DFT-D3 - Revision history

Ftran at 11:19, 2 March 2026

2026-03-02T11:19:47Z

← Older revision		Revision as of 11:19, 2 March 2026
Line 3:		Line 3:
	:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>		:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>

	Unlike in the ~~method~~ {{TAG\|DFT-D2}}, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. Two variants of DFT-D3, that differ in the damping functions <math>f_{d,n}</math>, are available.		Unlike in the older {{TAG\|DFT-D2}} method, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. Two variants of DFT-D3, that differ in the mathematical form of the damping functions <math>f_{d,n}</math>, are available. More variants of the damping function are available via the [[simple-DFT-D3]] external package ({{TAG\|IVDW}}=15).

	=== DFT-D3(zero) ===		=== DFT-D3(zero) ===
Line 10:		Line 10:
	:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>

	where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, ~~the parameters~~ <math>\alpha_6</math>, <math>\alpha_8~~</math>, <math>s_{R,8}</math> and <math>s_{6}~~</math> are fixed at values ~~of 14, 16, 1~~, and ~~1, respectively, while <math>s_{8}</math> and <math>s_{R~~,~~6}</math> are adjustable parameters~~ whose values depend on the choice of the exchange-correlation functional.		where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, <math>\alpha_6=14</math> and <math>\alpha_8=16</math> are fixed (there is no tag to change their values), and the others parameters, whose default values depend on the choice of the exchange-correlation functional, can be modified as follows:
			*{{TAG\|VDW_S6}}=[real] : scaling <math>s_6</math> of the dipole-dipole dispersion. '''Available since VASP.6.6.0'''.
	~~Optionally~~, ~~the following parameters~~ can be ~~defined in the {{FILE\|INCAR}} file (the given values are the default ones)~~:		*{{TAG\|VDW_S8}}=[real] : scaling <math>s_8</math> of the dipole-quadrupole dispersion
			*{{TAG\|VDW_SR}}=[real] : radii scaling <math>s_{r,6}</math> in the dipole-dipole damping function
	*{{TAG\|~~VDW_RADIUS~~}}=~~50.2~~ : ~~cutoff radius (in~~ <math>~~\AA~~</math>~~) for pair interactions considered in~~ the ~~equation of <math> E_{\mathrm{disp}}</math>~~		*{{TAG\|VDW_SR8}}=[real] : radii scaling <math>s_{r,8}</math> in the dipole-quadrupole damping function. '''Available since VASP.6.6.0'''.
	*{{TAG\|~~VDW_CNRADIUS~~}}=~~20.0~~ : ~~cutoff radius (in~~ <math>~~\AA~~</math>~~) for the calculation~~ of the ~~coordination numbers~~		*{{TAG\|VDW_RADIUS}}=[real] : two-body interaction cutoff (in Å)
	*{{TAG\|~~VDW_S8~~}}=[real] : ~~damping function parameter~~ <math>~~s_8~~</math>		*{{TAG\|VDW_CNRADIUS}}=[real] : coordination number cutoff (in Å)
	*{{TAG\|~~VDW_SR~~}}=[real] : ~~damping function parameter~~ <math>s_{R,6}</math>

	=== DFT-D3(BJ) ===		=== DFT-D3(BJ) ===
	In the Becke-Johnson (BJ) damping variant of DFT-D3,{{cite\|grimme:jcc:11}}, invoked by setting {{TAG\|IVDW}}=12, the damping function is given by		In the rational Becke-Johnson (BJ) damping variant of DFT-D3,{{cite\|grimme:jcc:11}}, invoked by setting {{TAG\|IVDW}}=12, the damping function is given by

	:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>

	~~with~~ <math>s_6=1</math> ~~and~~ <math>~~a_1~~</math>, <math>~~a_2~~</math>, and <math>~~s_8~~</math> ~~being adjustable~~ parameters~~. As before~~, ~~the parameters~~ {{TAG\|~~VDW_RADIUS~~}} ~~and~~ {{TAG\|~~VDW_CNRADIUS~~}} ~~can be used to change the default values for~~ the ~~cutoff radii.~~		where <math>s_6</math>, <math>s_8</math>, <math>a_1</math>, and <math>a_2</math> are parameters whose default values depend on the choice of the exchange-correlation functional, but can also be modified as follows:
			*{{TAG\|VDW_S6}}=[real] : scaling <math>s_6</math> of the dipole-dipole dispersion. '''Available since VASP.6.6.0'''.
	~~Optionally, the parameters of the damping function can be controlled using the following~~ {{~~FILE~~\|~~INCAR~~}} ~~tags~~:		*{{TAG\|VDW_S8}}=[real] : scaling <math>s_8</math> of the dipole-quadrupole dispersion
			*{{TAG\|VDW_A1}}=[real] : scaling <math>a_{1}</math> of the critical radii
	*{{TAG\|~~VDW_S8~~}}=[real]		*{{TAG\|VDW_A2}}=[real] : offset <math>a_{2}</math> of the critical radii
	*{{TAG\|~~VDW_A1~~}}=[real]		*{{TAG\|VDW_RADIUS}}=[real] : two-body interaction cutoff (in Å)
	*{{TAG\|~~VDW_A2~~}}=[real]		*{{TAG\|VDW_CNRADIUS}}=[real] : coordination number cutoff (in Å)

	{{NB\|mind\|		{{NB\|mind\|
Line 37:		Line 36:

	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|~~VDW_RADIUS~~}},		{{TAG\|IVDW}},
	{{TAG\|~~VDW_CNRADIUS~~}},		{{TAG\|VDW_S6}},
	{{TAG\|VDW_S8}},		{{TAG\|VDW_S8}},
	{{TAG\|VDW_SR}},		{{TAG\|VDW_SR}},
			{{TAG\|VDW_SR8}},
	{{TAG\|VDW_A1}},		{{TAG\|VDW_A1}},
	{{TAG\|VDW_A2}},		{{TAG\|VDW_A2}},
	{{TAG\|~~IVDW~~}},		{{TAG\|VDW_RADIUS}},
	{{TAG\|DFT-D2}},		{{TAG\|VDW_CNRADIUS}},
	~~{{TAG\|~~DFT-~~ulg}}~~,		[[DFT-D2]],
	[[DFT-D4]]		[[simple-DFT-D3]],
			[[DFT-D4]],
			[[DFT-ulg]]

	== References ==		== References ==

Ftran at 10:24, 28 February 2025

2025-02-28T10:24:05Z

← Older revision		Revision as of 10:24, 28 February 2025
Line 52:		Line 52:

	----		----
	[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]		[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]][[Category:Howto]]

Ftran at 15:04, 24 February 2025

2025-02-24T15:04:02Z

← Older revision		Revision as of 15:04, 24 February 2025
Line 45:		Line 45:
	{{TAG\|IVDW}},		{{TAG\|IVDW}},
	{{TAG\|DFT-D2}},		{{TAG\|DFT-D2}},
			{{TAG\|DFT-ulg}},
	[[DFT-D4]]		[[DFT-D4]]

Ftran at 15:01, 24 February 2025

2025-02-24T15:01:13Z

← Older revision		Revision as of 15:01, 24 February 2025
Line 1:		Line 1:
	In the DFT-D3 method of Grimme et al.{{cite\|grimme:jcp:10}}, the following expression for the vdW-dispersion energy-correction term is used:		In the DFT-D3 method of Grimme et al.{{cite\|grimme:jcp:10}}, the following expression for the vdW dispersion energy-correction term is used:

	:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>		:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>

	Unlike in the method {{TAG\|DFT-D2}}, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are ~~adjusted~~ on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. In the zero-damping variant of ~~the~~ DFT-D3 ~~method (DFT-D3(zero))~~, the damping function reads:		Unlike in the method {{TAG\|DFT-D2}}, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. Two variants of DFT-D3, that differ in the damping functions <math>f_{d,n}</math>, are available.

			=== DFT-D3(zero) ===
			In the zero-damping variant of DFT-D3,{{cite\|grimme:jcp:10}} invoked by setting {{TAG\|IVDW}}=11, the damping function reads

	:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>

	where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, the parameters <math>\alpha_6</math>, <math>\alpha_8</math>, <math>s_{R,8}</math> and <math>s_{6}</math> are fixed at values of 14, 16, 1, and 1, respectively, while <math>s_{8}</math> and <math>s_{R,6}</math> are adjustable parameters whose values depend on the choice of the exchange-correlation functional. ~~The DFT-D3(zero) method is invoked by setting {{TAG\|IVDW}}=11.~~ Optionally, the following parameters can be ~~user-~~defined (the given values are the default ones):		where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, the parameters <math>\alpha_6</math>, <math>\alpha_8</math>, <math>s_{R,8}</math> and <math>s_{6}</math> are fixed at values of 14, 16, 1, and 1, respectively, while <math>s_{8}</math> and <math>s_{R,6}</math> are adjustable parameters whose values depend on the choice of the exchange-correlation functional.

