ELPH SELFEN BROAD TOL - Revision history

Csheldon: Csheldon moved page Construction:ELPH SELFEN BROAD TOL to ELPH SELFEN BROAD TOL

2025-10-24T08:33:28Z

Csheldon moved page Construction:ELPH SELFEN BROAD TOL to ELPH SELFEN BROAD TOL

← Older revision	Revision as of 08:33, 24 October 2025
(No difference)

Csheldon at 08:33, 24 October 2025

2025-10-24T08:33:23Z

← Older revision		Revision as of 08:33, 24 October 2025
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	* {{TAG\|ELPH_TRANSPORT}}		* {{TAG\|ELPH_TRANSPORT}}

	~~<!--~~[[Category:INCAR tag]][[Category:Electron-phonon_interactions]]~~-->~~		[[Category:INCAR tag]][[Category:Electron-phonon_interactions]]

Miranda.henrique at 10:31, 23 October 2025

2025-10-23T10:31:30Z

← Older revision		Revision as of 10:31, 23 October 2025
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	----		----
	When evaluating delta-like quantities from the imaginary part of the electron self-energy, a finite broadening function <math>f(\epsilon)</math> is used.		When evaluating delta-like quantities from the imaginary part of the electron self-energy, a finite broadening function <math>f(\epsilon)</math> is used.
	{{TAG\|ELPH_SELFEN_BROAD_TOL}} determines what fraction of the integral of this function is retained inside the energy window <math>[-y, y]</math> around the chemical potential, such that the remaining tails are ignored.		{{TAG\|ELPH_SELFEN_BROAD_TOL}} determines what fraction of the integral of this function is retained inside the energy window <math>[-y, y]</math> around the chemical potential, such that the remaining tails are ignored.

	For a Lorentzian broadening of the form		For a Lorentzian broadening of the form
Line 39:		Line 39:

	Hence:		Hence:
	* A small value of {{TAG\|ELPH_SELFEN_BROAD_TOL}} (e.g. 1e-6) means that nearly the entire Lorentzian area is included — a wide energy window.		* A small value of {{TAG\|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.		* 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.		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.

Miranda.henrique at 10:27, 23 October 2025

2025-10-23T10:27:12Z

← Older revision		Revision as of 10:27, 23 October 2025
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	:<math>		:<math>
	f(x) = \frac{\~~Delta~~}{\~~Delta~~^2 + x^2},		f(x) = \frac{\delta}{\delta^2 + x^2},
	</math>		</math>

	where <math>\~~Delta~~ \equiv</math> {{TAG\|ELPH_SELFEN_DELTA}},		where <math>\delta \equiv</math> {{TAG\|ELPH_SELFEN_DELTA}},
	the integral between <math>-y</math> and <math>y</math> is		the integral between <math>-y</math> and <math>y</math> is

	:<math>		:<math>
	\int_{-y}^{y} \frac{\~~Delta~~}{\~~Delta~~^2 + x^2} \, dx = 2 \arctan\!\left(\frac{y}{\~~Delta~~}\right),		\int_{-y}^{y} \frac{\delta}{\delta^2 + x^2} \, dx = 2 \arctan\!\left(\frac{y}{\delta}\right),
	</math>		</math>

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	:<math>		:<math>
	2 \arctan\!\left(\frac{y}{\~~Delta~~}\right) = \pi (1 - \alpha),		2 \arctan\!\left(\frac{y}{\delta}\right) = \pi (1 - \alpha),
	</math>		</math>

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	:<math>		:<math>
	y = \~~Delta~~ \, \tan\!\left(\frac{\pi (1 - \alpha)}{2}\right).		y = \delta \, \tan\!\left(\frac{\pi (1 - \alpha)}{2}\right).
	</math>		</math>

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	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.		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}}.		The width parameter <math>\delta</math> is directly controlled by {{TAG\|ELPH_SELFEN_DELTA}}.

	==Related tags and articles==		==Related tags and articles==

Miranda.henrique at 10:26, 23 October 2025

2025-10-23T10:26:42Z

← Older revision		Revision as of 10:26, 23 October 2025
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	==Related tags and articles==		==Related tags and articles==
	* [[Electron self-energy from electron-phonon interactions\|Electron self-energy calculations]]
	* {{TAG\|ELPH_RUN}}		* {{TAG\|ELPH_RUN}}
	* {{TAG\|ELPH_SELFEN}}
	* {{TAG\|ELPH_SELFEN_IMAG_SKIP}}		* {{TAG\|ELPH_SELFEN_IMAG_SKIP}}
	* {{TAG\|ELPH_SELFEN_DELTA}}		* {{TAG\|ELPH_SELFEN_DELTA}}

Miranda.henrique at 10:26, 23 October 2025

2025-10-23T10:26:25Z

← Older revision		Revision as of 10:26, 23 October 2025
Line 42:		Line 42:
	* A large value (e.g. 0.1) restricts the integration to a smaller region around the resonance.		* 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]]-->

Miranda.henrique: Created page with "{{DISPLAYTITLE:ELPH_SELFEN_BROAD_TOL}} {{TAGDEF|ELPH_SELFEN_BROAD_TOL|[real]|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 {{TAG|ELPH_SELFEN_IMAG_SKIP}}=.TRUE. and {{TAG|ELPH_SELFEN_DELTA}}>0. {{Available|6.5.0}}..."

2025-10-23T10:25:30Z

Created page with "{{DISPLAYTITLE:ELPH_SELFEN_BROAD_TOL}} {{TAGDEF|ELPH_SELFEN_BROAD_TOL|[real]|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 {{TAG|ELPH_SELFEN_IMAG_SKIP}}=.TRUE. and {{TAG|ELPH_SELFEN_DELTA}}>0. {{Available|6.5.0}}..."

New page

{{DISPLAYTITLE:ELPH_SELFEN_BROAD_TOL}}
{{TAGDEF|ELPH_SELFEN_BROAD_TOL|[real]|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 {{TAG|ELPH_SELFEN_IMAG_SKIP}}=.TRUE. and {{TAG|ELPH_SELFEN_DELTA}}>0.
{{Available|6.5.0}}

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

For a Lorentzian broadening of the form

:<math>
f(x) = \frac{\Delta}{\Delta^2 + x^2},
</math>

where <math>\Delta \equiv</math> {{TAG|ELPH_SELFEN_DELTA}},
the integral between <math>-y</math> and <math>y</math> is

:<math>
\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>y \to \infty</math>) is <math>\pi</math>.
We thus require

:<math>
2 \arctan\!\left(\frac{y}{\Delta}\right) = \pi (1 - \alpha),
</math>

where <math>\alpha \equiv</math> {{TAG|ELPH_SELFEN_BROAD_TOL}}.

Solving for <math>y</math> gives the energy cutoff:

:<math>
y = \Delta \, \tan\!\left(\frac{\pi (1 - \alpha)}{2}\right).
</math>

Hence:
* A **small** value of {{TAG|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 delt

← Older revision		Revision as of 10:26, 23 October 2025
Line 46:		Line 46:

	==Related tags and articles==		==Related tags and articles==
	* [[Electron self-energy from electron-phonon interactions\|Electron self-energy calculations]]
	* {{TAG\|ELPH_RUN}}		* {{TAG\|ELPH_RUN}}
	* {{TAG\|ELPH_SELFEN}}
	* {{TAG\|ELPH_SELFEN_IMAG_SKIP}}		* {{TAG\|ELPH_SELFEN_IMAG_SKIP}}
	* {{TAG\|ELPH_SELFEN_DELTA}}		* {{TAG\|ELPH_SELFEN_DELTA}}