Category:Phonons - Revision history

Csheldon: /* Tutorials */

2025-05-28T13:15:32Z

Tutorials

← Older revision		Revision as of 13:15, 28 May 2025
Line 45:		Line 45:

	== Tutorials ==		== Tutorials ==
	*Tutorial for [https://vasp.at/tutorials/latest/phonon/ phonon calculations].		*Tutorial for [https://vasp.at/tutorials/latest/phonon/ lattice parameter, phonon dispersion and DOS, and long-range dipole-dipole interaction calculations].

	[[Category:VASP\|Phonons]][[Category:Linear response]]		[[Category:VASP\|Phonons]][[Category:Linear response]]

2025-05-28T13:09:04Z

← Older revision		Revision as of 13:09, 28 May 2025
Line 44:		Line 44:
	* [[Electron-phonon interactions from Monte-Carlo sampling]]		* [[Electron-phonon interactions from Monte-Carlo sampling]]

	~~----~~		== Tutorials ==
			*Tutorial for [https://vasp.at/tutorials/latest/phonon/ phonon calculations].

	[[Category:VASP\|Phonons]][[Category:Linear response]]		[[Category:VASP\|Phonons]][[Category:Linear response]]

2025-01-11T13:11:28Z

Electron-phonon interaction: Add link to perturbative approach

← Older revision		Revision as of 13:11, 11 January 2025
Line 36:		Line 36:
	The movement of the nuclei leads to changes in the electronic degrees of freedom with this		The movement of the nuclei leads to changes in the electronic degrees of freedom with this
	coupling between the electronic and phononic systems commonly referred to as [[Electron-phonon_interactions_theory \| electron-phonon interactions]].		coupling between the electronic and phononic systems commonly referred to as [[Electron-phonon_interactions_theory \| electron-phonon interactions]].
	These interactions can be captured by perturbative methods or [[Electron-phonon_interactions_from_Monte-Carlo_sampling \| Monte-Carlo sampling]] to populate a supercell with phonons and monitor how the electronic band-structure changes.		These interactions can be captured by [[:Category:Electron-phonon_interactions#Perturbative approach \| perturbative methods]] or [[Electron-phonon_interactions_from_Monte-Carlo_sampling \| Monte-Carlo sampling]] to populate a supercell with phonons and monitor how the electronic band-structure changes.

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

2024-10-08T07:59:25Z

← Older revision		Revision as of 07:59, 8 October 2024
Line 2:		Line 2:

	Here we will present a short summary with the complete derivation presented on the [[Phonons: Theory\|theory page]].		Here we will present a short summary with the complete derivation presented on the [[Phonons: Theory\|theory page]].
	Let us start by making the Taylor expansion of the total energy <math>E</math> in terms of the ionic displacement		Let us start by making the Taylor expansion of the total energy <math>E </math> in terms of the ionic displacement
	<math>		<math>
	u_{I\alpha} = R_{I\alpha} - R^0_{I\alpha}		u_{I\alpha} = R_{I\alpha} - R^0_{I\alpha}

2024-02-09T16:12:09Z

← Older revision		Revision as of 16:12, 9 February 2024
Line 45:		Line 45:

	----		----
	[[Category:VASP\|Phonons]][[Category:~~Linear response\|~~Linear response]]		[[Category:VASP\|Phonons]][[Category:Linear response]]

2024-02-07T11:38:17Z

← Older revision		Revision as of 11:38, 7 February 2024
Line 43:		Line 43:
	* [[Computing the phonon dispersion and DOS]]		* [[Computing the phonon dispersion and DOS]]
	* [[Electron-phonon interactions from Monte-Carlo sampling]]		* [[Electron-phonon interactions from Monte-Carlo sampling]]

			----
			[[Category:VASP\|Phonons]][[Category:Linear response\|Linear response]]

2023-10-23T09:17:34Z

← Older revision		Revision as of 09:17, 23 October 2023
Line 30:		Line 30:
	The computation of the second-order force constants using the supercell approach can be done using [[Phonons from finite differences\|finite-differences]] or [[Phonons from density-functional-perturbation theory \| density functional perturbation theory]].		The computation of the second-order force constants using the supercell approach can be done using [[Phonons from finite differences\|finite-differences]] or [[Phonons from density-functional-perturbation theory \| density functional perturbation theory]].

