Constructing Wannier orbitals - Revision history

Singraber at 08:03, 24 October 2025

2025-10-24T08:03:26Z

Csheldon: /* Example - diamond */

2025-04-15T07:59:53Z

Example - diamond

← Older revision		Revision as of 07:59, 15 April 2025
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	{{TAGBL\|LOCPROJ}} = 1 : sp3 : Hy 1 4. ! ... to map onto 4 sp-3 functions		{{TAGBL\|LOCPROJ}} = 1 : sp3 : Hy 1 4. ! ... to map onto 4 sp-3 functions

	The last part of the {{TAG\|LOCPROJ}} setting (<tt>Hy 1 4.</tt>) specifies that we want ~~Hyrdogen~~-like atomic orbitals (spherical harmonics) with main quantum number <math>n = 1</math> and a diffusivity of <math>\alpha = 4</math>.		The last part of the {{TAG\|LOCPROJ}} setting (<tt>Hy 1 4.</tt>) specifies that we want Hydrogen-like atomic orbitals (spherical harmonics) with main quantum number <math>n = 1</math> and a diffusivity of <math>\alpha = 4</math>.
	The diffusivity influences the spread of the local function.		The diffusivity influences the spread of the local function.
	A higher value generally results in a higher degree of localization.		A higher value generally results in a higher degree of localization.

Mani: Change INCAR blocks to use TAGBL

2024-06-18T09:07:36Z

Change INCAR blocks to use TAGBL

← Older revision		Revision as of 09:07, 18 June 2024
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	Once again, we choose {{TAGO\|NBANDS\|4}} and we set {{TAGO\|NUM_WANN\|4}} as well.		Once again, we choose {{TAGO\|NBANDS\|4}} and we set {{TAGO\|NUM_WANN\|4}} as well.
	The minimal [[INCAR]] file for this example looks like this:		The minimal [[INCAR]] file for this example looks like this:
	~~<pre>~~
	~~ismear~~ = 0 ! use Gaussian smearing for insulator		{{TAGBL\|ISMEAR}} = 0 ! use Gaussian smearing for insulator
	~~sigma~~ = 0.01 ! use small smearing		{{TAGBL\|SIGMA}} = 0.01 ! use small smearing
	~~nbands~~ = 4 ! use only 4 bands		{{TAGBL\|NBANDS}} = 4 ! use only 4 bands
	~~num_wann~~ = 4 ! ... to map onto 4 Wannier orbitals		{{TAGBL\|NUM_WANN}} = 4 ! ... to map onto 4 Wannier orbitals
	~~lscdm~~ = true ! ... using the SCDM method		{{TAGBL\|LSCDM}} = true ! ... using the SCDM method
	~~</pre>~~
	For this example calculation, we use the same course Γ-centered regular mesh of <tt>4x4x4</tt> k-points as before.		For this example calculation, we use the same course Γ-centered regular mesh of <tt>4x4x4</tt> k-points as before.
	We also specify the same k-point path for [[KPOINTS_OPT]] and [[KPOINTS_WAN]] to perform band-structure calculations.		We also specify the same k-point path for [[KPOINTS_OPT]] and [[KPOINTS_WAN]] to perform band-structure calculations.
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	The minimal [[INCAR]] file for this example is provided below:		The minimal [[INCAR]] file for this example is provided below:
	~~<pre>~~
	~~ismear~~ = 0 ! use Gaussian smearing for insulator		{{TAGBL\|ISMEAR}} = 0 ! use Gaussian smearing for insulator
	~~sigma~~ = 0.01 ! use small smearing		{{TAGBL\|SIGMA}} = 0.01 ! use small smearing
	~~nbands~~ = 16 ! use 16 bands, including unoccupied states		{{TAGBL\|NBANDS}} = 16 ! use 16 bands, including unoccupied states
	~~num_wann~~ = 9 ! ... to map to 9 Wannier orbitals		{{TAGBL\|NUM_WANN}} = 9 ! ... to map to 9 Wannier orbitals
	~~lscdm~~ = true ! ... using the SCDM method		{{TAGBL\|LSCDM}} = true ! ... using the SCDM method
	~~cutoff_type~~ = erfc ! choose erfc cutoff function		{{TAGBL\|CUTOFF_TYPE}} = erfc ! choose erfc cutoff function
	~~scdm_mu~~ = 10 ! ... and place it at 10 eV		{{TAGBL\|CUTOFF_MU}} = 10 ! ... and place it at 10 eV
	~~scdm_sigma~~ = 0.1 ! ... with a width of 0.1 eV		{{TAGBL\|CUTOFF_SIGMA}} = 0.1 ! ... with a width of 0.1 eV
	~~</pre>~~
	The initial k-point mesh is chosen to be <tt>8x8x8</tt> Γ-centered.		The initial k-point mesh is chosen to be <tt>8x8x8</tt> Γ-centered.

