Category:Van der Waals functionals - Revision history

Csheldon at 14:18, 27 February 2025

2025-02-27T14:18:23Z

← Older revision		Revision as of 14:18, 27 February 2025
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	== Types of approximations ==		== Types of approximations ==
	=== Atom-pairwise methods ===		=== Atom-pairwise methods ===
	[[File:Dft+d.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) and quadrupole-dipole interactions (purple arrows). All of these terms are pairwise. Adapted from Fig.2 in {{cite\|hermann:cr:2017}}.]]		[[File:Dft+d.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) and quadrupole-dipole interactions (purple arrows). All of these terms are pairwise. Adapted from Fig. 2 in Ref. {{cite\|hermann:cr:2017}}.]]
	They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:		They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:
	:<math>		:<math>
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	=== Many-body dispersion methods ===		=== Many-body dispersion methods ===
	[[File:Mbd.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) in many-body dispersions include the previously considered 2-body (pairwise) terms shown with purple arrows, in addition to the 3-, 4-, N-body dipole interaction terms shown with green arrows. Adapted from Fig.2 in {{cite\|hermann:cr:2017}}.]]		[[File:Mbd.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) in many-body dispersions include the previously considered 2-body (pairwise) terms shown with purple arrows, in addition to the 3-, 4-, N-body dipole interaction terms shown with green arrows. Adapted from Fig. 2 in Ref. {{cite\|hermann:cr:2017}}.]]
	These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:		These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:
	:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.		:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.
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	=== Nonlocal vdW-DF functionals ===		=== Nonlocal vdW-DF functionals ===
	[[File:Non_local_dft.png\|300px\|thumb\|Nonlocal DFT interaction (purple arrows) between pairwise dipole fluctuations in the density. Adapted from Fig.2 in {{cite\|hermann:cr:2017}}.]]		[[File:Non_local_dft.png\|300px\|thumb\|Nonlocal DFT interaction (purple arrows) between pairwise dipole fluctuations in the density. Adapted from Fig. 2 in Ref. {{cite\|hermann:cr:2017}}.]]
	These are density functionals that require a double spatial integration and are, therefore, nonlocal:		These are density functionals that require a double spatial integration and are, therefore, nonlocal:
	:<math>		:<math>

Csheldon at 14:17, 27 February 2025

2025-02-27T14:17:48Z

← Older revision		Revision as of 14:17, 27 February 2025
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	== Types of approximations ==		== Types of approximations ==
	=== Atom-pairwise methods ===		=== Atom-pairwise methods ===
	[[File:Dft+d.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) and quadrupole-dipole interactions (purple arrows). All of these terms are pairwise. Adapted from {{cite\|hermann:cr:2017}}.]]		[[File:Dft+d.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) and quadrupole-dipole interactions (purple arrows). All of these terms are pairwise. Adapted from Fig.2 in {{cite\|hermann:cr:2017}}.]]
	They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:		They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:
	:<math>		:<math>
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	=== Many-body dispersion methods ===		=== Many-body dispersion methods ===
	[[File:Mbd.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) in many-body dispersions include the previously considered 2-body (pairwise) terms shown with purple arrows, in addition to the 3-, 4-, N-body dipole interaction terms shown with green arrows. Adapted from {{cite\|hermann:cr:2017}}.]]		[[File:Mbd.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) in many-body dispersions include the previously considered 2-body (pairwise) terms shown with purple arrows, in addition to the 3-, 4-, N-body dipole interaction terms shown with green arrows. Adapted from Fig.2 in {{cite\|hermann:cr:2017}}.]]
	These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:		These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:
	:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.		:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.
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	=== Nonlocal vdW-DF functionals ===		=== Nonlocal vdW-DF functionals ===
	[[File:Non_local_dft.png\|300px\|thumb\|Nonlocal DFT interaction (purple arrows) between pairwise dipole fluctuations in the density. Adapted from {{cite\|hermann:cr:2017}}.]]		[[File:Non_local_dft.png\|300px\|thumb\|Nonlocal DFT interaction (purple arrows) between pairwise dipole fluctuations in the density. Adapted from Fig.2 in {{cite\|hermann:cr:2017}}.]]
	These are density functionals that require a double spatial integration and are, therefore, nonlocal:		These are density functionals that require a double spatial integration and are, therefore, nonlocal:
	:<math>		:<math>

