Extrapolating Unconverged GW Energies up to the Complete Basis Set Limit with Linear Regression

The GW approximation to the electronic
self-energy is now a well-recognized
approach to obtain the electron quasiparticle energies of molecules
and, in particular, their ionization potential and electron affinity.
Though much faster than the corresponding wavefunction methods, the
GW energies are still affected by slow convergence with respect to
the basis completeness. This limitation hinders a wider application
of the GW approach. Here, we show that we can reach the complete basis
set limit for the cumbersome GW calculations solely based on fast
preliminary calculations with an unconverged basis set. We introduce
a linear model that correlates the molecular orbital characteristics
and the basis convergence error for a large database of approximately
600 states in 104 organic molecules that contain H, C, O, N, F, P,
S, and Cl. The model employs molecular-orbital-based non-linear descriptors
that encode efficiently the chemical space offering outstanding transferability.
Using a low number of descriptors (17) the performance of this extrapolation
procedure is superior to that of the earlier more physically motivated
approaches. The predictive power of the method is finally demonstrated
for a selection of large acceptor molecules.