Category:DFT+U - Revision history

Csheldon: /* References */

2026-03-24T14:11:26Z

References

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	== References ==		== References ==

	~~----~~

	[[Category:VASP\|LDA+U]][[Category:Exchange-correlation functionals]]		[[Category:VASP\|LDA+U]][[Category:Exchange-correlation functionals]]

Csheldon at 14:11, 24 March 2026

2026-03-24T14:11:09Z

← Older revision		Revision as of 14:11, 24 March 2026
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	</math>		</math>

	==How to==		== Additional resources ==
			===How to===
	DFT+U can be switched on with the {{TAG\|LDAU}} tag, while the {{TAG\|LDAUTYPE}} tag determines the DFT+U flavor that is used. {{TAG\|LDAUL}} specifies the <math>l</math>-quantum number for which the on-site interaction is added, and the effective on-site Coulomb and exchange interactions are set (in eV) with the {{TAG\|LDAUU}} and {{TAG\|LDAUJ}} tags, respectively. Note that it is recommended to increase {{TAG\|LMAXMIX}} to 4 for ''d''-electrons or 6 for ''f''-elements.		DFT+U can be switched on with the {{TAG\|LDAU}} tag, while the {{TAG\|LDAUTYPE}} tag determines the DFT+U flavor that is used. {{TAG\|LDAUL}} specifies the <math>l</math>-quantum number for which the on-site interaction is added, and the effective on-site Coulomb and exchange interactions are set (in eV) with the {{TAG\|LDAUU}} and {{TAG\|LDAUJ}} tags, respectively. Note that it is recommended to increase {{TAG\|LMAXMIX}} to 4 for ''d''-electrons or 6 for ''f''-elements.

	==Tutorials==		===Tutorials===
	*Tutorial for ~~[https~~:~~//www.vasp.at/tutorials/latest/bulk/part3/#bulk-~~e09 DFT+U].		*Tutorial for {{Tutorial\|bulk:e09\|DFT+U}} on NiO.
	~~<!--~~*Tutorial for ~~[https~~:~~//www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09~~ DFT+U]. ~~ADD magnetism part e04 and e05 -->~~		*Tutorial for {{Tutorial\|magnetism:e04\|LSDA+U and pseudopotential selection of NiO}} and {{Tutorial\|magnetism:e05\|Heisenberg model for NiO using DFT+U}}.
	*Lecture on ~~[https~~:~~//youtu.be/6F_WNIh6V7I~~ the optical gap], introduces DFT+U towards the end of the lecture.
			=== Lectures ===
			*Lecture on {{Video\|optical:merzuk:2025\|the optical gap}}, introduces DFT+U towards the end of the lecture.

	== References ==		== References ==
	~~<references/>~~

	----		----

	[[Category:VASP\|LDA+U]][[Category:Exchange-correlation functionals]]		[[Category:VASP\|LDA+U]][[Category:Exchange-correlation functionals]]

Csheldon: /* Tutorials */

2025-12-12T11:29:21Z

Tutorials

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	==Tutorials==		==Tutorials==
	*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U].		*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U].
	<!--*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U]. ADD magnetism part e05 -->		<!--*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U]. ADD magnetism part e04 and e05 -->
	*Lecture on [https://youtu.be/6F_WNIh6V7I the optical gap], introduces DFT+U towards the end of the lecture.		*Lecture on [https://youtu.be/6F_WNIh6V7I the optical gap], introduces DFT+U towards the end of the lecture.

Csheldon: /* Tutorials */

2025-12-12T11:28:48Z

Tutorials

← Older revision		Revision as of 11:28, 12 December 2025
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	==Tutorials==		==Tutorials==
	*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U].		*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U].
			<!--*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U]. ADD magnetism part e05 -->
	*Lecture on [https://youtu.be/6F_WNIh6V7I the optical gap], introduces DFT+U towards the end of the lecture.		*Lecture on [https://youtu.be/6F_WNIh6V7I the optical gap], introduces DFT+U towards the end of the lecture.

Csheldon: /* Tutorials */

2025-12-11T10:35:36Z

Tutorials

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	==Tutorials==		==Tutorials==
			*Tutorial for [https://www.vasp.at/tutorials/latest/bulk/part3/#bulk-e09 DFT+U].
	*Lecture on [https://youtu.be/6F_WNIh6V7I the optical gap], introduces DFT+U towards the end of the lecture.		*Lecture on [https://youtu.be/6F_WNIh6V7I the optical gap], introduces DFT+U towards the end of the lecture.

