Electron propagator theory corresponding orbitals

Electron propagator theory generates a one-electron picture of electronic structure that includes electron correlation. One-electron energies may be obtained reliably for closed-shell molecules with the P3 method and more complex correlation effects can be treated with renormalized reference states and orbitals. To each electron binding energy, there corresponds a Dyson orbital that is a correlated generalization of a canonical molecular orbital. Electron propagator theory enables interpretation of precise ab initio calculations in terms of one-electron concepts. 

The lowest, virtual, canonical HF orbitals of the neutrals consist chiefly of valence s and p basis functions. Singly occupied spin orbitals that occur only in UHF calculations on the anion are composed of the same AOs. Both types of these one-electron wave funetions may be considered approximations to the Dyson orbitals [85,86] corresponding to the EAs of the beryllium clusters. In the framework of the electron propagator theory [85], the Dyson orbitals are overlaps between an N-electron reference state and final states with N electrons. They form an overcomplete set and are not necessarily normalized to unity. 

Coulson and Longuet-Higgins gave the theory an elegant formulation that readily connects to the propagator theory as discussed above. As the Hamiltonian is independent of electron spin, the discussion can be limited to situations where the labels such as r and s refer to orbitals rather than spin orbitals. Each orbital is associated with a particular atomic site in the molecule, and with one orbital per site there is a one-to-one correspondence between labels and sites. 

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