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A computational triage approach to the synthesis of novel difluorocyclopentenes and fluorinated cycloheptadienes using thermal rearrangements

Electronic structure calculations have been used for the effective triage of substituent effects on difluorinated vinylcyclopropane precursors and their ability to undergo vinyl cyclopropane rearrangements (VCPR).


Introduction
The continual rise in the processing power of modern computer systems has allowed the computational chemist to perform ever larger and more accurate calculations over shorter and shorter periods of time. Calculations are routinely performed for synthetically interesting reactions in order to characterise pathways in detail and rationalise experimental observations. 1 Typically, these calculations are performed aer considerable synthetic optimisation, which can be time consuming and expensive. Computational evaluation of reactions prior to the commitment of experimental resource is now becoming less rare having been shown to streamline investigations into a range of organic transformations. 2 We found that electronic structure calculations were extremely helpful in developing our understanding of the rearrangement of 1a to diuorocyclopentene 2 (Scheme 1). 3 We observed good agreement between calculated (29.8 kcal mol À1 , UM05-2X/6-31G*, with the conformationally simpler Me ester) and experimental (28.6 kcal mol À1 ) VCPR activation energies, but only the less expensive UB3LYP/6-31G* calculations predicted the order of reactivity between competing cyclopropane stereoisomerisation and [3,3]-sigmatropic rearrangement correctly. The system is most unusual in that reactions involving open shell singlets and triplet species are concurrent with a more classically concerted pericyclic Scheme 1 Correlation between experimental and calculated rates for ordering the rearrangement pathways of 1a (DG ‡ values (blue) calculated using UB3LYP/6-31G*, gas phase, 298 K, Gaussian'09, all energy values are in kcal mol À1 ). rearrangement to 3. Calculations also revealed the unexpected role that the alkene stereochemistry played in controlling rearrangement pathways; E-alkenoates underwent VCPR whereas Z-alkenoates reacted via initial [3,3]-rearrangement.
The two ring expansion rearrangements observed in our system have both been used successfully by other groups in total synthesis projects. VCPRs were utilised as key steps in securing the 5-membered cyclic cores for a range of complex structures, 4 including a-vetispirene 4 from the sesquiterpene family of compounds, 5 as well as the prostaglandin E 2 methyl ester 5 (Fig. 1a). 6 There have also been reports of related [3,3]sigmatropic rearrangements, 7 including divinylcyclopropane to cycloheptadiene rearrangements, 8 being used in a similar fashion to generate molecular complexity. However, despite being utilised in the successful synthesis of marine sponge derived natural product frondosin B 6 9 and the highly potent SIRT-inhibitor 7, 10 the [3,3]-rearrangements from our system are much less common (Fig. 1b).
The key rearrangements in the synthesis of 4 and 5 required high and very high temperatures of 190 C and 560 C, respectively. Substrate modications 11 and the utilisation of transition metal catalysts 12 have started to allow access to room temperature rearrangements. Fluorine atom substitution on the cyclopropane ring has also been shown to have a benecial effect. 13 The ring strain energy is $10 kcal mol À1 higher for gem-diuorinated VCP 8a than that for the parent hydrocarbon 8b (Scheme 2). 14 This induces regiospecic ring opening in 8a, due to the weakened distal C 3 -C 5 bond, and lowers the activation energy for VCPR (DDG ‡ ¼ 10.2 kcal mol À1 between 8a and 8b). 13b, 15 Our VCPR of precursor 1a exploited this effect, alongside stabilisation of the open shell singlet transition state through benzylic resonance, to lower the activation energy further (DDG ‡ ¼ 20.6 kcal mol À1 from 1a to 8b). This system offers a highly atom-efficient route into a novel diuorocyclopentene at practical rearrangement temperatures (100 C). 3 Despite recent synthetic advances for securing diuorinated 5-membered ring structures, 17 diuorinated cyclopentenes are still rare motifs in the literature. 18 To our knowledge, there are currently no reported routes for the synthesis of structures similar to uorinated benzocycloheptadiene 3. Since both of these desirable uorinated compounds were accessible from diuoro-VCP 1a, our system represents an exciting building block class for accessing new uorinated chemical space. 19 We now look to understand more fully what effect changing the functional groups around our diuorinated precursors has on the balance between these two rearrangement pathways; we wish to be able to design precursors which rearrange at relatively low temperatures. By securing accurate transition structures for all three possible rearrangement pathways (Fig. 2), we have ensured a relatively unique opportunity to start our study by assessing the scope and limitations of our system using electronic structure calculations before committing to any synthetic chemistry.