Csheldon at 14:17, 27 February 2025

2025-02-27T14:17:07Z

← Older revision		Revision as of 14:17, 27 February 2025
Line 7:		Line 7:
	== Types of approximations ==		== Types of approximations ==
	=== Atom-pairwise methods ===		=== Atom-pairwise methods ===
	[[File:Dft+d.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) and quadrupole-dipole interactions (purple arrows). All of these terms are pairwise.]]		[[File:Dft+d.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) and quadrupole-dipole interactions (purple arrows). All of these terms are pairwise. Adapted from {{cite\|hermann:cr:2017}}.]]
	They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:		They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:
	:<math>		:<math>
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	=== Many-body dispersion methods ===		=== Many-body dispersion methods ===
	[[File:Mbd.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) in many-body dispersions include the previously considered 2-body (pairwise) terms shown with purple arrows, in addition to the 3-, 4-, N-body dipole interaction terms shown with green arrows.]]		[[File:Mbd.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) in many-body dispersions include the previously considered 2-body (pairwise) terms shown with purple arrows, in addition to the 3-, 4-, N-body dipole interaction terms shown with green arrows. Adapted from {{cite\|hermann:cr:2017}}.]]
	These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:		These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:
	:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.		:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.
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	=== Nonlocal vdW-DF functionals ===		=== Nonlocal vdW-DF functionals ===
	[[File:Non_local_dft.png\|300px\|thumb\|Nonlocal DFT interaction (purple arrows) between pairwise dipole fluctuations in the density.]]		[[File:Non_local_dft.png\|300px\|thumb\|Nonlocal DFT interaction (purple arrows) between pairwise dipole fluctuations in the density. Adapted from {{cite\|hermann:cr:2017}}.]]
	These are density functionals that require a double spatial integration and are, therefore, nonlocal:		These are density functionals that require a double spatial integration and are, therefore, nonlocal:
	:<math>		:<math>
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	== References ==		== References ==
	~~<references/>~~

	~~----~~

	[[Category:VASP\|van der Waals]][[Category:Exchange-correlation functionals]]		[[Category:VASP\|van der Waals]][[Category:Exchange-correlation functionals]]

Ftran at 13:07, 27 February 2025

2025-02-27T13:07:39Z

← Older revision		Revision as of 13:07, 27 February 2025
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	=== Nonlocal vdW-DF functionals ===		=== Nonlocal vdW-DF functionals ===
	[[File:Non_local_dft.png\|300px\|thumb\|~~Non-local~~ DFT interaction (purple arrows) between pairwise dipole fluctuations in the density.]]		[[File:Non_local_dft.png\|300px\|thumb\|Nonlocal DFT interaction (purple arrows) between pairwise dipole fluctuations in the density.]]
	These are density functionals that require a double spatial integration and are, therefore, nonlocal:		These are density functionals that require a double spatial integration and are, therefore, nonlocal:
	:<math>		:<math>

Csheldon at 13:02, 27 February 2025

2025-02-27T13:02:58Z

← Older revision		Revision as of 13:02, 27 February 2025
Line 7:		Line 7:
	== Types of approximations ==		== Types of approximations ==
	=== Atom-pairwise methods ===		=== Atom-pairwise methods ===
			[[File:Dft+d.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) and quadrupole-dipole interactions (purple arrows). All of these terms are pairwise.]]
	They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:		They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:
	:<math>		:<math>
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	*[[DDsC dispersion correction]]{{cite\|steinmann:jcp:11}}{{cite\|steinmann:jctc:11}}		*[[DDsC dispersion correction]]{{cite\|steinmann:jcp:11}}{{cite\|steinmann:jctc:11}}
	*[[DFT-ulg]]{{cite\|kim:jpcl:2012}}		*[[DFT-ulg]]{{cite\|kim:jpcl:2012}}
			<div style="clear:both;"></div>

