ODDONLYGW

ODDONLYGW = [logical]
Default: ODDONLYGW = .FALSE.

Description: ODDONLYGW allows to avoid the inclusion of the $\Gamma$ point in the evaluation of response functions (in GW calculations).

The independent particle polarizability $\chi _{\mathbf {q} }^{0}({\mathbf {G} },{\mathbf {G} }',\omega )$ is given by:

$\chi _{\mathbf {q} }^{0}({\mathbf {G} },{\mathbf {G} }',\omega )={\frac {1}{\Omega }}\sum _{n,n',{\mathbf {k} }}2w_{\mathbf {k} }(f_{n'{\mathbf {k} }+{\mathbf {q} }}-f_{n{\mathbf {k} }})\times {\frac {\langle \psi _{n{\mathbf {k} }}|e^{-i({\mathbf {q} }+{\mathbf {G} }){\mathbf {r} }}|\psi _{n'{\mathbf {k} }+{\mathbf {q} }}\rangle \langle \psi _{n'{\mathbf {k} }+{\mathbf {q} }}|e^{i({\mathbf {q} }+{\mathbf {G} }'){\mathbf {r'} }}|\psi _{n{\mathbf {k} }}\rangle }{\epsilon _{n'{\mathbf {k} }+{\mathbf {q} }}-\epsilon _{n{\mathbf {k} }}-\omega -i\eta }}$

If the $\Gamma$ point is included in the summation over $\mathbf {k}$ , convergence is very slow for some materials (e.g. GaAs).

To deal with this problem the flag ODDONLYGW has been included. In the automatic mode, the $\mathbf {k}$ -grid is given by (see Sec. \ref{sec:autok}):

 ${\vec {k}}={\vec {b}}_{1}{\frac {n_{1}}{N_{1}}}+{\vec {b}}_{2}{\frac {n_{2}}{N_{2}}}+{\vec {b}}_{3}{\frac {n_{3}}{N_{3}}},\qquad n_{1}=0...,N_{1}-1\quad n_{2}=0...,N_{2}-1\quad n_{3}=0...,N_{3}-1.$

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