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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 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..

  • N.B. Please note that LPEAD = .TRUE. is not supported for metallic systems.

Related Tags and Sections

IPEAD, LEPSILON, LOPTICS, LCALCEPS, EFIELD_PEAD, Berry phases and finite electric fields

Examples that use this tag