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The expression for dispersion energy within the method of Tkatchenko and Scheffler<ref name="Tkatchenko09"/> (DFT-TS) is formally identical to that of the {{TAG|DFT-D2}} method. The important difference is, however, that the dispersion coefficients and damping function are charge-density dependent. The DFT-TS method is therefore able to take into account variations in vdW contributions of atoms due to their local chemical environment. In this method, polarizability, dispersion coefficients, and atomic radii of an atom in a molecule or a solid are computed from their free-atomic values using the following relations:
The expression for the dispersion energy within the method of Tkatchenko and Scheffler{{cite|tkatchenko:prl:09}} is formally identical to that of the {{TAG|DFT-D2}} method. The important difference is, however, that the dispersion coefficients and damping function are charge-density dependent. The Tkatchenko-Scheffler method is therefore able to take into account variations in vdW contributions of atoms due to their local chemical environment. In this method the polarizability, dispersion coefficients, and atomic radii of an atom in a molecule or a solid are computed from their free-atomic values using the following relations:


<math>\alpha_{i}  = \nu_{i}\, \alpha_{i}^{free},</math>
:<math>\alpha_{i}  = \nu_{i}\, \alpha_{i}^{free},</math>


<math>C_{6ii} = \nu_{i}^{2}\,C_{6ii}^{free},</math>
:<math>C_{6ii} = \nu_{i}^{2}\,C_{6ii}^{free},</math>


<math> R_{0i} = \left(\frac{\alpha_{i}}{\alpha_{i}^{free}} \right)^{\frac{1}{3}} R_{0i}^{free}. </math>
:<math> R_{0i} = \left(\frac{\alpha_{i}}{\alpha_{i}^{free}} \right)^{\frac{1}{3}} R_{0i}^{free}. </math>


The free-atomic quantities <math>\alpha_{i}^{free},C_{6ii}^{free}</math> and <math>R_{0i}^{free}</math> are tabulated for all elements from the first six rows of the periodic table except of lanthanides. If a DFT-TS calculation is performed for the system containing the unsupported elements, the user must define corresponding values using the tags {{TAG|VDW_ALPHA}}, {{TAG|VDW_C6}} and {{TAG|VDW_R0}} (see below). The effective atomic volumes <math>\nu_{i}</math> are determined using the Hirshfeld partitioning of the all-electron density:
The free-atomic quantities <math>\alpha_{i}^{free},C_{6ii}^{free}</math> and <math>R_{0i}^{free}</math> are tabulated for all elements from the first six rows of the periodic table except for lanthanides. If a Tkatchenko-Scheffler calculation is performed for the system containing an unsupported element, the user has to define the corresponding values using the tags {{TAG|VDW_ALPHA}}, {{TAG|VDW_C6}} and {{TAG|VDW_R0}} (see below). The effective atomic volumes <math>\nu_{i}</math> are determined using the Hirshfeld partitioning of the all-electron density:


<math>\nu_{i} = \frac{\int r^3 \,w_i({\mathbf{r}}) n({\mathbf{r}})\,d^3{\mathbf{r}}}{\int r^3\, n_{i}^{free}({\mathbf{r}})\,d^3{\mathbf{r}}}</math>
:<math>\nu_{i} = \frac{\int r^3 \,w_i({\mathbf{r}}) n({\mathbf{r}})\,d^3{\mathbf{r}}}{\int r^3\, n_{i}^{free}({\mathbf{r}})\,d^3{\mathbf{r}}}</math>


where <math>n({\mathbf{r}})</math> is the total electron density and <math>n_{i}^{free}({\mathbf{r}})</math> is the spherically averaged electron density of the neutral free atomic species <math>i</math>. The Hirshfeld weight <math>w_i({\mathbf{r}})</math> is defined by free atomic densities as follows:
where <math>n({\mathbf{r}})</math> is the total electron density and <math>n_{i}^{free}({\mathbf{r}})</math> is the spherically averaged electron density of the neutral free atomic species <math>i</math>. The Hirshfeld weight <math>w_i({\mathbf{r}})</math> is defined by free atomic densities as follows:


<math> w_i({\mathbf{r}}) = \frac{n_{i}^{free}({\mathbf{r}})}{\sum_{j=1}^{N_{at}} n_{j}^{free}({\mathbf{r}})}. </math>
:<math> w_i({\mathbf{r}}) = \frac{n_{i}^{free}({\mathbf{r}})}{\sum_{j=1}^{N_{at}} n_{j}^{free}({\mathbf{r}})}. </math>


The combination rule to define the strength of the dipole-dipole dispersion interaction between unlike species is:
The combination rule to define the strength of the dipole-dipole dispersion interaction between unlike species is:


<math> C_{6ij} = \frac{2C_{6ii}\,C_{6jj}}{[\frac{\alpha_{j}} {\alpha_{i}}C_{6ii}+\frac{\alpha_{i}}{\alpha_{j}}C_{6jj}]}. </math>
:<math> C_{6ij} = \frac{2C_{6ii}\,C_{6jj}}{[\frac{\alpha_{j}} {\alpha_{i}}C_{6ii}+\frac{\alpha_{i}}{\alpha_{j}}C_{6jj}]}. </math>


The parameter <math>R_{0ij}</math> used in the damping function of the {{TAG|DFT-D2}} method is obtained from the atom-in-molecule vdW radii as follows:
The parameter <math>R_{0ij}</math> used in the damping function of the {{TAG|DFT-D2}} method is obtained from the atom-in-molecule vdW radii as follows:


<math> R_{0ij} = R_{0i} + R_{0j}. </math>
:<math> R_{0ij} = R_{0i} + R_{0j}. </math>


The DFT-TS calculation is invoked by setting {{TAG|IVDW}}=2|20. The following parameters can be optionally defined in {{TAG|INCAR}}:
The Tkatchenko-Scheffler method is invoked by setting {{TAG|IVDW}}=2|20. The following parameters can be optionally defined in {{TAG|INCAR}} (the given values are the default ones):


*{{TAG|VDW_RADIUS}}=50.0 cutoff radius (in &Aring;) for pair interactions
*{{TAG|LVDWSCS}}=.FALSE. : activates the {{TAG|self-consistent screening in Tkatchenko-Scheffler method}}
*{{TAG|VDW_S6}}=1.00 global scaling factor <math>s_6</math>
*{{TAG|VDW_RADIUS}}=50.0 : cutoff radius (in &Aring;) for pair interactions
*{{TAG|VDW_SR}}=0.94 scaling factor <math>s_R</math>
*{{TAG|VDW_S6}}=1.00 : global scaling factor <math>s_6</math>
*{{TAG|VDW_D}}=20.0 damping parameter <math>d</math>
*{{TAG|VDW_SR}}=0.94 : scaling factor <math>s_R</math>
*{{TAG|VDW_ALPHA}}=[real array] free-atomic polarizabilities (atomic units) for each species defined in the {{TAG|POSCAR}} file
*{{TAG|VDW_D}}=20.0 : damping parameter <math>d</math>
*{{TAG|VDW_C6AU}}=[real array] free-atomic <math>C_6</math> parameters (atomic units) for each species defined in the {{TAG|POSCAR}} file
*{{TAG|VDW_ALPHA}}=[real array] : free-atomic polarizabilities (atomic units) for each species defined in the {{TAG|POSCAR}} file
*{{TAG|VDW_C6}}=[real array] free-atomic <math>C_6</math> parameters (<math>\mathrm{Jnm}^{6}\mathrm{mol}^{-1}</math>) for each species defined in the {{TAG|POSCAR}} file (this parameter overrides {{TAG|VDW_C6AU}})
*{{TAG|VDW_C6AU}}=[real array] : free-atomic <math>C_6</math> parameters (atomic units) for each species defined in the {{TAG|POSCAR}} file
*{{TAG|VDW_R0AU}}=[real array] free-atomic <math>R_0</math> parameters (atomic units) for each species defined in the {{TAG|POSCAR}} file
*{{TAG|VDW_C6}}=[real array] : free-atomic <math>C_6</math> parameters (<math>\mathrm{Jnm}^{6}\mathrm{mol}^{-1}</math>) for each species defined in the {{TAG|POSCAR}} file (this parameter overrides {{TAG|VDW_C6AU}})
*{{TAG|VDW_R0}}=[real array] <math>R_0</math> parameters (in &Aring;) for each species defined in the {{TAG|POSCAR}} file (this parameter overrides {{TAG|VDW_R0AU}})
*{{TAG|VDW_R0AU}}=[real array] : free-atomic <math>R_0</math> parameters (atomic units) for each species defined in the {{TAG|POSCAR}} file
*{{TAG|LVDW_EWALD}}=.FALSE. decides whether to compute the lattice summation in <math>E_{disp}</math> expression by means of Ewald's summation ({{TAG|LVDW_EWALD}}=''.TRUE.'') or not (tag available in VASP.5.3.4 and later)
*{{TAG|VDW_R0}}=[real array] : <math>R_0</math> parameters (in &Aring;) for each species defined in the {{TAG|POSCAR}} file (this parameter overrides {{TAG|VDW_R0AU}})
*{{TAG|LVDW_EWALD}}=.FALSE. : the lattice summation in <math>E_{\mathrm{disp}}</math> expression is computed by means of Ewald's summation (''.TRUE.'' ) or via a real space summation over all atomic pairs within cutoff radius {{TAG|VDW_RADIUS}} (''.FALSE.'')(available in VASP.5.3.4 and later)
*{{TAG|LTSSURF}}=.FALSE.: if set to .TRUE., the standard parametrization of the Tkatchenko-Scheffler method is replaced by the one designed to enable reliable modeling of structure and stability for a broad class of organic molecules adsorbed on metal surfaces is activated<ref>[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.035118 V. G. Ruiz, W. Liu, and A. Tkatchenko, Phys. Rev. B 93, 035118 (2016).]</ref>


