Category:Exchange-correlation functionals - Revision history

Ftran at 16:29, 13 March 2026

2026-03-13T16:29:58Z

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	*[[:Category:Hybrid_functionals\|Hybrid functionals]]		*[[:Category:Hybrid_functionals\|Hybrid functionals]]
			*[[:Hybrid_functionals:_formalism\|Hybrid_functionals - formalism]]

	=== Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI) ===		=== Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI) ===

Ftran: /* Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI) */

2026-03-06T14:40:21Z

Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI)

← Older revision		Revision as of 14:40, 6 March 2026
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	=== Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI) ===		=== Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI) ===
	In these methods the minimization of the exact-exchange HF energy expression is done with respect to the electron density <math>n</math>, instead of with respect to the orbitals <math>\psi_i</math>. That means that a local (in the sense of multiplicative) KS potential is calculated. EXX-OEP{{cite\|Sharp:pr:1992}} provides the exact potential, however, performing such calculations is non-trivial in particular since the unoccupied orbitals are required. LHF{{cite\|dellasala:jcp:2001}} is an approximation to EXX-OEP that alleviates the use of unoccupied orbitals, while KLI{{cite\|krieger:pra:1992}} is a further approximation.		In these methods the minimization of the exact-exchange HF energy expression is done with respect to the electron density <math>n</math>, instead of with respect to the orbitals <math>\psi_i</math>. That means that a local (in the sense of multiplicative) KS potential is calculated. EXX-OEP{{cite\|Sharp:pr:1992}} provides the exact exchange potential, however, performing such calculations is non-trivial in particular since the unoccupied orbitals are required. LHF{{cite\|dellasala:jcp:2001}} is an approximation to EXX-OEP that alleviates the use of unoccupied orbitals, while KLI{{cite\|krieger:pra:1992}} is a further approximation.

	These methods are available in VASP, but not documented.		These methods are available in VASP, but not documented. Note, however, that the tests SiC_OEP and SiC_OEPR of the testsuite use these methods.

	=== Density functional theory plus U (DFT+U) ===		=== Density functional theory plus U (DFT+U) ===

Ftran at 14:26, 6 March 2026

2026-03-06T14:26:16Z

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	Note that depending on the type of approximation for <math>E_{\rm xc}</math> the potential <math>\hat{v}_{\rm xc}</math> is calculated either as the derivative with respect to the density, <math>v_{\rm xc}=\delta E_{\rm xc}/\delta n</math> (KS scheme{{cite\|kohn:pr:1965}}), or as the derivative with respect to the orbitals, <math>\hat{v}_{\mathrm{xc}}\psi_{i}=\delta E_{\mathrm{xc}}/\delta\psi_{i}^{*}</math> (generalized KS scheme{{cite\|seidl:prb:96}}).		Note that depending on the type of approximation for <math>E_{\rm xc}</math> the potential <math>\hat{v}_{\rm xc}</math> is calculated either as the derivative with respect to the density, <math>v_{\rm xc}=\delta E_{\rm xc}/\delta n</math> (KS scheme{{cite\|kohn:pr:1965}}), or as the derivative with respect to the orbitals, <math>\hat{v}_{\mathrm{xc}}\psi_{i}=\delta E_{\mathrm{xc}}/\delta\psi_{i}^{*}</math> (generalized KS scheme{{cite\|seidl:prb:96}}).

	Several hundreds of approximations for the '''exchange and correlation''' have been proposed.{{cite\|libxc_list}}{{cite\|dellasala:ijqc:2016}}{{cite\|mardirossian:mp:2017}} They can be classified into families like the local density approximation (LDA), semilocal approximations (generalized gradient approximation ({{TAG\|GGA}}) and {{TAG\|METAGGA}}), or [[:Category:Hybrid functionals\|hybrid]]. There is also the possibility to include a [[:Category:Van der Waals functionals\|van der Waals correction]] or an on-site Coulomb repulsion using [[:Category:DFT+U\|DFT+U]] on top of another functional. The different types of approximations available in VASP are listed below. Also mentioned are the many-body methods for an accurate calculation of the correlation energy, which, however, are not DFT methods.		Several hundreds of approximations for the '''exchange and correlation''' have been proposed.{{cite\|libxc_list}}{{cite\|tran:arxiv:2026}}{{cite\|dellasala:ijqc:2016}}{{cite\|mardirossian:mp:2017}} They can be classified into families like the local density approximation (LDA), semilocal approximations (generalized gradient approximation ({{TAG\|GGA}}) and {{TAG\|METAGGA}}), or [[:Category:Hybrid functionals\|hybrid]]. There is also the possibility to include a [[:Category:Van der Waals functionals\|van der Waals correction]] or an on-site Coulomb repulsion using [[:Category:DFT+U\|DFT+U]] on top of another functional. The different types of approximations available in VASP are listed below. Also mentioned are the many-body methods for an accurate calculation of the correlation energy, which, however, are not DFT methods.