			Optionally, the following parameters can be defined in the {{FILE\|INCAR}} file (the given values are the default ones):

	*{{TAG\|VDW_RADIUS}}=50.2 : cutoff radius (in <math>\AA</math>) for pair interactions considered in the equation of <math> E_{\mathrm{disp}}</math>		*{{TAG\|VDW_RADIUS}}=50.2 : cutoff radius (in <math>\AA</math>) for pair interactions considered in the equation of <math> E_{\mathrm{disp}}</math>
Line 14:		Line 19:
	*{{TAG\|VDW_SR}}=[real] : damping function parameter <math>s_{R,6}</math>		*{{TAG\|VDW_SR}}=[real] : damping function parameter <math>s_{R,6}</math>

	~~Alternatively,~~ the Becke-Johnson (BJ) damping ~~can be used in the~~ DFT-D3 ~~method~~{{cite\|grimme:jcc:11}}:		=== DFT-D3(BJ) ===
			In the Becke-Johnson (BJ) damping variant of DFT-D3,{{cite\|grimme:jcc:11}}, invoked by setting {{TAG\|IVDW}}=12, the damping function is given by

	:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>

	with <math>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, and <math>s_8</math> being adjustable parameters.		with <math>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, and <math>s_8</math> being adjustable parameters. As before, the parameters {{TAG\|VDW_RADIUS}} and {{TAG\|VDW_CNRADIUS}} can be used to change the default values for the cutoff radii.
	~~This variant of DFT-D3 method (DFT-D3(BJ)) is invoked by setting {{TAG\|IVDW}}=12~~. As before, the parameters {{TAG\|VDW_RADIUS}} and {{TAG\|VDW_CNRADIUS}} can be used to change the default values for the cutoff radii. ~~The~~ parameters of the damping function can be controlled using the following tags:
			Optionally, the parameters of the damping function can be controlled using the following {{FILE\|INCAR}} tags:

	*{{TAG\|VDW_S8}}=[real]		*{{TAG\|VDW_S8}}=[real]
Line 26:		Line 33:

	{{NB\|mind\|		{{NB\|mind\|
	*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/ and follow the link "List of parametrized functionals").		*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/ and follow the link "List of parametrized functionals".
	*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited. Also carefully check the more extensive list of references found on https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/.}}		*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited. Also carefully check the more extensive list of references found on https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/.}}

Kresse: Link to Grimmes Web page updated

2024-07-05T13:14:24Z

Link to Grimmes Web page updated

← Older revision		Revision as of 13:14, 5 July 2024
Line 26:		Line 26:

	{{NB\|mind\|		{{NB\|mind\|
	*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.~~chemiebn~~.uni-bonn.de/~~pctc~~/~~mulliken-center~~/software/dft-d3/~~dft-d3~~.		*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/ and follow the link "List of parametrized functionals").
	*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}		*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited. Also carefully check the more extensive list of references found on https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/.}}

	== Related tags and articles ==		== Related tags and articles ==

Schlipf: /* Related tags and articles */

2024-06-13T10:23:31Z

Ftran at 15:05, 12 October 2023

2023-10-12T15:05:00Z

← Older revision		Revision as of 15:05, 12 October 2023
Line 25:		Line 25:
	*{{TAG\|VDW_A2}}=[real]		*{{TAG\|VDW_A2}}=[real]

	{{NB\|mind\|The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.}}		{{NB\|mind\|
	~~{{NB\|mind\|~~The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}		*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.
			*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}

	== Related tags and articles ==		== Related tags and articles ==

Ftran at 19:44, 1 February 2023

2023-02-01T19:44:41Z

← Older revision		Revision as of 19:44, 1 February 2023
Line 36:		Line 36:
	{{TAG\|VDW_A2}},		{{TAG\|VDW_A2}},
	{{TAG\|IVDW}},		{{TAG\|IVDW}},
	{{TAG\|DFT-D2~~}},~~		{{TAG\|DFT-D2}}
	~~{{TAG\|Tkatchenko-Scheffler method}},~~
	~~{{TAG\|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},~~
	~~{{TAG\|Self-consistent screening in Tkatchenko-Scheffler method}},~~
	~~{{TAG\|Many-body dispersion energy}},~~
	~~{{TAG\|dDsC dispersion correction~~}}