Csheldon: /* How to */

2025-09-22T10:39:29Z

How to

← Older revision		Revision as of 10:39, 22 September 2025
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	==How to==		==How to==
	DFT+U can be switched on with the {{TAG\|LDAU}} tag, while the {{TAG\|LDAUTYPE}} tag determines the DFT+U flavor that is used. {{TAG\|LDAUL}} specifies the <math>l</math>-quantum number for which the on-site interaction is added, and the effective on-site Coulomb and exchange interactions are set (in eV) with the {{TAG\|LDAUU}} and {{TAG\|LDAUJ}} tags, respectively. Note that it is recommended to increase {{TAG\|LMAXMIX}} to 4 for ''d''-electrons or 6 for ''f''-elements.		DFT+U can be switched on with the {{TAG\|LDAU}} tag, while the {{TAG\|LDAUTYPE}} tag determines the DFT+U flavor that is used. {{TAG\|LDAUL}} specifies the <math>l</math>-quantum number for which the on-site interaction is added, and the effective on-site Coulomb and exchange interactions are set (in eV) with the {{TAG\|LDAUU}} and {{TAG\|LDAUJ}} tags, respectively. Note that it is recommended to increase {{TAG\|LMAXMIX}} to 4 for ''d''-electrons or 6 for ''f''-elements.

			==Tutorials==
			*Lecture on [https://youtu.be/6F_WNIh6V7I the optical gap], introduces DFT+U towards the end of the lecture.

	== References ==		== References ==

Ftran at 16:05, 28 February 2025

2025-02-28T16:05:59Z

← Older revision		Revision as of 16:05, 28 February 2025
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	The LDA and semilocal GGA functionals 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 LDA/GGA functional:		The LDA and semilocal GGA functionals 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 LDA/GGA functional:
	:<math>E_{\text{xc}}^{\text{DFT}+U}[n,\hat{n}] = E_{\text{xc}}^{\text{~~LDA/GGA~~}}[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{DFT}}[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 and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach is known as the DFT+U method (traditionally called LSDA+U{{cite\|anisimov:prb:91}}).		where <math>E_{\text{dc}}[\hat{n}]</math> is the double-counting term and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach is known as the DFT+U method (traditionally called LSDA+U{{cite\|anisimov:prb:91}}).

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	:This particular flavour of DFT+U is of the form		:This particular flavour of DFT+U is of the form
	::<math>		::<math>
	E_{\rm HF}[{\hat n}]=\frac{1}{2} \sum_{\{\gamma\}}		E^{\rm HF}[{\hat n}]=\frac{1}{2} \sum_{\{\gamma\}}
	(U_{\gamma_1\gamma_3\gamma_2\gamma_4} -		(U_{\gamma_1\gamma_3\gamma_2\gamma_4} -
	U_{\gamma_1\gamma_3\gamma_4\gamma_2}){ \hat		U_{\gamma_1\gamma_3\gamma_4\gamma_2}){ \hat
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	::<math>		::<math>
	E^{\mathrm{DFT}+U}[n,\hat n]=E^{\mathrm{DFT}}[n]+~~E_{\mathrm{x}}~~^{\mathrm{HF}}[\hat n]-E_{\mathrm{dc}}[\hat n]		E^{\mathrm{DFT}+U}[n,\hat n]=E^{\mathrm{DFT}}[n]+E^{\mathrm{HF}}[\hat n]-E_{\mathrm{dc}}[\hat n]
	</math>		</math>

Ftran at 16:01, 28 February 2025

2025-02-28T16:01:49Z

← Older revision		Revision as of 16:01, 28 February 2025
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	The LDA and semilocal GGA functionals 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 LDA/GGA functional:		The LDA and semilocal GGA functionals 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 LDA/GGA functional:
	:<math>E_{\text{xc}}^{\text{~~LDA/GGA~~}+U}(n,\hat{n}) = E_{\text{xc}}^{\text{LDA/GGA}}(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{LDA/GGA}}[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 and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach is known as the DFT+U method (traditionally called LSDA+U{{cite\|anisimov:prb:91}}).		where <math>E_{\text{dc}}[\hat{n}]</math> is the double-counting term and <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach is known as the DFT+U method (traditionally called LSDA+U{{cite\|anisimov:prb:91}}).

