Phonons from density-functional-perturbation theory - Revision history

Csheldon at 10:03, 9 February 2026

2026-02-09T10:03:39Z

← Older revision		Revision as of 10:03, 9 February 2026
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	It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}
	{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported by VASP.5.1 and later versions.}}		{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported by VASP.5.1 and later versions.}}

	~~== Practical hints ==~~
	*Bear in mind that the choice of exchange-correlation functional can have a big impact on the [[Born effective charges]] and the [[:Category:Dielectric_properties#Dielectric_function \| dielectric function]], and thereby the LO-TO splitting.

	== Related tags and sections ==		== Related tags and sections ==

Csheldon: /* Output */

2026-02-09T10:01:45Z

Output

← Older revision		Revision as of 10:01, 9 February 2026
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	It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}
	{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported by VASP.5.1 and later versions.}}		{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported by VASP.5.1 and later versions.}}

			== Practical hints ==
			*Bear in mind that the choice of exchange-correlation functional can have a big impact on the [[Born effective charges]] and the [[:Category:Dielectric_properties#Dielectric_function \| dielectric function]], and thereby the LO-TO splitting.

	== Related tags and sections ==		== Related tags and sections ==

Mani: /* Output */ Fix broken link

2024-10-18T10:14:04Z

Output: Fix broken link

← Older revision		Revision as of 10:14, 18 October 2024
Line 41:		Line 41:
	The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.		The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.

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

	It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}

Huebsch at 09:41, 23 October 2023

2023-10-23T09:41:20Z

← Older revision		Revision as of 09:41, 23 October 2023
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	* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.		* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.

	If {{TAG\|LEPSILON}}=.TRUE. ~~is specified in the~~ {{TAG\|~~INCAR~~}} ~~file~~, ~~then Born effective charges, piezoelectric constants, and the ionic contributions to the~~ dielectric ~~tensor~~ are ~~calculated~~.		If {{TAG\|LEPSILON}}=.TRUE. or {{TAG\|LCALCEPS}}=.TRUE., additional dielectric properties are computed.

	== Output ==		== Output ==

Huebsch at 08:35, 23 October 2023

2023-10-23T08:35:06Z

← Older revision		Revision as of 08:35, 23 October 2023
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	In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons.		In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons.
	Therefore, ~~the code~~ offers few advantages over ~~the~~ [[Phonons_from_finite_differences\|finite differences ~~methods~~]].		Therefore, this approach offers few advantages over computing [[Phonons_from_finite_differences\|phonons from finite differences]].
	In particular, the DFPT routines are limited to LDA and GGA functionals and ~~it does~~ not determine the elastic tensors, since the perturbation with respect to the strain tensor is not implemented.		In particular, the DFPT routines are limited to LDA and GGA functionals, and they do not determine the elastic tensors, since the perturbation with respect to the strain tensor is not implemented.
	The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement {{TAG\|POTIM}}.		The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement {{TAG\|POTIM}}.
	Therefore, it might be helpful to first calculate phonon frequencies ~~using linear response~~ and then switch to [[Phonons from finite differences\|finite differences]] ~~and~~ determine the largest displacement that will produce results compatible with the linear response routines.		Therefore, it might be helpful to first calculate phonon frequencies within DFPT and then switch to the [[Phonons from finite differences\|finite differences approach]] in order to determine the largest displacement that will produce results compatible with the linear response routines.

	A few technical comments ~~are in order at this point.~~ VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals.		A few technical comments: VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals.
	Hence, unoccupied orbitals are not required.		Hence, unoccupied orbitals are not required.
	Internally, the VASP routines for linear response rely on finite differences in two places:		Internally, the VASP routines for linear response rely on finite differences in two places:
Line 14:		Line 14:
	# Second, after VASP has determined the first-order change of the orbitals, it computes all [[Phonons:_Theory#ForceConstantsDFPT\|second derivatives using finite displacements]].		# Second, after VASP has determined the first-order change of the orbitals, it computes all [[Phonons:_Theory#ForceConstantsDFPT\|second derivatives using finite displacements]].

