The characteristic property which some molecules have of transmitting influences from one part to another is an indication that the electrons constituting the bonds cannot be segregated into closed localized pairs. This feature is represented in the Pauling method by the super position of a number of canonical structures, each of which corresponds to a chemical picture of localized bonds. The state of the molecule has properties which are different from those of the individual canonical structures, but can be defined or interpreted in terms of a set of them. The energy of the lowest or normal state is usually lower than that of any one canonical structure, even than that which would appear from the orthodox method of drawing bonds to be the most stable. The amount by which the energy sinks as a result of the superposition has been called resonance energy by Pauling, and numerical estimates of its value have been made for a large number of organic molecules. In calculating this energy change, however, no account seems to have been taken of the change in the lengths of the links which may be caused by the interaction of the electrons. Links are regarded as single or double, and the appropriate energy content calculated as though they were isolated single or double links, whereas the interaction between adjoining links may result in a length and an energy of link, to which the description single or double is no longer appropriate. Pauling has recently discussed the relationship between the nature and the lengths of links in typical organic molecules. Taking the known lengths of links in ethylene, benzene, graphite, and ethane, and the fractional order of their links (as two, three-halves, four-thirds, and unity) derived from the coefficients which occur in the linear sum of canonical structures, Pauling has derived an empirical relation between them. From it he deduces in other cases the extent to which the double-bonded character enters into other links. Pauling’s method will be made more precise in a paper which follows this.
Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions
