Coulson’s hybridization

It can be further shown (Section 2.9.2) that the trigonometric relation (Equation 2.214) is equivalent to Coulson s hybridization condition (Coulson, 1961 Magnasco, 2007) provided the lone pair hybrid / = hys is Schmidt-orthogonalized against the bond hybrids b = hy and bi = hj2 directed towards the hydrogen atoms Hi and H2. 

Figure 3.17 Geometry of hybrid orbitals, (a) digonal sp hybrids oppositely directed along the same axis (b) trigonal sp2 hybrids pointing along three axes in a plane inclined at 120° (c) tetrahedral sp3 hybrids pointing towards the comers of a regular tetrahedron. (Reproduced with permission from R. McWeeny, Coulson s Valence, 1979, Oxford University Press, Oxford.)...

S. 0. Plastas, H. J. Huheey, C. L. Huhecy, J. E. Phosphorus 15171, /, 61-66. See also McWeeny, R. Coulson s Valence Oxford University Oxford, 1979 pp 195-198. The validity of this method has been questioned Magnusson, E.J. Am. Chem. Soc. 1984, 106, 1177-1185, 1185-1191. The lack of agreement revolves around the question of the orthogonality of hybrid orbitals. 

The electronic energy, AL/ i, is of interest mainly in connection with bonding theory since it is not an experimentally accessible quantity. A second quantity of this type is the intrinsic bond energy, the difference in energy between the atoms in the molecule and the separated atoms in the valence stafe, i.e., with all of the atoms in the same condition (with respect to spin and hybridization) as in the molecule. It is a measure of the strength of the bond after all other factors except the bringing together of valence state atoms have been eliminated (cf. the discussion of methane, Chapter 5 and McWeeny, R. Coulson s Valence, 3rd ed. Oxford University Oxford, 1979 Chapter 7). 

According to Coulson s Valence, hybridization is not a physical effect but merely a feature of [a] theoretical description . Despite flie fact that many authors of textbooks of general chemistry have written that CH4 has a tetrahedral structure because of sp hybridization, there neither exists now, nor has ever existed, any quantitative experimental or theoretical justification of such a statement. 

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. 

Coulson and Moffitt23 established a bent bond model of 1 by elaborating ideas first proposed by Forster24. They determined sp" (CC) and sp" (CH) hybrid orbitals with optimal hybridization ratios n and m to describe bonding in 1. Calculations showed that, for 1, the p-character of the CC hybrid orbitals has to be increased from sp3 to sp4 while the s-... 

V. K. Motlitt and C. A. Coulson. Phil. Mag. [7], 3S. 634 (1937 . These authors also give instructive contour diagrams of carlwn atom He, 2Ir, and 2di hybrid AO s, using orthogonalized Stater 25 AO s. 

The two concepts have on occasion been brought together Coulson and Duncanson[4] gave an explicit formula for sp-orbitals based on Slater type orbitals (STO s). Rozendaal and Baerends used hybrids to describe chemical bonding in a momentum representation [5], and more recently, Cooper considered the shape of sp hybrids in momentum space, and their impact on momentum densities [6], We would like to have a closer look at them, in terms of their functional behavior, their nodal structure and their topology. We will do... 

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