WAVEDER - Revision history

Liebetreu: Reverted edits by Liebetreu (talk) to last revision by Huebsch

2026-04-15T12:20:07Z

Reverted edits by Liebetreu (talk) to last revision by Huebsch

← Older revision		Revision as of 12:20, 15 April 2026
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	The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix		The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix

	:<math> \~~langle~~ \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} ~~\rangle~~ = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \braket{\tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} }= \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>\| {\tilde u_{n\mathbf{k}s}} ~~\rangle~~</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf{k} s}} ~~\rangle~~</math>.		where <math>\ket{\tilde u_{n\mathbf{k}s}}</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\ket{\tilde\psi_{n\mathbf k s}}</math>.

	These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].		These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].
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	* Plasmon frequency.		* Plasmon frequency.

	They are then followed by the matrix elements <math>\~~langle~~ {\tilde\psi_{n'\mathbf{k}} \| {\bf S} \| \frac{\partial \tilde\psi_{n\mathbf{k}}}{\partial k_i}} ~~\rangle~~</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the ~~<math>~~\uparrow\uparrow~~</math>~~ and ~~<math>~~\downarrow\downarrow~~</math>~~ matrix elements are computed. For ~~noncollinear~~ magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the ~~<math>~~\uparrow\uparrow~~</math>~~, ~~<math>~~\uparrow\downarrow~~</math>~~, ~~<math>~~\downarrow\uparrow~~</math>~~ and ~~<math>~~\downarrow\downarrow~~</math>~~ components are computed.		They are then followed by the matrix elements <math>\braket{\tilde\psi_{n'\mathbf k} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k}}{\partial k_i}}</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the $\uparrow\uparrow$ and $\downarrow\downarrow$ matrix elements are computed. For noncollienar magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the $\uparrow\uparrow$, $\uparrow\downarrow$, $\downarrow\uparrow$ and $\downarrow\downarrow$ components are computed.

	==Usage==		==Usage==

Liebetreu at 15:08, 14 April 2026

2026-04-14T15:08:10Z

← Older revision		Revision as of 15:08, 14 April 2026
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	:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf{k} s}} \rangle</math>.		where <math>\| {\tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf{k} s}} \rangle</math>.

	These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].		These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].

Liebetreu: /* Format */

2026-04-14T15:07:12Z

Format

← Older revision		Revision as of 15:07, 14 April 2026
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	* Plasmon frequency.		* Plasmon frequency.

	They are then followed by the matrix elements <math>\langle {\tilde\psi_{n'\mathbf k} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k}}{\partial k_i}} \rangle</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the <math>\uparrow\uparrow</math> and <math>\downarrow\downarrow</math> matrix elements are computed. For noncollinear magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the <math>\uparrow\uparrow</math>, <math>\uparrow\downarrow</math>, <math>\downarrow\uparrow</math> and <math>\downarrow\downarrow</math> components are computed.		They are then followed by the matrix elements <math>\langle {\tilde\psi_{n'\mathbf{k}} \| {\bf S} \| \frac{\partial \tilde\psi_{n\mathbf{k}}}{\partial k_i}} \rangle</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the <math>\uparrow\uparrow</math> and <math>\downarrow\downarrow</math> matrix elements are computed. For noncollinear magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the <math>\uparrow\uparrow</math>, <math>\uparrow\downarrow</math>, <math>\downarrow\uparrow</math> and <math>\downarrow\downarrow</math> components are computed.

	==Usage==		==Usage==

Liebetreu: /* Format */

2026-04-14T15:04:01Z

Format

← Older revision		Revision as of 15:04, 14 April 2026
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	* Plasmon frequency.		* Plasmon frequency.

	They are then followed by the matrix elements <math>\~~braket~~{\tilde\psi_{n'\mathbf k} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k}}{\partial k_i}}</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the <math>\uparrow\uparrow</math> and <math>\downarrow\downarrow</math> matrix elements are computed. For noncollinear magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the <math>\uparrow\uparrow</math>, <math>\uparrow\downarrow</math>, <math>\downarrow\uparrow</math> and <math>\downarrow\downarrow</math> components are computed.		They are then followed by the matrix elements <math>\langle {\tilde\psi_{n'\mathbf k} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k}}{\partial k_i}} \rangle</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the <math>\uparrow\uparrow</math> and <math>\downarrow\downarrow</math> matrix elements are computed. For noncollinear magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the <math>\uparrow\uparrow</math>, <math>\uparrow\downarrow</math>, <math>\downarrow\uparrow</math> and <math>\downarrow\downarrow</math> components are computed.

	==Usage==		==Usage==

Liebetreu at 15:03, 14 April 2026

2026-04-14T15:03:30Z

← Older revision		Revision as of 15:03, 14 April 2026
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	:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf k s}} \rangle</math>.		where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf{k} s}} \rangle</math>.

	These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].		These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].

Liebetreu at 15:02, 14 April 2026

2026-04-14T15:02:37Z

← Older revision		Revision as of 15:02, 14 April 2026
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	:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>~~\ket{~~\tilde u_{n\mathbf{k}s}}</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>~~\ket~~{\tilde\psi_{n\mathbf k s}}</math>.		where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf k s}} \rangle</math>.

