LPEAD: Difference between revisions

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where ''m'' runs over the ''N'' occupied bands of the system, <math>\Delta k=\mathbf{k}_{j+1}-\mathbf{k}_j</math>, and
where ''m'' runs over the ''N'' occupied bands of the system, &Delta;''k''='''k'''<sub>j+1</sub>-'''k'''<sub>j</sub>, and


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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


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