ELPH SELFEN NW: Difference between revisions

Latest revision as of 14:46, 17 October 2024

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ELPH_SELFEN_NW = [integer]
Default: ELPH_SELFEN_NW = 1

Description: Number of energies to use when computing the phonon-induced electron self-energy.

The electron self-energy, $\Sigma_{n \mathbf{k}}(\omega)$ , depends on the frequency $\omega$ (or energy $\hbar \omega$ ). ELPH_SELFEN_NW controls the number and location of frequencies when computing the self-energy in the following way:

ELPH_SELFEN_NW > 0: The self-energy is computed at ELPH_SELFEN_NW equally spaced energies between $\varepsilon_{n \mathbf{k}} - \frac{1}{2} E^{\text{W}}$ and $\varepsilon_{n \mathbf{k}} + \frac{1}{2} E^{\text{W}}$ . The interval is centered around each Kohn-Sham eigenvalue, $\varepsilon_{n \mathbf{k}}$ , and its width, $E^{\text{W}}$ , is controlled via ELPH_SELFEN_WRANGE. If ELPH_SELFEN_NW is an even number, it is automatically increased by one so that the center-most energy in each interval always coincides with the corresponding Kohn-Sham eigenvalue.
ELPH_SELFEN_NW < 0: The self-energy is computed at |ELPH_SELFEN_NW| equally spaced energies between $\varepsilon^{\text{min}}_{\mathbf{k}} - \frac{1}{2} E^{\text{W}}$ and $\varepsilon^{\text{max}}_{\mathbf{k}} + \frac{1}{2} E^{\text{W}}$ , where $\varepsilon^{\text{min}}_{\mathbf{k}}$ and $\varepsilon^{\text{max}}_{\mathbf{k}}$ are the minimum and maximum Kohn-Sham eigenvalues of the calculation, respectively. Once again, $E^{\text{W}}$ is controlled via ELPH_SELFEN_WRANGE and allows to extend the interval in both directions.

@@ Line 1: / Line 1: @@
 {{elph_release}}
 {{DISPLAYTITLE:ELPH_SELFEN_NW}}
-{{TAGDEF|ELPH_SELFEN_NW|integer|1}}
+{{TAGDEF|ELPH_SELFEN_NW|[integer]|1}}
 Description: Number of energies to use when computing the phonon-induced electron self-energy.
@@ Line 10: / Line 10: @@
 {{TAG|ELPH_SELFEN_NW}} controls the number and location of frequencies when computing the self-energy in the following way:
 ; {{TAGO|ELPH_SELFEN_NW|0|op=>}}
-: The self-energy is computed at {{TAG|ELPH_SELFEN_NW}} equally spaced energies between <math>\varepsilon_{n \mathbf{k}} - \frac{1}{2} E^{\text{W}}</math> and <math>\varepsilon_{n \mathbf{k}} + \frac{1}{2} E^{\text{W}}</math>. The interval is centered around each Kohn-Sham eigenvalue, <math>\varepsilon_{n \mathbf{k}}</math>, and its width, <math>E^{\text{W}}</math>, is controlled via {{TAG|ELPH_SELFEN_WRANGE}}. If {{TAG|ELPH_SELFEN_NW}} is an even number, it is automatically increased by one so that the middle-most energy always coincides with the Kohn-Sham eigenvalue.
+: The self-energy is computed at {{TAG|ELPH_SELFEN_NW}} equally spaced energies between <math>\varepsilon_{n \mathbf{k}} - \frac{1}{2} E^{\text{W}}</math> and <math>\varepsilon_{n \mathbf{k}} + \frac{1}{2} E^{\text{W}}</math>. The interval is centered around each Kohn-Sham eigenvalue, <math>\varepsilon_{n \mathbf{k}}</math>, and its width, <math>E^{\text{W}}</math>, is controlled via {{TAG|ELPH_SELFEN_WRANGE}}. If {{TAG|ELPH_SELFEN_NW}} is an even number, it is automatically increased by one so that the center-most energy in each interval always coincides with the corresponding Kohn-Sham eigenvalue.
 ; {{TAGO|ELPH_SELFEN_NW|0|op=<}}
 : The self-energy is computed at |{{TAG|ELPH_SELFEN_NW}}| equally spaced energies between <math>\varepsilon^{\text{min}}_{\mathbf{k}} - \frac{1}{2} E^{\text{W}}</math> and <math>\varepsilon^{\text{max}}_{\mathbf{k}} + \frac{1}{2} E^{\text{W}}</math>, where <math>\varepsilon^{\text{min}}_{\mathbf{k}}</math> and <math>\varepsilon^{\text{max}}_{\mathbf{k}}</math> are the minimum and maximum Kohn-Sham eigenvalues of the calculation, respectively. Once again, <math>E^{\text{W}}</math> is controlled via {{TAG|ELPH_SELFEN_WRANGE}} and allows to extend the interval in both directions.