The computational screening would start by separately predicting the effect different substituents, attached either to the diuorocyclopropane or the alkene portions of the precursor, would have on the barrier for VCPR. A selection of interesting compounds based on the predicted ease of rearrangement would then be synthesised to assess the accuracy of the theoretical predictions. As the overall goal is to identify computational models that can be easily implemented by synthetic chemists, off-the-peg and less computationally-intensive methods would be preferred over calculations which required bespoke methods and were more demanding in terms of computational resource. 20

Effect of diuorocyclopropane substitution
We reported that the most cost effective method for calculating VCPR activation energies was an unrestricted B3LYP 21 (UB3LYP) Fig. 1 Natural products and active pharmaceutical compounds synthesised using (a) VCPR and (b) aromatic-vinylcyclopropane rearrangements (key ring structures formed during the rearrangements are highlighted in blue).
We observed a dramatic rise in calculated activation energy when there was no additional substitution on the diuoro-VCP (9u, +11.9 kcal mol À1 ). Compounds with no aromatic functionality but one (9s and 9t) or two (9q and 9r) alkyl substituents were also found to have higher barriers for rearrangement (ranging from +6.5 to +8.6 kcal mol À1 ). We had observed previously that temperatures of 180 C facilitated a [3,3]-rearrangement pathway with a calculated activation energy of 32.9 kcal mol À1 (DG ‡ B3LYP , UB3LYP/6-31G*, gas phase, 298 K, Gaussian'09), 3 suggesting that low temperature rearrangement with alkyl substituents would be unlikely. Higher reaction temperatures also have the potential to activate a competitive [1,5]-hydride shi pathway 22 so these substitution patterns were ruled out of our synthetic study.
We observed a higher activation energy for 2,6-dimethylphenyl 9o (+3.3 kcal mol À1 ) due to steric interactions between the methyl protons and the proton (2.26Å) and uorine atoms (2.23 and 2.25Å) attached to the cyclopropane ring in the transition state. These small steric interactions are tolerated in the transition state to ensure the benzylic radical remains coplanar with the aromatic ring. Unlike the bis-alkyl substituents, no barrier-lowering was observed for bis-phenyl 9k (+0.5 kcal mol À1 ). Steric repulsion between the ortho-protons in TS1k induces a slight rotation of each ring, forcing stabilising aryl groups out of the plane of the benzylic radical (Fig. 4). Sustmann and co-workers investigated this twist angle effect in more detail, 23 but no further investigations into bis-arylated diuoro-VCP systems were undertaken because the DG ‡ B3LYP values were so similar to those for 9j. A wider range of effects was observed when R 1 was an heteroaryl group; 2-and 4-pyridyl groups raised the predicted barrier. 2-Furyl, 2-pyrrolyl and 2-thiophenyl groups lowered it signicantly, consistent with their known effects of free radical stabilisation as quantied by Creary. 24 A piperonyl group also activated the system (see the ESI † for a wider discussion of the systems screened and the substituent effects).

Effect of alkene substitution
We used 10 as a template for investigating modications to the alkene fragment of the precursors, focusing on the effects of alkene conguration (R 1 versus R 2 ) and radical stabilising substituents (Table 2 and Fig. 5).
