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| {{TAGDEF|INICS|0 {{!}} 1 {{!}} 2| 0}} | | {{not released}} |
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| Description: calculate the nucleus independent chemical shifts (NICS) by means of linear response.
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| ----
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| *{{TAG|INICS}}=0
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| :NICS are not calculated
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| *{{TAG|INICS}}=1
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| :NICS values are calculated at positions defined in POSNICS
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| *{{TAG|INICS}}=2
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| :NICS values are calculated at the grid points defined by the FFT.
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| ----
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| The chemical shielding tensor is defined as:
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| :<math>
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| \sigma_{ij}(\mathbf{R}) = - \frac{ \partial B^{\mathrm{in}}_i(\mathbf{R})}{ \partial B^{\mathrm{ext}}_j}
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| </math>
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| Using {{TAG|LCHIMAG}}, the chemical shielding is calculated at positions <math>\mathbf{R}</math> corresponding to the nuclei. It is also possible to calculate the chemical shielding "off-nucleus", i.e. ''nucleus-independent'' chemical shift (NICS) {{Cite|schleyer:1996}}.
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| 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{in}}(\mathbf{R})</math> the induced magnetic field at the nucleus.
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| 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:
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| :<math>
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| \delta_{ij}(\mathbf{R}) = \sigma_{ij}^{\mathrm{ref}} - \sigma_{ij}(\mathbf{R})
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| </math>
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| 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.
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| In VASP the chemical "shift" tensor is calculated as:
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| :<math>
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| \delta_{ij}(\mathbf{R})\mathrm{[VASP]} = \frac{ \partial B^{\mathrm{in}}_i(\mathbf{R})}{ \partial B^{\mathrm{ext}}_j}
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| </math>
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| 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
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| reference shielding:
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| :<math>
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| \delta_{ij}(\mathbf{R}) = \sigma_{ij}^{\mathrm{ref}} + \delta_{ij}(\mathbf{R})\mathrm{[VASP]}
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| </math>
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| 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}}
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| == Input ==
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| An example {{FILE|INCAR}} is given below:
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| {{TAGBL|PREC}} = Accurate
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| {{TAGBL|ENCUT}} = 600.0
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| {{TAGBL|EDIFF}} = 1E-8
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| {{TAGBL|ISMEAR}} = 0; {{TAGBL|SIGMA}} = 0.1
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| {{TAGBL|LREAL}} = A
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|
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| LCHIMAG = .TRUE.
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| {{TAGBL|DQ}} = 0.001
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| {{TAGBL|ICHIBARE}} = 1
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| {{TAGBL|LNMR_SYM_RED}} = .TRUE.
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| {{TAGBL|NLSPLINE}} = .TRUE.
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| {{NB|warning|The chemical shifts are calculated from the orbital magnetic response under the assumption that the system is an insulator. Smearing schemes intended for metals can generate nonsense.}}
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| <!--
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| There are also some additional tags relevant to {{TAG|LCHIMAG}} that are not used in the example {{FILE|INCAR}} that should be considered in special cases:
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| *{{TAG|LBONE}} adds the small B-component to the chemical shift tensor {{Cite|dewijs:laskowski:jcp:2017}}.
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| *{{TAG|LVGVCALC}} uses the vGv expression when calculating the orbital magnetic susceptibility {{Cite|avezac:prb:2007}}{{Cite|dewijs:havenith:jcp:2021}}.
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| *{{TAG|LVGVAPPL}} uses vGv orbital magnetic susceptibility when calculating the chemical shift anisotropy (CSA) tensor.
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| *{{TAG|LLRAUG}} calculates the two-center contributions to the chemical shielding tensor {{Cite|dewijs:jcp:2017}}{{Cite|dewijs:jcp:2018}}.
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| -->
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| The chemical shift is calculated via the induced current (cf. {{TAG|LWRTCUR}}) {{Cite|pickard:prb:2001}} {{Cite|yates:prb:2007}}.
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| It has contributions from the plane wave grid and one-center contributions (the induced field
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| 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 neglected by default. These contributions can be switched on using {{TAG|LLRAUG}}.
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| == Output ==
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| 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>.
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| ===Magnetic susceptibility===
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| By default the orbital '''magnetic susceptibility''' is calculated using the so-called ''pGv''-approximation, i.e. Eqs. 46-48 of Yates '' et al.'' {{Cite|yates:prb:2007}}. As of vasp.6.4.0 also the ''vGv''-approximation of the susceptibility is calculated. By default, the ''pGv'' result 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 the calculation of the ''vGv'' susceptibility. For details see {{TAG|LVGVCALC}}.