	=== Which exchange-correlation method to choose? ===		=== Which exchange-correlation method to choose? ===
	Among the hundreds of methods available,{{cite\|libxc_list}}{{cite\|~~dellasala~~:~~ijqc~~:~~2016~~}}{{cite\|~~mardirossian~~:mp:~~2017~~}}{{cite\|~~tran~~:~~arxiv~~:~~2026~~}} the choice for the exchange and correlation method should be done by considering the following points:		Among the hundreds of methods available,{{cite\|libxc_list}}{{cite\|tran:arxiv:2026}}{{cite\|dellasala:ijqc:2016}}{{cite\|mardirossian:mp:2017}} the choice for the exchange and correlation method should be done by considering the following points:
	*'''Appropriate for the studied system and property''':		*'''Appropriate for the studied system and property''':
	**Some functionals were constructed without emphasis on a particular property or class of systems, while others were developed specifically for van der Waals interactions, strongly correlated systems, or band gap calculation, for instance.		**Some functionals were constructed without emphasis on a particular property or class of systems, while others were developed specifically for van der Waals interactions, strongly correlated systems, or band gap calculation, for instance.

Ftran: /* Which exchange-correlation method to choose? */

2026-03-06T14:22:21Z

Which exchange-correlation method to choose?

← Older revision		Revision as of 14:22, 6 March 2026
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	=== Which exchange-correlation method to choose? ===		=== Which exchange-correlation method to choose? ===
	Among the hundreds of methods available,{{cite\|libxc_list}}{{cite\|dellasala:ijqc:2016}}{{cite\|mardirossian:mp:2017}} the choice for the exchange and correlation method should be done by considering the following points:		Among the hundreds of methods available,{{cite\|libxc_list}}{{cite\|dellasala:ijqc:2016}}{{cite\|mardirossian:mp:2017}}{{cite\|tran:arxiv:2026}} the choice for the exchange and correlation method should be done by considering the following points:
	*'''Appropriate for the studied system and property''':		*'''Appropriate for the studied system and property''':
	**Some functionals were constructed without emphasis on a particular property or class of systems, while others were developed specifically for van der Waals interactions, strongly correlated systems, or band gap calculation, for instance.		**Some functionals were constructed without emphasis on a particular property or class of systems, while others were developed specifically for van der Waals interactions, strongly correlated systems, or band gap calculation, for instance.

Ftran at 14:16, 6 March 2025

2025-03-06T14:16:14Z

← Older revision		Revision as of 14:16, 6 March 2025
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	E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{SL}} + E_{\mathrm{c}}^{\mathrm{SL}}		E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{SL}} + E_{\mathrm{c}}^{\mathrm{SL}}
	</math>		</math>
	where <math>\alpha</math> determines the relative amount of HF and semilocal exchange. The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like ~~HSE~~ are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).		where <math>\alpha</math> determines the relative amount of HF and semilocal exchange. The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or either at short or long range (called screened or range-separated hybrids). From the practical point of view, the short-range hybrid functionals like HSE06{{cite\|krukau:jcp:06}} are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).

	The HF method, where <math>E_{\mathrm{xc}}=E_{\mathrm{x}}^{\mathrm{HF}}</math>, is not accurate since correlation is entirely missing, however it is the basis of the many-body methods.		The HF method, where <math>E_{\mathrm{xc}}=E_{\mathrm{x}}^{\mathrm{HF}}</math>, is not accurate since correlation is entirely missing, however it is the basis of the many-body methods.

Ftran: /* Density functional theory plus U (DFT+U) */

2025-02-28T16:02:34Z

Density functional theory plus U (DFT+U)

← Older revision		Revision as of 16:02, 28 February 2025
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	=== Density functional theory plus U (DFT+U) ===		=== Density functional theory plus U (DFT+U) ===
	The semilocal approximations, LDA and GGA in particular, often fail to describe systems with localized (strongly correlated) <math>d</math> or <math>f</math> electrons (this manifests itself primarily in the form of unrealistic one-electron energies or too small magnetic moments). In some cases this can be remedied by introducing on the <math>d</math> or <math>f</math> atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner (<math>E_{\text{HF}}[\hat{n}]</math>), as an on-site replacement of the semilocal functional:		The semilocal approximations, LDA and GGA in particular, often fail to describe systems with localized (strongly correlated) <math>d</math> or <math>f</math> electrons (this manifests itself primarily in the form of unrealistic one-electron energies or too small magnetic moments). In some cases this can be remedied by introducing on the <math>d</math> or <math>f</math> atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner (<math>E_{\text{HF}}[\hat{n}]</math>), as an on-site replacement of the semilocal functional:
	:<math>E_{\text{xc}}^{\text{DFT}+U}[n,\hat{n}] = E_{\text{xc}}^{\text{SL}}[n] + ~~E_{\text{x}}~~^{\text{HF}}[\hat{n}] - E_{\text{dc}}[\hat{n}]</math>		:<math>E_{\text{xc}}^{\text{DFT}+U}[n,\hat{n}] = E_{\text{xc}}^{\text{SL}}[n] + E^{\text{HF}}[\hat{n}] - E_{\text{dc}}[\hat{n}]</math>
	where <math>E_{\text{dc}}[\hat{n}]</math> is the double-counting term, that removes some of the on-site exchange-correlation effects present in <math>E_{\text{xc}}^{\text{SL}}[n]</math>, and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach, known as the DFT+U method (traditionally called LSDA+U,{{cite\|anisimov:prb:91}}) can often be used as a cheap alternative to the much more costly hybrid functionals. Several variants of the DFT+U method exist, differing mostly in the expression for <math>E_{\text{dc}}[\hat{n}]</math>.		where <math>E_{\text{dc}}[\hat{n}]</math> is the double-counting term, that removes some of the on-site exchange-correlation effects present in <math>E_{\text{xc}}^{\text{SL}}[n]</math>, and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach, known as the DFT+U method (traditionally called LSDA+U,{{cite\|anisimov:prb:91}}) can often be used as a cheap alternative to the much more costly hybrid functionals. Several variants of the DFT+U method exist, differing mostly in the expression for <math>E_{\text{dc}}[\hat{n}]</math>.
	*[[:Category:DFT+U\|DFT+U]]		*[[:Category:DFT+U\|DFT+U]]

Ftran: /* Density functional theory plus U (DFT+U) */

2025-02-28T15:59:41Z

Density functional theory plus U (DFT+U)

