Relation of the States of the Carbon Atom to Its Valence in Methane

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Abstract
An extended Heitler-London-Pauling-Slater calculation is given for methane. In addition to the usual quadrivalent configuration of the carbon atom, divalent and other configurations with which it may ``resonate'' are considered, in order to ascertain whether or not s2p2 carbon plays a more important part than usually is supposed. The mathematical formulation, an example of the use of the vector model, leads to a seventh degree secular equation, which is solved for empirical values of the integrals. The influence of resonance upon the energy is found to be small, but not negligible, and increases the stability of the molecule about 1.2 volts over the value for the usual Pauling-Slater configuration. The state of the carbon atom when it forms four electron-pair bonds is obtained explicitly in terms of the atomic states, and is found to comprise 5S, 3D and 1D of sp3, together with 3P and 1D of s2p2 and of p4. This, the ``valence state'' of Van Vleck, is 7 volts above the ground state of the carbon atom; resonance lowers it about 2.5 volts. The resonance causes a greater modification in the wave function and in the valence state than it does in the energy. In the final section the relative energies of CH, CH2, CH3 and CH4 are examined under the approximation of electron pairing, and are shown to have the regularly graded values of 4.0, 8.0, 12.1 and 17.0 volts when the experimental values for CH and CH4 are used to determine the unknown integrals. There is no indication that CH2 occupies a favored position, and the valence of four for carbon remains understandable in the light of the theory.

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