ELPH TRANSPORT DFERMI TOL: Difference between revisions

Latest revision as of 13:55, 12 September 2025

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

Description: choose the fraction of the integral weight of the derivative of the Fermi–Dirac distribution that is excluded when defining the energy window for the Onsager coefficients. Must be between 0 and 1, and is only used when ELPH_TRANSPORT_DRIVER=1.

Mind: Available as of VASP 6.5.0

Using this parameter, ELPH_TRANSPORT_EMIN and ELPH_TRANSPORT_EMAX are automatically computed from the chemical potentials and the distribution $-\partial f^0/\partial \epsilon$ . Formally, the integration window $[\mu-e,\mu+e]$ is chosen such that

{\displaystyle \int_{\mu-e}^{\mu+e} \left(-\frac{\partial f^0}{\partial \epsilon}\right) d\epsilon = 1 - \alpha, }

where $\alpha \equiv$ ELPH_TRANSPORT_DFERMI_TOL. This gives

{\displaystyle e = k_B T \, \ln\!\left(\tfrac{2-\alpha}{\alpha}\right). }

A small value means that only the tails of the derivative of the Fermi-dirac distribution are excluded from the integral. A large value means that only a small energy window around the chemical potential is used.

The integral is then discretized with a number of energy points set by TRANSPORT_NEDOS and evaluated using the Simpson's rule.

@@ Line 2: / Line 2: @@
 {{TAGDEF|ELPH_TRANSPORT_DFERMI_TOL|[real]|1e-6}}
-Description: choose the percentage of the integral of the derivative of the Fermi-dirac distribution with respect to the energy that is excluded from the integral that yields the Onsager coefficients.
+Description: choose the fraction of the integral weight of the derivative of the Fermi–Dirac distribution that is excluded when defining the energy window for the Onsager coefficients. Must be between 0 and 1, and is only used when {{TAG|ELPH_TRANSPORT_DRIVER}}=1.
 {{Available|6.5.0}}
 ----
-Using this parameter, the values of {{TAG|ELPH_TRANSPORT_EMIN}} and {{TAG|ELPH_TRANSPORT_EMAX}} are automatically computed based on the list of chemical potential and the integral of the derivative of the Fermi-dirac distribution.
+Using this parameter, {{TAG|ELPH_TRANSPORT_EMIN}} and {{TAG|ELPH_TRANSPORT_EMAX}} are automatically computed from the chemical potentials and the distribution <math>-\partial f^0/\partial \epsilon</math>.
-This allows having a material independent parameter that is used to determine the energy window for which the electronic lifetimes must be computed.
+Formally, the integration window <math>[\mu-e,\mu+e]</math> is chosen such that
+:<math>
+\int_{\mu-e}^{\mu+e} \left(-\frac{\partial f^0}{\partial \epsilon}\right) d\epsilon
+= 1 - \alpha,
+</math>
+where <math>\alpha \equiv</math> {{TAG|ELPH_TRANSPORT_DFERMI_TOL}}.
+This gives
+:<math>
+e = k_B T \, \ln\!\left(\tfrac{2-\alpha}{\alpha}\right).
+</math>
 A small value means that only the tails of the derivative of the Fermi-dirac distribution are excluded from the integral.
 A large value means that only a small energy window around the chemical potential is used.
-The number of energy points is determined by {{TAG|TRANSPORT_NEDOS}}.
+The integral is then discretized with a number of energy points set by {{TAG|TRANSPORT_NEDOS}} and evaluated using the Simpson's rule.
 ==Related tags and articles==