← Older revision		Revision as of 15:59, 28 February 2025
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	=== Density functional theory plus U (DFT+U) ===		=== Density functional theory plus U (DFT+U) ===
	The semilocal approximations, LDA and GGA in particular, often fail to describe systems with localized (strongly correlated) <math>d</math> or <math>f</math> electrons (this manifests itself primarily in the form of unrealistic one-electron energies or too small magnetic moments). In some cases this can be remedied by introducing on the <math>d</math> or <math>f</math> atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner (<math>E_{\text{HF}}[\hat{n}]</math>), as an on-site replacement of the semilocal functional:		The semilocal approximations, LDA and GGA in particular, often fail to describe systems with localized (strongly correlated) <math>d</math> or <math>f</math> electrons (this manifests itself primarily in the form of unrealistic one-electron energies or too small magnetic moments). In some cases this can be remedied by introducing on the <math>d</math> or <math>f</math> atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner (<math>E_{\text{HF}}[\hat{n}]</math>), as an on-site replacement of the semilocal functional:
	:<math>E_{\text{xc}}^{\text{DFT}+U}[n,\hat{n}] = E_{\text{xc}}^{\text{SL}}[n] + E_{\text{HF}}[\hat{n}] - E_{\text{dc}}[\hat{n}]</math>		:<math>E_{\text{xc}}^{\text{DFT}+U}[n,\hat{n}] = E_{\text{xc}}^{\text{SL}}[n] + E_{\text{x}}^{\text{HF}}[\hat{n}] - E_{\text{dc}}[\hat{n}]</math>
	where <math>E_{\text{dc}}[\hat{n}]</math> is the double-counting term, that removes some of the on-site exchange-correlation effects present in <math>E_{\text{xc}}^{\text{SL}}[n]</math>, and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach, known as the DFT+U method (traditionally called LSDA+U,{{cite\|anisimov:prb:91}}) can often be used as a cheap alternative to the much more costly hybrid functionals. Several variants of the DFT+U method exist, differing mostly in the expression for <math>E_{\text{dc}}[\hat{n}]</math>.		where <math>E_{\text{dc}}[\hat{n}]</math> is the double-counting term, that removes some of the on-site exchange-correlation effects present in <math>E_{\text{xc}}^{\text{SL}}[n]</math>, and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach, known as the DFT+U method (traditionally called LSDA+U,{{cite\|anisimov:prb:91}}) can often be used as a cheap alternative to the much more costly hybrid functionals. Several variants of the DFT+U method exist, differing mostly in the expression for <math>E_{\text{dc}}[\hat{n}]</math>.
	*[[:Category:DFT+U\|DFT+U]]		*[[:Category:DFT+U\|DFT+U]]

Ftran: /* Hartree-Fock (HF) and hybrid functionals */

2025-02-28T13:02:59Z

Hartree-Fock (HF) and hybrid functionals

← Older revision		Revision as of 13:02, 28 February 2025
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	=== Hartree-Fock (HF) and hybrid functionals ===		=== Hartree-Fock (HF) and hybrid functionals ===
	In hybrid functionals the exchange part consists of a linear combination of the '''HF exchange''' and a semilocal (e.g., GGA) functional:		In hybrid functionals{{cite\|becke:jcp:93}} the exchange part consists of a linear combination of the '''HF exchange''' and a semilocal (e.g., GGA) functional:
	:<math>		:<math>
	E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{SL}} + E_{\mathrm{c}}^{\mathrm{SL}}		E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{SL}} + E_{\mathrm{c}}^{\mathrm{SL}}

Ftran at 08:48, 28 February 2025

2025-02-28T08:48:42Z

← Older revision		Revision as of 08:48, 28 February 2025
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	Note that depending on the type of approximation for <math>E_{\rm xc}</math> the potential <math>\hat{v}_{\rm xc}</math> is calculated either as the derivative with respect to the density, <math>v_{\rm xc}=\delta E_{\rm xc}/\delta n</math> (KS scheme{{cite\|kohn:pr:1965}}), or as the derivative with respect to the orbitals, <math>\hat{v}_{\mathrm{xc}}\psi_{i}=\delta E_{\mathrm{xc}}/\delta\psi_{i}^{*}</math> (generalized KS scheme{{cite\|seidl:prb:96}}).		Note that depending on the type of approximation for <math>E_{\rm xc}</math> the potential <math>\hat{v}_{\rm xc}</math> is calculated either as the derivative with respect to the density, <math>v_{\rm xc}=\delta E_{\rm xc}/\delta n</math> (KS scheme{{cite\|kohn:pr:1965}}), or as the derivative with respect to the orbitals, <math>\hat{v}_{\mathrm{xc}}\psi_{i}=\delta E_{\mathrm{xc}}/\delta\psi_{i}^{*}</math> (generalized KS scheme{{cite\|seidl:prb:96}}).

