Quantum-mechanical Description of the Quadrivalent Carbon Atom

Quantum-mechanical Description of the Quadrivalent Carbon Atom. —The description that is given above of the quadrivalent carbon atom as forming four sp8 bonds is somewhat idealized. In a later section (Sec. 4-5) it is pointed out that the bond orbitals have some d and / character. Moreover, the four valence electrons are not closely described by the electron configuration sp8, even aside from the contribution of configurations involving d and / orbitals. v 

7 Pauling and Sherman, loc. cit. (4). Calculations of the bonding power of 2 -2p hybrid orbitals have been reported also by R. S. Mulliken, J. Chem. Phys. 19, 900, 912 (1951). C. A. Coulson and G. R. Lester, Trans. Faraday Soc. 51, 1605 (1955), have made calculations for excited states of the hydrogen molecule-ion that agree reasonably well with the postulate that the strength S of an orbital determines its bond-forming power. 

A detailed quantum-mechanical treatment of methane has been carried out by Voge. He took into consideration the configurations 2s22p2, 2s2ps, and 2p4 and minimized the energy of the molecule in 

Since tetrahedral orbitals form stronger bonds than other orbitals it might be thought that hybridization to tetrahedral orbitals would always occur in bond formation. The tendency to use the best bond orbitals is, however, resisted in the case of atoms with an unshared pair (or more than one) by the tendency to keep the unshared pair in the 8 orbital, which is more stable than the p orbitals. In OFi, for example, the use of tetrahedral orbitals in bond formation would require that half of the 8 orbital (which is divided equally among the four tetrahedral orbitals) be used for shared pairs and only half for unshared pairs. Since a shared pair counts as only one electron for each atom, this would involve the loss of one-quarter of the extra stability due to a pair of s electrons, and the atom will strive to prevent this. On the 

A simple quantitative treatment of the amount of hybridization of bond orbitals of this kind can easily be carried out. Let us represent the bond orbital as 

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