Dear Martijn,

the difference between ri-cd-gw and gw/ri-ac-gw is mainly that ri-cd-gw does not use linearization in G0W0. Therefore, all z's are 1. You calculations only differ by this linearization as far as I can see.

To use ri-cd-gw for G0W0 it is recommended to iteratively solve the quasiparticle equation (by adding for example qpeiter 10 to the $rigw keyword group) - note that this, unlike for ri-ac-gw or linearization in general, will also work properly for non-valence orbitals (though the results may be different to linearized ones, especially if linearization is not well-suited). Further ri-cd-gw is the recommended method for the iterative evGW approach when the molecule is too large for full GW ($gw). But for IP/EA G0W0 (so HOMO/LUMO) I just recommend to use ri-ac-gw, as it is the fastest by far for large molecules - also quite some effort was invested into yielding good linearized values in this case (we employ a unique double-grid double-Pade expansion for this case, which is simply theoretically not compatible with ri-cd-gw).

Concerning the accuracy of ri-ac-gw and ri-cd-gw in general:

- For HOMO and LUMO in linearized G0W0: ri-ac-gw will in nearly any case yield quasiparticle energies VERY close to those of full G0W0. Therefore it is brilliant if one only needs to know the IP/EA, but not much else. This is often the case though.
- Beyond HOMO and LUMO the quality of ri-ac-gw will degrade significantly, as does the quality of linearized results.
- ri-cd-gw will yield correlation self-energies (Sigma_C) which are always VERY close to the of full GW. This holds for valence and core orbitals, making it the best suited for itertive approaches as evGW or G0W0 where quasiparticle energies are solved iteratively. Basically if one treats all orbitals within ri-cd-gw and an iterative treatment the results will be nearly identical to those of the corresponsing full $gw approach. However, the trick is of course to limit the orbital range for making calculations feasible.

One final remark: You molecule features degenerate orbitals. This is the single case where more integration points (npoints 256 or 512) really helps in improving the results of ri-ac-gw and ri-cd-gw. This behaviour originates from the sharp step in the Green's function at the poles, were the description actually suffers from numerical noise when they become degenerate.

Otherwise the default of 128 integration points will yield deviations between gw & ri-ac-gw for HOMO and LUMO that are usually well below 0.01 eV. Though the deviation of 0.015 eV between gw & ri-ac-gw in your calculation is probably also not critical.

All the best,

Christof