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	To generate MLWFs from VASP orbitals, you can add the following lines to your [[INCAR]] file:		To generate MLWFs from VASP orbitals, you can add the following lines to your [[INCAR]] file:
	~~<pre>~~
	~~lwannier90~~ = true # or lwannier90_run = true		{{TAGBL\|LWANNIER90}} = true # or lwannier90_run = true
	~~wannier90_win~~ = "		{{TAGBL\|WANNIER90_WIN}} = "
	dis_num_iter = 100		dis_num_iter = 100
	num_iter = 100		num_iter = 100
	"		"
	~~</pre>~~
	where <tt>dis_num_iter</tt> specifies the number of iteration during Wannier90's disentanglement procedure and <tt>num_iter</tt> the number of iteration during the MLWF procedure.		where <tt>dis_num_iter</tt> specifies the number of iteration during Wannier90's disentanglement procedure and <tt>num_iter</tt> the number of iteration during the MLWF procedure.
	{{NB\|important\|Make sure that VASP is compiled with the [[Precompiler options#-DVASP2WANNIER90\|VASP2WANNIER90]] precompiler option.}}		{{NB\|important\|Make sure that VASP is compiled with the [[Precompiler options#-DVASP2WANNIER90\|VASP2WANNIER90]] precompiler option.}}

Mani: /* Example - diamond */ Change INCAR example to use TAGBL

2024-06-18T08:50:07Z

Example - diamond: Change INCAR example to use TAGBL

← Older revision		Revision as of 08:50, 18 June 2024
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	We seek to map the four bands in the simulation to four Wannier orbitals, so we choose to setup four sp-3 hybrids on one atom.		We seek to map the four bands in the simulation to four Wannier orbitals, so we choose to setup four sp-3 hybrids on one atom.
	The minimal INCAR file used in this example looks like this:		The minimal INCAR file used in this example looks like this:
	~~<pre>~~
	~~ismear~~ = 0 ! use Gaussian smearing for insulator		{{TAGBL\|ISMEAR}} = 0 ! use Gaussian smearing for insulator
	~~sigma~~ = 0.01 ! use small smearing		{{TAGBL\|SIGMA}} = 0.01 ! use small smearing
	~~nbands~~ = 4 ! use only 4 bands		{{TAGBL\|NBANDS}} = 4 ! use only 4 bands
	~~locproj~~ = 1 : sp3 : Hy 1 4. ! ... to map onto 4 sp-3 functions		{{TAGBL\|LOCPROJ}} = 1 : sp3 : Hy 1 4. ! ... to map onto 4 sp-3 functions
	~~</pre>~~
	The last part of the {{TAG\|LOCPROJ}} setting (<tt>Hy 1 4.</tt>) specifies that we want Hyrdogen-like atomic orbitals (spherical harmonics) with main quantum number <math>n = 1</math> and a diffusivity of <math>\alpha = 4</math>.		The last part of the {{TAG\|LOCPROJ}} setting (<tt>Hy 1 4.</tt>) specifies that we want Hyrdogen-like atomic orbitals (spherical harmonics) with main quantum number <math>n = 1</math> and a diffusivity of <math>\alpha = 4</math>.
	The diffusivity influences the spread of the local function.		The diffusivity influences the spread of the local function.

