Fulminic acid, 1,3-dipolar cycloaddition

The combination of modem valence bond theory, in its spin-coupled (SC) form, and intrinsic reaction coordinate calculations utilizing a complete-active-space self-consistent field (CASSCF) wavefunction, is demonstrated to provide quantitative and yet very easy-to-visualize models for the electronic mechanisms of three gas-phase six-electron pericyclic reactions, namely the Diels-Alder reaction between butadiene and ethene, the 1,3-dipolar cycloaddition of fulminic acid to ethyne, and the disrotatory electrocyclic ringopening of cyclohexadiene. 

The article is organized as follows. In the next Section we present a brief outline of the theoretical background for the present work. Section 3 contains summaries of the SC models for the electronic mechanisms of the gas-phase Diels-Alder reaction between butadiene andethene [11] and the 1,3-dipolar cycloaddition of fulminic acid to ethyne [12]. In Section 4 we provide, for the first time, a description of the SC model for the electronic mechanism of the gas-phase disrotatory electrocyclic ring-opening of cyclohexadiene. Conclusions and final comments are presented in Section 5. 

We now turn to the gas-phase 1,3-dipolar cycloaddition of fulminic acid to ethyne. The concerted, almost synchronous nature of this reaction might create the impression that the electronic mechanism of this process should be very similar to that of the Diels-Alder reaction. Such an expectation is reinforced by frontier orbital theory, which treats both reactions in very much the same way (see Ref. 32). The only significant differences are related to the fact that the lowest unoccupied MO (LUMO) for a linear 1,3-dipole... 

We believe that reactions that follow a scheme with fill-arrows, such as the gas-phase 1,3-dipolar cycloaddition of fulminic acid to ethyne, are most likely to remain nonaromatic along the whole reaction coordinate. 

At the RHF level of theory, which uses a wavefunction that is relatively straightforward to interpret, the subtle differences between the half- and full-arrow reaction schemes would remain well-hidden within the doubly-occupied, usually delocalized orbitals. While it can be argued that the application of an orbital localization procedure could produce a semblance of the SC description for the 1,3-dipolar cycloaddition of fulminic acid to ethyne, the double-occupancy restriction makes it impossible to obtain the analogue of a half-arrow SC mechanism using an RHF wavefunction. 

Figure 2. SC orbitals for the gas-phase 1,3-dipolar cycloaddition of fulminic acid to ethyne along the CASSCF(6,6) IRC at IRC -1.2 amu bohr (leftmost column), the IS (IRC = 0) and IRC = +1.2 amu bohr (rightmost column). The plot details are as for Fig. I except that the isovalue surfaces correspond to V / = 0.1.

Figure 5. Symmetry-unique spin-coupled orbitals for the 1,3-dipolar cycloaddition of fulminic acid to ethyne.

Fig. 6. Transition structures for the 1,3-dipolar cycloadditions of fulminic acid with acetylene (left) and ethene (middle) and of nitrone with ethylene (right)...

Examples of 1,3-dipoles include diazoalkanes, nitrones, carbonyl ylides and fulminic acid. Organic chemists typically describe 1,3-dipolar cycloaddition reactions [15] in terms of four out-of-plane 71 electrons from the dipole and two from the dipolarophile. Consequently, most of the interest in the electronic structure of 1,3-dipoles has been concentrated on the distribution of the four Jt electrons over the three heavy atom centres. Of course, a characteristic feature of this class of molecules is that it presents awkward problems for classical valence theories a conventional fashion of representing such systems invokes resonance between a number of zwitterionic and diradical structures [16-19]. Much has been written on the amount of diradical character, with widely differing estimates of the relative weights of the different bonding schemes. 

The most extensively studied 1,3-dipolar cycloaddition reaction so far is the prototype reaction of acetylene with fulminic acid (Scheme 1-4). The early GVB calculations by Harcourt and Little attempted to resolve the controversy between Firestone s stepwise biradical mechanism and the concerted mechanism for the 1,3-dipolar reaction [95]. Which mechanism... 

A number of ab initio theoretical investigations on 1,3 dipolar cycloadditions have appeared in the literature in the last decade with the purpose of providing information on the mechanism of these reactions. Here we review the theoretical results obtained for the reaction between fulminic acid and acetylene (see Scheme XVIII), since this is the 1,3 dipolar cycloaddition most extensively investigated at the theoretical level. 

As specified above, the reaction investigated at the MC-SCF level is the 1,3 dipolar cycloaddition of fulminic acid to acetylene to give isoxazole. The fulminic acid can be thought of as having two allyl-like systems of three n orbitals, an in-plane n set and an out-of-plane n set. Similarly the acetylene has two sets of n orbitals, an in-plane and an out-of-plane set. These orbitals are... 

In summary, the MC-SCF results suggest that for the 1,3 dipolar cycloaddition of fulminic acid to acetylene the concerted synchronous pathway is preferred, in agreement with the mechanism proposed by Huisgen. However, contrary to Huisgen s prediction, the related transition state is found to be planar. 

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