Bonding and the shapes of molecules

The simplest models of covalently bonded chemical substances are the so-called ball-and-stick models, in which the atoms are represented by balls and the sticks represent the bonds. In constructing such models it is usual to make use of so-called standard bond lengths and standard bond angles . In addition, certain orientations of groups of atoms around bonds are also assumed, i.e. preferred torsional angles . These standards correspond approximately to properties of the real molecules and control the possible shapes that the molecules can take. What are the reasons for these values and what are they for various types of molecule  

The simplest covalent bonds consist of pairs of electrons, one electron from each of the two bonded atoms, contributed by its outermost shell of electrons. The two electrons of each pair have the same spatial wave function, but have opposite spins to comply with the Pauli exclusion principle, which 

Particular types of bond, e.g. C—C, C—O, etc., generally have lengths that are approximately independent of their position in a molecule. The reason for this is that the pair of electrons forming the bond is fairly well localised to the region of the bond, so the bond is unaffected, to a first approximation, by the nature of the other bonds formed with the atom. Atomic bond lengths are always specified as the distances between the corresponding atomic nuclei. Table 3.1 shows the standard lengths for the bonds most commonly encountered in polymer molecules. 

The energy in the trans conformation is lower than that in the gauche conformations, which are the conformations of next lowest energy, because 

CH3—CH2—CH2—CH3 as a function of the torsion angle of the central C—C bond measured from the eclipsed conformation. (Reproduced from The Science of Polymer Molecules by R. H. Boyd and P. J. Phillips. Cambridge University Press 1993.) 

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