The dramatic reactivity difference between the E-and Zalkene isomers of 9j previously reported 3 was maintained when a wider range of substituents was examined. Calculated activation energies for E-substituted precursors (Table 2, entries 1-5) were lower than for the unsubstituted precursor 10e (Table 2, entry 6), whilst the barriers for the corresponding Z-diastereoisomers were higher (Table 2, entries 7-9). The narrow range

Fig. 3
Difference in free energies of activation (DG ‡ B3LYP ) between cyclopropane-substituted difluoro-VCP and reference 9j. Green ¼ lower DG ‡ (<25.3 kcal mol À1 ), orange ¼ 0-5 kcal mol À1 higher DG ‡ and red ¼ >5 kcal mol À1 increase in DG ‡ . of free energies of activation observed for the E-diastereoisomers (23.2 to 25.5 kcal mol À1 ) suggests that all of these precursors should rearrange at temperatures close to or below 100 C. The narrow spread of barrier heights (DDG ‡ B3LYP ¼ 6.5 kcal mol À1 ) as the alkene substituents vary is half that observed when the similar changes were made on the cyclopropane (see Table 1). This suggests that a wider range of substituents could be tolerated on the alkene fragment since the radical is already stabilised through allylic resonance.
The transition states for the Z-diastereoisomers of Weinreb amide 10b and methyl ester 10i failed to optimise, but the alcohol (10f, +3.2 kcal mol À1 ), methyl (10g, +4.4 kcal mol À1 ) and cyanide (10h, +4.4 kcal mol À1 ) species all optimised with higher activation energies than the corresponding E-series. Disubstituted alkene 10i (Table 2, entry 10) had a higher free energy of activation than ester 9j (+3.0 kcal mol À1 ) but the introduction of the ester functionality lowered the activation energy for the rearrangement of Z-methyl 10g (difference of 1.4 kcal mol À1 between 10i and 10g).

Synthetic investigations
Aer the systematic examination of the functional group tolerance of the VCPR using electronic structure calculations, the synthesis of a selection of compounds was undertaken in order to test the computational predictions. While the literature describing the synthesis of diuorocyclopropanes by diuorocarbene transfer is extensive, 17h,25 reaction substrates oen seem to have been selected for electron-richness and low levels of functionality. We have challenged the published methods extensively in securing this set of compounds; our studies are described fully in the ESI. † The approach described below is a pragmatic one, arrived at aer extensive optimisation for this focussed set of compounds.

Synthesis of substituted diuoro-VCP
The efficient synthesis of phenyl-VCP 1a (73% over three steps) previously reported, relied on the successful diuorocyclopropanation of commercially available cinnamyl acetate with methyl 2,2-diuoro-2-(uorosulfonyl)acetate (MDFA,11). It was believed that the more electron-rich heteroarene substituents would help the cyclopropanation reaction by raising the nucleophilicity of the alkene. However, only decomposition was observed when 13a was exposed to the MDFA conditions (Scheme 3).
A 2 nd generation synthesis of precursor 16 from alkenoate 13 was proposed (Scheme 4); alkenoates 13 are easily accessible on a gram scale from the corresponding commercial or easy-toprepare aldehydes and are more stable olens for the high temperature reactions involving electron-rich aromatic substituents than allyl acetate 14.
Furyl alkenoate 13a proved to be more stable under MDFAmediated diuorocyclopropanation conditions than acetate 14a but only when a shorter reaction time of 4 hours was used ( Table 3, entry 1); prolonged reaction times of 24 h resulted in a decreased conversion to ester 15a (66% compared with 50%, respectively). The conversion to 15a could be increased to 87% by using sodium chlorodiuoroacetate (Na-CDFA, 10 eq.) conditions, 25e,26 but a drop in isolated yield was observed (22%) and attributed to product decomposition at the higher reaction temperature of 180 C over a longer reaction time of 25 hours. 10i
Reactions with ethyl cinnamate 13b (Table 3, entries 2-4) showed that this 2 nd generation route is less efficient than our previously published entry from cinnamyl acetate, due to the alkene reactivity rather than the conditions used to access alkenoates.
