ELPH TRANSPORT DRIVER

ELPH_TRANSPORT_DRIVER = [integer]
Default: ELPH_TRANSPORT_DRIVER = 2 

Description: choose method to compute the Onsager coefficients, which are then used to compute the transport coefficients.

Mind: Available as of VASP 6.5.0

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The Onsager coefficients can be computed using either of the options bellow, each with its own advantages and disadvantages. They are defined as

[math]\displaystyle{ L_{ij} = \int d\epsilon \, \sigma(\epsilon) \, (\epsilon-\mu)^{i+j-2} \left( -\frac{\partial f^0}{\partial \epsilon} \right), }[/math]

where [math]\displaystyle{ \sigma(\epsilon) }[/math] is the transport distribution function, [math]\displaystyle{ \mu }[/math] the chemical potential, and [math]\displaystyle{ f^0 }[/math] the Fermi–Dirac distribution.

ELPH_TRANSPORT_DRIVER = 1

The discretized Onsager coefficient is evaluated as

[math]\displaystyle{ L_{ij} \;\approx\; \sum_{k=1}^{N} w_k \; \sigma(\epsilon_k)\; (\epsilon_k - \eta)^{\,i+j-2}\; \left( -\frac{\partial f^0}{\partial \epsilon} \right). }[/math]

with [math]\displaystyle{ \epsilon_k = \epsilon_\text{min}+(k-1)\Delta \epsilon,\;\; k=1,\dots,N }[/math] and [math]\displaystyle{ \Delta \epsilon = \tfrac{\epsilon_\text{max}-\epsilon_\text{min}}{N-1} }[/math] and [math]\displaystyle{ \epsilon_\text{min} }[/math]=ELPH_TRANSPORT_EMIN and [math]\displaystyle{ \epsilon_\text{max} }[/math]=ELPH_TRANSPORT_EMAX or alternatively both [math]\displaystyle{ \epsilon_\text{min} }[/math] and [math]\displaystyle{ \epsilon_\text{max} }[/math] are set by ELPH_TRANSPORT_DFERMI_TOL, [math]\displaystyle{ w_k }[/math] the weights due to the Simpson integration rule and N=TRANSPORT_NEDOS.

ELPH_TRANSPORT_DRIVER = 2

Use Gauss-Legendre integration to evaluate the Onsager coefficients. The convergence of the integral can be checked by performing a convergence study with respect to N=TRANSPORT_NEDOS alone. In this case the Onsager coefficients are evaluated using the following discretization

[math]\displaystyle{ L_{ij} \;\approx\; \tfrac{1}{2} \sum_{k=1}^N w_k \, \left( \frac{k_B T}{-e} \ln \frac{1+x_k}{1-x_k} \right)^{i+j-2} \sigma\!\left(\eta + k_B T \ln\frac{1+x_k}{1-x_k}\right), }[/math]

with [math]\displaystyle{ w_k }[/math] and [math]\displaystyle{ x_k }[/math] the weights and abcissae of the Gauss-Legendre quadrature rule.

Related tags and articles

• Transport calculations
• ELPH_RUN
• ELPH_TRANSPORT
• TRANSPORT_NEDOS
• ELPH_TRANSPORT_DFERMI_TOL
• ELPH_TRANSPORT_EMIN
• ELPH_TRANSPORT_EMAX