	To do this, VASP displaces the selected atom in the selected directions [[Phonons:_Theory#FiniteDiffWF\|adds the calculated linear response to the orbitals]], and finally determines the differences in the forces and the stress tensor for positive and negative displacements.		To this end, VASP displaces the selected atom in the selected directions [[Phonons:_Theory#FiniteDiffWF\|adds the calculated linear response to the orbitals]], and finally determines the differences in the forces and the stress tensor for positive and negative displacements.
	It can be shown that this yields ~~exactly~~ the [[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and the [[Phonons:_Theory#InternalStrainDFPT\|internal strain tensor]], respectively.		It can be shown that this yields precisely the [[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and the [[Phonons:_Theory#InternalStrainDFPT\|internal strain tensor]], respectively.

	== Input ==		== Input ==

	To use DFPT the tag [[IBRION#ibrion78\|'''IBRION'''=7 or 8]] ~~has to be set~~ in the {{TAG\|INCAR}} file.		To use DFPT, set the tag [[IBRION#ibrion78\|'''IBRION'''=7 or 8]] in the {{TAG\|INCAR}} file.
	There are two options ~~to use~~ the DFPT routines to compute the second order force-constants		There are two options for using the DFPT routines to compute the second-order force-constants
	* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,		* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,
	* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.		* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.

	If {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file then Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated.		If {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file, then Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated.

	== Output ==		== Output ==
Line 44:		Line 44:

	It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}
	{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported ~~from~~ VASP.5.1 and later versions.}}		{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported by VASP.5.1 and later versions.}}

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

Miranda.henrique at 09:19, 12 August 2022

2022-08-12T09:19:56Z

← Older revision		Revision as of 09:19, 12 August 2022
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	== Output ==		== Output ==

	The ~~output is similar as for~~ [[~~IBRION~~#~~ibrion56~~\|~~'''IBRION'''=5 and 6~~]].		The second derivates of the total energy with respect to ionic displacements (interatomic force constants) are computed,
			the [[Phonons:_Theory#DynamicalMatrix\|dynamical matrix]] is constructed, diagonalized and the phonon modes and frequencies of the system are reported after the following lines:

	~~The second derivates~~ of the ~~total energy with respect to ionic displacements (interatomic force constants) are computed,~~		Eigenvectors and eigenvalues of the dynamical matrix
	~~the [[Phonons:_Theory#DynamicalMatrix\|~~dynamical matrix~~]] is constructed, diagonalized and the phonon modes and frequencies of the system are reported.~~		----------------------------------------------------

	The mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated and reported.		The mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated and reported.

Miranda.henrique at 08:28, 12 August 2022

2022-08-12T08:28:43Z

← Older revision		Revision as of 08:28, 12 August 2022
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	The phonon calculations using [[Phonons:_Theory#Density_functional_perturbation_theory\|density-functional-perturbation theory (DFPT)]] are carried out by setting ~~{{TAG~~\|IBRION}}=7 or 8 in the {{FILE\|INCAR}} file.		The phonon calculations using [[Phonons:_Theory#Density_functional_perturbation_theory\|density-functional-perturbation theory (DFPT)]] are carried out by setting [[IBRION#ibrion78\|'''IBRION'''=7 or 8]] in the {{FILE\|INCAR}} file.
	{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}		{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}

Line 19:		Line 19:
	== Input ==		== Input ==

	To use DFPT the tag ~~{{TAG~~\|IBRION}}=7 or 8 has to be set in the {{TAG\|INCAR}} file.		To use DFPT the tag [[IBRION#ibrion78\|'''IBRION'''=7 or 8]] has to be set in the {{TAG\|INCAR}} file.
	There are two options to use the DFPT routines to compute the second order force-constants		There are two options to use the DFPT routines to compute the second order force-constants
	* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,		* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,

Miranda.henrique at 07:49, 12 August 2022

2022-08-12T07:49:36Z

← Older revision		Revision as of 07:49, 12 August 2022
Line 43:		Line 43:

	It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}
	{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 ~~and {{TAG\|IBRION}}{{=}}~~8 are supported from VASP.5.1 and later versions.}}		{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported from VASP.5.1 and later versions.}}