A wider range of heteroarene functionalised diuorocyclopropyl esters could be isolated in moderate to good yields (40-71%) using our shorter diuorocyclopropanation conditions from the corresponding alkenoates (Table 3). 2-Pyridyl 13e and 2-thiazoyl 13g failed to show any signs of reaction. Successful diuorocyclopropanation of a more reactive vinyl pyridine was reported in the patent literature using higher temperature decomposition of sodium chlorodiuoroacetate (Na-CDFA); 27 these conditions also failed to cause alkenoate 13e to react. The lack of reactivity was attributed to side reactions between the substituents and diuorocarbene; a full discussion can be found the ESI. † DIBAL-mediated reduction of the isolated diuorocyclopropyl esters to the corresponding alcohols gave mixed results with moderate to excellent yields (50-94%) observed for furyl 17a, thiophenyl 17c, piperonyl 17d and 3 0 -methyl-furyl 17g analogues (Table 3). Unfortunately, N-Boc pyrrolyl 15f was unstable under reduction conditions and gave a poor 6% yield of 17f.
Vatele's room temperature tandem oxidation/olenation conditions were utilised as the nal step in the precursor synthesis, minimising rearrangements during alkenoate formation. 28 The one-pot method previously found to be successful with ethyl ester functionalisation only worked with a selection of commercially available phosphoranes (Scheme 5, Method A). However, aldehyde 18b could be isolated in good yield using the same room temperature oxidation chemistry, allowing direct Wittig reactions to proceed smoothly (Scheme 5, Method B).
Although 2-furyl 9b and 2-thiophenyl 9d had some of the lowest predicted VCPR activation energies (21.0 and 21.3 kcal mol À1 , respectively), the observed low temperature rearrangements were still surprising; all reactions were conducted at room temperature and only warmed briey during the evaporation of solvent (maximum temperature 40 C). A repeated synthesis of VCP-23 (furan) evaporated the reaction solvent under a stream of nitrogen at ambient temperature and Scheme 4 1 st and 2 nd generation synthetic routes for accessing difluoro-VCP 16.  resulted in a similar mixture of products. These results suggest that the rearrangements occurred at room temperature (<20 C) and not during work up. To our knowledge these are the rst examples of VCP precursors undergoing low temperature thermolysis without additional additives; previously only transition metal mediated 12a,29 or charge accelerated rearrangements 11,30 occurred at temperatures close to ambient. Deconvolution of crude oxidation/Wittig reaction mixtures for furyl and thiophenyl substrates was difficult due to the presence of triphenylphosphine oxide side product. All of these reaction mixtures were puried twice, rst to remove reaction impurities in order to try to reveal the reaction outcome (see ESI † for crude reaction spectra), then a nal separation to isolate products free from phosphine oxide ( Table 5).
Precursor 23 (furyl) was absent aer the reaction; instead mixed fractions from the rst purication conrmed that mono-uorinated cycloheptadiene 28a was the favoured rearrangement product over diuorocyclopentene 30a (Table 5, entry 1). Attempts at isolating rearrangement product failed due to product decomposition but distinctive 19 F NMR signals which were consistent with isolated thiophene product were used for assigning rearrangement outcomes.
The synthesis of thiophenyl 24a/24b resulted in more complex fraction mixtures from the rst purication, with NMR evidence for VCP 24a and 24b, as well as rearrangement products 29a and 31a (Table 5, entry 2). Further thermolysis reactions of mixtures containing VCP precursors showed that E-isomer 24a rearranged at 40 C whereas the corresponding Z-isomer 24b required the higher temperature of 50 C (see ESI † for full discussion). The major mono-uorinated cycloheptadiene 29a could be isolated in 12% yield and minor diuorocyclopentene 31a in a lower 3% yield (but of only 50% purity because of the presence of cycloheptadiene 29a).
