Frank H.
Allen
*a,
Mary F.
Mahon
b,
Paul R.
Raithby
*b,
Gregory P.
Shields
a and
Hazel A.
Sparkes
b
aCambridge Crystallographic Data Centre, 12 Union Road, Cambridge, UK CB2 IEZ. E-mail: allen@ccdc.cam.ac.uk
bDepartment of Chemistry, University of Bath, Bath, UK BA2 7AY. E-mail: p.r.raithby@bath.ac.uk
First published on 8th December 2004
The mechanism of the solid state [2 + 2] cycloaddition of alkenes has been investigated using the structure correlation method based on geometrical data calculated from single crystal X-ray diffraction studies retrieved from the Cambridge Structural Database (CSD). Searches were carried out for non-bonded alkene⋯alkene reactant interactions, within a limiting C⋯C separation of the sum of van der Waals radii plus 20%, and for bonded cyclobutane product fragments. The results were visualised and interpreted using principal component analysis and symmetry deformation coordinates. The reaction pathway for [2 + 2] cycloaddition was established and it was shown that (a) the alkene moieties are not required to be parallel for the reaction to occur and (b) a large twist angle of the reacting alkene fragments is permissible to form a puckered cyclobutane reaction product, as long as similar intra-annular valence angles are maintained around the four-membered ring.
Since the interest in solid state reactions continues to grow, particularly due to the potential applications of the resultant products in the pharmaceutical and electronics industries, it is timely to further investigate their mechanisms. Here we present an analysis of the solid state [2 + 2] cycloaddition reaction of alkenes using structural information available in the Cambridge Structural Database (CSD)8 and the knowledge mining techniques that are now available. Fundamental to the methodology used is the structure correlation principle of Bürgi and Dunitz9 which views each specific observation of a chemical substructure in a specific crystal structure as a structural ‘snapshot’ which is determined by the chemical environment and energetics of the compound. If large numbers of these snapshots are plotted together, they can trace out energetically accessible sections of the pathway followed during a chemical reaction (Scheme 1).9,10 A key question in applying the structure correlation principle concerns the structural parameters, or combination of parameters, that should be plotted so as to best visualise the reaction pathway, interpreted as a low energy valley in the relevant potential energy hypersurface. In the present study, we use principal component analysis to visualise the structural data and to detect interconversion pathways, which are then interpreted using symmetry deformation coordinates.
![]() | ||
Scheme 1 |
![]() | ||
Fig. 1 Non-bonded reactant search fragment with geometrical parameters defined. |
![]() | ||
Fig. 2 Bonded cyclobutane product search fragment with geometrical parameters defined. |
![]() | ||
Fig. 3 Definition of the cyclobutane ring-puckering angle θ. |
In order to account for the D2h topological symmetry of the non-bonded fragment (Fig. 1) the resultant geometrical dataset was symmetry expanded in accordance with the permutational operators listed in Table 1(a) using an external program written by one of us (GPS), since the automated PERMUTE function built into Quest3D does not operate on datasets arising from non-bonded searches. For the bonded searches, the topological symmetry of the fragment is D4h and the PERMUTE function in Quest3D generated the symmetry-expanded dataset according to the permutational operators listed in Table 1(b).
Two factors are relevant to the application of PCA to datasets of geometrical parameters derived from crystal structure data: (a) PCA should only be applied to sets of data of similar type, e.g. distances, angles or torsion angles, and (b) when PCA is applied to datasets that have been expanded according to the highest topological symmetry of the search fragment (i.e. the dataset includes all permutational isomers), then the PCs are directly correlated to the symmetry deformation coordinates (SDCs) generated using group theory.
In the present work we have carried out separate PCAs on the 4D symmetry-expanded datasets of the distances (B1–B4), angles (A1–A4) and torsions (T1–T4), for both the non-bonded and bonded fragments depicted in Fig. 1 and 2. We have also derived the SDCs for both types of search fragments, and these are given in Table 2(a) and (b). We have then used the PC results to identify the SDCs which show the most variation in each dataset (non-bonded and bonded), and these SDCs were then used to construct scatterplots to identify any systematic geometrical trends that might indicate a reaction coordinate for [2 + 2] cycloaddition.
