ODDONLYGW

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

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

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

${\chi }_{\mathbf{𝐪}}^0(\mathbf{𝐆},{\mathbf{𝐆}}^{\prime },\omega )=\frac{1}{\mathrm{\Omega }}\sum _{n,n^{\prime },\mathbf{𝐤}}2w_{\mathbf{𝐤}}(f_{n^{\prime }\mathbf{𝐤}+\mathbf{𝐪}}-f_{n\mathbf{𝐤}})\times \frac{⟨{\psi }_{n\mathbf{𝐤}}|e^{-i(\mathbf{𝐪}+\mathbf{𝐆})\mathbf{𝐫}}|{\psi }_{n^{\prime }\mathbf{𝐤}+\mathbf{𝐪}}⟩⟨{\psi }_{n^{\prime }\mathbf{𝐤}+\mathbf{𝐪}}|e^{i(\mathbf{𝐪}+{\mathbf{𝐆}}^{\prime }){\mathbf{𝐫}}^{\prime }}|{\psi }_{n\mathbf{𝐤}}⟩}{{ϵ}_{n^{\prime }\mathbf{𝐤}+\mathbf{𝐪}}-{ϵ}_{n\mathbf{𝐤}}-\omega -i\eta }$

If the $\mathrm{\Gamma }$ 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}):

$\overrightarrow{k}={\overrightarrow{b}}_1\frac{n_1}{N_1}+{\overrightarrow{b}}_2\frac{n_2}{N_2}+{\overrightarrow{b}}_3\frac{n_3}{N_3},n_1=0...,N_1-1n_2=0...,N_2-1n_3=0...,N_3-1.$

Related Tags and Sections

EVENONLYGW, GW calculations

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