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# GW and dielectric matrix

The GW routine also determines the frequency dependent dielectric matrix without local field effects and with local field effects in the random phase approximation (RPA, LRPA=.TRUE.), or the DFT approximation (LRPA=.FALSE., see Sec. \ref{incar-rpa}). The calculated microscopic frequency dependent dielectric function, must match exactly those determined using the optical routine (LOPTICS=.TRUE., and, in the static limit, the density functional perturbation routines (LEPSILON=.TRUE.). In fact, it is guaranteed that the results are identical to those determined using a summation over conduction band states (LOPTICS). Differences for LSPECTRAL=.FALSE. must be negligible, and can be solely related to a different complex shift CSHIFT (defaults for CSHIFT are different in both routines). Setting CSHIFT manually in the INCAR file will remedy this issue. If differences prevail, it might be required to increase NEDOS (in this case the LOPTICS routine was suffering from an inaccurate frequency sampling, and the GW routine was most likely performing perfectly well). For LSPECTRAL=.TRUE. differences can arise, because (i) the GW routine uses less frequency points and different frequency grids than the optics routine or again (ii) from a different complex shift. Increasing NOMEGA should remove all discrepancies. Finally, the GW routine is the only routine capable to include local field effects for the frequency dependent dielectric function.

The imaginary and real part of frequency dependent dielectric function is always determined by the GW routine. It can be conveniently grepped from the file using the command (note two blanks between the two words)

grep " dielectric  constant" OUTCAR


The first value is the frequency (in eV) and the other two are the real and imaginary part of the trace of the dielectric matrix. Note that two sets can be found on the OUTCAR file. The first one corresponds to the head of the microscopic dielectric matrix (and therefore does not include local field effects), whereas the second one is the inverse of the dielectric matrix with local field effects included in the random phase approximation or density functional approximation (depending on LRPA).

If full GW calculations are not required, it is possible to greatly accelerate the calculations, by calculating the response functions only at the ${\displaystyle \Gamma }$-point. This can be achieved by setting the following values in the INCAR file:

 NKREDX = number of k-points in direction of first lattice vector
NKREDY = number of k-points in direction of second lattice vector
NKREDZ = number of k-points in direction of third lattice vector


The calculation of the QP shifts can be bypassed by setting ALGO=CHI. Furthermore, if only the static response function is required the number of frequency points should be set to NOMEGA=1 and LSPECTRAL=.FALSE.