  For many-body methods such as MCSCF and CASSCF, in which the number of
one-electron orbitals are optimized and independent of basis set used, there
are no problems with using plane-wave basis sets. However, for methods
currently used in quantum computing such as select configuration interaction
(CI) and coupled cluster (CC) methods, it is necessary to have a virtual space
that is able to capture a significant amount of electron-electron correlation
in the system. The virtual orbitals in a pseudopotential plane-wave
Hartree--Fock calculation, because of Coulomb repulsion, are often scattering
states that interact very weakly with the filled orbitals. As a result, very
little correlation energy is captured from them. The use of virtual spaces
derived from the one-electron operators have also been tried, and while some
correlation is captured, the amount is quite low. To overcome these
limitations, we have been developing new classes of algorithms to define
virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians,
which we term as correlation optimized virtual orbitals with the abbreviation
COVOs. With these procedures we have been able to derive virtual spaces,
containing only a few orbitals, that are able to capture a significant amount
of correlation. Besides, using these derived basis sets for quantum computing
calculations targeting full CI (FCI) quality-results, they can also be used in
other many-body approaches, including CC and M{\o}ller--Plesset perturbation
theories, and open up the door to many-body calculations for pseudopotential
plane-wave basis set methods. For the H$_2$ molecule, we were able to obtain
good agreement with FCI/cc-pVTZ results with just 4 virtual orbitals, for both
FCI and quantum simulations.