SDC label | Symmetry deformation coordinate (SDC) | Symmetry operator | Eigen value | Variance |
---|---|---|---|---|
SA1 | 1/2 × (A1 + A2 + A3 + A4) | Ag | 0.075 | 1.886 |
SA2 | 1/2 × (A1 − A2 + A3 − A4) | B1g | 3.773 | 94.330 |
SA3 | 1/2 × (A1 + A2 − A3 − A4) | B2u | 0.001 | 0.037 |
SA4 | 1/2 × (A1 − A2 − A3 + A4) | B3u | 0.150 | 3.747 |
ST1 | 1/2 × (T1 + T2 + T3 + T4) | Au (a) | 0.016 | 0.401 |
ST2 | 1/2 × (T1 − T2 − T3 + T4) | Au (b) | 3.977 | 99.415 |
ST3 | 1/√2 × (T1 − T4) | B2g | 0.002 | 0.057 |
ST4 | 1/√2 × (T3 − T2) | B3g | 0.005 | 0.127 |
SB1 | 1/2 × (B1 + B2 + B3 + B4) | Ag (a) | 1.475 | 36.876 |
SB2 | 1/2 × (B1 − B2 + B3 − B4) | Ag (b) | 1.872 | 46.807 |
SB3 | 1/√2 × (B1 − B3) | B2u | 0.299 | 7.479 |
SB4 | 1/√2 × (B2 − B4) | B3u | 0.354 | 8.839 |
SDC label | Symmetry deformation coordinate (SDC) | Symmetry operator | Eigen value | Variance |
---|---|---|---|---|
SA1 | 1/2 × (A1 + A2 + A3 + A4) | A1g | 2.119 | 52.982 |
SA2 | 1/2 × (A1 − A2 + A3 − A4) | B2g | 1.183 | 29.575 |
SA3 | 1/√2 × (A1 − A3) | Eu (a) | 0.349 | 8.722 |
SA4 | 1/√2 × (A4 − A2) | Eu (b) | 0.349 | 8.722 |
ST1 | 1/2 × (T1 + T2 + T3 + T4) | A1u | 0.000 | 0.007 |
ST2 | 1/2 × (T1 − T2 − T3 + T4) | B1u | 3.999 | 99.980 |
ST3 | 1/√2 × (T1 − T4) | Eg (a) | 0.000 | 0.006 |
ST4 | 1/√2 × (T3 − T2) | Eg (b) | 0.000 | 0.006 |
SB1 | 1/2 × (B1 + B2 + B3 + B4) | A1g | 1.298 | 32.438 |
SB2 | 1/2 × (B1 − B2 + B3 − B4) | B1g | 0.931 | 23.272 |
SB3 | 1/√2 × (B1 − B3) | Eu (a) | 0.886 | 22.145 |
SB4 | 1/√2 × (B4 − B2) | Eu (b) | 0.886 | 22.145 |
In discussing the conformational variations exhibited by the developing (Fig. 1) and actual (Fig. 2) four-membered rings, we have used the puckering angle θ (Fig. 3) throughout, since this is the well-understood single conformational parameter. We note however that ST2 in Table 2(a) and (b), which maps this conformational variation in terms of the intra-annular torsion angles in both symmetries, is linearly related to θ,14 hence plots involving ST2 or θ convey equivalent information.
![]() | ||
Fig. 4 (a) Plot of SB1 vs. SB2. (b) Plot of SA2 vs. SB2. (c) Plot of the ring-puckering angle θ for non-bonded dataset. |
Fig. 4(a) (SB1 vs. SB2) indicates that as the sum of the distances (SB1) decreases so does SB2, i.e. the difference between (B1 + B3) (the sum of the bonded alkene distances) and (B2 + B4) (the sum of the non-bonded C⋯C contact distances). The major proportion of this decrease in SB2 arises from a significant decrease in the non-bonded C⋯C distances (B2 and B4) as the transition state is approached, since there is only a relatively small increase in the bonded distances (B1and B3) as the alkene bond loses double bond character.
Similarly, Fig. 4(b) (SA2 vs. SB2) indicates that as the non-bonded distance between the two alkene groups decreases so does the difference between (A1 + A3) and (A2 + A4) (see Fig. 1). This suggests that as the non-bonded distances decrease all of the angles within the putative cyclic reaction product tend towards similar values; however, these values are not necessarily 90°. This observation is supported by the wide range of puckering angles θ (Fig. 3) that are observed for the developing cyclobutane ring. It is well known9,14,15 that changing the intra-annular valence angles in cyclobutane by just 2° induces quite significant ring puckering, yielding a θ-value of 30°. Taken together, Fig. 4(b) and (c) provide evidence that the cyclobutane product is being generated in puckered as well as planar forms.