Mani: /* Related tags and articles */ Add LOCPROJ to related tags

2024-05-17T11:52:07Z

Related tags and articles: Add LOCPROJ to related tags

← Older revision		Revision as of 11:52, 17 May 2024
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	== Related tags and articles==		== Related tags and articles==
	{{TAG\|LSCDM}},		{{TAG\|LSCDM}},
			{{TAG\|LOCPROJ}},
	{{TAG\|CUTOFF_TYPE}},		{{TAG\|CUTOFF_TYPE}},
	{{TAG\|CUTOFF_MU}},		{{TAG\|CUTOFF_MU}},

Mani: Mani moved page Wannier orbitals from VASP to Constructing Wannier orbitals

2024-05-17T11:46:08Z

Mani moved page Wannier orbitals from VASP to Constructing Wannier orbitals

← Older revision	Revision as of 11:46, 17 May 2024
(No difference)

Mani: /* Wannier90 */ Remove warning

2024-03-21T10:24:59Z

Wannier90: Remove warning

← Older revision		Revision as of 10:24, 21 March 2024
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	Afterwards, run Wannier90 to generate MLWFs (all of this can be done in one run when setting {{TAGO\|LWANNIER90_RUN\|true}}).		Afterwards, run Wannier90 to generate MLWFs (all of this can be done in one run when setting {{TAGO\|LWANNIER90_RUN\|true}}).
	At this point, you can use the functionality available in Wannier90 to plot the band structure, the orbitals, etc.		At this point, you can use the functionality available in Wannier90 to plot the band structure, the orbitals, etc.
	~~{{NB\|warning\|The <code>exclude_bands</code> parameter in the <tt>wannier90.win</tt> input file is currently not properly supported in VASP when using the SCDM method. Use with caution!\|\|Bug:}}~~

	When plotting orbitals using Wannier90, in addition to {{TAGO\|LWRITE_MMN_AMN\|true}}, it may also be necessary to set {{TAGO\|LWRITE_UNK\|true}}.		When plotting orbitals using Wannier90, in addition to {{TAGO\|LWRITE_MMN_AMN\|true}}, it may also be necessary to set {{TAGO\|LWRITE_UNK\|true}}.

Huebsch: Huebsch moved page Construction:Wannier orbitals from VASP to Wannier orbitals from VASP without leaving a redirect

2024-03-19T12:59:09Z

Huebsch moved page Construction:Wannier orbitals from VASP to Wannier orbitals from VASP without leaving a redirect

← Older revision	Revision as of 12:59, 19 March 2024
(No difference)

Huebsch at 12:58, 19 March 2024

2024-03-19T12:58:55Z

← Older revision		Revision as of 12:58, 19 March 2024
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	In general, <math>A_{mn \mathbf{k}}</math> is not going to be a unitary matrix.		In general, <math>A_{mn \mathbf{k}}</math> is not going to be a unitary matrix.
	It could in principle be used to transform the Bloch orbitals into a set of non-orthogonal Wannier orbitals.		It could, in principle, be used to transform the Bloch orbitals into a set of non-orthogonal Wannier orbitals.
	However, for many applications it is desirable to have orthonormal Wannier orbitals, such as for Wannier interpolation.		However, for many applications, it is desirable to have orthonormal Wannier orbitals, such as for Wannier interpolation.
	Therefore, <math>A_{mn \mathbf{k}}</math> needs to ~~first~~ be orthonormalized.		Therefore, <math>A_{mn \mathbf{k}}</math> needs first to be orthonormalized.

	In VASP, we employ a one-shot orthonormalization procedure that uses the [https://en.wikipedia.org/wiki/Singular_value_decomposition singular-value decomposition] (SVD) of <math>A_{mn \mathbf{k}}</math>:		In VASP, we employ a one-shot orthonormalization procedure that uses the [https://en.wikipedia.org/wiki/Singular_value_decomposition singular-value decomposition] (SVD) of <math>A_{mn \mathbf{k}}</math>:
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	U_{mn\mathbf{k}} = [DV^\dagger]_{mn\mathbf{k}}.		U_{mn\mathbf{k}} = [DV^\dagger]_{mn\mathbf{k}}.
	</math>		</math>
	~~The SVD orthogonalization operates simultaneously on all local functions, in~~ contrast to iterative methods (e.g. Gram-Schmidt orthogonalization).		In contrast to iterative methods (e.g., Gram-Schmidt orthogonalization), the SVD orthogonalization operates simultaneously on all local functions.
	This ensures that the symmetry properties of the local functions encoded in <math>A_{mn \mathbf{k}}</math> are preserved during the orthonormalization procedure.		This ensures that the symmetry properties of the local functions encoded in <math>A_{mn \mathbf{k}}</math> are preserved during the orthonormalization procedure.