	The first VASP DFT+U calculations, including some additional technical details on the VASP implementation, can be found in Ref. {{cite\|rohrbach:jcp:03}} (the original implementation was done by Olivier Bengone {{cite\|Bengone:prb:00}} and Georg Kresse).		The first VASP DFT+U calculations, including some additional technical details on the VASP implementation, can be found in Ref. {{cite\|rohrbach:jcp:03}} (the original implementation was done by Olivier Bengone {{cite\|Bengone:prb:00}} and Georg Kresse).
Line 8:		Line 8:

	==Theory==		==Theory==
	DFT+U is a method that was proposed to improve the description of systems with strongly correlated <math>d</math> or <math>f</math> electrons, like antiferromagnetic NiO for instance, that are usually inaccurately described with the standard LDA and GGA functionals{{cite\|anisimov:prb:91}}. Several variants of the DFT+U method exist (see Refs. {{cite\|Ylvisaker:prb:2009}}{{cite\|Himmetoglu:ijqc:2014}} for reviews) that differ for instance in the way the double counting term <math>E_{\text{dc}}(\hat{n})</math> is calculated. Three variants of them are implemented in VASP, whose formalism is briefly summarized below.		DFT+U is a method that was proposed to improve the description of systems with strongly correlated <math>d</math> or <math>f</math> electrons, like antiferromagnetic NiO for instance, that are usually inaccurately described with the standard LDA and GGA functionals{{cite\|anisimov:prb:91}}. Several variants of the DFT+U method exist (see Refs. {{cite\|Ylvisaker:prb:2009}}{{cite\|Himmetoglu:ijqc:2014}} for reviews) that differ for instance in the way the double counting term <math>E_{\text{dc}}[\hat{n}]</math> is calculated. Three variants of them are implemented in VASP, whose formalism is briefly summarized below.

	*{{TAG\|LDAUTYPE}}=1: The rotationally invariant DFT+U introduced by Liechtenstein ''et al.''{{cite\|liechtenstein:prb:95}}		*{{TAG\|LDAUTYPE}}=1: The rotationally invariant DFT+U introduced by Liechtenstein ''et al.''{{cite\|liechtenstein:prb:95}}
	:This particular flavour of DFT+U is of the form		:This particular flavour of DFT+U is of the form
	::<math>		::<math>
	E_{\rm HF}({\hat n})=\frac{1}{2} \sum_{\{\gamma\}}		E_{\rm HF}[{\hat n}]=\frac{1}{2} \sum_{\{\gamma\}}
	(U_{\gamma_1\gamma_3\gamma_2\gamma_4} -		(U_{\gamma_1\gamma_3\gamma_2\gamma_4} -
	U_{\gamma_1\gamma_3\gamma_4\gamma_2}){ \hat		U_{\gamma_1\gamma_3\gamma_4\gamma_2}){ \hat
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	::<math>		::<math>
	E_{\mathrm{~~tot~~}}(n,\hat n)=E_{\mathrm{DFT}}(n)+E_{\mathrm{HF}}(\hat n)-E_{\mathrm{dc}}(\hat n)		E^{\mathrm{DFT}+U}[n,\hat n]=E^{\mathrm{DFT}}[n]+E_{\mathrm{x}}^{\mathrm{HF}}[\hat n]-E_{\mathrm{dc}}[\hat n]
	</math>		</math>

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	::<math>		::<math>
	E_{\mathrm{dc}}(\hat n) = \frac{U}{2} {\hat n}_{\mathrm{tot}}({\hat n}_{\mathrm{tot}}-1) -		E_{\mathrm{dc}}[\hat n] = \frac{U}{2} {\hat n}_{\mathrm{tot}}({\hat n}_{\mathrm{tot}}-1) -
	\frac{J}{2} \sum_\sigma {\hat n}^\sigma_{\mathrm{tot}}({\hat n}^\sigma_{\mathrm{tot}}-1).		\frac{J}{2} \sum_\sigma {\hat n}^\sigma_{\mathrm{tot}}({\hat n}^\sigma_{\mathrm{tot}}-1).
	</math>		</math>
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	::<math>		::<math>
	E_{\mathrm{DFT+U}}=E_{\mathrm{~~LSDA~~}}+\frac{(U-J)}{2}\sum_\sigma \left[		E^{\mathrm{DFT+U}}=E^{\mathrm{DFT}}+\frac{(U-J)}{2}\sum_\sigma \left[
	\left(\sum_{m_1} n_{m_1,m_1}^{\sigma}\right) - \left(\sum_{m_1,m_2}		\left(\sum_{m_1} n_{m_1,m_1}^{\sigma}\right) - \left(\sum_{m_1,m_2}
	\hat n_{m_1,m_2}^{\sigma} \hat n_{m_2,m_1}^{\sigma} \right) \right].		\hat n_{m_1,m_2}^{\sigma} \hat n_{m_2,m_1}^{\sigma} \right) \right].
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	::<math>		::<math>
	E_{\mathrm{dc}}(\hat n) = \frac{U}{2} {\hat n}_{\mathrm{tot}}({\hat n}_{\mathrm{tot}}-1) -		E_{\mathrm{dc}}[\hat n] = \frac{U}{2} {\hat n}_{\mathrm{tot}}({\hat n}_{\mathrm{tot}}-1) -
	\frac{J}{2} \sum_\sigma {\hat n}^\sigma_{\mathrm{tot}}({\hat n}^\sigma_{\mathrm{tot}}-1).		\frac{J}{2} \sum_\sigma {\hat n}^\sigma_{\mathrm{tot}}({\hat n}^\sigma_{\mathrm{tot}}-1).
	</math>		</math>