Using the same search criteria as described previously for the non-bonded reactant searches, separate datasets for intra- and intermolecular alkenes were created. SDC plots analogous to those in Fig. 4(a) and (b) showed similar characteristics to those for the composite dataset and indicate that intra- and intermolecular alkenes follow the same reaction pathway. However, the intramolecular dataset does exhibit a somewhat different θ-range, as illustrated in Fig. 5(a) and (b). We also examined scatterplots derived from the separate ‘organic’ and ‘metal–organic’ searches and observed that both of these datasets exhibit the same trends as those observed in the composite dataset.
![]() | ||
Fig. 5 (a) Plot of the ring-puckering angle θ for intermolecular alkenes. (b) Plot of the ring-puckering angle θ for intramolecular alkenes. |
The SDCs that map on to the PCs that account for almost all of the variance within the dataset are SA1, SA2, ST2, SB1, SB2, SB3 and SB4. Pairwise scatterplots were examined for trends within the dataset and these reveal only small variations in bond lengths and valence angles around the ring. However examination of Fig. 6, the histogram of the puckering angle (θ, equivalent to ST2 as noted above), shows that the cyclobutane product forms across the well known range of planar and puckered forms.6,14,15 Further analysis of the bonded dataset shows that intramolecular [2 + 2] cycloadditions would have resulted in the formation of all of the structures where the puckering angle, θ, exceeds 45°. This may well result from the mutual orientation of the reactant alkene groups being imposed by the rest of the molecule and by the constraints imposed by the solid state reaction conditions.
![]() | ||
Fig. 6 Plot of the ring-puckering angle (θ) for cyclobutane products. |
A proposed mechanism7 for the [2 + 2] cycloaddition reaction in the gas phase suggests that one of the non-bonded distances, say B2 in Fig. 1, shortens first, and this is followed by a twisting of the alkene component before the other non-bonded distance, B4, shortens to form the cyclobutane product. Clearly, the large amount of atomic movement involved here would be impossible in a solid state reaction, and this is borne out by Fig. 7(a) and (b). Thus, Fig. 7(a) shows that as the alkenes approach each other the non-bonded distances (B2 and B4) tend towards similar values, as do the bonded distances (B1 and B3). This suggests that, in the solid state at least, there is a concerted shortening of both B2 and B4, and a concerted elongation of B1 and B3, as the reaction proceeds. Once formed, the cyclobutane product has closely similar bond lengths and valence angles, as illustrated by the compact nature of the (grey) product cluster.
![]() | ||
Fig. 7 (a) The reaction pathway—superimposed plot of SB1 vs. SB2 for the reactants and products (black—alkene reactants, grey—cyclobutane products). (b) The reaction pathway—superimposed plot of SA2 vs. SB2 for the reactants and products (black—alkene reactants, grey—cyclobutane products). |
Fig. 7(b) shows that as the non-bonded distances decrease the angles A1–A4 tend towards the same value although this is not necessarily the 90° required to form a planar cyclobutane product. The wide range of ST2 [the difference between the values of (T1 + T4) and (T2 + T3)] and of the cyclobutane puckering angle (θ) indicate that the cyclobutane fragment can form in either the planar or puckered form6,14,15 and this is possibly dependant on the steric requirements of the groups directly attached to the alkene carbons that form the ring.
Our mapping of the reaction pathway, derived from many thousands of crystallographic observations, is strongly supported by the available crystallographic observations of individual solid state [2 + 2] cycloaddition reaction products. Thus, we have searched the CSD for examples of cyclobutane reaction products by restricting the substructural search query of Fig. 2 to those CSD entries containing the text string ‘irrad’ (to locate the phrases ‘irradiation product’ or ‘irradiated product’. This combined search yielded 22 CSD entries which, after the permutational symmetry had been accounted for, contained 264 cyclobutane fragments for which the puckering angle (θ) was calculated in each case. The resulting histogram (Fig. 8) shows that 80 (30%) of these examples have planar rings, while 184 (70%) have θ-values between 6° and 45°, reinforcing the conclusion from the more general analysis that solid state [2 + 2] cycloadditions of alkenes can result in both planar and puckered cyclobutane products.
![]() | ||
Fig. 8 Histogram of the ring-puckering angle (θ) for cyclobutane fragments that have been generated by solid state photochemical reactions. |
This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2005 |