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	To find a good representation of the electronic band structure in terms of Wannier orbitals, it is important to choose suitable projection targets.		To find a good representation of the electronic band structure in terms of Wannier orbitals, it is important to choose suitable projection targets.
	In general, this can be a difficult task as some bands hybridize and disperse, changing electronic character as a function of the Bloch vector <math>\mathbf{k}</math>.		In general, this can be a difficult task as some bands hybridize and disperse, changing electronic character as a function of the Bloch vector <math>\mathbf{k}</math>.
	It is thus expedient to ~~have a good understanding of~~ the relevant electronic bands before attempting a Wannierization using {{TAG\|LOCPROJ}}.		It is thus expedient to understand the relevant electronic bands before attempting a Wannierization using {{TAG\|LOCPROJ}}.

	To gain insight into the electronic character of certain bands, you can use the {{TAG\|LORBIT}} tag.		To gain insight into the electronic character of certain bands, you can use the {{TAG\|LORBIT}} tag.
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	This decomposes the bands into <math>l</math> and <math>m</math> quantum numbers in terms of spherical harmonics.		This decomposes the bands into <math>l</math> and <math>m</math> quantum numbers in terms of spherical harmonics.
	We get information on each k-point in the [[PROCAR]] file.		We get information on each k-point in the [[PROCAR]] file.
	Here is the start of the file which contains information about the Γ-point:		Here is the start of the file, which contains information about the Γ-point:
	<pre>		<pre>
	PROCAR lm decomposed		PROCAR lm decomposed
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	A higher value generally results in a higher degree of localization.		A higher value generally results in a higher degree of localization.
	This is beneficial for Wannier interpolation and yields Wannier orbitals of higher quality in that regard.		This is beneficial for Wannier interpolation and yields Wannier orbitals of higher quality in that regard.
	{{NB:tip:You may also choose to use the PAW information to specify local orbitals with {{TAG\|LOCPROJ}}. In this case, you should use {{TAGO\|LORBIT\|11}} to extract the relevant information from the basis.}}		{{NB\|tip\|You may also choose to use the PAW information to specify local orbitals with {{TAG\|LOCPROJ}}. In this case, you should use {{TAGO\|LORBIT\|11}} to extract the relevant information from the basis.}}

	For this example calculation, we use a relatively course Γ-centered regular mesh of <tt>4x4x4</tt> k-points.		For this example calculation, we use a relatively course Γ-centered regular mesh of <tt>4x4x4</tt> k-points.
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	== References ==		== References ==
	<references/>		<references/>

			[[Category:Wannier functions]][[Category:Howto]]

Mani: /* SCDM and Wannier90 */ Make more general

2024-02-09T10:40:54Z

SCDM and Wannier90: Make more general

← Older revision		Revision as of 10:40, 9 February 2024
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	{{NB\|mind\|The quality of the Wannierization can depend strongly on the choice of [[CUTOFF_MU]] and [[CUTOFF_SIGMA]]. It will often take some trial and error to find reasonable parameters.}}		{{NB\|mind\|The quality of the Wannierization can depend strongly on the choice of [[CUTOFF_MU]] and [[CUTOFF_SIGMA]]. It will often take some trial and error to find reasonable parameters.}}

