Phonons: Theory - Revision history

Csheldon: /* Related tags and sections */

2025-11-12T10:42:38Z

Related tags and sections

← Older revision		Revision as of 10:42, 12 November 2025
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	{{TAG\|IBRION}},		{{TAG\|IBRION}},
	[[Phonons from finite differences]],		[[Phonons from finite differences]],
	[[Phonons from density-functional-perturbation theory]]		[[Phonons from density-functional-perturbation theory]],
			[[Static linear response: theory]]

	== References ==		== References ==

Huebsch: /* Related Tags and Sections */

2023-10-20T07:23:08Z

Related Tags and Sections

← Older revision		Revision as of 07:23, 20 October 2023
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	The results should be equivalent to the ones obtained using {{TAG\|LCALCEPS}} and {{TAG\|LEPSILON}}.		The results should be equivalent to the ones obtained using {{TAG\|LCALCEPS}} and {{TAG\|LEPSILON}}.

	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and sections ==
	{{TAG\|IBRION}},		{{TAG\|IBRION}},
	[[Phonons from finite differences]],		[[Phonons from finite differences]],

Miranda.henrique: /* Long-range interatomic force constants (LO-TO splitting) */

2022-09-23T07:09:39Z

Long-range interatomic force constants (LO-TO splitting)

← Older revision		Revision as of 07:09, 23 September 2022
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	e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}		e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}
	</math>		</math>
	with <math display="inline">\epsilon^\infty</math> the clamped ~~ion~~ dielectric tensor, <math display="inline">\mathbf{Z}^*_{I\alpha}</math> the Born effective charges, <math display="inline">\alpha</math> the Ewald parameter which is chosen such that the contributions from <math display="inline">e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}</math> are negligible within a certain <math display="inline">\mathbf{G}</math> vector cutoff sphere {{TAG\|PHON_G_CUTOFF}}.		with <math display="inline">\epsilon^\infty</math> the ion-clamped dielectric tensor, <math display="inline">\mathbf{Z}^*_{I\alpha}</math> the Born effective charges, <math display="inline">\alpha</math> the Ewald parameter which is chosen such that the contributions from <math display="inline">e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}</math> are negligible within a certain <math display="inline">\mathbf{G}</math> vector cutoff sphere {{TAG\|PHON_G_CUTOFF}}.

	This also allows us to separate the dynamical matrix into short and long-range parts		This also allows us to separate the dynamical matrix into short and long-range parts

Miranda.henrique: /* Long-range interatomic force constants (LO-TO splitting) */

2022-09-23T07:09:09Z

Long-range interatomic force constants (LO-TO splitting)

← Older revision		Revision as of 07:09, 23 September 2022
Line 121:		Line 121:
	e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}		e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}
	</math>		</math>
	with <math display="inline">\epsilon^\infty</math> the clamped ion dielectric ~~function~~, <math display="inline">\mathbf{Z}^*_{I\alpha}</math> the Born effective charges, <math display="inline">\alpha</math> the Ewald parameter which is chosen such that the contributions from <math display="inline">e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}</math> are negligible within a certain <math display="inline">\mathbf{G}</math> vector cutoff sphere {{TAG\|PHON_G_CUTOFF}}.		with <math display="inline">\epsilon^\infty</math> the clamped ion dielectric tensor, <math display="inline">\mathbf{Z}^*_{I\alpha}</math> the Born effective charges, <math display="inline">\alpha</math> the Ewald parameter which is chosen such that the contributions from <math display="inline">e^\frac{-\mathbf{G} \cdot \epsilon^\infty \cdot \mathbf{G}}{4\lambda^2}</math> are negligible within a certain <math display="inline">\mathbf{G}</math> vector cutoff sphere {{TAG\|PHON_G_CUTOFF}}.