	It is possible to [[~~Computing_the_phonon_dispersion~~ \|obtain the phonon dispersion at different '''q''' points]] by computing the second-order force constants on a sufficiently large supercell and Fourier interpolating the dynamical matrices in the unit cell.		It is possible to [[Computing_the_phonon_dispersion_and_DOS \|obtain the phonon dispersion at different '''q''' points]] by computing the second-order force constants on a sufficiently large supercell and Fourier interpolating the dynamical matrices in the unit cell.

	== Electron-phonon interaction ==		== Electron-phonon interaction ==

2023-10-23T09:17:08Z

How to

← Older revision		Revision as of 09:17, 23 October 2023
Line 41:		Line 41:
	* [[Phonons from finite differences]]		* [[Phonons from finite differences]]
	* [[Phonons from density-functional-perturbation theory]]		* [[Phonons from density-functional-perturbation theory]]
	* [[Computing the phonon dispersion]]		* [[Computing the phonon dispersion and DOS]]
	* [[Electron-phonon interactions from Monte-Carlo sampling]]		* [[Electron-phonon interactions from Monte-Carlo sampling]]

2022-09-23T06:54:04Z

How to

← Older revision		Revision as of 06:54, 23 September 2022
Line 41:		Line 41:
	* [[Phonons from finite differences]]		* [[Phonons from finite differences]]
	* [[Phonons from density-functional-perturbation theory]]		* [[Phonons from density-functional-perturbation theory]]
			* [[Computing the phonon dispersion]]
	* [[Electron-phonon interactions from Monte-Carlo sampling]]		* [[Electron-phonon interactions from Monte-Carlo sampling]]

2022-08-11T07:33:30Z

← Older revision		Revision as of 07:33, 11 August 2022
Line 22:		Line 22:
	:<math>		:<math>
	\sum_{J\beta} \frac{1}{\sqrt{M_I M_J}} \Phi_{I\alpha J\beta} e^{i\mathbf{q} \cdot (\mathbf{R}_J-\mathbf{R}_I)} (\mathbf{q})		\sum_{J\beta} \frac{1}{\sqrt{M_I M_J}} \Phi_{I\alpha J\beta} e^{i\mathbf{q} \cdot (\mathbf{R}_J-\mathbf{R}_I)} (\mathbf{q})
	\~~xi^{\nu }_~~{J\beta}(\mathbf{q}) =		\varepsilon_{J\beta,\nu}(\mathbf{q}) =
	\~~omega^~~\nu(\mathbf{q})^2 \~~xi^{\nu }_~~{I\alpha}(\mathbf{q})		\omega_\nu(\mathbf{q})^2 \varepsilon_{I\alpha,\nu}(\mathbf{q})
	</math>		</math>
	where the normal modes <math>\~~xi^{\nu }_~~{I\alpha}(\mathbf{q})</math>		where the normal modes <math>\varepsilon_{I\alpha,\nu}(\mathbf{q})</math>
	and corresponding frequencies <math>\~~omega^~~\nu(\mathbf{q})^2</math> are the phonons in the adiabatic harmonic approximation.		and corresponding frequencies <math>\omega_\nu(\mathbf{q})^2</math> are the phonons in the adiabatic harmonic approximation.

	The computation of the second-order force constants using the supercell approach can be done using [[Phonons from finite differences\|finite-differences]] or [[Phonons from density-functional-perturbation theory \| density functional perturbation theory]].		The computation of the second-order force constants using the supercell approach can be done using [[Phonons from finite differences\|finite-differences]] or [[Phonons from density-functional-perturbation theory \| density functional perturbation theory]].