In Configuration Interaction scheme Why does inclusion of excited states (unfilled states) in the basis set improve accuracy? What is missing in the model which is accounted for by inclusion of suc h virtual states. My guess is the the born-oppenheimer approximation but not sure??
CI spans a larger space of possible solutions than Hartree-Fock alone. A CI wavefunction may be interpreted to include partial occupancy of orbitals unfilled in the Hartree-Fock model where all MO's are constrained to have 1 or 2 electrons. The occupancy of such orbitals is chosen to give the lowest possible energy. The Born-Oppenheimer approximation has nothing to do with CI. It allows one to decouple nuclear motion from that of the electrons. This leads to a simple 1/r description of nuclear-electron attractions. Since you've asked several questions on this topic, I suggest you have a look at: "Modern Quantum Chemistry" by A. Szabo and N.S. Ostlund. -Jim