LEPSILON

LEPSILON = .TRUE. | .FALSE.
Default: LEPSILON = .FALSE. 

Description: LEPSILON=.TRUE. determines the static dielectric matrix, ion-clamped piezoelectric tensor and the Born effective charges using density functional perturbation theory.

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Determines the static ion-clamped dielectric matrix using density functional perturbation theory. The dielectric matrix is calculated with and without local field effects. Usually local field effects are determined on the Hartree level, i.e. including changes of the Hartree potential. To include microscopic changes of the exchange correlation potential the tag LRPA=.FALSE. must be set. The method is explained in detail in paper by Gajdoš et al., and closely follows the original work of Baroni and Resta. A summation over empty conduction band states is not required, instead the usual expressions in perturbation theory (LOPTICS=.TRUE.),

$|\nabla _{\mathbf {k} }|{\tilde {u}}_{n\mathbf {k} }\rangle =\sum _{n'\neq n}{\frac {|{\tilde {u}}_{n'\mathbf {k} }\rangle \langle {\tilde {u}}_{n'\mathbf {k} }|{\frac {\partial \,(\mathbf {H} (\mathbf {k} )-\epsilon _{n\mathbf {k} }\mathbf {S} (\mathbf {k} ))}{\partial {\mathbf {k} }}}|{\tilde {u}}_{n\mathbf {k} }\rangle }{\epsilon _{n\mathbf {k} }-\epsilon _{n'\mathbf {k} }}}.$

are rewritten as linear Sternheimer equations:

$\left(\mathbf {H} (\mathbf {k} )-\epsilon _{n\mathbf {k} }\mathbf {S} (\mathbf {k} )\right)|\nabla _{\mathbf {k} }{\tilde {u}}_{n\mathbf {k} }\rangle =-{\frac {\partial \,(\mathbf {H} (\mathbf {k} )-\epsilon _{n\mathbf {k} }\mathbf {S} (\mathbf {k} ))}{\partial {\mathbf {k} }}}|{\tilde {u}}_{n\mathbf {k} }\rangle .$

Related Tags and Sections

LOPTICS, LRPA

References

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