Ftran at 16:21, 27 February 2025

2025-02-27T16:21:36Z

← Older revision		Revision as of 16:21, 27 February 2025
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	The first VASP DFT+U calculations, including some additional technical details on the VASP implementation, can be found in Ref. {{cite\|rohrbach:jcp:03}} (the original implementation was done by Olivier Bengone {{cite\|Bengone:prb:00}} and Georg Kresse).		The first VASP DFT+U calculations, including some additional technical details on the VASP implementation, can be found in Ref. {{cite\|rohrbach:jcp:03}} (the original implementation was done by Olivier Bengone {{cite\|Bengone:prb:00}} and Georg Kresse).

	~~For more details, read the article~~ about the ~~[[DFT+U:~~ formalism~~\|formalism of the DFT+U method]]~~.		More detail about the formalism is provided below.

	==Theory==		==Theory==

Ftran at 15:37, 27 February 2025

2025-02-27T15:37:31Z

← Older revision		Revision as of 15:37, 27 February 2025
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	For more details, read the article about the [[DFT+U: formalism\|formalism of the DFT+U method]].		For more details, read the article about the [[DFT+U: formalism\|formalism of the DFT+U method]].

			==Theory==
			DFT+U is a method that was proposed to improve the description of systems with strongly correlated <math>d</math> or <math>f</math> electrons, like antiferromagnetic NiO for instance, that are usually inaccurately described with the standard LDA and GGA functionals{{cite\|anisimov:prb:91}}. Several variants of the DFT+U method exist (see Refs. {{cite\|Ylvisaker:prb:2009}}{{cite\|Himmetoglu:ijqc:2014}} for reviews) that differ for instance in the way the double counting term <math>E_{\text{dc}}(\hat{n})</math> is calculated. Three variants of them are implemented in VASP, whose formalism is briefly summarized below.

			*{{TAG\|LDAUTYPE}}=1: The rotationally invariant DFT+U introduced by Liechtenstein ''et al.''{{cite\|liechtenstein:prb:95}}
			:This particular flavour of DFT+U is of the form
			::<math>
			E_{\rm HF}({\hat n})=\frac{1}{2} \sum_{\{\gamma\}}
			(U_{\gamma_1\gamma_3\gamma_2\gamma_4} -
			U_{\gamma_1\gamma_3\gamma_4\gamma_2}){ \hat
			n}_{\gamma_1\gamma_2}{\hat n}_{\gamma_3\gamma_4}
			</math>
			:and is determined by the <span id="occmat">PAW on-site occupancies
			::<math>
			{\hat n}_{\gamma_1\gamma_2} = \langle \Psi^{s_2} \mid m_2 \rangle
			\langle m_1 \mid \Psi^{s_1} \rangle
			</math></span>
			:and the (unscreened) on-site electron-electron interaction
			::<math>
			U_{\gamma_1\gamma_3\gamma_2\gamma_4}= \langle m_1 m_3 \mid
			\frac{1}{\|\mathbf{r}-\mathbf{r}^\prime\|} \mid m_2 m_4 \rangle
			\delta_{s_1 s_2} \delta_{s_3 s_4}
			</math>
			:where <math>\|m\rangle</math> represents a real spherical harmonics of angular momentum <math>l</math>={{TAG\|LDAUL}}.

			:The unscreened electron-electron interaction <math>U_{\gamma_{1}\gamma_{3}\gamma_{2}\gamma_{4}}</math> can be written in terms of the Slater integrals <math>F^0</math>, <math>F^2</math>, <math>F^4</math>, and <math>F^6</math> (<math>f</math> electrons). Using values for the Slater integrals calculated from atomic orbitals, however, would lead to a large overestimation of the true electron-electron interaction, since in solids the Coulomb interaction is screened (especially <math>F^0</math>).