	Several hundreds of approximations for the '''exchange and correlation''' have been proposed.{{cite\|libxc_list}}{{cite\|mardirossian:mp:2017}} They can be classified into families like the local density approximation (LDA), semilocal approximations (generalized gradient approximation ({{TAG\|GGA}}) and {{TAG\|METAGGA}}), or [[:Category:Hybrid functionals\|hybrid]]. There is also the possibility to include a [[:Category:Van der Waals functionals\|van der Waals correction]] or an on-site Coulomb repulsion using [[:Category:DFT+U\|DFT+U]] on top of another functional. The different types of approximations available in VASP are listed. Also mentioned are the many-body methods for an accurate calculation of the correlation energy, which, however, are not DFT methods.		Several hundreds of approximations for the '''exchange and correlation''' have been proposed.{{cite\|libxc_list}}{{cite\|dellasala:ijqc:2016}}{{cite\|mardirossian:mp:2017}} They can be classified into families like the local density approximation (LDA), semilocal approximations (generalized gradient approximation ({{TAG\|GGA}}) and {{TAG\|METAGGA}}), or [[:Category:Hybrid functionals\|hybrid]]. There is also the possibility to include a [[:Category:Van der Waals functionals\|van der Waals correction]] or an on-site Coulomb repulsion using [[:Category:DFT+U\|DFT+U]] on top of another functional. The different types of approximations available in VASP are listed below. Also mentioned are the many-body methods for an accurate calculation of the correlation energy, which, however, are not DFT methods.

	=== Which exchange-correlation method to choose? ===		=== Which exchange-correlation method to choose? ===
			Among the hundreds of methods available,{{cite\|libxc_list}}{{cite\|dellasala:ijqc:2016}}{{cite\|mardirossian:mp:2017}} the choice for the exchange and correlation method should be done by considering the following points:
	~~The~~ choice for the exchange and correlation method should be done by considering the following points:		*'''Appropriate for the studied system and property''':
	*'''~~Literature research~~''':		**Some functionals were constructed without emphasis on a particular property or class of systems, while others were developed specifically for van der Waals interactions, strongly correlated systems, or band gap calculation, for instance.
	**~~Among the hundreds of methods available, some of them~~ were constructed without emphasis on a particular property or class of systems, while others were developed specifically for van der Waals interactions, strongly correlated systems, or band gap calculation, for instance.
	**Therefore, a method should be appropriately chosen according to the information found in the literature.		**Therefore, a method should be appropriately chosen according to the information found in the literature.
	*'''Computational power''':		*'''Computational power''':

Ftran at 08:27, 28 February 2025

2025-02-28T08:27:34Z

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	\left(-\frac{1}{2}\nabla^{2} -\sum_{A}\frac{Z_{A}}{\left\vert{\bf r}-{\bf R}_{A}\right\vert} + \int\frac{n({\bf r'})}{\left\vert{\bf r}-{\bf r'}\right\vert}d^{3}r' + \hat{v}_{\rm xc}({\bf r})\right)\psi_{i}({\bf r}) = \epsilon_{i}\psi_{i}({\bf r}).		\left(-\frac{1}{2}\nabla^{2} -\sum_{A}\frac{Z_{A}}{\left\vert{\bf r}-{\bf R}_{A}\right\vert} + \int\frac{n({\bf r'})}{\left\vert{\bf r}-{\bf r'}\right\vert}d^{3}r' + \hat{v}_{\rm xc}({\bf r})\right)\psi_{i}({\bf r}) = \epsilon_{i}\psi_{i}({\bf r}).
	</math>		</math>
	The only terms in <math>E_{\rm tot}^{\rm DFT}</math> and in the (g)KS equations that are not known exactly are the '''exchange-correlation energy functional''' <math>E_{\rm xc}</math> and '''potential''' <math>\hat{v}_{\rm xc}</math>. Therefore, the accuracy of the calculated properties depends strongly on the approximations used for <math>E_{\rm xc}</math> and <math>\hat{v}_{\rm xc}</math>. The potential <math>\hat{v}_{\rm xc}</math> is calculated either as <math>v_{\rm xc}=\delta E_{\rm xc}/\delta n</math> (KS scheme{{cite\|kohn:pr:1965}}) or as <math>\hat{v}_{\mathrm{xc}}\psi_{i}=\delta E_{\mathrm{xc}}/\delta\psi_{i}^{*}</math> (generalized KS scheme{{cite\|seidl:prb:96}}).		The only terms in <math>E_{\rm tot}^{\rm DFT}</math> and in the (g)KS equations that are not known exactly are the '''exchange-correlation energy functional''' <math>E_{\rm xc}</math> and '''potential''' <math>\hat{v}_{\rm xc}</math>. Therefore, the accuracy of the calculated properties depends strongly on the approximations used for <math>E_{\rm xc}</math> and <math>\hat{v}_{\rm xc}</math>.

