LPEAD: Difference between revisions
No edit summary |
|||
Line 49: | Line 49: | ||
== Related Tags and Sections == | == Related Tags and Sections == | ||
{{TAG|IPEAD}}, | {{TAG|IPEAD}}, | ||
{{TAG|LEPSILON}}, | {{TAG|LEPSILON}}, | ||
{{TAG|LOPTICS}}, | {{TAG|LOPTICS}}, | ||
{{TAG|LCALCEPS}}, | |||
{{TAG|EFIELD_PEAD}}, | |||
[[Berry_phases_and_finite_electric_fields|Berry phases and finite electric fields]] | [[Berry_phases_and_finite_electric_fields|Berry phases and finite electric fields]] | ||
---- | ---- |
Revision as of 17:53, 20 March 2011
LPEAD = .TRUE. | .FALSE
Default: LPEAD = .FALSE.
Description: for LPEAD=.TRUE., the derivative of the cell-periodic part of the orbitals w.r.t. k, |∇kunk⟩, is calculated using finite differences.
The derivative of the cell-periodic part of the orbitals w.r.t. k, k, |∇kunk⟩, may be written as:
where H(k) and S(k) are the Hamiltonian and overlap operator for the cell-periodic part of the orbitals, and the sum over n´ must include a sufficiently large number of unoccupied states.
It may also be found as the solution to the following linear Sternheimer equation (see LEPSILON):
Alternatively one may compute |∇kunk⟩ from finite differences:
where m runs over the N occupied bands of the system, Δk=kj+1-kj, and
- .
As mentioned in the context of the self-consistent response to finite electric fields one may derive analoguous expressions for |∇kunk⟩ using higher-order finite difference approximations.
When LPEAD=.TRUE., VASP will compute |∇kunk⟩ using the aforementioned finite difference scheme. The order of the finite difference approximation can be specified by means of the IPEAD-tag (default: IPEAD=4).
These tags may be used in combination with LOPTICS=.TRUE. and LEPSILON=.TRUE..
Related Tags and Sections
IPEAD, LEPSILON, LOPTICS, LCALCEPS, EFIELD_PEAD, Berry phases and finite electric fields