@Blaise Welcome! In here we generally talk stuffs about every kind of calculation

@eimrek Also: Welcome! You should add that img to your question. It'll provide visual aid, and why this all is a bit tedious.

I would try a def2-SVP basis set first, then move up to def2-TZVP later. You might also try other functionals, like PBE or one of the Minnesota functionals, although I do not know enough to tell you which functional should work best for your type of system. Also, if the SCF oscillation continues with def2-SVP, I'd activate the damping function. I'm not sure what the exact command is for damping in Gaussian, but I see in your output that "damping=F," so there must be a way to make it true.

Well, depending on how far you are with your calculations, you may prefer to stay with 6-311++G so you can publish with the same basis set on all your molecules. In that case, I'd still go to a database and take a smaller basis set to see if it helps initial convergence. You can always upgrade the basis set afterward.

@eimrek

Thanks for the ideas, I managed to get the rb3lyp to converge with 6-311G** (so without diffuse functions). Hopefully I can get most of my stuff done this way.