On the Theory of the Structure of CH₄ and Related Molecules: Part II

Explicit calculations are made to examine whether the tetrahedral model of CH₄ is really the most stable in the Hund‐Mulliken and Slater‐Pauling theories. The secular determinant involved in the H‐M procedure is too complicated (degree 8) to solve generally, but three methods of approximation are given applicable in three different limiting cases, in all of which the tetrahedral model proves to be that of least energy quite irrespective of repulsions between the H atoms. The fact that two of the methods do not assume the carbon s‐p separation to be small shows that s‐p hybridization is not a necessary condition for tetrahedral valence bonds. Calculations are also given which show that in the Heitler‐London‐Pauling‐Slater method the regular tetrahedron is superior to other models of somewhat lower symmetry. It is further calculated according to both the H‐M and H‐L‐P‐S schemes that in compounds of the form CH₂X₂, CHX₃, and CH₃X, the most stable models are tetrahedra of less symmetry than the regular tetrahedron; i.e., models with the valence angles somewhat distorted from 109.5° unless the C – H and C — X bonds are of equal intensity. The predicted directions of the deviations from 109.5° are in agreement with x‐ray diffraction data for CH₂Cl₂ and CHCl₃. The conclusion is rather prevalent in the literature that with s‐p hybridization and electron pairing two bond axes tend to set themselves at 109.5°. This is shown incorrect; instead the angle can be anything between 90° and 180° depending on the relative intensities of the s and p bonds. If the s bonding power is not negligible, the angle between an NH axis and the pyramidal axis in NH₃ should be somewhat greater than the value 54.7° which is obtained if the three NH axes are orthogonal and which is characteristic of pure p‐bonding. Actually Dennison and Uhlenbeck find 68°, and Lueg and Hedfeld 73°, from band spectra. It is shown that CH₄⁺ should be a flattened rather than regular tetrahedron, conceivably even being plane. Also CH₃ should be a flatter pyramid than NH₃.