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| 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:
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| <pre>
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| -------------------------------------------------------------
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| ORBITAL MAGNETIC SUSCEPTIBILITY, excluding core contribution
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| -------------------------------------------------------------
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| Approximate magnetic susceptibility, pGv (10^-6 cm^3/mole)
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| 1 -70.928534 -0.000000 0.000000
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| 2 -0.000000 -70.928534 0.000000
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| 3 0.000000 0.000000 -70.928534
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| -------------------------------------------------------------
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| Approximate magnetic susceptibility, vGv (10^-6 cm^3/mole)
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| 1 -63.412095 -0.000000 0.000000
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| 2 -0.000000 -63.412095 0.000000
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| 3 0.000000 0.000000 -63.412095
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| principal value axis
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| (10^-6 cm^3/mole) x, y, z
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| --------------------------------------------------------
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| -63.412095 0.1652 -0.9863 0.0000
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| -63.412095 -0.9863 -0.1652 0.0000
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| -63.412095 0.0000 0.0000 1.0000
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| -------------------------------------------------------------
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| </pre>
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| ===Chemical shielding===
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| 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.
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| The reference shift experienced by the core is given first:
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| <pre>
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| Core NMR properties
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| typ El Core shift (ppm)
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| ----------------------------
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| 1 C -200.5098801
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| ----------------------------
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| Core contribution to magnetic susceptibility: -0.31 10^-6 cm^3/mole
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| --------------------------------------------------------------------------
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| </pre>
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| {{NB|important|The chemical shieldings calculated are the negative of the chemical shift. Note that the isotropic chemical shift <math>\delta_{\mathrm{iso}}\mathrm{[VASP]}</math> (ISO_SHIFT) is actually minus the isotropic shielding. To make it a ''real shift'' one should add the reference shielding.}}
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| 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:
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| <pre>
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| ---------------------------------------------------------------------------------
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| CSA tensor (J. Mason, Solid State Nucl. Magn. Reson. 2, 285 (1993))
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| ---------------------------------------------------------------------------------
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| EXCLUDING G=0 CONTRIBUTION INCLUDING G=0 CONTRIBUTION
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| ----------------------------------- -----------------------------------
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| ATOM ISO_SHIFT SPAN SKEW ISO_SHIFT SPAN SKEW
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| ---------------------------------------------------------------------------------
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| (absolute, valence only)
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| 1 4598.8125 0.0000 0.0000 4589.9696 0.0000 0.0000
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| 2 291.5486 0.0000 0.0000 282.7058 0.0000 0.0000
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| 3 736.5979 344.8803 1.0000 727.7550 344.8803 1.0000
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| 4 736.5979 344.8803 1.0000 727.7550 344.8803 1.0000
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| 5 736.5979 344.8803 1.0000 727.7550 344.8803 1.0000
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| ---------------------------------------------------------------------------------
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| (absolute, valence and core)
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| 1 -6536.1417 0.0000 0.0000 -6547.9848 0.0000 0.0000
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| 2 -5706.3864 0.0000 0.0000 -5718.2296 0.0000 0.0000
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| 3 -2369.4015 344.8803 1.0000 -2381.2446 344.8803 1.0000
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| 4 -2369.4015 344.8803 1.0000 -2381.2446 344.8803 1.0000
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| 5 -2369.4015 344.8803 1.0000 -2381.2446 344.8803 1.0000
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| ---------------------------------------------------------------------------------
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| IF SPAN.EQ.0, THEN SKEW IS ILL-DEFINED
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| ---------------------------------------------------------------------------------
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| </pre>
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| 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>.
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| {{NB|important|
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| *The columns excluding the <math>\mathbf{G=0}</math> contribution are useful for supercell calculations on molecules.
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| *The columns including the <math>\mathbf{G=0}</math> contribution are for crystals.
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| *The upper block gives the shielding due to only the electrons included in the SCF calculation.
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| *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.}}
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| | The {{FILE|NICS}} file contains the NMR nucleus-independent chemical shielding (NICS) in ppm. It is written if {{TAG|NUCIND}} = .TRUE. is set and no {{FILE|POSNICS}} is present. The format is the same as {{FILE|CHGCAR}} with a header to define the grid and then 9 blocks that correspond to the indices of the chemical shielding tensor <math>\sigma_{ij}</math>: <math>\sigma_{xx}</math>, <math>\sigma_{xy}</math>, <math>\sigma_{xz}</math>, <math>\sigma_{yx}</math>, <math>\sigma_{yy}</math>, <math>\sigma_{yz}</math>, <math>\sigma_{zx}</math>, <math>\sigma_{zy}</math>, and <math>\sigma_{zz}</math>. |
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| == Related tags and articles == | | == Related tags and articles == |
| | {{FILE|LCHIMAG}}, |
| | {{TAG|NUCIND}}, |
| | {{TAG|LNICSALL}} |
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|
| | | [[Category:INCAR tag]][[Category:NMR]] |
| {{sc|LCHIMAG|Examples|Examples that use this tag}}
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| == References ==
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| <!--[[Category:INCAR tag]][[Category:NMR]]-->
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