ELPH_SELFEN_BROAD_TOL
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.