On the Theory of the Structure of CH4 and Related Molecules. Part I1

Abstract

The primary purpose of the present series of papers is to give more explicit mathematical form to the theory of Mulliken and Hund, and in some instances to the alternative theories of Pauling and Slater and of Heitler and Rumer, for valence in carbon compounds. A critical comparison is given of the Slater-Pauling and Hund-Mulliken concepts of CH4, which are based respectively on localized bonds (``electron pairs'') with the Heitler-London method, and on one-electron wave functions (Mulliken's ``orbitals'') for a self-consistent field with tetrahedral symmetry. The H-M procedure avoids hybridization of the carbon 2s and 2p wave functions, but allows two (though never three or more) electrons to accumulate on one H atom, as well as up to eight on a C atom. Inadequate cognizance is thus taken of the tendency of inter-electronic Coulomb forces to keep two electrons apart. The S-P procedure avoids this excessive accumulation, but at the expense of not letting an individual wave function be of a symmetry type (irreducible group representation) appropriate to a tetrahedral field. In particular, its s-p hybridization ``undiagonalizes'' the internal energy of the C atom. These points are illustrated by explicit exhibition of the secular determinant, which is the main new feature. Because inter-electronic repulsions make the dynamical problem more complicated than a one-electron one, the tetrahedral symmetry need only be preserved in the properties of the total wave function of the entire system rather than that of one electron, but the departures from individual tetrahedral symmetry should be less than in the Slater-Pauling theory if the Hartree self-consistent field is really a good approximation. Thus both the H-M and S-P methods, though qualitatively exceedingly illuminating, have their own characteristic drawbacks from a quantitative standpoint unless refined by inclusion of higher approximations which ultimately merge the two methods but which practically are very difficult to make.