LPEAD: Difference between revisions

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Alternatively one may compute |&nabla;<sub>'''k'''</sub>u<sub>n'''k'''</sub>&rang; <math>\nabla_{k} \tilde{u}</math> from finite differences:
Alternatively one may compute <math>\nabla_{\mathbf{k}} \tilde{u}_{n\mathbf{k}}</math> from finite differences:


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These tags may be used in combination with {{TAG|LOPTICS}}=.TRUE. and {{TAG|LEPSILON}}=.TRUE..
These tags may be used in combination with {{TAG|LOPTICS}}=.TRUE. and {{TAG|LEPSILON}}=.TRUE..
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*N.B. Please note that {{TAG|LPEAD}} = .TRUE. '''is not supported for metallic systems'''.


== Related Tags and Sections ==
== Related tags and articles ==
{{TAG|IPEAD}},
{{TAG|IPEAD}},
{{TAG|LEPSILON}},
{{TAG|LEPSILON}},
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[[Berry_phases_and_finite_electric_fields|Berry phases and finite electric fields]]
[[Berry_phases_and_finite_electric_fields|Berry phases and finite electric fields]]


== Example Calculations using this Tag ==
{{sc|LPEAD|Examples|Examples that use this tag}}
{{TAG|bandgap of Si in GW}}, {{TAG|Dielectric properties of Si using BSE}}, {{TAG|dielectric properties of Si}}, {{TAG|dielectric properties of SiC}}, {{TAG|Model BSE calculation on Si}}
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[[The_VASP_Manual|Contents]]


[[Category:INCAR]][[Category:Berry phases]]
[[Category:INCAR tag]][[Category:Linear response]][[Category:Dielectric properties]][[Category:Berry phases]]

Latest revision as of 07:59, 19 July 2022

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 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 articles

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

Examples that use this tag