Abstract
There are two fairly distinct methods of attempting the solution of the structure of polyatomic molecules. One is associated principally with the names Hund and Mulliken, while the other owes its development chiefly to Heitler, London, Slater, and Pauling. The former of these, which following Van Vleck, we shall denote as the H-M procedure, allows the electrons to be fed, one at a time, into a self-consistent field possessing the symmetry of the nuclear framework. Each energy level can absorb two electrons on account of the spin degeneracy, and the levels are filled in succession until all of the electrons have been used up. In contrast, the H-L-S-P method is based on the idea of electron pairs. The spin of an electron on one nucleus is coupled with that of another electron on another nucleus to give a resultant spin or zero, and the pair then form a saturated bond. Pairing occurs between the spins in such a way as to give a maximum bonding energy, and the number of free spins capable of being paired with electrons on other atoms constitutes the valency of an atom. While the two modes of attack, when carried to a complete solution, are equivalent, they often bear little resemblance to each other, to the approximation to which they are generally tractable. It is therefore important, when considering any problem of valency, to make calculations both ways, and if the results agree, one can feel fairly sure of their accuracy. It is the principal aim of the present paper to attempt such an attack on the ethylene molecule CH
2
-CH
2
. In addition, some interesting results will be given on the ethane molecule CH
3
-CH
3
. Pauling and Slater| have suggested rather tentatively that with ethylene the four valence electrons on the C nuclei are arranged with tetrahedral symmetry, just as they are in the methane molecule. This would make the HCH angle 109·5°, and the two pairs of electrons comprising the double bond, similar. In order to get the maximum overlapping, and hence presumably the least energy, all six nuclei must lie in one plane. We shall discuss this model in some detail and show that by a slight redistribution of the bonds an even more stable arrangement is possible. Mulliken has proposed essentially the same type of double bond as we employ, but he did not make any detailed calculations to establish the point. Hückel has also considered the ethylene molecule, and he concluded that it is the π-π bonds which prevent free rotation about the C-C joint. We shall establish this point in much greater detail than he did, and prove at the same time that if one of the CH
2
groups is rotated, the position of minimum energy is attained when all six nuclei lie in one plane.