where the caligraphic operators denote they have been projected into a subspace defined by P ˆ; that is, H = P ˆH ˆP ˆ. It is important to note that the projector only acts on matter operators, so we need only consider the impact of truncation on H ˆe, H ˆblc , and H ˆdse . The projected molecular electronic Hamiltonian has the form