Abstract General representations for symmetrical and asymmetrical intermediate sp-hybridization are provided, with which the development of electronic structure in C3v-symmetrical C2H6 and the bonding configuration in C60 have been analyzed as an example. The spherical structure of C60 does not necessarily require the fourth hybrid, h4, to lie along the radial direction. Rather, h4 runs at an angle of 3.83° from the radius, in the plane bisecting a pentagon, to achieve maximum overlap with adjacent h4-hybrids. By virtue of these representations, a number of properties of covalent molecules and solids can be conveniently calculated. This work might be particularly helpful for the study of C-C bonding in curved structures of carbon, such as fullerenes, carbon nanotubes, and buckled graphene.
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