	Several hundreds of approximations for the '''exchange and correlation''' have been proposed.{{cite\|libxc_list}} They can be classified into families like the local density approximation (LDA), semilocal approximations (generalized gradient approximation ({{TAG\|GGA}}) and {{TAG\|METAGGA}}), or [[:Category:Hybrid functionals\|hybrid]]. There is also the possibility to include a [[:Category:Van der Waals functionals\|van der Waals correction]] or an on-site Coulomb repulsion using [[:Category:DFT+U\|DFT+U]] on top of another functional. The different types of approximations available in VASP are listed. Also mentioned are the many-body methods for an accurate calculation of the correlation energy, which, however, are not DFT methods.		Note that depending on the type of approximation for <math>E_{\rm xc}</math> the potential <math>\hat{v}_{\rm xc}</math> is calculated either as the derivative with respect to the density, <math>v_{\rm xc}=\delta E_{\rm xc}/\delta n</math> (KS scheme{{cite\|kohn:pr:1965}}), or as the derivative with respect to the orbitals, <math>\hat{v}_{\mathrm{xc}}\psi_{i}=\delta E_{\mathrm{xc}}/\delta\psi_{i}^{*}</math> (generalized KS scheme{{cite\|seidl:prb:96}}).

			Several hundreds of approximations for the '''exchange and correlation''' have been proposed.{{cite\|libxc_list}}{{cite\|mardirossian:mp:2017}} They can be classified into families like the local density approximation (LDA), semilocal approximations (generalized gradient approximation ({{TAG\|GGA}}) and {{TAG\|METAGGA}}), or [[:Category:Hybrid functionals\|hybrid]]. There is also the possibility to include a [[:Category:Van der Waals functionals\|van der Waals correction]] or an on-site Coulomb repulsion using [[:Category:DFT+U\|DFT+U]] on top of another functional. The different types of approximations available in VASP are listed. Also mentioned are the many-body methods for an accurate calculation of the correlation energy, which, however, are not DFT methods.

	=== Which exchange-correlation method to choose? ===		=== Which exchange-correlation method to choose? ===
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	=== Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI) ===		=== Exact exchange optimized-effective potential (EXX-OEP), localized Hartree-Fock (LHF), and Krieger-Li-Iafrate (KLI) ===
	In these methods the minimization of the exact-exchange HF energy expression is done with respect to the electron density <math>n</math>, instead of with respect to the orbitals <math>\psi_i</math>. That means that a local (in the sense of multiplicative) KS potential is calculated. EXX-OEP{{cite\|Sharp:pr:1992}} provides the exact potential, however, performing such calculations is non-trivial in particular since the unoccupied orbitals are required. LHF{{cite\|dellasala:jcp:2001}} is an approximation to EXX-OEP that alleviates the use of unoccupied orbitals, while KLI{{cite\|krieger:pra:1992}} is a further approximation.		In these methods the minimization of the exact-exchange HF energy expression is done with respect to the electron density <math>n</math>, instead of with respect to the orbitals <math>\psi_i</math>. That means that a local (in the sense of multiplicative) KS potential is calculated. EXX-OEP{{cite\|Sharp:pr:1992}} provides the exact potential, however, performing such calculations is non-trivial in particular since the unoccupied orbitals are required. LHF{{cite\|dellasala:jcp:2001}} is an approximation to EXX-OEP that alleviates the use of unoccupied orbitals, while KLI{{cite\|krieger:pra:1992}} is a further approximation.

			These methods are available in VASP, but not documented.

	=== Density functional theory plus U (DFT+U) ===		=== Density functional theory plus U (DFT+U) ===