			== Related Tags and Sections ==
			{{TAG\|IBRION}},
			[[Phonons: Theory]],
			[[Phonons from finite differences]]

	== References ==		== References ==

Miranda.henrique at 07:37, 12 August 2022

2022-08-12T07:37:11Z

← Older revision		Revision as of 07:37, 12 August 2022
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			The phonon calculations using [[Phonons:_Theory#Density_functional_perturbation_theory\|density-functional-perturbation theory (DFPT)]] are carried out by setting {{TAG\|IBRION}}=7 or 8 in the {{FILE\|INCAR}} file.
			{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}

	This approach determines the Hessian matrix (matrix of second derivatives with respect to the position of the ions) using density-functional-perturbation theory (DFPT). To use DFPT the tag {{TAG\|IBRION}} has to be set in the {{TAG\|INCAR}} file. Setting {{TAG\|IBRION}}=7 does not exploit the symmetry of the crystal, whereas {{TAG\|IBRION}}=8 uses symmetry to reduce the number of needed displacements. The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]]. Specifically, the second derivates of the total energy with respect to ionic displacements (interatomic force constants) and the mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated. Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined. Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated if {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file.		In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons.
	~~{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}~~		Therefore, the code offers few advantages over the [[Phonons_from_finite_differences\|finite differences methods]].
	In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons. ~~In other words, VASP can only determine phonon frequencies at the Gamma point of the supercell.~~ Therefore, the code offers few advantages over the finite differences methods ~~discussed above~~. In particular, the ~~linear response is~~ limited to LDA and GGA functionals and it does not determine the elastic tensors, since the ~~linear response~~ with respect to the strain tensor is not implemented. The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement. Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.		In particular, the DFPT routines are limited to LDA and GGA functionals and it does not determine the elastic tensors, since the perturbation with respect to the strain tensor is not implemented.
			The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement {{TAG\|POTIM}}.
			Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.

	A few technical comments are in order at this point. VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals. Hence, unoccupied orbitals are not required. Internally, the VASP routines for linear response rely on finite differences in two places:		A few technical comments are in order at this point. VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals.
			Hence, unoccupied orbitals are not required.
			Internally, the VASP routines for linear response rely on finite differences in two places:
	# The first place is the determination of the second derivative of the [[:Category:Exchange-correlation_functionals\|exchange-correlation functional]]: Since most functionals do not support an algebraic determination of second derivatives, VASP always resorts to finite differences to determine the second-order change of the exchange correlation-potential and the PAW one-center terms for each atomic displacement.		# The first place is the determination of the second derivative of the [[:Category:Exchange-correlation_functionals\|exchange-correlation functional]]: Since most functionals do not support an algebraic determination of second derivatives, VASP always resorts to finite differences to determine the second-order change of the exchange correlation-potential and the PAW one-center terms for each atomic displacement.
	# Second, after VASP has determined the first-order change of the orbitals, it computes all second derivatives using finite displacements.		# Second, after VASP has determined the first-order change of the orbitals, it computes all [[Phonons:_Theory#ForceConstantsDFPT\|second derivatives using finite displacements]].

			To do this, VASP displaces the selected atom in the selected directions [[Phonons:_Theory#FiniteDiffWF\|adds the calculated linear response to the orbitals]], and finally determines the differences in the forces and the stress tensor for positive and negative displacements.
			It can be shown that this yields exactly the [[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and the [[Phonons:_Theory#InternalStrainDFPT\|internal strain tensor]], respectively.

			== Input ==

			To use DFPT the tag {{TAG\|IBRION}}=7 or 8 has to be set in the {{TAG\|INCAR}} file.
			There are two options to use the DFPT routines to compute the second order force-constants
			* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,
			* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.

			If {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file then Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated.

			== Output ==

			The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]].

			The second derivates of the total energy with respect to ionic displacements (interatomic force constants) are computed,
			the [[Phonons:_Theory#DynamicalMatrix\|dynamical matrix]] is constructed, diagonalized and the phonon modes and frequencies of the system are reported.