	These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].		These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].

Liebetreu at 15:01, 14 April 2026

2026-04-14T15:01:19Z

← Older revision		Revision as of 15:01, 14 April 2026
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	The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix		The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix

	:<math> \~~braket{~~\tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} }= \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>\ket{\tilde u_{n\mathbf{k}s}}</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\ket{\tilde\psi_{n\mathbf k s}}</math>.		where <math>\ket{\tilde u_{n\mathbf{k}s}}</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\ket{\tilde\psi_{n\mathbf k s}}</math>.

Liebetreu at 14:54, 14 April 2026

2026-04-14T14:54:10Z

← Older revision		Revision as of 14:54, 14 April 2026
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	* Plasmon frequency.		* Plasmon frequency.

	They are then followed by the matrix elements <math>\braket{\tilde\psi_{n'\mathbf k} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k}}{\partial k_i}}</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the $\uparrow\uparrow$ and $\downarrow\downarrow$ matrix elements are computed. For ~~noncollienar~~ magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the $\uparrow\uparrow$, $\uparrow\downarrow$, $\downarrow\uparrow$ and $\downarrow\downarrow$ components are computed.		They are then followed by the matrix elements <math>\braket{\tilde\psi_{n'\mathbf k} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k}}{\partial k_i}}</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the <math>\uparrow\uparrow</math> and <math>\downarrow\downarrow</math> matrix elements are computed. For noncollinear magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the <math>\uparrow\uparrow</math>, <math>\uparrow\downarrow</math>, <math>\downarrow\uparrow</math> and <math>\downarrow\downarrow</math> components are computed.

	==Usage==		==Usage==

Huebsch: /* Format */

2025-10-24T10:06:42Z

Format

← Older revision		Revision as of 10:06, 24 October 2025
Line 17:		Line 17:
	* Plasmon frequency.		* Plasmon frequency.

	They are then followed by the matrix elements <math>\braket{\tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}}</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k~~, s~~, i)</math>, where ~~<math>s</math> stands for the spin channel and~~ <math>i=1,2,3</math> for the ~~cartesian~~ direction. The maximum value of each index is defined in the file header, as mentioned above.		They are then followed by the matrix elements <math>\braket{\tilde\psi_{n'\mathbf k} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k}}{\partial k_i}}</math>. This is stored in an five-indexed array, with the indices' order being <math>(n',n,\mathbf k, i)</math>, where <math>i=1,2,3</math> for the Cartesian direction. The maximum value of each index is defined in the file header, as mentioned above. For collinear spin-polarized calculations ({{TAG\|ISPIN\|2}}) the $\uparrow\uparrow$ and $\downarrow\downarrow$ matrix elements are computed. For noncollienar magnetic calculations ({{TAG\|LNONCOLLINEAR\|True}}) the KS orrbitals are stored as spinors and the $\uparrow\uparrow$, $\uparrow\downarrow$, $\downarrow\uparrow$ and $\downarrow\downarrow$ components are computed.

	==Usage==		==Usage==

Pmelo at 12:09, 20 October 2025

2025-10-20T12:09:44Z

← Older revision		Revision as of 12:09, 20 October 2025
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	The {{FILE\|WAVEDER}} file contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix		The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix

	:<math> \braket{\tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} }= \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \braket{\tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} }= \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
Line 7:		Line 7:

	In the case of degenerate states, the matrix elements are set to zero, within numerical accuracy.		In the case of degenerate states, the matrix elements are set to zero, within numerical accuracy.

	~~The {{FILE\|WAVEDER}} file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file.~~
	{{NB\|important\| Please note that only the matrix elements where <math>n</math> or <math>n'</math> correspond to a pair of an occupied and an unoccupied state are calculated and written to the {{FILE\|WAVEDER}} file. Matrix elements involving both occupied or both unoccupied states are not computed.}}		{{NB\|important\| Please note that only the matrix elements where <math>n</math> or <math>n'</math> correspond to a pair of an occupied and an unoccupied state are calculated and written to the {{FILE\|WAVEDER}} file. Matrix elements involving both occupied or both unoccupied states are not computed.}}
	To include more empty states in the calculation, set the {{TAG\|NBANDS}} tag in the {{TAG\|INCAR}} file to a larger value with respect to the default. The default value of {{TAG\|NBANDS}} can be obtained with a VASP [[Command-line_arguments#--dry-run_/_-n \| a dry run]]. Setting {{TAG\|NBANDS}} is generally recommended for {{TAGDEF\|LOPTICS\|True}}, since the [[:Category:Dielectric properties\|dielectric function]] is computed using a summation over empty states (see the page for {{TAG\|LOPTICS}} for more information).		To include more empty states in the calculation, set the {{TAG\|NBANDS}} tag in the {{TAG\|INCAR}} file to a larger value with respect to the default. The default value of {{TAG\|NBANDS}} can be obtained with a VASP [[Command-line_arguments#--dry-run_/_-n \| a dry run]]. Setting {{TAG\|NBANDS}} is generally recommended for {{TAGDEF\|LOPTICS\|True}}, since the [[:Category:Dielectric properties\|dielectric function]] is computed using a summation over empty states (see the page for {{TAG\|LOPTICS}} for more information).

