LPEAD: Difference between revisions
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where ''m'' runs over the ''N'' occupied bands of the system, | where ''m'' runs over the ''N'' occupied bands of the system, Δ''k''='''k'''<sub>j+1</sub>-'''k'''<sub>j</sub>, and | ||
:<math> | :<math> |
Revision as of 17:41, 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
- .
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
LPEAD, IPEAD, LEPSILON, LOPTICS, Berry phases and finite electric fields