Trivalent Carbocations

One of the main aims of quantum mechanical methods in chemistry is the calculation of energies of molecules as a function of their geometries. This requires the generation of potential energy hypersurfaces. If these surfaces can be calculated with sufficient accuracy, they may be employed to predict equilibrium geometries of molecules, relative energies of isomers, the rates of their interconversions, NMR chemical shifts, vibrational spectra, and other properties. Carbocations are ideally suited for calculations because relative energies of well-defined structural isomers are frequently not easily determined experimentally. It should, however, be kept in mind that theoretical calculations usually refer to isolated ion structures in the gas phase. 

Over the years, several computational methods have been developed. The variational theory can be used either without using experimental data other than the fundamental constants (i.e., ab initio methods) or by using empirical data to reduce the needed amount of numerical work (i.e., semiempirical data methods). There are various levels of sophistication in both ab initio [HF(IGLO), DFT GIAO-MP2, GIAO-CCSD(T)] and semiempirical methods. In the ab initio methods, various kinds of basic sets can be employed, while in the semiempirical methods, different choices of empirical parameters and parametric functions exist. The reader is referred to reviews of the subject.18,77 

Recent developments in computational chemistry have established the exact structure of carbocations by combining computational and experimental results.78,79 Furthermore, accurate 1H and 13C NMR chemical shifts of carbocations and other organic molecules can be calculated with the application of recent coupled cluster methods, such as GIAO-CCSD(T).80 

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Trivalent ( classical carbenium ions contain an sp -hybridized electron-deficient carbon atom, which tends to be planar in the absence of constraining skeletal rigidity or steric interference. The carbenium carbon contains six valence electrons thus it is highly electron deficient. The structure of trivalent carbocations can always be adequately described by using only two-electron two-center bonds (Lewis valence bond structures). CH3 is the parent for trivalent ions. 

The reverse reaction of the protolytic ionization of hydrocarbons to carbocations, that is, the reaction of trivalent carbocations with molecular hydrogen giving their parent hydrocarbons, involves the same five-coordinate carbonium ions. 

The reaction of trivalent carbocations with carbon monoxide giving acyl cations is the key step in the well-known and industrially used Koch-Haaf reaction of preparing branched carboxylic acids from al-kenes or alcohols. For example, in this way, isobutylene or tert-hutyi alcohol is converted into pivalic acid. In contrast, based on the superacidic activation of electrophiles leading the superelectrophiles (see Chapter 12), we found it possible to formylate isoalkanes to aldehydes, which subsequently rearrange to their corresponding branched ketones. 

The destabilizing effect of a silyl group compared with an alkyl group in trivalent carbocations was explained by the weaker hyperconjugation of the Si-R a-bond (R = alkyl) relative to a C-R cr-bond (R = H or alkyl) and by electrostatic repulsion between the adjacent positively charged cationic carbon and the electropositive silicon (10). 

The RC60+ cations are carbenium ions (trivalent carbocations), which are formally conjugated with the entire 7i-system of the fullerene cage. This chapter focuses on recent developments in the author s laboratory regarding the prepara-... 

In contrast, cracking of longer-chain alkanes with conventional acid catalysts is considered to proceed via p scission involving initial formation of trivalent carbocations ... 

There is clear differentiation of the alkylation of alkenes (jt-donor nucleophiles) and alkanes (a donors). The former follows Markovnikov addition, giving a trivalent carbocation and derived branched products. The latter proceeds through a five-coordinate carbocation without involvement of trivalent carbenium ions and thus without necessary branching. 

Schleyer, Olah, and co-workers.55 In this method, the sums of all 13C chemical shifts of carbocations with their respective hydrocarbon precursors are compared. A trivalent carbocation has a sum of chemical shifts of at least 350 ppm higher than the sum for the corresponding neutral hydrocarbon. This difference can be rationalized by partly attributing it to the hybridization change to sp2 and to the deshielding influence of an unit positive charge in the trivalent carbocation. Since higher coordinate carbocations (nonclassical ions) have penta- and hexa-coordinate centers, the sum of their chemical shifts relative to their neutral hydrocarbons is much smaller, often by less than 200 ppm. 

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