			:In practice these integrals are often treated as parameters, ''i.e.'', adjusted to reach agreement with experiment for a property like for instance the equilibrium volume, the magnetic moment or the band gap. They are normally specified in terms of the effective on-site Coulomb- and exchange parameters, <math>U</math> and <math>J</math> ({{TAG\|LDAUU}} and {{TAG\|LDAUJ}}, respectively). <math>U</math> and <math>J</math> can also be extracted from constrained-DFT calculations{{cite\|vaugier:prb:2012}}{{cite\|kaltak:thesis2015}}.

			:These translate into values for the Slater integrals in the following way (as implemented in VASP at the moment):

			::{\| cellpadding="5" cellspacing="0" border="1"
			\| <math>L\;</math> \|\| <math>F^0\;</math> \|\| <math>F^2\;</math> \|\| <math>F^4\;</math> \|\| <math>F^6\;</math>
			\|-
			\| <math>1\;</math> \|\| <math>U\;</math> \|\| <math>5J\;</math> \|\| - \|\| -
			\|-
			\| <math>2\;</math> \|\| <math>U\;</math> \|\| <math>\frac{14}{1+0.625}J</math> \|\| <math>0.625 F^2\;</math> \|\| -
			\|-
			\| <math>3\;</math> \|\| <math>U\;</math> \|\| <math>\frac{6435}{286+195 \cdot 0.668+250 \cdot 0.494}J</math> \|\| <math>0.668 F^2\;</math> \|\| <math>0.494 F^2\;</math>
			\|}

			:The essence of the DFT+U method consists of the assumption that one may now write the total energy as:

			::<math>
			E_{\mathrm{tot}}(n,\hat n)=E_{\mathrm{DFT}}(n)+E_{\mathrm{HF}}(\hat n)-E_{\mathrm{dc}}(\hat n)
			</math>

			:where the Hartree-Fock-like interaction replaces the semilocal on-site due to the fact that one subtracts a double-counting energy <math>E_{\mathrm{dc}}</math>, which supposedly equals the on-site semilocal contribution to the total energy,

			::<math>
			E_{\mathrm{dc}}(\hat n) = \frac{U}{2} {\hat n}_{\mathrm{tot}}({\hat n}_{\mathrm{tot}}-1) -
			\frac{J}{2} \sum_\sigma {\hat n}^\sigma_{\mathrm{tot}}({\hat n}^\sigma_{\mathrm{tot}}-1).
			</math>

			*{{TAG\|LDAUTYPE}}=2: The simplified (rotationally invariant) approach to the DFT+U, introduced by Dudarev ''et al.''{{cite\|dudarev:prb:98}}
			:This flavour of DFT+U is of the following form:

			::<math>
			E_{\mathrm{DFT+U}}=E_{\mathrm{LSDA}}+\frac{(U-J)}{2}\sum_\sigma \left[
			\left(\sum_{m_1} n_{m_1,m_1}^{\sigma}\right) - \left(\sum_{m_1,m_2}
			\hat n_{m_1,m_2}^{\sigma} \hat n_{m_2,m_1}^{\sigma} \right) \right].
			</math>

			:This can be understood as adding a penalty functional to the semilocal total energy expression that forces the [[#occmat\|on-site occupancy matrix]] in the direction of idempotency,
			::<math>\hat n^{\sigma} = \hat n^{\sigma} \hat n^{\sigma}</math>.

			:Real matrices are only idempotent when their eigenvalues are either 1 or 0, which for an occupancy matrix translates to either fully occupied or fully unoccupied levels.

			:'''Note''': in Dudarev's approach the parameters <math>U</math> and <math>J</math> do not enter seperately, only the difference <math>U-J</math> is meaningful.

			*{{TAG\|LDAUTYPE}}=3: This option is for the calculation of the parameter <math>U</math> using the linear response approach from Ref. {{cite\|cococcioni:2005}}. The steps to use this method are shown for [[Calculate U for LSDA+U\|the example of NiO]].

			*{{TAG\|LDAUTYPE}}=4: same as {{TAG\|LDAUTYPE}}=1, but without exchange splitting (i.e., the total spin-up plus spin-down occupancy matrix is used). The double-counting term is given by

			::<math>
			E_{\mathrm{dc}}(\hat n) = \frac{U}{2} {\hat n}_{\mathrm{tot}}({\hat n}_{\mathrm{tot}}-1) -
			\frac{J}{2} \sum_\sigma {\hat n}^\sigma_{\mathrm{tot}}({\hat n}^\sigma_{\mathrm{tot}}-1).
			</math>

	==How to==		==How to==