	~~To do this, VASP displaces~~ the ~~selected atom in~~ the ~~selected directions adds~~ the ~~calculated linear response~~ to the ~~orbitals~~, ~~and finally determines~~ the ~~differences in the forces and the stress~~ tensor ~~for positive and negative displacements. It can be shown that this yields exactly~~ the ~~[[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and~~ the ~~[[Phonons:_Theory#InternalStrainDFPT\|internal~~ strain tensor~~]], respectively~~.		The mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated and reported.
			Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined because the perturbation with respect to the strain tensor is not implemented.

	Furthermore, the [[Phonons:_Theory#BornChargeDFPT\|Born effective charges]] are determined "analytically" by contracting the linear response of the orbitals over the "polarization" vector Eq. (30) in Ref. {{cite\|gajdos:prb:2006}}. These should agree well with the Born effective charges that were previously determined when the linear response with respect to external fields {{TAG\|LEPSILON}}=.TRUE. was calculated (there are two different routes to calculate mixed derivatives). The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.		Furthermore, the [[Phonons:_Theory#BornChargeDFPT\|Born effective charges]] are determined analytically by contracting the linear response of the orbitals over the "polarization" vector Eq. (30) in Ref. {{cite\|gajdos:prb:2006}}.
			These should agree well with the Born effective charges that were previously determined when the linear response with respect to external fields {{TAG\|LEPSILON}}=.TRUE. was calculated (there are two different routes to calculate mixed derivatives).
			The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.

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

	It is also possible to use phonopy{{cite\|phonopy}} to ~~post-process~~ the results of a ~~finite differences~~ calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}
	{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 and {{TAG\|IBRION}}{{=}}8 are supported from VASP.5.1 and later versions.}}		{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 and {{TAG\|IBRION}}{{=}}8 are supported from VASP.5.1 and later versions.}}

Miranda.henrique at 07:34, 11 August 2022

2022-08-11T07:34:57Z

← Older revision		Revision as of 07:34, 11 August 2022
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	This approach determines the Hessian matrix (matrix of second derivatives with respect to the position of the ions) using density-functional-perturbation theory (DFPT). To use DFPT the tag {{TAG\|IBRION}} has to be set in the {{TAG\|INCAR}} file. Setting {{TAG\|IBRION}}=7 does not exploit the symmetry of the crystal, whereas {{TAG\|IBRION}}=8 uses symmetry to reduce the number of needed displacements. The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]]. Specifically, the second derivates of the total energy with respect to ionic displacements (interatomic force constants) and the mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated. Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined. Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated if {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file.		This approach determines the Hessian matrix (matrix of second derivatives with respect to the position of the ions) using density-functional-perturbation theory (DFPT). To use DFPT the tag {{TAG\|IBRION}} has to be set in the {{TAG\|INCAR}} file. Setting {{TAG\|IBRION}}=7 does not exploit the symmetry of the crystal, whereas {{TAG\|IBRION}}=8 uses symmetry to reduce the number of needed displacements. The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]]. Specifically, the second derivates of the total energy with respect to ionic displacements (interatomic force constants) and the mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated. Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined. Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated if {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file.
			{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}
	In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons. In other words, VASP can only determine phonon frequencies at the Gamma point of the supercell. Therefore, the code offers few advantages over the finite differences methods discussed above. In particular, the linear response is limited to LDA and GGA functionals and it does not determine the elastic tensors, since the linear response with respect to the strain tensor is not implemented. The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement. Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.		In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons. In other words, VASP can only determine phonon frequencies at the Gamma point of the supercell. Therefore, the code offers few advantages over the finite differences methods discussed above. In particular, the linear response is limited to LDA and GGA functionals and it does not determine the elastic tensors, since the linear response with respect to the strain tensor is not implemented. The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement. Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.

← Older revision		Revision as of 10:14, 18 October 2024
Line 41:		Line 41:
	The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.		The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.

