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# LNABLA

LNABLA = .TRUE. | .FALSE.
Default: LNABLA = .FALSE.

Description: LNABLA=.TRUE. evaluates the transversal expression for the frequency dependent dielectric matrix.

Usually VASP uses the longitudinal expression for the frequency dependent dielectric matrix. It is however possible to switch to the computationally somewhat simpler transversal expressions by selecting LNABLA=.TRUE. (Eqs. 17 and 20 in Ref.[1]). In this simplification the imaginary part of the macroscopic dielectric function is given by

${\displaystyle \epsilon _{{\alpha \beta }}^{{(2)}}(\omega )={\frac {4\pi ^{2}e^{2}\hbar ^{4}}{\Omega \omega ^{2}m_{e}^{2}}}{\mathrm {lim}}_{{{\mathbf {q}}\rightarrow 0}}\sum _{{c,v,{\mathbf {k}}}}2w_{{\mathbf {k}}}\delta (\epsilon _{{c{\mathbf {k+q}}}}-\epsilon _{{v{\mathbf {k}}}}-\omega )\times \langle u_{{c{\mathbf {k}}}}|i{{\mathbf {\nabla }}_{{\alpha }}-{\mathbf {k}}}_{{\alpha }}|u_{{v{\mathbf {k}}}}\rangle \langle u_{{c{\mathbf {k}}}}|i{{\mathbf {\nabla }}_{{\beta }}-{\mathbf {k}}}_{{\beta }}|u_{{v{\mathbf {k}}}}\rangle ^{*}.}$

Except for the purpose of testing, there is however hardly ever a reason to use the transversal expression, since it is less accurate.