We also attempted the synthesis of 3-methyl furyl precursor 27 expecting that the methyl group would cause unfavourable steric interactions in the [3,3]-transition state and instead favour VCPR (Scheme 6a). However, like all other heteroarene substituted precursors, rearrangement was observed before isolation, but 19 F NMR reaction monitoring of the tandem oxidation/olenation of alcohol 17h suggested that rearrangement had occurred from aldehyde 18h (see ESI † for further discussion).
The two major products were tentatively assigned as dihydrofuran 33 and benzooxepine 34 due to the strong similarities between 19 F NMR chemical shis reported by Hammond 31 and ourselves, 3 respectively. Electronic structure calculations for the [3,3]-rearrangement via TS3 supported room temperature Scheme 5 Oxidation and olefination chemistry used to access a range of alkene functionality. Conditions: (i) BAIB (1.1 eq.), TEMPO (0.1 eq.), DCM, r.t., 5-6 h, (ii) Ph 3 P]C(R 1 )R 2 , DCM, r.t., 15-16 h.  a and b correspond to E-and Z-isomers, respectively. b Synthetic methodology based on Scheme 5. c Isolated yields unless otherwise stated. d 21a and 21b could not be separated by column chromatography and instead were isolated as a 3 : 2 mixture, respectively (mixture determined by 1 H NMR). e 22b formed during the reaction but could not be separated from a mixture with 22a (21% isolated yield of 22a/22b mixture). f All precursors were successfully formed but reactions resulted in complex mixtures due to competing low temperature rearrangements. rearrangement with a low DG ‡ UB3LYP value of 20.8 kcal mol À1 (Scheme 6b). Analysis of the VCPR of aldehyde 18h through TS4 gave a higher calculated barrier for rearrangement (DG ‡ UB3LYP ¼ 25.0 kcal mol À1 ), but a low spin operator value (S 2 ¼ 0.291) suggested that the rearrangement is more likely to be concerted or through a donor-acceptor ring opening/ring closing mechanism. 32 Purication of the resulting crude reaction mixture failed, due to either decomposition or volatility of the proposed products. Further synthetic and computational investigations into these appealing uorinated products are underway but they do not contribute to the development of the computational model in this study.
The observed experimental results with heterocyclic precursors link well to the calculated low activation energies for VCPR. However the lack of control, and in some cases dominance of the [3,3]-pathway, was surprising because temporary dearomatisation is required. Experimental activation energies were required from more controlled rearrangements in order to screen for the best computational methods for assessing this competing pathway.

Thermal rearrangement of isolated diuoro-VCP
The rearrangement temperatures for precursors which could be isolated were optimised to give full consumption of VCP aer 17 hours (AE5 C) (Scheme 7). Normalising the reaction temperature against a xed reaction time allows for the role that different substituents play on rearrangement rates (Table 6) to be appreciated more readily.
Weinreb amide 19a rearranged at 95 C, 5 C lower than the corresponding ethyl ester 1a, to afford a near quantitative yield of diuorocyclopentene 35 (Table 6, entry 1), consistent with the slightly lower calculated activation energy (DG ‡ ¼ À0.9 kcal mol À1 ). Minor stereoisomer 19b required higher temperatures to induce rearrangement, favouring what seemed to be a [3,3]-pathway over VCPR, consistent with previously investigated Z-alkenoates. Diene 40 was proposed as one of the major products ( Fig. 6) but these harsher conditions resulted in some decomposition and poor recovery of observed products (Table 6, entry 2). Despite the slightly lower temperature of 155 C required for methylated alkenoate 20a (Table 6, entry 3), decomposition was again observed and only rm 19 F NMR identication of diene 41 could be achieved (see ESI † for further discussion). The higher temperature required for rearrangement of 20a compared with ester 1a was entirely consistent with an increased calculated barrier height (+3.0 kcal mol À1 , vide supra).