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

	It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}

← Older revision		Revision as of 08:35, 23 October 2023
Line 3:		Line 3:

	In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons.		In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons.
	Therefore, ~~the code~~ offers few advantages over ~~the~~ [[Phonons_from_finite_differences\|finite differences ~~methods~~]].		Therefore, this approach offers few advantages over computing [[Phonons_from_finite_differences\|phonons from finite differences]].
	In particular, the DFPT routines are limited to LDA and GGA functionals and ~~it does~~ not determine the elastic tensors, since the perturbation with respect to the strain tensor is not implemented.		In particular, the DFPT routines are limited to LDA and GGA functionals, and they do not determine the elastic tensors, since the perturbation with respect to the strain tensor is not implemented.
	The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement {{TAG\|POTIM}}.		The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement {{TAG\|POTIM}}.
	Therefore, it might be helpful to first calculate phonon frequencies ~~using linear response~~ and then switch to [[Phonons from finite differences\|finite differences]] ~~and~~ determine the largest displacement that will produce results compatible with the linear response routines.		Therefore, it might be helpful to first calculate phonon frequencies within DFPT and then switch to the [[Phonons from finite differences\|finite differences approach]] in order to determine the largest displacement that will produce results compatible with the linear response routines.

	A few technical comments ~~are in order at this point.~~ VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals.		A few technical comments: VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals.
	Hence, unoccupied orbitals are not required.		Hence, unoccupied orbitals are not required.
	Internally, the VASP routines for linear response rely on finite differences in two places:		Internally, the VASP routines for linear response rely on finite differences in two places:
Line 14:		Line 14:
	# Second, after VASP has determined the first-order change of the orbitals, it computes all [[Phonons:_Theory#ForceConstantsDFPT\|second derivatives using finite displacements]].		# Second, after VASP has determined the first-order change of the orbitals, it computes all [[Phonons:_Theory#ForceConstantsDFPT\|second derivatives using finite displacements]].

	To do this, VASP displaces the selected atom in the selected directions [[Phonons:_Theory#FiniteDiffWF\|adds the calculated linear response to the orbitals]], and finally determines the differences in the forces and the stress tensor for positive and negative displacements.		To this end, VASP displaces the selected atom in the selected directions [[Phonons:_Theory#FiniteDiffWF\|adds the calculated linear response to the orbitals]], and finally determines the differences in the forces and the stress tensor for positive and negative displacements.
	It can be shown that this yields ~~exactly~~ the [[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and the [[Phonons:_Theory#InternalStrainDFPT\|internal strain tensor]], respectively.		It can be shown that this yields precisely the [[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and the [[Phonons:_Theory#InternalStrainDFPT\|internal strain tensor]], respectively.

	== Input ==		== Input ==

	To use DFPT the tag [[IBRION#ibrion78\|'''IBRION'''=7 or 8]] ~~has to be set~~ in the {{TAG\|INCAR}} file.		To use DFPT, set the tag [[IBRION#ibrion78\|'''IBRION'''=7 or 8]] in the {{TAG\|INCAR}} file.
	There are two options ~~to use~~ the DFPT routines to compute the second order force-constants		There are two options for using the DFPT routines to compute the second-order force-constants
	* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,		* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,
	* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.		* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.

	If {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file then Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated.		If {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file, then Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated.

	== Output ==		== Output ==
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	It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}
	{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported ~~from~~ VASP.5.1 and later versions.}}		{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 or 8 are supported by VASP.5.1 and later versions.}}

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

← Older revision		Revision as of 07:37, 12 August 2022
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			The phonon calculations using [[Phonons:_Theory#Density_functional_perturbation_theory\|density-functional-perturbation theory (DFPT)]] are carried out by setting {{TAG\|IBRION}}=7 or 8 in the {{FILE\|INCAR}} file.
			{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}