	== References ==		== References ==

Ftran at 14:54, 25 January 2023

2023-01-25T14:54:57Z

← Older revision		Revision as of 14:54, 25 January 2023
Line 25:		Line 25:
	*{{TAG\|VDW_A2}}=[real]		*{{TAG\|VDW_A2}}=[real]

	{{NB\|mind\|The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.}}		{{NB\|mind\|The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.}}
	{{NB\|mind\|The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}		{{NB\|mind\|The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}

Ftran at 14:52, 25 January 2023

2023-01-25T14:52:01Z

← Older revision		Revision as of 14:52, 25 January 2023
Line 25:		Line 25:
	*{{TAG\|VDW_A2}}=[real]		*{{TAG\|VDW_A2}}=[real]

	{{NB\|mind\|The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBE0) functionals. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.}}		{{NB\|mind\|The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.}}
	{{NB\|mind\|The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}		{{NB\|mind\|The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}

← Older revision		Revision as of 11:19, 2 March 2026
Line 3:		Line 3:
	:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>		:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>

	Unlike in the ~~method~~ {{TAG\|DFT-D2}}, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. Two variants of DFT-D3, that differ in the damping functions <math>f_{d,n}</math>, are available.		Unlike in the older {{TAG\|DFT-D2}} method, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. Two variants of DFT-D3, that differ in the mathematical form of the damping functions <math>f_{d,n}</math>, are available. More variants of the damping function are available via the [[simple-DFT-D3]] external package ({{TAG\|IVDW}}=15).

	=== DFT-D3(zero) ===		=== DFT-D3(zero) ===
Line 10:		Line 10:
	:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>

	where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, ~~the parameters~~ <math>\alpha_6</math>, <math>\alpha_8~~</math>, <math>s_{R,8}</math> and <math>s_{6}~~</math> are fixed at values ~~of 14, 16, 1~~, and ~~1, respectively, while <math>s_{8}</math> and <math>s_{R~~,~~6}</math> are adjustable parameters~~ whose values depend on the choice of the exchange-correlation functional.		where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, <math>\alpha_6=14</math> and <math>\alpha_8=16</math> are fixed (there is no tag to change their values), and the others parameters, whose default values depend on the choice of the exchange-correlation functional, can be modified as follows:
			*{{TAG\|VDW_S6}}=[real] : scaling <math>s_6</math> of the dipole-dipole dispersion. '''Available since VASP.6.6.0'''.
	~~Optionally~~, ~~the following parameters~~ can be ~~defined in the {{FILE\|INCAR}} file (the given values are the default ones)~~:		*{{TAG\|VDW_S8}}=[real] : scaling <math>s_8</math> of the dipole-quadrupole dispersion
			*{{TAG\|VDW_SR}}=[real] : radii scaling <math>s_{r,6}</math> in the dipole-dipole damping function
	*{{TAG\|~~VDW_RADIUS~~}}=~~50.2~~ : ~~cutoff radius (in~~ <math>~~\AA~~</math>~~) for pair interactions considered in~~ the ~~equation of <math> E_{\mathrm{disp}}</math>~~		*{{TAG\|VDW_SR8}}=[real] : radii scaling <math>s_{r,8}</math> in the dipole-quadrupole damping function. '''Available since VASP.6.6.0'''.
	*{{TAG\|~~VDW_CNRADIUS~~}}=~~20.0~~ : ~~cutoff radius (in~~ <math>~~\AA~~</math>~~) for the calculation~~ of the ~~coordination numbers~~		*{{TAG\|VDW_RADIUS}}=[real] : two-body interaction cutoff (in Å)
	*{{TAG\|~~VDW_S8~~}}=[real] : ~~damping function parameter~~ <math>~~s_8~~</math>		*{{TAG\|VDW_CNRADIUS}}=[real] : coordination number cutoff (in Å)
	*{{TAG\|~~VDW_SR~~}}=[real] : ~~damping function parameter~~ <math>s_{R,6}</math>

	=== DFT-D3(BJ) ===		=== DFT-D3(BJ) ===
	In the Becke-Johnson (BJ) damping variant of DFT-D3,{{cite\|grimme:jcc:11}}, invoked by setting {{TAG\|IVDW}}=12, the damping function is given by		In the rational Becke-Johnson (BJ) damping variant of DFT-D3,{{cite\|grimme:jcc:11}}, invoked by setting {{TAG\|IVDW}}=12, the damping function is given by

	:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>

	~~with~~ <math>s_6=1</math> ~~and~~ <math>~~a_1~~</math>, <math>~~a_2~~</math>, and <math>~~s_8~~</math> ~~being adjustable~~ parameters~~. As before~~, ~~the parameters~~ {{TAG\|~~VDW_RADIUS~~}} ~~and~~ {{TAG\|~~VDW_CNRADIUS~~}} ~~can be used to change the default values for~~ the ~~cutoff radii.~~		where <math>s_6</math>, <math>s_8</math>, <math>a_1</math>, and <math>a_2</math> are parameters whose default values depend on the choice of the exchange-correlation functional, but can also be modified as follows:
			*{{TAG\|VDW_S6}}=[real] : scaling <math>s_6</math> of the dipole-dipole dispersion. '''Available since VASP.6.6.0'''.
	~~Optionally, the parameters of the damping function can be controlled using the following~~ {{~~FILE~~\|~~INCAR~~}} ~~tags~~:		*{{TAG\|VDW_S8}}=[real] : scaling <math>s_8</math> of the dipole-quadrupole dispersion
			*{{TAG\|VDW_A1}}=[real] : scaling <math>a_{1}</math> of the critical radii
	*{{TAG\|~~VDW_S8~~}}=[real]		*{{TAG\|VDW_A2}}=[real] : offset <math>a_{2}</math> of the critical radii
	*{{TAG\|~~VDW_A1~~}}=[real]		*{{TAG\|VDW_RADIUS}}=[real] : two-body interaction cutoff (in Å)
	*{{TAG\|~~VDW_A2~~}}=[real]		*{{TAG\|VDW_CNRADIUS}}=[real] : coordination number cutoff (in Å)

	{{NB\|mind\|		{{NB\|mind\|
Line 37:		Line 36:

	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|~~VDW_RADIUS~~}},		{{TAG\|IVDW}},
	{{TAG\|~~VDW_CNRADIUS~~}},		{{TAG\|VDW_S6}},
	{{TAG\|VDW_S8}},		{{TAG\|VDW_S8}},
	{{TAG\|VDW_SR}},		{{TAG\|VDW_SR}},
			{{TAG\|VDW_SR8}},
	{{TAG\|VDW_A1}},		{{TAG\|VDW_A1}},
	{{TAG\|VDW_A2}},		{{TAG\|VDW_A2}},
	{{TAG\|~~IVDW~~}},		{{TAG\|VDW_RADIUS}},
	{{TAG\|DFT-D2}},		{{TAG\|VDW_CNRADIUS}},
	~~{{TAG\|~~DFT-~~ulg}}~~,		[[DFT-D2]],
	[[DFT-D4]]		[[simple-DFT-D3]],
			[[DFT-D4]],
			[[DFT-ulg]]

	== References ==		== References ==

← Older revision		Revision as of 15:01, 24 February 2025
Line 1:		Line 1:
	In the DFT-D3 method of Grimme et al.{{cite\|grimme:jcp:10}}, the following expression for the vdW-dispersion energy-correction term is used:		In the DFT-D3 method of Grimme et al.{{cite\|grimme:jcp:10}}, the following expression for the vdW dispersion energy-correction term is used:

	:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>		:<math> E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>

	Unlike in the method {{TAG\|DFT-D2}}, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are ~~adjusted~~ on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. In the zero-damping variant of ~~the~~ DFT-D3 ~~method (DFT-D3(zero))~~, the damping function reads:		Unlike in the method {{TAG\|DFT-D2}}, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. Two variants of DFT-D3, that differ in the damping functions <math>f_{d,n}</math>, are available.

			=== DFT-D3(zero) ===
			In the zero-damping variant of DFT-D3,{{cite\|grimme:jcp:10}} invoked by setting {{TAG\|IVDW}}=11, the damping function reads

	:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>

	where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, the parameters <math>\alpha_6</math>, <math>\alpha_8</math>, <math>s_{R,8}</math> and <math>s_{6}</math> are fixed at values of 14, 16, 1, and 1, respectively, while <math>s_{8}</math> and <math>s_{R,6}</math> are adjustable parameters whose values depend on the choice of the exchange-correlation functional. ~~The DFT-D3(zero) method is invoked by setting {{TAG\|IVDW}}=11.~~ Optionally, the following parameters can be ~~user-~~defined (the given values are the default ones):		where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, the parameters <math>\alpha_6</math>, <math>\alpha_8</math>, <math>s_{R,8}</math> and <math>s_{6}</math> are fixed at values of 14, 16, 1, and 1, respectively, while <math>s_{8}</math> and <math>s_{R,6}</math> are adjustable parameters whose values depend on the choice of the exchange-correlation functional.

