ODDONLYGW

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

Description: ODDONLYGW allows to avoid the inclusion of the [math]\displaystyle{ \Gamma }[/math] point in the evaluation of response functions (in GW calculations).

---

The independent particle polarizability [math]\displaystyle{ \chi_{{\mathbf{q}}}^0 ({\mathbf{G}}, {\mathbf{G}}', \omega) }[/math] is given by:

[math]\displaystyle{ \chi_{{\mathbf{q}}}^0 ({\mathbf{G}}, {\mathbf{G}}', \omega) = \frac{1}{\Omega} \sum_{n,n',{\mathbf{k}}}2 w_{{\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 } }[/math]

If the [math]\displaystyle{ \Gamma }[/math] point is included in the summation over [math]\displaystyle{ \mathbf{k} }[/math], 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 [math]\displaystyle{ \mathbf{k} }[/math]-grid is given by (see Sec. \ref{sec:autok}):

[math]\displaystyle{  \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.  }[/math]

Related Tags and Sections

EVENONLYGW, GW calculations

---

Contents