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.

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.,^[1] and closely follows the original work of Baroni and Resta.^[2] A summation over empty conduction band states is not required, instead the usual expressions in perturbation theory (LOPTICS=.TRUE.),

{\displaystyle | \nabla_{\mathbf{k}} |\tilde{u}_{n\mathbf{k}} \rangle = \sum_{n'\ne 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:

{\displaystyle \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 . }

The solution of this equation involves similar iterative techniques as the conventional selfconsistency cycles. Hence, for each element of the dielectric matrix several lines will be written to the stdout and OSZICAR. These possess a similar structure as for conventional selfconsistent or non-selfconsistent calculations (a residual minimization scheme is used to solve the linear equation, other schemes such as Davidson do not apply to a linear equation):

       N       E              dE             d eps       ncg     rms          rms(c)
RMM:   1    -0.14800E+01   -0.85101E-01   -0.72835E+00   220   0.907E+00    0.146E+00
RMM:   2    -0.14248E+01    0.55195E-01   -0.27994E-01   221   0.449E+00    0.719E-01
RMM:   3    -0.13949E+01    0.29864E-01   -0.10673E-01   240   0.322E+00    0.131E-01
RMM:   4    -0.13949E+01    0.13883E-04   -0.31511E-03   242   0.600E-01    0.336E-02
RMM:   5    -0.13949E+01    0.28357E-04   -0.25757E-04   228   0.177E-01    0.126E-02

It is important to note that exact values for the dielectric matrix are obtained even if only valence band states are calculated. Hence this method does not require to increase the NBANDS parameter. The final values for the static dielectric matrix can be found in the OUTCAR file after the lines

 MACROSCOPIC STATIC DIELECTRIC TENSOR (excluding local field effects)

and

 MACROSCOPIC STATIC DIELECTRIC TENSOR (including local field effects in DFT)

Related Tags and Sections

LOPTICS, LRPA

References

Contents

[gajdos:prb:06-1] M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, Phys. Rev. B 73, 045112 (2006).

[baroni:prb:86-2] S. Baroni and R. Resta, Phys. Rev. B 33, 7017, (1986).

[1]

[2]