ELPH SELFEN BROAD TOL: Difference between revisions

Revision as of 10:26, 23 October 2025

ELPH_SELFEN_BROAD_TOL = [real]
Default: ELPH_SELFEN_BROAD_TOL = 1e-6

Description: defines the fraction of the total weight of the broadening function (derived from the imaginary part of the electron self-energy) that is excluded when setting the energy window beyond which the delta function is considered zero. Must be between 0 and 1. This tag is only used when ELPH_SELFEN_IMAG_SKIP=.TRUE. and ELPH_SELFEN_DELTA>0.

Mind: Available as of VASP 6.5.0

When evaluating delta-like quantities from the imaginary part of the electron self-energy, a finite broadening function [math]\displaystyle{ f(\epsilon) }[/math] is used. ELPH_SELFEN_BROAD_TOL determines what fraction of the integral of this function is **retained** inside the energy window [math]\displaystyle{ [-y, y] }[/math] around the chemical potential, such that the remaining tails are ignored.

For a Lorentzian broadening of the form

[math]\displaystyle{ f(x) = \frac{\Delta}{\Delta^2 + x^2}, }[/math]

where [math]\displaystyle{ \Delta \equiv }[/math] ELPH_SELFEN_DELTA, the integral between [math]\displaystyle{ -y }[/math] and [math]\displaystyle{ y }[/math] is

[math]\displaystyle{ \int_{-y}^{y} \frac{\Delta}{\Delta^2 + x^2} \, dx = 2 \arctan\!\left(\frac{y}{\Delta}\right), }[/math]

while the total integral over all energies ([math]\displaystyle{ y \to \infty }[/math]) is [math]\displaystyle{ \pi }[/math]. We thus require

[math]\displaystyle{ 2 \arctan\!\left(\frac{y}{\Delta}\right) = \pi (1 - \alpha), }[/math]

where [math]\displaystyle{ \alpha \equiv }[/math] ELPH_SELFEN_BROAD_TOL.

Solving for [math]\displaystyle{ y }[/math] gives the energy cutoff:

[math]\displaystyle{ y = \Delta \, \tan\!\left(\frac{\pi (1 - \alpha)}{2}\right). }[/math]

Hence:

A **small** value of ELPH_SELFEN_BROAD_TOL (e.g. 1e-6) means that nearly the entire Lorentzian area is included — a wide energy window.
A **large** value (e.g. 0.1) restricts the integration to a smaller region around the resonance.

This parameter ensures a consistent and physically meaningful truncation of the Lorentzian tails when transforming the imaginary part of the self-energy into an effective delta function. The width parameter [math]\displaystyle{ \Delta }[/math] is directly controlled by ELPH_SELFEN_DELTA.

@@ Line 42: / Line 42: @@
 * A **large** value (e.g. 0.1) restricts the integration to a smaller region around the resonance.
-This parameter ensures a consistent and physically meaningful truncation of the Lorentzian tails when transforming the imaginary part of the self-energy into an effective delt
+This parameter ensures a consistent and physically meaningful truncation of the Lorentzian tails when transforming the imaginary part of the self-energy into an effective delta function.
+The width parameter <math>\Delta</math> is directly controlled by {{TAG|ELPH_SELFEN_DELTA}}.
+==Related tags and articles==
+* [[Electron self-energy from electron-phonon interactions|Electron self-energy calculations]]
+* {{TAG|ELPH_RUN}}
+* {{TAG|ELPH_SELFEN}}
+* {{TAG|ELPH_SELFEN_IMAG_SKIP}}
+* {{TAG|ELPH_SELFEN_DELTA}}
+* {{TAG|ELPH_TRANSPORT}}
+<!--[[Category:INCAR tag]][[Category:Electron-phonon_interactions]]-->