	This also allows us to separate the dynamical matrix into short and long-range parts		This also allows us to separate the dynamical matrix into short and long-range parts

Miranda.henrique: /* Long-range interatomic force constants (LO-TO splitting) */

2022-09-22T07:22:53Z

Long-range interatomic force constants (LO-TO splitting)

← Older revision		Revision as of 07:22, 22 September 2022
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	* Compute <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}=\Phi_{I\alpha J\beta}-\Phi^\text{LR}_{I\alpha J\beta}</math>		* Compute <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}=\Phi_{I\alpha J\beta}-\Phi^\text{LR}_{I\alpha J\beta}</math>
	* Compute <math display="inline">D^\text{SR}_{i\alpha j\beta}(\mathbf{q})</math> using <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}</math>		* Compute <math display="inline">D^\text{SR}_{i\alpha j\beta}(\mathbf{q})</math> using <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}</math>
	* Compute <math>D^\text{LR}_{i\alpha j\beta}(\mathbf{q})</math> in the unit cell and add to <math>D^\text{SR}_{i\alpha i\beta}(\mathbf{q})</math>		* Compute <math>D^\text{LR}_{i\alpha j\beta}(\mathbf{q})</math> in the unit cell and add to <math>D^\text{SR}_{i\alpha j\beta}(\mathbf{q})</math>

	The treatment is done automatically inside VASP using the {{TAG\|LPHON_POLAR}}=.TRUE. tag and specifying the dielectric tensor with {{TAG\|PHON_DIELECTRIC}} and the Born effective charges with {{TAG\|PHON_BORN_CHARGES}}.		The treatment is done automatically inside VASP using the {{TAG\|LPHON_POLAR}}=.TRUE. tag and specifying the dielectric tensor with {{TAG\|PHON_DIELECTRIC}} and the Born effective charges with {{TAG\|PHON_BORN_CHARGES}}.

Miranda.henrique: /* Long-range interatomic force constants (LO-TO splitting) */

2022-09-22T07:22:32Z

Long-range interatomic force constants (LO-TO splitting)

← Older revision		Revision as of 07:22, 22 September 2022
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	* Compute <math display="inline">\Phi_{I\alpha J\beta}</math> using a finite size supercell		* Compute <math display="inline">\Phi_{I\alpha J\beta}</math> using a finite size supercell
	* Compute <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}=\Phi_{I\alpha J\beta}-\Phi^\text{LR}_{I\alpha J\beta}</math>		* Compute <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}=\Phi_{I\alpha J\beta}-\Phi^\text{LR}_{I\alpha J\beta}</math>
	* Compute <math display="inline">D^\text{SR}_{i\alpha i\beta}(\mathbf{q})</math> using <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}</math>		* Compute <math display="inline">D^\text{SR}_{i\alpha j\beta}(\mathbf{q})</math> using <math display="inline">\Phi_{I\alpha J\beta}^\text{SR}</math>
	* Compute <math>D^\text{LR}_{i\alpha i\beta}(\mathbf{q})</math> in the unit cell and add to <math>D^\text{SR}_{i\alpha i\beta}(\mathbf{q})</math>		* Compute <math>D^\text{LR}_{i\alpha j\beta}(\mathbf{q})</math> in the unit cell and add to <math>D^\text{SR}_{i\alpha i\beta}(\mathbf{q})</math>

	The treatment is done automatically inside VASP using the {{TAG\|LPHON_POLAR}}=.TRUE. tag and specifying the dielectric tensor with {{TAG\|PHON_DIELECTRIC}} and the Born effective charges with {{TAG\|PHON_BORN_CHARGES}}.		The treatment is done automatically inside VASP using the {{TAG\|LPHON_POLAR}}=.TRUE. tag and specifying the dielectric tensor with {{TAG\|PHON_DIELECTRIC}} and the Born effective charges with {{TAG\|PHON_BORN_CHARGES}}.