			Optionally, the following parameters can be defined in the {{FILE\|INCAR}} file (the given values are the default ones):

	*{{TAG\|VDW_RADIUS}}=50.2 : cutoff radius (in <math>\AA</math>) for pair interactions considered in the equation of <math> E_{\mathrm{disp}}</math>		*{{TAG\|VDW_RADIUS}}=50.2 : cutoff radius (in <math>\AA</math>) for pair interactions considered in the equation of <math> E_{\mathrm{disp}}</math>
Line 14:		Line 19:
	*{{TAG\|VDW_SR}}=[real] : damping function parameter <math>s_{R,6}</math>		*{{TAG\|VDW_SR}}=[real] : damping function parameter <math>s_{R,6}</math>

	~~Alternatively,~~ the Becke-Johnson (BJ) damping ~~can be used in the~~ DFT-D3 ~~method~~{{cite\|grimme:jcc:11}}:		=== DFT-D3(BJ) ===
			In the Becke-Johnson (BJ) damping variant of DFT-D3,{{cite\|grimme:jcc:11}}, invoked by setting {{TAG\|IVDW}}=12, the damping function is given by

	:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>		:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>

	with <math>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, and <math>s_8</math> being adjustable parameters.		with <math>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, and <math>s_8</math> being adjustable parameters. As before, the parameters {{TAG\|VDW_RADIUS}} and {{TAG\|VDW_CNRADIUS}} can be used to change the default values for the cutoff radii.
	~~This variant of DFT-D3 method (DFT-D3(BJ)) is invoked by setting {{TAG\|IVDW}}=12~~. As before, the parameters {{TAG\|VDW_RADIUS}} and {{TAG\|VDW_CNRADIUS}} can be used to change the default values for the cutoff radii. ~~The~~ parameters of the damping function can be controlled using the following tags:
			Optionally, the parameters of the damping function can be controlled using the following {{FILE\|INCAR}} tags:

	*{{TAG\|VDW_S8}}=[real]		*{{TAG\|VDW_S8}}=[real]
Line 26:		Line 33:

	{{NB\|mind\|		{{NB\|mind\|
	*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/ and follow the link "List of parametrized functionals").		*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/ and follow the link "List of parametrized functionals".
	*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited. Also carefully check the more extensive list of references found on https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/.}}		*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited. Also carefully check the more extensive list of references found on https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/.}}

← Older revision		Revision as of 10:23, 13 June 2024
Line 37:		Line 37:
	{{TAG\|VDW_A2}},		{{TAG\|VDW_A2}},
	{{TAG\|IVDW}},		{{TAG\|IVDW}},
	{{TAG\|DFT-D2}}		{{TAG\|DFT-D2}},
			[[DFT-D4]]

	== References ==		== References ==

← Older revision		Revision as of 15:05, 12 October 2023
Line 25:		Line 25:
	*{{TAG\|VDW_A2}}=[real]		*{{TAG\|VDW_A2}}=[real]

	{{NB\|mind\|The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.}}		{{NB\|mind\|
	~~{{NB\|mind\|~~The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}		*The default values for the damping function parameters are available for several {{TAG\|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG\|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals\|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals\|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG\|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.
			*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite\|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite\|grimme:jcp:10}} and {{cite\|grimme:jcc:11}} should also be cited.}}

	== Related tags and articles ==		== Related tags and articles ==

← Older revision		Revision as of 19:44, 1 February 2023
Line 36:		Line 36:
	{{TAG\|VDW_A2}},		{{TAG\|VDW_A2}},
	{{TAG\|IVDW}},		{{TAG\|IVDW}},
	{{TAG\|DFT-D2~~}},~~		{{TAG\|DFT-D2}}
	~~{{TAG\|Tkatchenko-Scheffler method}},~~
	~~{{TAG\|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},~~
	~~{{TAG\|Self-consistent screening in Tkatchenko-Scheffler method}},~~
	~~{{TAG\|Many-body dispersion energy}},~~
	~~{{TAG\|dDsC dispersion correction~~}}

	== References ==		== References ==