# Accelerating GW in 2D systems

Since Yambo v5.1 it is possible to use an algorithm able to accelerate convergences of GW calculations in two-dimensional systems with respect to the k point sampling.

The method is explained in the paper:

Efficient GW calculations in two-dimensional materials through a stochastic integration of the screened potential

A. Guandalini, P. D'Amico, A. Ferretti and D. Varsano

The method makes use of a truncated Coulomb potential in a slab geometry that in Fourier space reads:

$\displaystyle{ V_G(q)=\frac{4\pi}{\vert q+G \vert^2}[1-e^{-\vert q_\parallel+G_\parallel\vert L/2}cos[(q_z+G_z)L/2)] }$

where L is the length of the cell in the non-periodic z direction. As the q-grid is 2D, we have $\displaystyle{ q_z = 0. }$

To activate the algorithm it is needed to add the RIM_W in your GW input file: Convergence of the quasiparticle band gap of MoS2 , hBN and phosphorene with respect to the number of sampling points of the BZ. Blue lines: standard integration methods. The extrapolated values are indicated with an horizontal dashed line. Orange lines: W-av method. The grey shaded regions show the converge tolerance (±50 meV) centered at the extrapolated values.
rim_cut                          # [R] Coulomb potential
HF_and_locXC                     # [R] Hartree-Fock
gw0                              # [R] GW approximation
ppa                              # [R][Xp] Plasmon Pole Approximation for the Screened Interaction
dyson                            # [R] Dyson Equation solver
em1d                             # [R][X] Dynamically Screened Interaction
RIM_W                            # Activate the RIM_W algorithm


and set the "slab z" Coulomb cutoff:

CUTGeo= "slab z"                   # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere/ws/slab X/Y/Z/XY..


where z is the non periodic direction.

and finally define the variable governing the Monte Carlo integration e.g.:

RandQpts=3000000                  # [RIM] Number of random q-points in the BZ
RandGvec= 97                RL    # [RIM] Coulomb interaction RS components
RandGvecW = 15              RL


here RandGvecW defines the number of G vectors to integrate W outside the BZ.