Category:Linear response: Difference between revisions
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(Refer to phonons category. Strictly speaking berry phases is not linear response but it can be used to compute response) |
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Currently, we can consider three types of perturbations: | Currently, we can consider three types of perturbations: | ||
# external electric field | # external electric field | ||
# | # atomic displacements | ||
# | # homogeneous strains | ||
If we restrict ourselves to the first order of the perturbation then we are in the linear regime and thus we talk about linear response. | If we restrict ourselves to the first order of the perturbation then we are in the linear regime and thus we talk about linear response. | ||
A central quantity in linear response is the [[Dielectric properties|dielectric function]] which relates an external electric field with the internal electric displacement. | |||
The response to atomic displacements includes [[:Category:Phonons|phonons]] and [[:Category:electron-phonon interactions|electron-phonon interactions]]. | |||
The response to homogeneous strains is related to the elastic tensor and piezoelectric tensor when combined with a response to and external electric field. | |||
== Polarization, berry phases, and finite electric fields == | == Polarization, berry phases, and finite electric fields == | ||
The polarization in a periodic system can be computed using the [[Berry_phases_and_finite_electric_fields#Modern_Theory_of_Polarization| berry phase formulation of the polarization]] (often referred to as the modern theory of polarization). With a method to compute the polarization, we can apply a [[Berry_phases_and_finite_electric_fields#Berry_phases_and_finite_electric_fields#Self-consistent_response_to_finite_electric_fields| finite electric field]] to the system. | The polarization in a periodic system can be computed using the [[Berry_phases_and_finite_electric_fields#Modern_Theory_of_Polarization| berry phase formulation of the polarization]] (often referred to as the modern theory of polarization). With a method to compute the polarization, we can apply a [[Berry_phases_and_finite_electric_fields#Berry_phases_and_finite_electric_fields#Self-consistent_response_to_finite_electric_fields| finite electric field]] to the system. | ||
Strictly speaking, polarization, as well as the application of a finite electric field, are ground-state properties, however, because they can be used to compute the static dielectric tensor, born effective charges, and piezoelectric tensors which are response properties, we refer to this approach here. | |||
== Static response == | == Static response == | ||
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=== Born effective charges === | === Born effective charges === | ||
=== Elastic tensor === | |||
=== Piezoelectric tensor === | === Piezoelectric tensor === | ||
--> | --> | ||
== Dynamic response == | == Dynamic response == | ||
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Another case of interest is the absorption of core electrons as measured in [[XAS theory | X-ray absorption near edge spectroscopy (XANES)]]. | Another case of interest is the absorption of core electrons as measured in [[XAS theory | X-ray absorption near edge spectroscopy (XANES)]]. | ||
== How to == | == How to == | ||
Revision as of 06:25, 8 February 2024
Apart from ground-state properties, VASP can compute how a system reacts to external perturbations. Currently, we can consider three types of perturbations:
- external electric field
- atomic displacements
- homogeneous strains
If we restrict ourselves to the first order of the perturbation then we are in the linear regime and thus we talk about linear response. A central quantity in linear response is the dielectric function which relates an external electric field with the internal electric displacement. The response to atomic displacements includes phonons and electron-phonon interactions. The response to homogeneous strains is related to the elastic tensor and piezoelectric tensor when combined with a response to and external electric field.
Polarization, berry phases, and finite electric fields
The polarization in a periodic system can be computed using the berry phase formulation of the polarization (often referred to as the modern theory of polarization). With a method to compute the polarization, we can apply a finite electric field to the system. Strictly speaking, polarization, as well as the application of a finite electric field, are ground-state properties, however, because they can be used to compute the static dielectric tensor, born effective charges, and piezoelectric tensors which are response properties, we refer to this approach here.
Static response
Dielectric tensor
For the case where the external electric field is static, the static dielectric function is sufficient to determine the response. This static response can be computed by finite differences (LCALCEPS) of the polarization with respect to a finite external electric field or by using density functional perturbation theory (LEPSILON).
Both LEPSILON or LCALCEPS yield the same converged results for the dielectric tensor, however, the former can only be used for local or semi-local exchange-correlation functionals and applies to both semiconductors and metals while the second can be used for meta-GGA or hybrid but only for systems with a gap.
Dynamic response
There are different approaches and levels of theory implemented in VASP to compute the frequency-dependent dielectric tensor. The simplest of these is done using the Green-kubo formula and is activated using LOPTICS = .TRUE.. This however neglects local-field effects which means that it only reproduces calculations from DFPT or finite differences of a finite electric field when LRPA = .TRUE. when the frequency is zero (static limit). To include local field effects one should use ALGO = CHI.
Another case of interest is the absorption of core electrons as measured in X-ray absorption near edge spectroscopy (XANES).
How to
Subcategories
This category has the following 5 subcategories, out of 5 total.
Pages in category "Linear response"
The following 26 pages are in this category, out of 26 total.