Single reference electronic structure

Establishing a hierarchy of rapidly converging, generally applicable, systematic approximations of exact electronic wave functions is the holy grail of electronic structure theory [1]. The basis of these approximations is the Hartree-Fock (HF) method, which defines a simple noncorrelated reference wave function consisting of a single Slater determinant (an antisymmetrized product of orbitals). To introduce electron correlation into the description, the wave function is expanded as a combination of the reference and excited Slater determinants obtained by promotion of one, two, or more electrons into vacant virtual orbitals. The approximate wave functions thus defined are characterized by the manner of the expansion (linear, nonlinear), the maximum excitation rank, and by the size of one-electron basis used to represent the orbitals. 

The discussion in Section 1-3 about the element of arbitrariness in the concept of resonance may be recalled at this point with reference to the nitrous oxide molecule and the other molecules that are described in this chapter as resonating among several valence-bond structures. It is not necessary that the structures A, B, and C be used as the basis of discussion of the nitrous oxide molecule. We might say instead that the molecule cannot be satisfactorily represented by any single valence-bond structure, and abandon the effort to correlate its structure and properties with those of other molecules. By using valence-bond structures as the basis for discussion, howrever, with the aid of the concept of resonance, we are able to account for the properties of the molecule in terms of those of other molecules in a straightforward and simple way. It is for this practical reason that we find it convenient to speak of the resonance of molecules among several electronic structures. 

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