	== ~~SCDM and~~ Wannier90 ==		== Wannier90 ==
	Wannier orbitals obtained inside VASP via the SCDM ~~method~~ can be passed to [http://www.wannier.org Wannier90] for further processing.		Wannier orbitals obtained inside VASP via the {{TAG\|LOCPROJ}} or SCDM methods can be passed to [http://www.wannier.org Wannier90] for further processing.
	Wannier90 employs an iterative algorithm that generates so-called maximally-localized Wannier functions (MLWF).		Wannier90 employs an iterative algorithm that generates so-called maximally-localized Wannier functions (MLWF).
	MLWFs are usually superior in terms of quality for band structure calculations.		MLWFs are usually superior in terms of quality for band structure calculations.
	However, even though they are generated from an iterative procedure, Wannier90 still relies on good first guesses for the localized functions.		However, even though they are generated from an iterative procedure, Wannier90 still relies on good first guesses for the localized functions.
	This is where the SCDM method can provide a suitable set of initial functions for the MLWF procedure.		This is where the SCDM method can provide a suitable set of initial functions for the MLWF procedure.
			In the case of the {{TAG\|LOCPROJ}} tag, the projection matrix <math>A_{mn\mathbf{k}}</math> is passed directly to Wannier90 where the Wannier transformation is constructed.
			VASP handles the communication of the projection targets and matrix dimensions automatically.

	To generate MLWFs from ~~SCDM~~ orbitals, you can add the following lines to your [[INCAR]] file:		To generate MLWFs from VASP orbitals, you can add the following lines to your [[INCAR]] file:
	<pre>		<pre>
	lwannier90 = true # or lwannier90_run = true		lwannier90 = true # or lwannier90_run = true
	wannier90_win = "		wannier90_win = "
	dis_num_iter = 0		dis_num_iter = 100
	num_iter = 100		num_iter = 100
	"		"
	</pre>		</pre>
			where <tt>dis_num_iter</tt> specifies the number of iteration during Wannier90's disentanglement procedure and <tt>num_iter</tt> the number of iteration during the MLWF procedure.
	{{NB\|important\|Make sure that VASP is compiled with the [[Precompiler options#-DVASP2WANNIER90\|VASP2WANNIER90]] precompiler option.}}		{{NB\|important\|Make sure that VASP is compiled with the [[Precompiler options#-DVASP2WANNIER90\|VASP2WANNIER90]] precompiler option.}}
			{{NB\|important\|When using the SCDM method together with Wannier90, it is recommended to set <code>dis_num_iter {{=}} 0</code> via {{TAG\|WANNIER90_WIN}} or in the Wannier90 input file.}}
	{{TAG\|LWANNIER90}} activates the interface between VASP and Wannier90 and writes a <tt>wannier90.win</tt> input file that can then be read by Wannier90.		{{TAG\|LWANNIER90}} activates the interface between VASP and Wannier90 and writes a <tt>wannier90.win</tt> input file that can then be read by Wannier90.
	In addition to the basic input parameters, VASP also writes the overlap matrices <math>M_{mn}</math> and <math>A_{mn}</math> to the corresponding files, <tt>wannier90.mmn</tt> and <tt>wannier90.amn</tt>.		In addition to the basic input parameters, VASP also writes the overlap matrices <math>M_{mn}</math> and <math>A_{mn}</math> to the corresponding files, <tt>wannier90.mmn</tt> and <tt>wannier90.amn</tt>.
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	Meanwhile, <math>A_{mn}</math> contains the overlaps between the Bloch orbitals and the projection targets (in this case, the SCDM orbitals obtained from VASP).		Meanwhile, <math>A_{mn}</math> contains the overlaps between the Bloch orbitals and the projection targets (in this case, the SCDM orbitals obtained from VASP).
	{{NB\|tip\|The <tt>wannier90.mmn</tt> and <tt>wannier90.amn</tt> files can be explicitly written via {{TAGO\|LWRITE_MMN_AMN\|true}}. This is switched on by default when {{TAGO\|LWANNIER90\|true}}. It is unnecessary to write these files when {{TAGO\|LWANNIER90_RUN\|true}} as they are directly passed to Wannier90.}}		{{NB\|tip\|The <tt>wannier90.mmn</tt> and <tt>wannier90.amn</tt> files can be explicitly written via {{TAGO\|LWRITE_MMN_AMN\|true}}. This is switched on by default when {{TAGO\|LWANNIER90\|true}}. It is unnecessary to write these files when {{TAGO\|LWANNIER90_RUN\|true}} as they are directly passed to Wannier90.}}
	~~{{NB\|important\|When using the SCDM method together with Wannier90, it is recommended to set <code>dis_num_iter {{=}} 0</code> via {{TAG\|WANNIER90_WIN}} or in the Wannier90 input file.}}~~


