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Supplementing Nike's answer above.. This is actually quite elementary math. Let's say I have an orbital in a basis $|\psi\rangle = \sum_i c_i |i\rangle$ and I want to find the expansion in some other basis set $|J\rangle$. How do I do this? In the new basis set, one has the resolution of the identity $\sum_{JK} |J\rangle \langle J|K\rangle^{-1} \langle K|\... 8 What you're describing is very common, and is not limited to GAMESS and Q-Chem. First, here's how to do it in MOLPRO, MRCC, GAMESS, Q-Chem (in fact the only electronic structure software that I regularly use which doesn't allow this type of projection into a bigger basis set, is CFOUR): 1) MOLPRO: basis=cc-pVDZ hf basis=cc-pVQZ hf The HF ... 6 I think Nike has answered to all questions adequately enough. I am sharing my understanding as one of the developers of the PNO-based local coupled-cluster (CC) methods, codes for computing response properties in particular. In coupled-cluster theory, the correlated wavefunction is described in terms of "cluster amplitudes" (which are the ... 6 I'll answer each of your three questions separately, but the one you say is "most important" will go first 😊 And most importantly, why are they used for correlation calculation? They can significantly reduce the cost of a calculation on a big system, especially when there is a large number of "virtual" orbitals (unoccupied orbitals) in ... 5 Note: I have corrected some omissions from my initial answer to avoid any confusion. For a rigorous explanation of the process, I would recommend looking at Susi's answer. The projection process for MOs is actually fairly straightforward. In the following, let$m$be the dimension of the new basis,$n\$ the dimension of the old. Even though getting a guess ...