The Roles of Simple Numbers and Symmetry in Chemical Reactivity

The Roles of Simple Numbers and Symmetry in Chemical Reactivity 

Simple numbers play a huge role in understanding chemical reactivity. For example, the periodic table has 18 columns (families) of chemical elements and (for now) 7 rows or periods. The periods correspond to Bohr s orbits (n = 1,2,3.) which are simple integers. When the new quantum mechanics appeared during the 1920s, simple integers for quantum numbers n, 1, and m specified atomic orbitals. 

The 4n + 2 rule, developed by Hiickel in the 1930s, is another example. Allowed values for n are integers only (n = 0, 1, 2, 3.). Benzene, the stable aromatic compound, has 6 n electrons satisfying the 4n + 2 rule (n = 1). Cyclobutadiene (see chapter 4) has 4 it electrons, does not satisfy the 

4n + 2 rule, and is extremely reactive and short-lived. The 1960s witnessed widespread testing of concepts of aromaticity with NMR furnishing a sensitive probe. Particularly striking is [18]-annulene (see structure below), prepared by Franz Sondheimer (1926-81) in London. This planar 18-membered ring satisfies the 4n + 2 rule (n = 4), is stable and displays aromatic chemical and NMR properties. In 1964, Rowland Pettit (1927-81), University of Texas, prepared a stable iron complex containing square cyclobutadiene (see structure below). The complex satisfies the 18-elec-tron rule and releases its short-lived captive upon oxidation by Ce.  

The type of pictorial, back-of-the-envelope, application of theory exemplified by the 4n + 2 rule would soon be applied toward understanding a wide range of no-mechanism reactions. The Diels-Alder reaction (see chapter 3) is one example. The reverse reaction ( retro-Diels-Alder ) also occurs readily. In one step (one transition state), three n bonds are broken and two new o bonds and one n bond are created. The simultaneous cleavage and formation of all bonds in one step is referred to as concerted and such reactions often occur under mild conditions and form specific stereoisomers. Since the bonds made and broken form a continuous cycle in the transition state, the Diels-Alder is an example of an electrocyclic reaction. In contrast to the Diels-Alder reaction, dimerizations of two alkene molecules (R2C=CR2) to cyclobutanes typically fail (as do the reverse thermal decompositions of cyclobutanes). These reactions often succeed when ultraviolet light (photochemistry) is used in place of heat (thermal chemistry). 

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