	Run VASP with the above [[INCAR]] ~~file~~ to generate Wannier orbitals via SCDM and to generate the required Wannier90 input files.		Run VASP with the above [[INCAR]] tags to generate Wannier orbitals via SCDM or {{TAG\|LOCPROJ}} and to generate the required Wannier90 input files.
	Afterwards, run Wannier90 to generate MLWFs (all of this can be done in one run when setting {{TAGO\|LWANNIER90_RUN\|true}}).		Afterwards, run Wannier90 to generate MLWFs (all of this can be done in one run when setting {{TAGO\|LWANNIER90_RUN\|true}}).
	At this point, you can use the functionality available in Wannier90 to plot the band structure, the orbitals, etc.		At this point, you can use the functionality available in Wannier90 to plot the band structure, the orbitals, etc.
	{{NB\|warning\|The <code>exclude_bands</code> parameter in the <tt>wannier90.win</tt> input file is currently not properly supported in VASP when using the SCDM method. Use with caution!\|\|Bug:}}		{{NB\|warning\|The <code>exclude_bands</code> parameter in the <tt>wannier90.win</tt> input file is currently not properly supported in VASP when using the SCDM method. Use with caution!\|\|Bug:}}

			When plotting orbitals using Wannier90, in addition to {{TAGO\|LWRITE_MMN_AMN\|true}}, it may also be necessary to set {{TAGO\|LWRITE_UNK\|true}}.
			This writes the cell-periodic part of the Bloch orbitals to disk.

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

← Older revision		Revision as of 11:52, 17 May 2024
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	== Related tags and articles==		== Related tags and articles==
	{{TAG\|LSCDM}},		{{TAG\|LSCDM}},
			{{TAG\|LOCPROJ}},
	{{TAG\|CUTOFF_TYPE}},		{{TAG\|CUTOFF_TYPE}},
	{{TAG\|CUTOFF_MU}},		{{TAG\|CUTOFF_MU}},

← Older revision		Revision as of 08:03, 24 October 2025
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	VASP will then apply the [[#One-shot Wannierization using a singular-value decomposition\|one-shot orthonormalization]] internally to obtain the Wannier transformation matrix <math>U_{mn\mathbf{k}}</math>.		VASP will then apply the [[#One-shot Wannierization using a singular-value decomposition\|one-shot orthonormalization]] internally to obtain the Wannier transformation matrix <math>U_{mn\mathbf{k}}</math>.
	The number of Wannier orbitals is the same as the total number of local functions.		The number of Wannier orbitals is the same as the total number of local functions.
	{{NB\|tip\|You can write the Wannier transformation matrix to disk by setting {{~~TAGO~~\|LWRITE_WANPROJ\|true}}.}}		{{NB\|tip\|You can write the Wannier transformation matrix to disk by setting {{TAG\|LWRITE_WANPROJ\|true}}.}}
	This information can then be used to perform Wannier interpolation of the electronic band structure (for example, using the [[KPOINTS_WAN]] file).		This information can then be used to perform Wannier interpolation of the electronic band structure (for example, using the [[KPOINTS_WAN]] file).
	It can also be passed to [http://www.wannier.org Wannier90] (more on that [[#SCDM and Wannier90\|later]]).		It can also be passed to [http://www.wannier.org Wannier90] (more on that [[#SCDM and Wannier90\|later]]).
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	To gain insight into the electronic character of certain bands, you can use the {{TAG\|LORBIT}} tag.		To gain insight into the electronic character of certain bands, you can use the {{TAG\|LORBIT}} tag.
	This decomposes the bands into local contributions either in terms of spherical harmonics ({{~~TAGO~~\|LORBIT\|10\|op=<}}) or in terms of PAW projector functions ({{~~TAGO~~\|LORBIT\|10\|op=≥}}).		This decomposes the bands into local contributions either in terms of spherical harmonics ({{TAG\|LORBIT\|10\|op=<}}) or in terms of PAW projector functions ({{TAG\|LORBIT\|10\|op=≥}}).
	The relevant information is written to the [[PROCAR]] file and can be used to determine suitable projection targets for {{TAG\|LOCPROJ}}.		The relevant information is written to the [[PROCAR]] file and can be used to determine suitable projection targets for {{TAG\|LOCPROJ}}.

