Theory of Separated Electron Pairs

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Abstract
Electron pairs in a molecule are said to be separated if (i) the molecular electronic wave function is accurately expressible as an antisymmetrized product of individual pair wave functions, and (ii) the individual pair functions are mutually exclusive in the sense that if all pair functions are linearily expressed in terms of Slater determinants built from some orthogonal one‐electron spin orbitals, no spin orbital enters the description of more than one pair function. It is shown that the electronic energy of a system of separated electron pairs may be written in a particularly simple form, and the problem of determining the best separated electron‐pair description of a particular molecule is discussed. The best orbital description of an electron‐pair bond is defined to be the best wave function for the pair that can be built from two atomic orbitals, one on each of two atoms. Systematic adjustment of individual pair descriptions one at a time is shown to provide a rigorous yet practicable procedure for obtaining best orbital descriptions for several separated electron‐pair bonds in a molecule. The equations obtained are shown to simplify considerably when Mulliken approximations are introduced for certain electronic repulsion integrals. Under these approximations a single property of each bond is shown to dominate its effect on other bonds, the net charge transferred from one atom to the other in the bond. This charge is called the bond polarity parameter. The equations are rewritten in terms of polarity parameters, and a scheme is thereby obtained which is convenient for discussion of intrabond charge transfer effects in a molecule. Formulas are given for the terms to be added to the absolute electronegativity of an atom in a bond to correct for charge transfers in other bonds. It is shown that the total molecular energy of a system of separated electron‐pair bonds can be expressed quite rigorously as a sum of bond energies, and the approximate invariance of bond energy to molecular environment is verified. Limitations of the assumption of separability and methods for transcending it are discussed.

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