Category:Wannier functions - Revision history

Huebsch at 13:11, 27 February 2025

2025-02-27T13:11:50Z

← Older revision		Revision as of 13:11, 27 February 2025
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	Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is built from <math>A_{mn\mathbf{k}}</math>. The latter can be built from projections onto some localized-orbital basis.		Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is built from <math>A_{mn\mathbf{k}}</math>. The latter can be built from projections onto some localized-orbital basis.

	Comprehensive instructions on how to construct Wannier orbitals ~~in VASP can be found [[Constructing_Wannier_orbitals\|here~~]].		* Comprehensive instructions on [[Constructing Wannier orbitals\|how to construct Wannier orbitals]].

	== One-shot singular-value decomposition (SVD)==		== One-shot singular-value decomposition (SVD)==

Mani: Typo

2024-08-20T08:48:58Z

Typo

← Older revision		Revision as of 08:48, 20 August 2024
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	Here, <math>U_{mn\mathbf{k}}</math> is a unitary matrix which can be generated using different approaches discussed below, <math>m</math> is an index enumerating Wannier functions with position <math>\mathbf{R}</math>, <math>n</math> is the band index, and <math>\mathbf{k}</math> is the Bloch vector.		Here, <math>U_{mn\mathbf{k}}</math> is a unitary matrix which can be generated using different approaches discussed below, <math>m</math> is an index enumerating Wannier functions with position <math>\mathbf{R}</math>, <math>n</math> is the band index, and <math>\mathbf{k}</math> is the Bloch vector.
	Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is ~~build~~ from <math>A_{mn\mathbf{k}}</math>. The latter can be built from projections onto some localized-orbital basis.		Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is built from <math>A_{mn\mathbf{k}}</math>. The latter can be built from projections onto some localized-orbital basis.

	Comprehensive instructions on how to construct Wannier orbitals in VASP can be found [[Constructing_Wannier_orbitals\|here]].		Comprehensive instructions on how to construct Wannier orbitals in VASP can be found [[Constructing_Wannier_orbitals\|here]].

Miranda.henrique: /* Maximally localized Wannier functions using Wannier90 */

2024-06-14T06:12:16Z

Maximally localized Wannier functions using Wannier90

← Older revision		Revision as of 06:12, 14 June 2024
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	== Maximally localized Wannier functions using Wannier90 ==		== Maximally localized Wannier functions using Wannier90 ==

	The interface of VASP with the Wannier90 code is mainly controlled by {{TAG\|LWANNIER90}} and {{TAG\|LWANNIER90_RUN}}. First, the initial guess for <math>A_{mn\mathbf{k}}</math> can be created by providing the ''projections block'' in the '''wannier90.win''' file (also see {{TAG\|WANNIER90_WIN}}) and setting {{TAG\|LWANNIER90}}=True.		The interface of VASP with the Wannier90 code{{cite\|mostofi:cpc:2014}}{{cite\|pizzi:jpcm:2020}} is mainly controlled by {{TAG\|LWANNIER90}} and {{TAG\|LWANNIER90_RUN}}. First, the initial guess for <math>A_{mn\mathbf{k}}</math> can be created by providing the ''projections block'' in the '''wannier90.win''' file (also see {{TAG\|WANNIER90_WIN}}) and setting {{TAG\|LWANNIER90}}=True.

	In order to obtain maximally localized Wannier functions, <math>U_{mn\mathbf{k}}</math> is constructed in a second step. For this, <math>A_{mn\mathbf{k}}</math> could be created using any projection method in the first step, i.e., single-shot SVD method ({{TAG\|LOCPROJ}}), SCDM method ({{TAG\|LSCDM}}), or Wannier90 ({{TAG\|LWANNIER90}}). Then, Wannier90 can be executed directly or through VASP with the {{TAG\|LWANNIER90_RUN}} tag.		In order to obtain maximally localized Wannier functions, <math>U_{mn\mathbf{k}}</math> is constructed in a second step. For this, <math>A_{mn\mathbf{k}}</math> could be created using any projection method in the first step, i.e., single-shot SVD method ({{TAG\|LOCPROJ}}), SCDM method ({{TAG\|LSCDM}}), or Wannier90 ({{TAG\|LWANNIER90}}). Then, Wannier90 can be executed directly or through VASP with the {{TAG\|LWANNIER90_RUN}} tag.

Mani: Add link to Wannierization how-to page

2024-05-17T11:51:01Z

Add link to Wannierization how-to page

← Older revision		Revision as of 11:51, 17 May 2024
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	Here, <math>U_{mn\mathbf{k}}</math> is a unitary matrix which can be generated using different approaches discussed below, <math>m</math> is an index enumerating Wannier functions with position <math>\mathbf{R}</math>, <math>n</math> is the band index, and <math>\mathbf{k}</math> is the Bloch vector.		Here, <math>U_{mn\mathbf{k}}</math> is a unitary matrix which can be generated using different approaches discussed below, <math>m</math> is an index enumerating Wannier functions with position <math>\mathbf{R}</math>, <math>n</math> is the band index, and <math>\mathbf{k}</math> is the Bloch vector.
	Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is build from <math>A_{mn\mathbf{k}}</math>. The latter can be built from projections onto some localized-orbital basis.		Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is build from <math>A_{mn\mathbf{k}}</math>. The latter can be built from projections onto some localized-orbital basis.

			Comprehensive instructions on how to construct Wannier orbitals in VASP can be found [[Constructing_Wannier_orbitals\|here]].

	== One-shot singular-value decomposition (SVD)==		== One-shot singular-value decomposition (SVD)==

Mani: Fix typo

2024-05-17T11:47:33Z

Fix typo

← Older revision		Revision as of 11:47, 17 May 2024
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	Here, <math>U_{mn\mathbf{k}}</math> is a unitary matrix which can be generated using different approaches discussed below, <math>m</math> is an index enumerating Wannier functions with position <math>\mathbf{R}</math>, <math>n</math> is the band index, and <math>\mathbf{k}</math> is the Bloch vector.		Here, <math>U_{mn\mathbf{k}}</math> is a unitary matrix which can be generated using different approaches discussed below, <math>m</math> is an index enumerating Wannier functions with position <math>\mathbf{R}</math>, <math>n</math> is the band index, and <math>\mathbf{k}</math> is the Bloch vector.
	Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is build from <math>A_{mn\mathbf{k}}</math>. The latter can be ~~build~~ from projections onto some localized-orbital basis.		Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is build from <math>A_{mn\mathbf{k}}</math>. The latter can be built from projections onto some localized-orbital basis.

	== One-shot singular-value decomposition (SVD)==		== One-shot singular-value decomposition (SVD)==

Mani: /* One-shot single value decomposition (SVD) */

2024-02-08T21:20:46Z

One-shot single value decomposition (SVD)

← Older revision		Revision as of 21:20, 8 February 2024
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	Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is build from <math>A_{mn\mathbf{k}}</math>. The latter can be build from projections onto some localized-orbital basis.		Generally, one starts with an initial guess for <math>U_{mn\mathbf{k}}</math> that is build from <math>A_{mn\mathbf{k}}</math>. The latter can be build from projections onto some localized-orbital basis.

	== One-shot ~~single~~ value decomposition (SVD)==		== One-shot singular-value decomposition (SVD)==

	In one-shot SVD, <math>A_{mn\mathbf{k}}</math> is computed by projecting the KS orbitals onto localized orbitals basis <math>\phi_{m\mathbf{k}}</math> that is specified by the {{TAG\|LOCPROJ}} tag:		In one-shot SVD, <math>A_{mn\mathbf{k}}</math> is computed by projecting the KS orbitals onto localized orbitals basis <math>\phi_{m\mathbf{k}}</math> that is specified by the {{TAG\|LOCPROJ}} tag:

Mani: Update reference

2024-02-07T10:20:50Z

Update reference

← Older revision		Revision as of 10:20, 7 February 2024
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	== Selected columns of the density matrix (SCDM) ==		== Selected columns of the density matrix (SCDM) ==

	The SCDM method {{cite\|~~dale~~:mms:2018}} is switched on using {{TAG\|LSCDM}}. It has the advantage that the specification of a local basis in terms of atomic quantum numbers is omitted.		The SCDM method {{cite\|damle:mms:2018}} is switched on using {{TAG\|LSCDM}}. It has the advantage that the specification of a local basis in terms of atomic quantum numbers is omitted.