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	This is a group of bands that is energetically isolated (they are surrounded by band gaps).		This is a group of bands that is energetically isolated (they are surrounded by band gaps).
	Since there is no mixing with any other states, the Wannierization process of these four bands is relatively simple.		Since there is no mixing with any other states, the Wannierization process of these four bands is relatively simple.
	With the standard C POTCAR distributed with VASP, we can conveniently set {{~~TAGO~~\|NBANDS\|4}} to only consider those states.		With the standard C POTCAR distributed with VASP, we can conveniently set {{TAG\|NBANDS\|4}} to only consider those states.

	First, let us run a calculation with {{~~TAGO~~\|LORBIT\|1}} and {{~~TAGO~~\|RWIGS\|1.1}}.		First, let us run a calculation with {{TAG\|LORBIT\|1}} and {{TAG\|RWIGS\|1.1}}.
	This decomposes the bands into <math>l</math> and <math>m</math> quantum numbers in terms of spherical harmonics.		This decomposes the bands into <math>l</math> and <math>m</math> quantum numbers in terms of spherical harmonics.
	We get information on each k-point in the [[PROCAR]] file.		We get information on each k-point in the [[PROCAR]] file.
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	A higher value generally results in a higher degree of localization.		A higher value generally results in a higher degree of localization.
	This is beneficial for Wannier interpolation and yields Wannier orbitals of higher quality in that regard.		This is beneficial for Wannier interpolation and yields Wannier orbitals of higher quality in that regard.
	{{NB\|tip\|You may also choose to use the PAW information to specify local orbitals with {{TAG\|LOCPROJ}}. In this case, you should use {{~~TAGO~~\|LORBIT\|11}} to extract the relevant information from the basis.}}		{{NB\|tip\|You may also choose to use the PAW information to specify local orbitals with {{TAG\|LOCPROJ}}. In this case, you should use {{TAG\|LORBIT\|11}} to extract the relevant information from the basis.}}

	For this example calculation, we use a relatively course Γ-centered regular mesh of <tt>4x4x4</tt> k-points.		For this example calculation, we use a relatively course Γ-centered regular mesh of <tt>4x4x4</tt> k-points.
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	== SCDM method ==		== SCDM method ==
	In contrast to the {{TAG\|LOCPROJ}} method, the SCDM method does not rely on the specification of a local basis.		In contrast to the {{TAG\|LOCPROJ}} method, the SCDM method does not rely on the specification of a local basis.
	To activate the SCDM method, set {{~~TAGO~~\|LSCDM\|true}}.		To activate the SCDM method, set {{TAG\|LSCDM\|true}}.
	This will use the information contained in the electronic one-particle density matrix to construct localized functions from the original Bloch (Kohn-Sham) orbitals.		This will use the information contained in the electronic one-particle density matrix to construct localized functions from the original Bloch (Kohn-Sham) orbitals.
	These localized functions are then orthonormalized using the [[#One-shot Wannierization using a singular-value decomposition\|one-shot SVD approach]] to obtain orthonormal Wannier orbitals.		These localized functions are then orthonormalized using the [[#One-shot Wannierization using a singular-value decomposition\|one-shot SVD approach]] to obtain orthonormal Wannier orbitals.

	The number of Wannier orbitals obtained is controlled via the {{TAG\|NUM_WANN}} tag.		The number of Wannier orbitals obtained is controlled via the {{TAG\|NUM_WANN}} tag.
	{{NB\|mind\|You must ensure that {{~~TAGO~~\|NUM_WANN\|{{TAG\|NBANDS}}\|op=≤}} in order to have enough information to construct the Wannier orbitals.}}		{{NB\|mind\|You must ensure that {{TAG\|NUM_WANN\|{{TAG\|NBANDS}}\|op=≤}} in order to have enough information to construct the Wannier orbitals.}}