	=== Many-body dispersion methods ===		=== Many-body dispersion methods ===
			[[File:Mbd.png\|300px\|thumb\|Dipole-dipole interactions between atoms (black dots) in many-body dispersions include the previously considered 2-body (pairwise) terms shown with purple arrows, in addition to the 3-, 4-, N-body dipole interaction terms shown with green arrows.]]
	These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:		These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency <math>\omega</math> involving the frequency-dependent polarizability <math>{\mathbf{A}}_{LR}</math>:
	:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.		:<math>E_{\mathrm{c,disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \}.
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	*[[Many-body dispersion energy with fractionally ionic model for polarizability]]{{cite\|gould:jctc:2016_a}}{{cite\|gould:jctc:2016_b}}		*[[Many-body dispersion energy with fractionally ionic model for polarizability]]{{cite\|gould:jctc:2016_a}}{{cite\|gould:jctc:2016_b}}
	*[[LIBMBD_METHOD\|Library libMBD of many-body dispersion methods]]{{cite\|libmbd_1}}{{cite\|libmbd_2}}{{cite\|hermann:jcp:2023}}		*[[LIBMBD_METHOD\|Library libMBD of many-body dispersion methods]]{{cite\|libmbd_1}}{{cite\|libmbd_2}}{{cite\|hermann:jcp:2023}}
			<div style="clear:both;"></div>

	=== Nonlocal vdW-DF functionals ===		=== Nonlocal vdW-DF functionals ===
			[[File:Non_local_dft.png\|300px\|thumb\|Non-local DFT interaction (purple arrows) between pairwise dipole fluctuations in the density.]]
	These are density functionals that require a double spatial integration and are, therefore, nonlocal:		These are density functionals that require a double spatial integration and are, therefore, nonlocal:
	:<math>		:<math>
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	where the kernel <math>\Phi</math> depends on the electronic density <math>n</math>, its derivative <math>\nabla n</math> as well as on the interelectronic distance <math>\left\vert\bf{r}-\bf{r}'\right\vert</math>. The nonlocal functionals are more expensive to calculate than semilocal functionals, however, they are efficiently implemented by using FFTs {{cite\|romanperez:prl:09}}. These methods are selected with the {{TAG\|LUSE_VDW}} and {{TAG\|IVDW_NL}} tags.		where the kernel <math>\Phi</math> depends on the electronic density <math>n</math>, its derivative <math>\nabla n</math> as well as on the interelectronic distance <math>\left\vert\bf{r}-\bf{r}'\right\vert</math>. The nonlocal functionals are more expensive to calculate than semilocal functionals, however, they are efficiently implemented by using FFTs {{cite\|romanperez:prl:09}}. These methods are selected with the {{TAG\|LUSE_VDW}} and {{TAG\|IVDW_NL}} tags.
	*[[Nonlocal vdW-DF functionals]]		*[[Nonlocal vdW-DF functionals]]
			<div style="clear:both;"></div>

	== References ==		== References ==

Ftran at 11:38, 27 February 2025

2025-02-27T11:38:10Z

← Older revision		Revision as of 11:38, 27 February 2025
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	The semilocal (SL) and hybrid exchange-correlation functionals do not include the London dispersion forces. Therefore, they can not be applied reliably on systems where the London dispersion forces play an important role. To account more properly for the London dispersion forces in DFT, a correlation dispersion term can be added to the semilocal or hybrid functional. This leads to the so-called '''van der Waals functionals''':		The semilocal (SL) and hybrid exchange-correlation functionals do not include the London dispersion forces. Therefore, they can not be applied reliably on systems where the London dispersion forces play an important role. To account more properly for the London dispersion forces in DFT, a correlation dispersion term can be added to the semilocal or hybrid functional.{{cite\|grimme:cr:2016}}{{cite\|hermann:cr:2017}} This leads to the so-called '''van der Waals functionals''':
	:<math>		:<math>
	E_{\text{xc}}^{\text{vdW}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.		E_{\text{xc}}^{\text{vdW}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.