	== Maximally localized Wannier functions using Wannier90 ==		== Maximally localized Wannier functions using Wannier90 ==

Huebsch: Huebsch moved page Category:Wannier Functions to Category:Wannier functions without leaving a redirect

2022-07-19T12:04:50Z

Huebsch moved page Category:Wannier Functions to Category:Wannier functions without leaving a redirect

← Older revision	Revision as of 12:04, 19 July 2022
(No difference)

Huebsch at 11:52, 5 April 2022

2022-04-05T11:52:56Z

← Older revision		Revision as of 11:52, 5 April 2022
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	Wannier functions <math>\|w_{m\mathbf{R}}\rangle</math> are constructed by a linear combination of Bloch states <math>\|\psi_{n\mathbf{k}}\rangle</math>, i.e., the computed Kohn-Sham (KS) orbitals, as follows:		Wannier functions <math>\|w_{m\mathbf{R}}\rangle</math> are constructed by a linear combination of Bloch states <math>\|\psi_{n\mathbf{k}}\rangle</math>, i.e., the computed Kohn-Sham (KS) orbitals, as follows:

	<math>		::<math>
	\|w_{m\mathbf{R}}\rangle =		\|w_{m\mathbf{R}}\rangle =
	\sum_{n\mathbf{k}}		\sum_{n\mathbf{k}}
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	In one-shot SVD, <math>A_{mn\mathbf{k}}</math> is computed by projecting the KS orbitals onto localized orbitals basis <math>\phi_{m\mathbf{k}}</math> that is specified by the {{TAG\|LOCPROJ}} tag:		In one-shot SVD, <math>A_{mn\mathbf{k}}</math> is computed by projecting the KS orbitals onto localized orbitals basis <math>\phi_{m\mathbf{k}}</math> that is specified by the {{TAG\|LOCPROJ}} tag:

	<math>		::<math>
	A_{mn\mathbf{k}} =		A_{mn\mathbf{k}} =
	\langle \psi_{n\mathbf{k}} \| S \|\phi_{m\mathbf{k}}\rangle,		\langle \psi_{n\mathbf{k}} \| S \|\phi_{m\mathbf{k}}\rangle,
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	where		where

	<math>		::<math>
	\phi_{i\mathbf{k}}(\mathbf{r}) = e^{\mathrm{i}\mathbf{k}\cdot\mathbf{r}} Y_{lm}(\hat{r})R_n(r).		\phi_{i\mathbf{k}}(\mathbf{r}) = e^{\mathrm{i}\mathbf{k}\cdot\mathbf{r}} Y_{lm}(\hat{r})R_n(r).
	</math>		</math>
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	Then, VASP performs one-shot SVD for each k point		Then, VASP performs one-shot SVD for each k point

	<math>		::<math>
	A_{mn\mathbf{k}} = [D \Sigma V^*]_{mn\mathbf{k}}		A_{mn\mathbf{k}} = [D \Sigma V^*]_{mn\mathbf{k}}
	</math>		</math>
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	to obtain the unitary matrix		to obtain the unitary matrix

	<math>		::<math>
	U_{mn\mathbf{k}} = [DV^*]_{mn\mathbf{k}}.		U_{mn\mathbf{k}} = [DV^*]_{mn\mathbf{k}}.
	</math>		</math>

Huebsch: Huebsch moved page Wannier Functions to Category:Wannier Functions

2022-04-01T14:46:46Z

Huebsch moved page Wannier Functions to Category:Wannier Functions

← Older revision	Revision as of 14:46, 1 April 2022
(No difference)