It sounds like you’re interested in quantum computation for quantum chemistry, but don’t have a strong background in quantum chemistry. Please read Sections IIIB2 and IIID of https://doi.org/10.1103/RevModPhys.92.015003, as well as Appendix A of https://doi.org/10.1021/acs.chemrev.8b00803, if you haven’t already.

Changing between 6-31G and CC-PVDZ is not a unitary transformation. Those give different sets of atomic orbitals for a given molecular geometry, which are not related by *any* linear transformation, unitary or otherwise. You cannot write one set of atomic orbitals as a linear combination of the others.

It sounds like your method is truncating the space of virtual orbitals based on occupation numbers?

If this is a quantum computing project, then the Hamiltonians are certainly not directly calculated from the 2RDM. However, they cannot possibly be computed from the overlap matrix either. *On its own*, the overlap matrix gives zero information about the Hamiltonian. You need to combine that with OEI and TEI integrals in a not-necessarily orthogonal basis set for that to be at all useful. Look over your code again and figure out what it is you need. “How do I use the Psi interface,” I can help with. “What exactly do I need for my research project/external software,” I cannot.