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# ENCUTGW

ENCUTGW = [real]
Default: ENCUTGW = 2/3 ENCUT

Description: The tag ENCUTGW sets the energy cutoff for response function. It controls the basis set for the response functions in exactly the same manner as ENCUT does for the orbitals.

## Contents

In GW and RPA calculations, storing and manipulating the response function dominates the computational work load:

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

ENCUTGW controls how many ${\displaystyle {\mathbf {G}}}$ vectors are included in the the response function ${\displaystyle \chi _{{{{\mathbf {q}}}}}^{0}({{\mathbf {G}}},{{\mathbf {G}}}',\omega )}$ .

Our experience suggests that choosing ENCUTGW= 2/3 ENCUT yields reasonable results at fairly modest computational cost, although, the response function contains contributions up to twice the plane wave cutoff ${\displaystyle G_{{{\rm {cut}}}}}$ (see ALGO). Furthermore, RPA correlation energies are reported using an internal extrapolation of the correlation energy by varying ENCUTGW internally (inside VASP) between the largest value given in the INCAR file and smaller values [1]. The extrapolated value is only reliable, if ENCUTGW is smaller then ENCUT (the cutoff extrapolation with respect to ENCUTGW would be very precise, if the plane wave basis for the orbitals were infinite). Again the VASP defaults yield very reasonable values for the extrapolated correlation energy. In fact, it is unwise to increase ENCUTGW only, without increasing ENCUT . To converge RPA correlation energies, simply increase ENCUT and the number of orbitals, and use the VASP default for ENCUTGW.

For QP gaps, it is sometimes possible to set ENCUTGW to values between 150 to 200 eV, and even 100 eV can yield gaps that are accurate to within a few tens of an eV for main group elements. Be aware, however, that the absolute values of the QP energies depend inverse proportionally on the number of plane waves. Thus convergence of absolute QP energies is always very slow, although QP gaps might seem converged.

The recommended procedure to obtain accurate QP energies is discussed in the reference below. Specifically, for reference type calculations we recommend the following procedure:

• use the default for ENCUTGW, or even decrease ENCUTGW to half the value of ENCUT.
• Calculate all orbitals that the plane wave basis set allows to calculate. This number can be determined by searching for "maximum number of plane-waves" in the groundstate DFT OUTCAR file, and setting NBANDS to this value.
• Increase ENCUT systematically and plot the QP energies versus the number of plane wave coefficients (which equals the number of orbitals). This means ENCUTGW and NBANDS increase as ENCUT increases.

This procedure can be carried out using few k-points. Other commonly applied methods can yield less accurate results and are not considered to be reliable.

## FFT grid and PRECFOCK

The flag PRECFOCK determines the FFT grid in all GW (and Hartree-Fock) related routines. For small systems (which are often dominated by FFT operations), the flag can have a significant impact on the compute time for QP calculations. For large systems, the FFT's usually do not dominating the computational work load and savings are expected to be small for PRECFOCK = fast. QP shifts are usually not very sensitive to the setting of PRECFOCK (and it therefore does not harm to set PRECFOCK = fast), whereas for RPA calculations we recommend to set PRECFOCK = normal to avoid numerical errors.