# Subsampling (NNS and CSI)

GW and BSE calculations are considerably more computationally demanding when applied to systems with reduced dimensionality, since the electronic confinement leads to a slower convergence of sums over the Brillouin zone due to a much more complicated screening environment that manifests in the 'head' and 'neck' elements of the dielectric matrix. BerkeleyGW implements two schemes to speedup GW and BSE calculations for systems with reduced dimensionality: the nonuniform neck subsampling method (NNS) and the clustered sampling interpolation (CSI) method, which can lead to orders-of-magnitude savings in computer time. Please see PRB 95, 035109 (2017) for further information, and please cite the paper if use this functionality!

## Mean-field

The first step before running NNS and CSI is to perform a ground-state DFT calculation on a relatively coarse k-point grid that is enough to sample different transitions in the Brillouin zone. This is roughly the same k-grid that one would use to converge a DFT calculation. For instance, for monolayer MoS2, a uniform, Gamma-centered 6x6x1 k-point grid is enough. Make sure you generate a number of unoccupied states necessary to converge your GW calculation. We will refer to the generated wavefunction file as WFN. The subsampling scheme both NNS and CSI) will then automatically generate a set of shifted wavefunction files which will allow you to compute the dielectric matrix at arbitrarily small wavevectors $q$. Note that these shifted calculations will only involve occupied states, so they are fairly inexpensive.

Note

For now, the script only automatically generates k-points for Quantum ESPRESSO. However, it is fairly straightforward to convert the list of k-points to be used with another mean-field code.

## NNS and CSI

After you perform the mean-field calculation, follow the documentation to perform an NNS calculation to obtain the electronic self-energy of a quasi-2D system, or an CSI calculation to obtain the optical absorption spectrum.