Category:Linear response: Difference between revisions

Revision as of 16:12, 6 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
strain perturbation
ionic displacements

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. The central quantity in linear response is the dielectric function which relates an external electric field with the internal electric displacement.

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.

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

X-ray absorption near edge spectra (XANES) spectra from the supercell core-hole method

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.

@@ Line 1: / Line 1: @@
-== Theory ==
+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
+# strain perturbation
+# ionic displacements
-*Static dielectric matrix, ion-clamped piezoelectric tensor and the Born effective charges using density functional perturbation theory: {{TAG|LEPSILON}}.
+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.
-*Frequency dependent dielectric properties: {{TAG|LOPTICS}}.
+The central quantity in linear response is the [[Dielectric properties|dielectric function]] which relates an external electric field with the internal electric displacement.
-*Berry phases and finite electric fields: {{TAG|Berry phases and finite electric fields}}.
-*Calculation of X-ray abpsorption spectra (XAS): {{TAG|XAS theory}}.
+== 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.
+== 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 ({{TAG|LCALCEPS}}) of the polarization with respect to a finite external electric field or by using density functional perturbation theory ({{TAG|LEPSILON}}).
+Both {{TAG|LEPSILON}} or {{TAG|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 [[:Category:Meta-GGA|meta-GGA]] or [[:Category:Hybrid functionals|hybrid]] but only for systems with a gap.
+<!--
+=== Born effective charges ===
+=== Piezoelectric tensor ===
+-->
+== 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 {{TAGO|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 {{TAGO|LRPA|.TRUE.}} when the frequency is zero (static limit). To include local field effects one should use [[:Category:Dielectric_properties#ALGO_=_CHI:_polarizability_within_GW_approximation| ALGO = CHI]].
+Another case of interest is the absorption of core electrons as measured in [[XAS theory | X-ray absorption near edge spectroscopy (XANES)]].
 == How to ==
-*Static dielectric matrix, ion-clamped piezoelectric tensor and the Born effective charges using density functional perturbation theory: {{TAG|LEPSILON}}.
+*[[SCH calculations|X-ray absorption near edge spectra (XANES) spectra from the supercell core-hole method]]
-*Frequency dependent dielectric properties: {{TAG|LOPTICS}}.
-*Berry phases and finite electric fields: {{TAG|LBERRY}}, {{TAG|LCALCEPS}}.
-*XAS (XANES) spectra from the super-cell core-hole method: {{TAG|SCH calculations}}.
-----
 [[Category:VASP|Linear response]]