	This approach determines the Hessian matrix (matrix of second derivatives with respect to the position of the ions) using density-functional-perturbation theory (DFPT). To use DFPT the tag {{TAG\|IBRION}} has to be set in the {{TAG\|INCAR}} file. Setting {{TAG\|IBRION}}=7 does not exploit the symmetry of the crystal, whereas {{TAG\|IBRION}}=8 uses symmetry to reduce the number of needed displacements. The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]]. Specifically, the second derivates of the total energy with respect to ionic displacements (interatomic force constants) and the mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated. Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined. Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated if {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file.		In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons.
	~~{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}~~		Therefore, the code offers few advantages over the [[Phonons_from_finite_differences\|finite differences methods]].
	In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons. ~~In other words, VASP can only determine phonon frequencies at the Gamma point of the supercell.~~ Therefore, the code offers few advantages over the finite differences methods ~~discussed above~~. In particular, the ~~linear response is~~ limited to LDA and GGA functionals and it does not determine the elastic tensors, since the ~~linear response~~ with respect to the strain tensor is not implemented. The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement. Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.		In particular, the DFPT routines are limited to LDA and GGA functionals and it does not determine the elastic tensors, since the perturbation with respect to the strain tensor is not implemented.
			The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement {{TAG\|POTIM}}.
			Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.

	A few technical comments are in order at this point. VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals. Hence, unoccupied orbitals are not required. Internally, the VASP routines for linear response rely on finite differences in two places:		A few technical comments are in order at this point. VASP solves the [[Phonons:_Theory#IonSternheimer\|linear Sternheimer equation]] to determine the linear response of the orbitals.
			Hence, unoccupied orbitals are not required.
			Internally, the VASP routines for linear response rely on finite differences in two places:
	# The first place is the determination of the second derivative of the [[:Category:Exchange-correlation_functionals\|exchange-correlation functional]]: Since most functionals do not support an algebraic determination of second derivatives, VASP always resorts to finite differences to determine the second-order change of the exchange correlation-potential and the PAW one-center terms for each atomic displacement.		# The first place is the determination of the second derivative of the [[:Category:Exchange-correlation_functionals\|exchange-correlation functional]]: Since most functionals do not support an algebraic determination of second derivatives, VASP always resorts to finite differences to determine the second-order change of the exchange correlation-potential and the PAW one-center terms for each atomic displacement.
	# Second, after VASP has determined the first-order change of the orbitals, it computes all second derivatives using finite displacements.		# Second, after VASP has determined the first-order change of the orbitals, it computes all [[Phonons:_Theory#ForceConstantsDFPT\|second derivatives using finite displacements]].

			To do this, VASP displaces the selected atom in the selected directions [[Phonons:_Theory#FiniteDiffWF\|adds the calculated linear response to the orbitals]], and finally determines the differences in the forces and the stress tensor for positive and negative displacements.
			It can be shown that this yields exactly the [[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and the [[Phonons:_Theory#InternalStrainDFPT\|internal strain tensor]], respectively.

			== Input ==

			To use DFPT the tag {{TAG\|IBRION}}=7 or 8 has to be set in the {{TAG\|INCAR}} file.
			There are two options to use the DFPT routines to compute the second order force-constants
			* {{TAG\|IBRION}}=7, all the atoms are displaced in all three Cartesian directions,
			* {{TAG\|IBRION}}=8, uses symmetry to reduce the number of displacements.

			If {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file then Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated.

			== Output ==

			The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]].

			The second derivates of the total energy with respect to ionic displacements (interatomic force constants) are computed,
			the [[Phonons:_Theory#DynamicalMatrix\|dynamical matrix]] is constructed, diagonalized and the phonon modes and frequencies of the system are reported.

	~~To do this, VASP displaces~~ the ~~selected atom in~~ the ~~selected directions adds~~ the ~~calculated linear response~~ to the ~~orbitals~~, ~~and finally determines~~ the ~~differences in the forces and the stress~~ tensor ~~for positive and negative displacements. It can be shown that this yields exactly~~ the ~~[[Phonons:_Theory#InternalStrainDFPT\|second-order force constants]] and~~ the ~~[[Phonons:_Theory#InternalStrainDFPT\|internal~~ strain tensor~~]], respectively~~.		The mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated and reported.
			Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined because the perturbation with respect to the strain tensor is not implemented.