← Older revision		Revision as of 15:08, 14 April 2026
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	:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf{k} s}} \rangle</math>.		where <math>\| {\tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf{k} s}} \rangle</math>.

	These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].		These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].

← Older revision		Revision as of 15:03, 14 April 2026
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	:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf k s}} \rangle</math>.		where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf{k} s}} \rangle</math>.

	These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].		These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].

← Older revision		Revision as of 15:02, 14 April 2026
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	:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>~~\ket{~~\tilde u_{n\mathbf{k}s}}</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>~~\ket~~{\tilde\psi_{n\mathbf k s}}</math>.		where <math>\| \tilde u_{n\mathbf{k}s}} \rangle</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\| {\tilde\psi_{n\mathbf k s}} \rangle</math>.

	These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].		These matrix elements correspond to the dipole moment between the states <math>\tilde\psi_{n'\mathbf k s}</math> and <math>\tilde\psi_{n\mathbf k s}</math>, which are important in the context of dielectric properties. They serve as input for [[Practical guide to GW calculations\|GW]] and [[Bethe-Salpeter-equations calculations\|Bethe-Salpeter]] calculations, as well as the [[time-evolution algorithm]].

← Older revision		Revision as of 15:01, 14 April 2026
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	The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix		The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix

	:<math> \~~braket{~~\tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} }= \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \langle \tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} \rangle = \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
	where <math>\ket{\tilde u_{n\mathbf{k}s}}</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\ket{\tilde\psi_{n\mathbf k s}}</math>.		where <math>\ket{\tilde u_{n\mathbf{k}s}}</math> is the [[Projector-augmented-wave formalism\|cell periodic part of the pseudo-wave function]], <math>\ket{\tilde\psi_{n\mathbf k s}}</math>.

← Older revision		Revision as of 12:09, 20 October 2025
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	The {{FILE\|WAVEDER}} file contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix		The {{FILE\|WAVEDER}} binary file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file. It contains the derivative of the Kohn-Sham orbitals with respect to the Bloch vector '''k''', written in units of <math>\AA</math>. More precisely, it contains the following matrix

	:<math> \braket{\tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} }= \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>		:<math> \braket{\tilde u_{n'\mathbf{k}s} \| \tilde u_{n\mathbf{k}+k_i s} }= \langle \tilde\psi_{n'\mathbf k s} \|{\bf S} \| \frac{\partial \tilde\psi_{n\mathbf k s}}{\partial k_i}\rangle = \frac{1}{\epsilon_{n\mathbf k s} -\epsilon_{n'\mathbf k s}} \langle \tilde\psi_{n'\mathbf k s} \| \frac{\partial (\mathbf{ H} - \epsilon_{n\mathbf k s} \mathbf{S})}{\partial k_i} \| \tilde\psi_{n\mathbf k s} \rangle,</math>
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	In the case of degenerate states, the matrix elements are set to zero, within numerical accuracy.		In the case of degenerate states, the matrix elements are set to zero, within numerical accuracy.

	~~The {{FILE\|WAVEDER}} file is written when {{TAGDEF\|LOPTICS\|True}} is set in the {{FILE\|INCAR}} file.~~
	{{NB\|important\| Please note that only the matrix elements where <math>n</math> or <math>n'</math> correspond to a pair of an occupied and an unoccupied state are calculated and written to the {{FILE\|WAVEDER}} file. Matrix elements involving both occupied or both unoccupied states are not computed.}}		{{NB\|important\| Please note that only the matrix elements where <math>n</math> or <math>n'</math> correspond to a pair of an occupied and an unoccupied state are calculated and written to the {{FILE\|WAVEDER}} file. Matrix elements involving both occupied or both unoccupied states are not computed.}}
	To include more empty states in the calculation, set the {{TAG\|NBANDS}} tag in the {{TAG\|INCAR}} file to a larger value with respect to the default. The default value of {{TAG\|NBANDS}} can be obtained with a VASP [[Command-line_arguments#--dry-run_/_-n \| a dry run]]. Setting {{TAG\|NBANDS}} is generally recommended for {{TAGDEF\|LOPTICS\|True}}, since the [[:Category:Dielectric properties\|dielectric function]] is computed using a summation over empty states (see the page for {{TAG\|LOPTICS}} for more information).		To include more empty states in the calculation, set the {{TAG\|NBANDS}} tag in the {{TAG\|INCAR}} file to a larger value with respect to the default. The default value of {{TAG\|NBANDS}} can be obtained with a VASP [[Command-line_arguments#--dry-run_/_-n \| a dry run]]. Setting {{TAG\|NBANDS}} is generally recommended for {{TAGDEF\|LOPTICS\|True}}, since the [[:Category:Dielectric properties\|dielectric function]] is computed using a summation over empty states (see the page for {{TAG\|LOPTICS}} for more information).