	=== Example - diamond ===		=== Example - diamond ===
	Let us repeat the example calculation [[#LOCPROJ method#Example - diamond\|shown earlier]] to obtain Wannier orbitals in diamond using the SCDM method.		Let us repeat the example calculation [[#LOCPROJ method#Example - diamond\|shown earlier]] to obtain Wannier orbitals in diamond using the SCDM method.
	Once again, we choose {{~~TAGO~~\|NBANDS\|4}} and we set {{~~TAGO~~\|NUM_WANN\|4}} as well.		Once again, we choose {{TAG\|NBANDS\|4}} and we set {{TAG\|NUM_WANN\|4}} as well.
	The minimal [[INCAR]] file for this example looks like this:		The minimal [[INCAR]] file for this example looks like this:

Line 190:		Line 190:

	== Disentanglement ==		== Disentanglement ==
	When {{~~TAGO~~\|NBANDS\|{{TAG\|NUM_WANN}}\|op=>}} or when the bands are not energetically isolated, Wannierization becomes more involved.		When {{TAG\|NBANDS\|{{TAG\|NUM_WANN}}\|op=>}} or when the bands are not energetically isolated, Wannierization becomes more involved.
	The difficulty lies in determining which electronic states to select when transforming the initial Bloch orbitals to the Wannier orbitals.		The difficulty lies in determining which electronic states to select when transforming the initial Bloch orbitals to the Wannier orbitals.
	This process is known as disentanglement.		This process is known as disentanglement.
Line 259:		Line 259:
	<math>M_{mn}</math> contains the overlaps between all pairs of Bloch orbitals.		<math>M_{mn}</math> contains the overlaps between all pairs of Bloch orbitals.
	Meanwhile, <math>A_{mn}</math> contains the overlaps between the Bloch orbitals and the projection targets (in this case, the SCDM orbitals obtained from VASP).		Meanwhile, <math>A_{mn}</math> contains the overlaps between the Bloch orbitals and the projection targets (in this case, the SCDM orbitals obtained from VASP).
	{{NB\|tip\|The <tt>wannier90.mmn</tt> and <tt>wannier90.amn</tt> files can be explicitly written via {{~~TAGO~~\|LWRITE_MMN_AMN\|true}}. This is switched on by default when {{~~TAGO~~\|LWANNIER90\|true}}. It is unnecessary to write these files when {{~~TAGO~~\|LWANNIER90_RUN\|true}} as they are directly passed to Wannier90.}}		{{NB\|tip\|The <tt>wannier90.mmn</tt> and <tt>wannier90.amn</tt> files can be explicitly written via {{TAG\|LWRITE_MMN_AMN\|true}}. This is switched on by default when {{TAG\|LWANNIER90\|true}}. It is unnecessary to write these files when {{TAG\|LWANNIER90_RUN\|true}} as they are directly passed to Wannier90.}}

	Run VASP with the above [[INCAR]] tags to generate Wannier orbitals via SCDM or {{TAG\|LOCPROJ}} and to generate the required Wannier90 input files.		Run VASP with the above [[INCAR]] tags to generate Wannier orbitals via SCDM or {{TAG\|LOCPROJ}} and to generate the required Wannier90 input files.
	Afterwards, run Wannier90 to generate MLWFs (all of this can be done in one run when setting {{~~TAGO~~\|LWANNIER90_RUN\|true}}).		Afterwards, run Wannier90 to generate MLWFs (all of this can be done in one run when setting {{TAG\|LWANNIER90_RUN\|true}}).
	At this point, you can use the functionality available in Wannier90 to plot the band structure, the orbitals, etc.		At this point, you can use the functionality available in Wannier90 to plot the band structure, the orbitals, etc.

	When plotting orbitals using Wannier90, in addition to {{~~TAGO~~\|LWRITE_MMN_AMN\|true}}, it may also be necessary to set {{~~TAGO~~\|LWRITE_UNK\|true}}.		When plotting orbitals using Wannier90, in addition to {{TAG\|LWRITE_MMN_AMN\|true}}, it may also be necessary to set {{TAG\|LWRITE_UNK\|true}}.
	This writes the cell-periodic part of the Bloch orbitals to disk.		This writes the cell-periodic part of the Bloch orbitals to disk.