Ftran at 11:36, 27 February 2025

2025-02-27T11:36:20Z

← Older revision		Revision as of 11:36, 27 February 2025
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	The semilocal (SL) and hybrid exchange-correlation functionals do not include the London dispersion forces. Therefore, they can not be applied reliably on systems where the London dispersion forces play an important role. To account more properly for the London dispersion forces in DFT, a correlation dispersion term can be added to the semilocal or hybrid functional. This leads to the so-called '''van der Waals functionals''':		The semilocal (SL) and hybrid exchange-correlation functionals do not include the London dispersion forces. Therefore, they can not be applied reliably on systems where the London dispersion forces play an important role. To account more properly for the London dispersion forces in DFT, a correlation dispersion term can be added to the semilocal or hybrid functional. This leads to the so-called '''van der Waals functionals''':
	:<math>		:<math>
	E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.		E_{\text{xc}}^{\text{vdW}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.
	</math>		</math>
	There are essentially three types of dispersion terms <math>E_{\text{c,disp}}</math> that are available in VASP, and a brief sketch of them is given below along with links to pages that provide more detail. Note that [[LIBMBD_METHOD\|libMBD]] is an external package that provides the Tkatchenko-Scheffler atom-pairwise methods and their many-body dispersion extensions.		There are essentially three types of dispersion terms <math>E_{\text{c,disp}}</math> that are available in VASP, and a brief sketch of them is given below along with links to pages that provide more detail. Note that [[LIBMBD_METHOD\|libMBD]] is an external package that provides the Tkatchenko-Scheffler atom-pairwise methods and their many-body dispersion extensions.

Ftran at 14:51, 26 February 2025

2025-02-26T14:51:09Z

← Older revision		Revision as of 14:51, 26 February 2025
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	There are essentially three types of dispersion terms <math>E_{\text{c,disp}}</math> that are available in VASP, and a brief sketch of them is given below along with links to pages that provide more detail. Note that [[LIBMBD_METHOD\|libMBD]] is an external package that provides the Tkatchenko-Scheffler atom-pairwise methods and their many-body dispersion extensions.		There are essentially three types of dispersion terms <math>E_{\text{c,disp}}</math> that are available in VASP, and a brief sketch of them is given below along with links to pages that provide more detail. Note that [[LIBMBD_METHOD\|libMBD]] is an external package that provides the Tkatchenko-Scheffler atom-pairwise methods and their many-body dispersion extensions.

	== ~~Approximations~~ ==		== Types of approximations ==
	=== Atom-pairwise methods ===		=== Atom-pairwise methods ===
	They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:		They consist of a sum over the atoms pairs <math>A</math>-<math>B</math>:

Ftran at 15:57, 25 February 2025

2025-02-25T15:57:46Z

← Older revision		Revision as of 15:57, 25 February 2025
Line 1:		Line 1:
	The semilocal and hybrid exchange-correlation functionals do not include the London dispersion forces. Therefore, they can not be applied reliably on systems where the London dispersion forces play an important role. To account more properly for the London dispersion forces in DFT, a correlation dispersion term can be added to the semilocal or hybrid functional. This leads to the so-called '''van der Waals functionals''':		The semilocal (SL) and hybrid exchange-correlation functionals do not include the London dispersion forces. Therefore, they can not be applied reliably on systems where the London dispersion forces play an important role. To account more properly for the London dispersion forces in DFT, a correlation dispersion term can be added to the semilocal or hybrid functional. This leads to the so-called '''van der Waals functionals''':
	:<math>		:<math>
	E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.		E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.
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	E_{\text{c,disp}} = -\sum_{A<B}\sum_{n=6,8,10,\ldots}f_{n}^{\text{damp}}(R_{AB})\frac{C_{n}^{AB}}{R_{AB}^{n}},		E_{\text{c,disp}} = -\sum_{A<B}\sum_{n=6,8,10,\ldots}f_{n}^{\text{damp}}(R_{AB})\frac{C_{n}^{AB}}{R_{AB}^{n}},
	</math>		</math>
	where <math>C_{n}^{AB}</math> are the dispersion coefficients, <math>R_{AB}</math> is the distance between atoms <math>A</math> and <math>B</math>, and <math>f_{n}^{\text{damp}}</math> is a damping function. ~~Many~~ variants of such atom-pair corrections exist and the most popular of them, listed below, are available in VASP and are selected with the {{TAG\|IVDW}} tag.		where <math>C_{n}^{AB}</math> are the dispersion coefficients, <math>R_{AB}</math> is the distance between atoms <math>A</math> and <math>B</math>, and <math>f_{n}^{\text{damp}}</math> is a damping function. Several variants of such atom-pair corrections exist and the most popular of them, listed below, are available in VASP and are selected with the {{TAG\|IVDW}} tag.
	*{{TAG\|IVDW}}
	*[[DFT-D2]]{{cite\|grimme:jcc:06}}		*[[DFT-D2]]{{cite\|grimme:jcc:06}}
	*[[DFT-D3]]{{cite\|grimme:jcp:10}}{{cite\|grimme:jcc:11}}		*[[DFT-D3]]{{cite\|grimme:jcp:10}}{{cite\|grimme:jcc:11}}
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	</math>		</math>
	These methods, listed below, are selected with the {{TAG\|IVDW}} tag.		These methods, listed below, are selected with the {{TAG\|IVDW}} tag.
	*{{TAG\|IVDW}}
	*[[Many-body dispersion energy]]{{cite\|tkatchenko:prl:12}}{{cite\|ambrosetti:jcp:14}}		*[[Many-body dispersion energy]]{{cite\|tkatchenko:prl:12}}{{cite\|ambrosetti:jcp:14}}
	*[[Many-body dispersion energy with fractionally ionic model for polarizability]]{{cite\|gould:jctc:2016_a}}{{cite\|gould:jctc:2016_b}}		*[[Many-body dispersion energy with fractionally ionic model for polarizability]]{{cite\|gould:jctc:2016_a}}{{cite\|gould:jctc:2016_b}}
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	</math>		</math>
	where the kernel <math>\Phi</math> depends on the electronic density <math>n</math>, its derivative <math>\nabla n</math> as well as on the interelectronic distance <math>\left\vert\bf{r}-\bf{r}'\right\vert</math>. The nonlocal functionals are more expensive to calculate than semilocal functionals, however, they are efficiently implemented by using FFTs {{cite\|romanperez:prl:09}}. These methods are selected with the {{TAG\|LUSE_VDW}} and {{TAG\|IVDW_NL}} tags.		where the kernel <math>\Phi</math> depends on the electronic density <math>n</math>, its derivative <math>\nabla n</math> as well as on the interelectronic distance <math>\left\vert\bf{r}-\bf{r}'\right\vert</math>. The nonlocal functionals are more expensive to calculate than semilocal functionals, however, they are efficiently implemented by using FFTs {{cite\|romanperez:prl:09}}. These methods are selected with the {{TAG\|LUSE_VDW}} and {{TAG\|IVDW_NL}} tags.
	*{{TAG\|LUSE_VDW}}
	*{{TAG\|IVDW_NL}}
	*[[Nonlocal vdW-DF functionals]]		*[[Nonlocal vdW-DF functionals]]

Ftran at 15:43, 25 February 2025

2025-02-25T15:43:03Z

← Older revision		Revision as of 15:43, 25 February 2025
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	E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.		E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.
	</math>		</math>
	There are essentially three types of dispersion terms <math>E_{\text{c,disp}}</math> that are available in VASP~~. A~~ brief sketch of ~~the methods~~ is given below along with links to pages that provide more detail. Note that [[LIBMBD_METHOD\|libMBD]] is an external package that provides the Tkatchenko-Scheffler atom-pairwise methods and their many-body dispersion extensions.		There are essentially three types of dispersion terms <math>E_{\text{c,disp}}</math> that are available in VASP, and a brief sketch of them is given below along with links to pages that provide more detail. Note that [[LIBMBD_METHOD\|libMBD]] is an external package that provides the Tkatchenko-Scheffler atom-pairwise methods and their many-body dispersion extensions.

	== Approximations ==		== Approximations ==