ODDONLYGW and EVENONLYGW: reducing the $k$-grid for the response functions

 EVENONLYGW = logical
 ODDONLYGW  = logical

ODDONLYGW allows to avoid the inclusion of the $\Gamma$-point in the evaluation of response functions. The independent particle polarizability $\chi_{\mathbf{q}}^0 (\mathbf{G}, \mathbf{G}', \omega)$ is given by:

$$\chi_{\mathbf{q}}^0 (\mathbf{G}, \mathbf{G}', \omega) = \fr... ...thbf{k}+\mathbf{q}}-\epsilon_{n\mathbf{k}} - \omega - i \eta }$$ (42)

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 $k$-grid is given by (see Sec. 5.5.3):

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

If the three integers $n_i$ sum to an odd value, the $k$-point is included in the previous summation in the GW routine ( ODDONLYGW=.TRUE.). Note that other routines (linear optical properties) presently do not recognize this flag. EVENONLYGW =.TRUE. is only of limited use and restricts the summation to $k$-points with $n_1+n_2+n_3$ being even ($\Gamma$-point and from there on ever second k-point included).

Accelerations are also possible by evaluating the response function itself at a restricted number of $\bf q$-points. Note that the GW loop, involves a sum over $\bf k$, and a second one over $\bf q$ (the index in the response function). To some extend both can be varied independently. The former one by using ODDONLYGW, and the latter one using the HF related flags NKRED, NKREDX, NKREDY, NKREDZ and EVENONLY, ODDONLY. As explained in Sec. 6.64.8 the index ${\bf q}$ can be restricted to the values

$${\vec q} = {\vec b}_1 \frac{n_1 C_1}{N_1} + {\vec b}_2 \frac... ...+ {\vec b}_3 \frac{n_3 C_3}{N_3}, \hspace{3mm}(n_i=0,..,N_i-1)$$ (43)

The integer grid reduction factors are either set separately through $C_1$= NKREDX, $C_2$= NKREDY, and $C_3$= NKREDZ, or simultaneously through $C_1=C_2=C_3$= NKRED.