	Furthermore, the [[Phonons:_Theory#BornChargeDFPT\|Born effective charges]] are determined "analytically" by contracting the linear response of the orbitals over the "polarization" vector Eq. (30) in Ref. {{cite\|gajdos:prb:2006}}. These should agree well with the Born effective charges that were previously determined when the linear response with respect to external fields {{TAG\|LEPSILON}}=.TRUE. was calculated (there are two different routes to calculate mixed derivatives). The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.		Furthermore, the [[Phonons:_Theory#BornChargeDFPT\|Born effective charges]] are determined analytically by contracting the linear response of the orbitals over the "polarization" vector Eq. (30) in Ref. {{cite\|gajdos:prb:2006}}.
			These should agree well with the Born effective charges that were previously determined when the linear response with respect to external fields {{TAG\|LEPSILON}}=.TRUE. was calculated (there are two different routes to calculate mixed derivatives).
			The final summary output towards the end of the {{TAG\|OUTCAR}} file writes the Born effective charges determined from the linear response with respect to external fields.

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

	It is also possible to use phonopy{{cite\|phonopy}} to ~~post-process~~ the results of a ~~finite differences~~ calculation done with VASP.{{cite\|phonopy_dfpt}}		It is also possible to use phonopy{{cite\|phonopy}} to use the results of a density-functional-perturbation theory calculation done with VASP.{{cite\|phonopy_dfpt}}
	{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 and {{TAG\|IBRION}}{{=}}8 are supported from VASP.5.1 and later versions.}}		{{NB\|mind\|{{TAG\|IBRION}}{{=}}7 and {{TAG\|IBRION}}{{=}}8 are supported from VASP.5.1 and later versions.}}

← Older revision		Revision as of 07:34, 11 August 2022
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	This approach determines the Hessian matrix (matrix of second derivatives with respect to the position of the ions) using density-functional-perturbation theory (DFPT). To use DFPT the tag {{TAG\|IBRION}} has to be set in the {{TAG\|INCAR}} file. Setting {{TAG\|IBRION}}=7 does not exploit the symmetry of the crystal, whereas {{TAG\|IBRION}}=8 uses symmetry to reduce the number of needed displacements. The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]]. Specifically, the second derivates of the total energy with respect to ionic displacements (interatomic force constants) and the mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated. Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined. Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated if {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file.		This approach determines the Hessian matrix (matrix of second derivatives with respect to the position of the ions) using density-functional-perturbation theory (DFPT). To use DFPT the tag {{TAG\|IBRION}} has to be set in the {{TAG\|INCAR}} file. Setting {{TAG\|IBRION}}=7 does not exploit the symmetry of the crystal, whereas {{TAG\|IBRION}}=8 uses symmetry to reduce the number of needed displacements. The output is similar as for [[IBRION#ibrion56\|'''IBRION'''=5 and 6]]. Specifically, the second derivates of the total energy with respect to ionic displacements (interatomic force constants) and the mixed second derivative with respect to the strain and the ionic displacement (internal strain tensor) are evaluated. Although the contributions from the ionic relaxations to the elastic tensor are calculated, the ion-clamped elastic tensor (rigid ion) is not determined. Born effective charges, piezoelectric constants, and the ionic contributions to the dielectric tensor are calculated if {{TAG\|LEPSILON}}=.TRUE. is specified in the {{TAG\|INCAR}} file.
			{{NB\|mind\|Only zone-center (Γ-point) frequencies are calculated.}}
	In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons. In other words, VASP can only determine phonon frequencies at the Gamma point of the supercell. Therefore, the code offers few advantages over the finite differences methods discussed above. In particular, the linear response is limited to LDA and GGA functionals and it does not determine the elastic tensors, since the linear response with respect to the strain tensor is not implemented. The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement. Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.		In general, the DFPT routines in VASP are somewhat rudimentary and only support displacements commensurate with the supercell, i.e., so-called q=0 phonons. In other words, VASP can only determine phonon frequencies at the Gamma point of the supercell. Therefore, the code offers few advantages over the finite differences methods discussed above. In particular, the linear response is limited to LDA and GGA functionals and it does not determine the elastic tensors, since the linear response with respect to the strain tensor is not implemented. The only advantage of the linear response routines is that they eliminate the need to choose the magnitude of the finite displacement. Therefore, it might be helpful to first calculate phonon frequencies using linear response and then switch to [[Phonons from finite differences\|finite differences]] and determine the largest displacement that will produce results compatible with the linear response routines.