It was predicted that the E-isomer (21a) would rearrange more rapidly in the isolated mixture of nitriles-21a and 21b since the calculated activation energy for 21a was 6.5 kcal mol À1 lower than that of the Z-isomer (21b). Thermolysis of the mixture at 90 C over 17 hours gave full conversion of 21a to diuorocyclopentene 37; 21b only showed cyclopropane stereoisomerisation to cis-42 at this temperature ( Table 6, entry 4). Only when the resulting mixture was re-heated to 160 C was full conversion of the Z-isomers observed ( Table 6, entry 5), affording diuorocyclopentene 37 in a 48% yield in a 6 : 1 ratio with alkene regioisomer 43. The computational triage was not limited to uorinated precursors; VCP 47 had a calculated activation barrier of 33.4 kcal mol À1 for rearrangement through TS5 (Scheme 8). Simmons-Smith cyclopropanation 33 of commercially available cinnamyl alcohol 46, followed by tandem oxidation/olenation, afforded the desired precursor 47 in an unoptimised 35% yield over two steps. A much higher temperature of 220 C was required for full conversion of 47 to cyclopentene 38 over 17 hours (Table 6, entry 6), 120 C higher than required for the corresponding diuorinated precursor 1a. A mixture of trans-38a and cis-38b diastereoisomers was observed and chromatographic separation gave 40% and 22% yields of the two products, respectively. Electronic structure calculations showed that transition states representing the VCPR from both trans-47 (TS5a, DG ‡ B3LYP ¼ 33.4 kcal mol À1 ) and the corresponding cisisomer (TS5b, DG ‡ B3LYP ¼ 34.5 kcal mol À1 ) had similar energies and could therefore be competitive at high temperatures.
This result conclusively shows the accelerative effect of gem-diuorination, and justies the decision not to invest time in the synthesis of precursors predicted to have activation energies greater than 30 kcal mol À1 . In fact, experimental results from compounds 20a and 21b suggest that the maximum temperature for synthetically useful VCPR with uorinated precursors could be much lower than expected.
Piperonyl species 22a had a much lower predicted activation energy (DG ‡ B3LYP ¼ 23.0 kcal mol À1 ) and subsequently rearranged at much lower optimised temperature of 70 C (Table 6, entry 7). However, like compounds containing the highly activating heteroarene substituents, both diuorocyclopentene 39 and heptadiene 44 were observed and could be isolated aer preparative HPLC in low yields (18% and 11% respectively). Diene 44 was the exclusive product of the [3,3]-rearrangement, despite the possibility of the formation of regioisomer 45 via reaction at aromatic carbon centre C4 (Scheme 9). Electronic structure calculations were consistent with experimental results, showing that the observed pathway through TS6a had a lower activation energy than that through TS6b (DDG ‡ ¼ 5.3 kcal mol À1 ).
The greater thermal control observed from the rearrangement of 22a, allowed the competition between VCPR and [3,3]pathways to be examined fully and for the rst time, using VT  ]toluene (see the ESI † d Decomposition was observed. e Clean product could not be isolated from crude reaction mixture. f 3 : 2 mixture of 21a and 21b, respectively. g Crude mixture also contains 26% 21b and 3% cis-42 (determined by 19 F NMR). h Using crude reaction mixture from entry 4. i 6 : 1 ratio of diuorocyclopentene 37 and alkene isomer 43 (by 1 H NMR). j 22% of cis-cyclopentene 38b was also isolated. k Crude reaction mixture also contains 58% of [3,3]-product (44, by 19 F NMR). l 11% of 44 was also isolated.

