding. To make it a ''real shift'' one should add the reference shielding. Also note that <math>\Omega</math> (SPAN) and <math>\kappa</math> (SKEW) are unambiguously defined.<ref name="mason:ssn:93"/> Units are ppm, except for the skew. This typically looks like:
+<pre>
     ---------------------------------------------------------------------------------
      CSA tensor (J. Mason, Solid State Nucl. Magn. Reson. 2, 285 (1993))
@@ Line 105: / Line 133: @@
      IF SPAN.EQ.0, THEN SKEW IS ILL-DEFINED
     ---------------------------------------------------------------------------------
+</pre>
-The columns excluding the <math>\mathbf{G=0}</math> contribution are useful for supercell calculations on molecules.
-The columns including the <math>\mathbf{G=0}</math> contribution are for crystals.
-The upper block gives the shielding due to only the electrons included in the SCF calculation.
-The lower block has the contributions due to the frozen PAW cores added. These core contributions are rigid.<ref name="gregor:jcp:99"/> They depend on {{FILE|POTCAR}} and are isotropic, i.e. affect neither SPAN nor SKEW.
+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 <code>ISO_SHIFT</code>, <code>SPAN</code>, and <code>SKEW</code>.
+{{NB|important|
+*The columns excluding the <math>\mathbf{G=0}</math> contribution are useful for supercell calculations on molecules.
+*The columns including the <math>\mathbf{G=0}</math> contribution are for crystals.
+*The upper block gives the shielding due to only the electrons included in the SCF calculation.
+*The lower block has the contributions due to the frozen PAW cores added. These core contributions are rigid  {{Cite|gregor:jcp:1999}}. They depend on {{FILE|POTCAR}} and are isotropic, i.e. affect neither SPAN nor SKEW.}}
 <!--
 As of VASP.? on OUTCAR also a summary of the tensors per ion is printed. This is done both excluding and including the '''G'''=0 contribution.
 The summary starts with, for each ion, its number, the isotropic shielding, the shielding tensor and the symmetrized shielding tensor.
 Next the principal components and the principal axes are printed (from the symmetrized tensor).
-They are ordered following Mason,<ref name="mason:ssn:93"/> i.e. &sigma;<sub>11</sub> < &sigma;<sub>22</sub> < &sigma;<sub>33</sub>.
+They are ordered following Mason {{Cite|mason:ssn:1993}}, i.e. σ<sub>11</sub> < σ<sub>22</sub> < σ<sub>33</sub>.
-Finally a line is printed with (again) the isotropic shielding &sigma;<sub>iso</sub>, the span &Omega; &amp; skew &kappa; (Herzfeld-Berger, Mason sections 2.2 and 2.3) and the shielding anistropy &Delta; &amp; asymmetry &eta; (Haeberlen, Mason section 2.6).
+Finally a line is printed with (again) the isotropic shielding σ<sub>iso</sub>, the span Ω & skew κ (Herzfeld-Berger, Mason sections 2.2 and 2.3) and the shielding anisotropy Δ & asymmetry η (Haeberlen, Mason section 2.6).
--->
+<pre>
-By default the orbital '''magnetic susceptibility''' is calculated using the so-called ''pGv''-approximation, i.e. Eqs. 46-48 of Yates '' et al.''<ref name="yates:prb:07"/>
+ ---------------------------------------------------------------------------------------
-As of vasp.6.4.0 also the ''vGv''-approximation of the susceptibility is calculated. By default, the ''pGv'' result
+  CSA tensor (J. Mason, Solid State Nucl. Magn. Reson. 2, 285 (1993))
-is applied for the <math>\mathbf{G=0}</math> contribution to the shifts. With {{TAG|LVGVAPPL}} one can force VASP to use the ''vGv'' result for the <math>\mathbf{G=0}</math> contribution instead. With {{TAG|LVGVCALC}} one can suppress calculation of the ''vGv'' susceptibility. For details see {{TAG|LVGVCALC}}.
+  for chemical shielding  (including the isotropic core contribution)
-== Advice ==
+  BDIR labels direction of applied magnetic field (i.e. B0)
+  For BDIR==1, B0 along x-axis, etc.
+  Induced field listed along cartesian directions for each BDIR
+ ---------------------------------------------------------------------------------------
+                 EXCLUDING G=0 CONTRIBUTION             INCLUDING G=0 CONTRIBUTION
+            ------------------------------------   ------------------------------------
+  ion  BDIR            X           Y           Z              X           Y           Z
+          (   iso_shield        span        skew) (  iso_shield        span        skew)
+ ---------------------------------------------------------------------------------------
+     1     142.5256     -0.0000      0.0000       229.8645     -0.0000      0.0000
+      -0.0000    142.5256      0.0000        -0.0000    229.8645     -0.0000
+      -0.0000      0.0000    142.5256        -0.0000      0.0000    229.8645
+          (     142.5256      0.0000      0.0000) (    229.8645      0.0000      0.0000)
-'''Beware''' the treatment of the orbital magnetism is non-relativistic. This is fine for light nuclei.
+     1     142.5256     -0.0000      0.0000       229.8645     -0.0000      0.0000
-The standard POTCARs are scalar-relativistic and account partially for relativistic effects.
+      -0.0000    142.5256      0.0000        -0.0000    229.8645     -0.0000
-The accuracy can be improved using {{TAG|LBONE}}, that restores the small B-component of the wave function inside the PAW spheres.
+      -0.0000      0.0000    142.5256        -0.0000      0.0000    229.8645
-Spin-orbit coupling is not implemented for chemical shift calculations.
+          (     142.5256      0.0000      0.0000) (    229.8645      0.0000      0.0000)
+ ---------------------------------------------------------------------------------------
-'''What to do in case of insufficient memory?''' VASP trades off memory savings against speed, opting for the latter.
+  IF SPAN.EQ.0, THEN SKEW IS ILL-DEFINED
-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 {{FILE|CHGCAR}} file.
+</pre>
-Next do a chemical shift calculation for each ''k''-point in the IBZ separately, starting from {{FILE|CHGCAR}}, ''i.e.'', using {{TAG|ICHARG}}=11.
+-->
-Finally calculate the shifts as a ''k''-point weighted average of the symmetrized shifts of the individual ''k''-points.
 == Related tags and articles ==
@@ Line 148: / Line 189: @@
 == References ==
-<references>
-<ref name="pickard:prb:01">[http://link.aps.org/doi/10.1103/PhysRevB.63.245101 C. J. Pickard, F. Mauri, Phys. Rev. B 63, 245101 (2001).]</ref>
-<ref name="yates:prb:07">[http://link.aps.org/doi/10.1103/PhysRevB.76.024401 J. R. Yates, C. J. Pickard, F. Mauri, Phys. Rev. B 76, 024401 (2007).]</ref>
-<ref name="mason:ssn:93">[http://dx.doi.org/10.1016/0926-2040(93)90010-K J. Mason, Solid State Nucl. Magn. Reson. 2, 285 (1993).]</ref>
-<ref name="gregor:jcp:99">[http://dx.doi.org/10.1063/1.479451 T. Gregor, F. Mauri, R. Car, J. Chem. Phys. 111, 1815 (1999).]</ref>
-</references>
-----
-[[Category:INCAR tag]][[Category:NMR]][[Category:Chemical shifts]]
+[[Category:INCAR tag]][[Category:NMR]]