Extrapolating unconverged GW energies to the complete basis set limit with linear regression

International audienceThe GW approximation to the electronic self-energy is now a well-recognized approach toobtain the electron quasiparticle energies ofmolecules and in particular their ionization po-tential and electron affinity. Though muchfaster than the corresponding wavefunctionmethods, the GW energies are still affected bya slow convergence with respect to the basiscompleteness. This limitation hinders a widerapplication of the GW approach. Here weshow we can reach the complete basis set limitfor the cumbersome GW calculations solelybased on fast preliminary calculations with anunconverged basis set. We introduce a lin-ear model that correlates the molecular orbitalcharacteristics and the basis convergence er-ror for a large database of about 600 statesin 104 organic molecules that contain H, C,O, N, F, P, S, and Cl. The model employsmolecular-orbital-based non-linear descriptorsthat encode efficiently the chemical space offer-ing an outstanding transferability. Using a lownumber of descriptors (17) the performance ofthis extrapolation procedure is superior to theearlier more physically-motivated approaches.The predictive power of the method is finallydemonstrated for a selection of large acceptormolecules