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minimum with a barrier of for its lowest-energy isomerization path, to the tricyclic carbene, which lies above it. This presents us with the astonishing possibility that the exotic hydrocarbon may be isolable at room temperature. The threshold barrier for isolability at room temperature is about for example, (E)-cycloheptene, with a barrier of to isomerization, has a roomtemperature halflife of about 47 s [8], and the halflife rises steeply with the barrier. Other properties of pyramidane, including ionization energy and electron affinity (section 5.5.5), heat of formation (section 5.5.2.2c), and NMR spectra (section 5.5.5) were calculated [7b].

8.1.1.4 Beyond dinitrogen

There has in recent years been considerable interest in the possibility of making allotropes of nitrogen with more than two atoms per molecule. Curiously, almost all (the cation has been made [9, 10]) the work reported has been computational rather than experimental. These compounds are interesting because to any chemist with imagination the idea of a form of pure nitrogen that is not a gas at room temperature is fascinating, and because any such compound would be thermodynamically very unstable with respect to decomposition to dinitrogen.

Perhaps the first serious computational study of nitrogen oligomers was by Engelke, who studied the analogues of the benzene isomers in Fig. 8.4, first at the uncorrelated [11] then at the MP2 [12] level. The uncorrelated calculations suggested that 1–5 were “stable”, i.e. kinetically stable, although thermodynamically much higher in energy than dinitrogen. However, on the MP2/6-31G* potential energy surface 1 is a hilltop (section 2.2) and 5 is a transition state (section 2.2). This illustrates the not-so-rare fact that optimistic predictions at low levels of theory may not be sustained at higher levels. Noncorrelated ab initio, and in particular, semiempirical (chapter 6) calculations, tend to be too permissive in granting reality to exotic molecules.

8.1.2Mechanisms

We have seen, above, that computational chemistry can sometimes tell us with good reliability whether a molecule can exist. Another important application is to indicate how one molecule gets to be another: how chemical reactions occur. Indeed, the prime architect of one of the most useful computational tools, the AM1 method (chapter 6), questioned “whether the mechanism of any organic reaction was really known” [13] before the advent of computational chemistry! This skepticism was

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engendered by the difficulties and ambiguities in studying very transient intermediates, and the impossibility (at the time) of observing transition states.

8.1.2.1 The Diels–Alder reaction

This is one of the most important reactions in all of organic synthesis, as it unites two moieties in a predictable stereochemical relationship, with the concomitant formation of two carbon–carbon bonds (Fig. 8.5) [14]. The reaction has been used in the synthesis of complex natural products, for example, in an efficient synthesis of the antihypertensive drug reserpine [15]. Such a reaction seems to be well worth studying.

The Diels–Alder reaction and related pericyclic reactions, which can be treated qualitatively by the Woodward–Hoffmann rules (section 4.3.5), have been reviewed in the context of computational chemistry [16]. The reaction is clearly nonionic, and the main controversy was whether it proceeds in a concerted fashion (as indicated in Fig. 8.5) or through a diradical, in which one bond has formed and two unpaired electrons have yet to form the other bond. A subtler question was whether the reaction, if concerted, was synchronous or asynchronous: whether both new bonds were formed to the same extent as the reaction proceeded, or whether the formation of one ran ahead of the formation of the other. Using the CASSCF method (section 5.4.3) Li and Houk [17] concluded that the butadiene–ethene reaction is concerted and synchronous, and chided Dewar and Jie [18] for stubbornly adhering to the diradical (biradical) mechanism. A DFT (chapter 7) study also supported the concerted mechanism [19].

8.1.2.2Abstraction of H from amino acids by the OH radical

This reaction seems more esoteric than the Diels–Alder, and although not “used” at all, may be very important. Proteins are combinations of amino acid residues, and