Performance of PBE-TS method in optimization of various crystalline systems has been examined in reference <ref name="bucko"/>.
The performance of the Tkatchenko-Scheffler method in optimization of various crystalline systems has been examined in reference {{cite|bucko:prb:13}}.


== IMPORTANT NOTES ==
{{NB|mind|
 
*This method requires the use of {{TAG|POTCAR}} files from the PAW dataset version 52 or later.
*This method requires the use of {{TAG|POTCAR}} files from the PAW dataset version 52 or later.
*The input reference data for non-interacting atoms is available only for elements of the first six rows of the periodic table except for lanthanides. If the system contains other elements, the user must provide the free-atomic parameters for all atoms in the system via {{TAG|VDW_ALPHA}}, {{TAG|VDW_C6}}, {{TAG|VDW_R0}} defined in the {{TAG|INCAR}} file.
*The input reference data for non-interacting atoms is available only for elements of the first six rows of the periodic table except of lanthanides. If the system contains other elements, the user must provide the free-atomic parameters for all atoms in the system via {{TAG|VDW_ALPHA}}, {{TAG|VDW_C6}}, {{TAG|VDW_R0}} defined in the {{TAG|INCAR}} file.
*The charge-density dependence of gradients is neglected.
*The charge-density dependence of gradients is neglected.
*The DFT-TS method is incompatible with the setting {{TAG|ADDGRID}}=''.TRUE.''.
*The DFT-TS method is incompatible with the setting {{TAG|ADDGRID}}{{=}}''.TRUE.''.
*It is essential that a sufficiently dense FFT grid (controlled via {{TAG|NGFX(Y,Z)}}) is used in the DFT-TS calculation - we strongly recommend to use {{TAG|PREC}}=''Accurate'' for this type of calculations (in any case, avoid using {{TAG|PREC}}=''Low'').
*It is essential that a sufficiently dense FFT grid (controlled via {{TAG|NGXF}}, {{TAG|NGYF}} and {{TAG|NGZF}}) is used in the DFT-TS calculation - we strongly recommend to use {{TAG|PREC}}{{=}}''Accurate'' for this type of calculations (in any case, avoid using {{TAG|PREC}}{{=}}''Low'').
*Defaults for the parameters controlling the damping function ({{TAG|VDW_S6}}, {{TAG|VDW_SR}}, {{TAG|VDW_D}}) are available only for the PBE functional. If a functional other than PBE is used, the value of {{TAG|VDW_SR}} must be specified in the {{TAG|INCAR}} file.
*Defaults for the parameters controlling the damping function ({{TAG|VDW_S6}}, {{TAG|VDW_SR}}, {{TAG|VDW_D}}) are available for the PBE, PBE0, HSE03, HSE06, TPSS, and M06L functionals. If any other functional is used, the value of {{TAG|VDW_SR}} must be specified in the {{TAG|INCAR}} file.
*Ewald's summation in the calculation of <math>E_{disp}</math> (controlled via {{TAG|LVDW_EWALD}}) implemented according to reference <ref name="kerber"/> is available as of VASP.5.3.4.
*Ewald's summation in the calculation of <math>E_{disp}</math> (controlled via {{TAG|LVDW_EWALD}}) implemented according to reference {{cite|kerber:jcc:08}} is available as of VASP.5.3.4.
*Parameters {{TAG|VDW_C6AU}} and {{TAG|VDW_R0AU}}  are available as of VASP.5.3.4.
*Parameters {{TAG|VDW_C6AU}} and {{TAG|VDW_R0AU}}  are available as of VASP.5.3.4.
*Hirshfeld charges for all configurations generated in a calculation are written out in the {{TAG|OUTCAR}} file. The corresponding table is introduced by the expression ''Hirshfeld charges:''.
*Hirshfeld charges for all configurations generated in a calculation are written out in the {{TAG|OUTCAR}} file. The corresponding table is introduced by the expression ''Hirshfeld charges:''.}}