Miranda.henrique: /* Density functional perturbation theory */

2022-08-18T11:46:57Z

Density functional perturbation theory

← Older revision		Revision as of 11:46, 18 August 2022
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	-\frac{		-\frac{
	\left(		\left(
	\mathbf{F}[\{\psi^{u_{J\beta}}_{\lambda/2}\}]-		\mathbf{F}[\{\psi^{u_{J\beta}}_{\lambda}\}]-
	\mathbf{F}[\{\psi^{u_{J\beta}}_{-\lambda/2}\}]		\mathbf{F}[\{\psi^{u_{J\beta}}_{-\lambda}\}]
	\right)_{I\alpha}}{\lambda},		\right)_{I\alpha}}{2\lambda},
	\quad {I=1,..,N_\text{atoms}}		\quad {I=1,..,N_\text{atoms}}
	\quad {J=1,..,N_\text{atoms}}		\quad {J=1,..,N_\text{atoms}}
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	\frac{		\frac{
	\left(		\left(
	\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{\lambda/2}\}]-		\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{\lambda}\}]-
	\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{-\lambda/2}\}]		\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{-\lambda}\}]
	\right)_l		\right)_l
	}{\lambda}		}{2\lambda}
	,\qquad {l=xx, yy, zz, xy, yz, zx} \quad {\alpha=x,y,z} \quad {J=1,..,N_\text{atoms}}		,\qquad {l=xx, yy, zz, xy, yz, zx} \quad {\alpha=x,y,z} \quad {J=1,..,N_\text{atoms}}
	</math>		</math>

Miranda.henrique: /* Finite differences */

2022-08-18T11:46:19Z

Finite differences

← Older revision		Revision as of 11:46, 18 August 2022
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	-\frac{		-\frac{
	\left(		\left(
	\mathbf{F}[\{\psi^{u_{J\beta}}_{\lambda/2}\}]-		\mathbf{F}[\{\psi^{u_{J\beta}}_{\lambda}\}]-
	\mathbf{F}[\{\psi^{u_{J\beta}}_{-\lambda/2}\}]		\mathbf{F}[\{\psi^{u_{J\beta}}_{-\lambda}\}]
	\right)_{I\alpha}}{\lambda},		\right)_{I\alpha}}{2\lambda},
	\quad {I=1,..,N_\text{atoms}}		\quad {I=1,..,N_\text{atoms}}
	\quad {J=1,..,N_\text{atoms}}		\quad {J=1,..,N_\text{atoms}}
Line 178:		Line 178:
	\frac{		\frac{
	\left(		\left(
	\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{\lambda/2}\}]-		\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{\lambda}\}]-
	\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{-\lambda/2}\}]		\mathbf{\sigma}[\{\psi^{u_{I\alpha}}_{-\lambda}\}]
	\right)_l		\right)_l
	}{\lambda}		}{2\lambda}
	,\qquad {l=xx, yy, zz, xy, yz, zx} \quad {\alpha=x,y,z} \quad {J=1,..,N_\text{atoms}}		,\qquad {l=xx, yy, zz, xy, yz, zx} \quad {\alpha=x,y,z} \quad {J=1,..,N_\text{atoms}}
	</math>		</math>

Miranda.henrique: /* Taylor expansion in ionic displacements */

2022-08-18T09:18:53Z

Taylor expansion in ionic displacements

← Older revision		Revision as of 09:18, 18 August 2022
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	== Taylor expansion in ionic displacements ==		== Taylor expansion in ionic displacements ==
	To compute ~~them~~ we start by Taylor expanding the total energy (<math>E</math>) around the set of equilibrium positions of the nuclei (<math>\{\mathbf{R}^0\}</math>)		To compute the phonon modes and frequencies we start by Taylor expanding the total energy (<math>E</math>) around the set of equilibrium positions of the nuclei (<math>\{\mathbf{R}^0\}</math>)
	:<math>		:<math>
	E(\{\mathbf{R}\})=		E(\{\mathbf{R}\})=

Miranda.henrique at 07:45, 12 August 2022

2022-08-12T07:45:29Z

← Older revision		Revision as of 07:45, 12 August 2022
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	and <math>\| \vec{\beta}_{n\mathbf{k}} \rangle</math> is the polarization vector defined in Eq. (30) in Ref. {{cite\|gajdos:prb:2006}}.		and <math>\| \vec{\beta}_{n\mathbf{k}} \rangle</math> is the polarization vector defined in Eq. (30) in Ref. {{cite\|gajdos:prb:2006}}.
	The results should be equivalent to the ones obtained using {{TAG\|LCALCEPS}} and {{TAG\|LEPSILON}}.		The results should be equivalent to the ones obtained using {{TAG\|LCALCEPS}} and {{TAG\|LEPSILON}}.

			== Related Tags and Sections ==
			{{TAG\|IBRION}},
			[[Phonons from finite differences]],
			[[Phonons from density-functional-perturbation theory]]

	== References ==		== References ==