== Related Tags and Sections ==
== Related tags and articles ==
{{TAG|VDW_RADIUS}},
{{TAG|VDW_S6}},
{{TAG|VDW_SR}},
{{TAG|VDW_D}},
{{TAG|VDW_ALPHA}},
{{TAG|VDW_C6AU}},
{{TAG|VDW_C6}},
{{TAG|VDW_R0AU}},
{{TAG|VDW_R0}},
{{TAG|LVDW_EWALD}},
{{TAG|IVDW}},
{{TAG|IVDW}},
{{TAG|IALGO}},
{{TAG|DFT-D2}},
{{TAG|DFT-D3}},
{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},
{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},
{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}},
{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}},
{{TAG|Many-body dispersion energy}},
{{TAG|Many-body dispersion energy}},
{{TAG|dDsC dispersion correction}}
{{TAG|Many-body dispersion energy with fractionally ionic model for polarizability}}


{{sc|Tkatchenko-Scheffler method|Examples|Examples that use this tag}}
== References ==
<references/>


== References ==
<references>
<ref name="Tkatchenko09">[https://doi.org/10.1103/PhysRevLett.102.073005 A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009).]</ref>
<ref name="bucko">[http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.064110 T. Bučko, S. Lebègue, J. Hafner, and J. G. Ángyán, Phys. Rev. B 87, 064110 (2013).]</ref>
<ref name="kerber">[http://onlinelibrary.wiley.com/doi/10.1002/jcc.21069/abstract Kerber and J. Sauer, J. Comp. Chem. 29, 2088 (2008).]</ref>
</references>
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[[The_VASP_Manual|Contents]]
[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]
 
[[Category:XC Functionals]][[Category:van der Waals]][[Category:Theory]][[Category:Howto]]

Latest revision as of 10:48, 19 January 2024

The expression for the dispersion energy within the method of Tkatchenko and Scheffler[1] is formally identical to that of the DFT-D2 method. The important difference is, however, that the dispersion coefficients and damping function are charge-density dependent. The Tkatchenko-Scheffler method is therefore able to take into account variations in vdW contributions of atoms due to their local chemical environment. In this method the polarizability, dispersion coefficients, and atomic radii of an atom in a molecule or a solid are computed from their free-atomic values using the following relations:

The free-atomic quantities and are tabulated for all elements from the first six rows of the periodic table except for lanthanides. If a Tkatchenko-Scheffler calculation is performed for the system containing an unsupported element, the user has to define the corresponding values using the tags VDW_ALPHA, VDW_C6 and VDW_R0 (see below). The effective atomic volumes are determined using the Hirshfeld partitioning of the all-electron density:

where is the total electron density and is the spherically averaged electron density of the neutral free atomic species . The Hirshfeld weight is defined by free atomic densities as follows:

The combination rule to define the strength of the dipole-dipole dispersion interaction between unlike species is:

The parameter used in the damping function of the DFT-D2 method is obtained from the atom-in-molecule vdW radii as follows:

The Tkatchenko-Scheffler method is invoked by setting IVDW=2|20. The following parameters can be optionally defined in INCAR (the given values are the default ones):

  • LVDWSCS=.FALSE. : activates the self-consistent screening in Tkatchenko-Scheffler method
  • VDW_RADIUS=50.0 : cutoff radius (in Å) for pair interactions
  • VDW_S6=1.00 : global scaling factor
  • VDW_SR=0.94 : scaling factor
  • VDW_D=20.0 : damping parameter
  • VDW_ALPHA=[real array] : free-atomic polarizabilities (atomic units) for each species defined in the POSCAR file
  • VDW_C6AU=[real array] : free-atomic parameters (atomic units) for each species defined in the POSCAR file
  • VDW_C6=[real array] : free-atomic parameters () for each species defined in the POSCAR file (this parameter overrides VDW_C6AU)
  • VDW_R0AU=[real array] : free-atomic parameters (atomic units) for each species defined in the POSCAR file
  • VDW_R0=[real array] : parameters (in Å) for each species defined in the POSCAR file (this parameter overrides VDW_R0AU)
  • LVDW_EWALD=.FALSE. : the lattice summation in expression is computed by means of Ewald's summation (.TRUE. ) or via a real space summation over all atomic pairs within cutoff radius VDW_RADIUS (.FALSE.). (available in VASP.5.3.4 and later)
  • LTSSURF=.FALSE.: if set to .TRUE., the standard parametrization of the Tkatchenko-Scheffler method is replaced by the one designed to enable reliable modeling of structure and stability for a broad class of organic molecules adsorbed on metal surfaces is activated[2]

The performance of the Tkatchenko-Scheffler method in optimization of various crystalline systems has been examined in reference [3].


Mind:
  • This method requires the use of POTCAR files from the PAW dataset version 52 or later.
  • The input reference data for non-interacting atoms is available only for elements of the first six rows of the periodic table except for lanthanides. If the system contains other elements, the user must provide the free-atomic parameters for all atoms in the system via VDW_ALPHA, VDW_C6, VDW_R0 defined in the INCAR file.
  • The charge-density dependence of gradients is neglected.
  • The DFT-TS method is incompatible with the setting ADDGRID=.TRUE..
  • It is essential that a sufficiently dense FFT grid (controlled via NGXF, NGYF and NGZF) is used in the DFT-TS calculation - we strongly recommend to use PREC=Accurate for this type of calculations (in any case, avoid using PREC=Low).
  • Defaults for the parameters controlling the damping function (VDW_S6, VDW_SR, VDW_D) are available for the PBE, PBE0, HSE03, HSE06, TPSS, and M06L functionals. If any other functional is used, the value of VDW_SR must be specified in the INCAR file.
  • Ewald's summation in the calculation of (controlled via LVDW_EWALD) implemented according to reference [4] is available as of VASP.5.3.4.
  • Parameters VDW_C6AU and VDW_R0AU are available as of VASP.5.3.4.
  • Hirshfeld charges for all configurations generated in a calculation are written out in the OUTCAR file. The corresponding table is introduced by the expression Hirshfeld charges:.

Related tags and articles

VDW_RADIUS, VDW_S6, VDW_SR, VDW_D, VDW_ALPHA, VDW_C6AU, VDW_C6, VDW_R0AU, VDW_R0, LVDW_EWALD, IVDW, Tkatchenko-Scheffler method with iterative Hirshfeld partitioning, Self-consistent screening in Tkatchenko-Scheffler method, Many-body dispersion energy, Many-body dispersion energy with fractionally ionic model for polarizability

References