Fig. 6
Potential side products from the rearrangement of difluorinated VCP discussed in Table 6.
for experimental details and a full discussion on kinetic modelling)). Unlike the VCPR of phenyl 1a monitored previously, no evidence of the cis-VCP was observed during thermolysis because the [3,3]-pathway was now competitive with VCPR. At this higher rearrangement temperature (100 C), full consumption of 22a was observed aer 30 minutes, contrasting with the 10 hours required for full conversion of 1a and providing further experimental evidence that the activation energy for the latter was higher, as predicted. An Arrhenius determination of activation parameters was carried out; the value for VCPR E a from piperonyl 22a of (23.4 AE 0.2) kcal mol À1 was very close to the calculated DG ‡ B3LYP (23.0 kcal mol À1 ). A slightly higher E a value of (24.9 AE 0.3) kcal mol À1 was calculated for the [3,3]-pathway; these values were used to screen for the best computational method for treating this manifold of reactions.

Predictive electronic structure calculations
We carried out an extensive set of calculations to determine the most appropriate methods for the treatment of VCPR and competing [3,3]-rearrangement. The study is reported fully in the ESI † and only the main ndings will be summarised here. The UM05-2X/6-31+G* method gave the closest agreement between experimental values for the VCPR of 1a and 22a, while the M06-2X/6-31G* method was the best for the [3,3]-rearrangement of 48; these Minnesota functionals were selected as the most accurate methods for assessing the two pathways. Because of its consistency of performance, the (U)B3LYP/6-31G* was also retained as a low cost method able to handle both rearrangements at a useful level of accuracy. The calculated DG ‡ values for VCPR using each of these methods were corrected by the average error (DG ‡ ) from 9f and 9j; these values are +2.7 kcal mol À1 for UB3LYP and À1.2 kcal mol À1 for UM05-2X. Since the experimental activation energy for the [3,3]-rearrangement could only be determined for 48, the correcting values are based solely on this compound's DG ‡ values, which are +2.4 kcal mol À1 for B3LYP and +0.5 kcal mol À1 for M06-2X.
The differences in corrected DG ‡ VCPR and corrected DG ‡ [3,3] values ((DG ‡ VCPR D) À (DG ‡ [3,3] )) were then used to predict which rearrangement pathway would be favoured by either B3LYP or Minnesota methods; values greater than +1.0 kcal mol À1 would favour VCPR and values less than À1.0 kcal mol À1 would favour sigmatropic rearrangement. Small differences between these values could result from computational error (AE0.5 kcal mol À1 ) and would represent the limit of our ability to predict the composition of rearrangement product mixtures or the identity of the dominant pathway (Table 7).
Since the correction factors were derived from their experimental values, it was no surprise that phenyl 1a was correctly predicted to undergo VCPR and that piperonyl 22a was predicted to give a mixture of products (Table 7, entry 1 and 2, respectively). More pleasingly, the major rearrangement pathways for the nine out of the ten novel diuoro-VCP systems examined were all predicted correctly using B3LYP/6-31G* calculations; for phenyl 1a, the VCPR pathway was correctly predicted as the major one but is within computational error (DG ‡ ¼ +0.9 kcal mol À1 , Fig. 7).
VCPs 25 and 26, but it is unknown whether the errors arise from the VCPR or [3,3]-rearrangement calculations, or from a combination of both. These results strongly suggest that the lowest cost method is comparable and in some case better than the more expensive Minnesota methods (we refer to implementation in Spartan), consistent with studies carried out by Simón and Goodman. 34 Since all experimental rearrangements were optimised to give full conversion of VCP aer 17 hours, a strong trend was apparent between the corrected DG ‡ values for VCPR with reaction temperatures using either M05-2X/6-31+G* (Fig. 8) or B3LYP/6-31G* methods (see ESI †).
As more compounds are synthesised, the error associated with these models may be reduced. However, from the small set of varied diuorinated vinylcyclopropanes that were examined, the most effective computational models look reliable enough to be used with condence in the design and assessment of new precursors before any synthetic commitments are required.
A set of VCP from the literature were selected to test the predictive capability of the developed computational models and the rearrangement pathway for all four compounds was successfully predicted using the lower cost UB3LYP/6-31G* method (Fig. 9). The indole-vinylcyclopropane rearrangement of 50 8b and divinylcyclopropane rearrangement of 49 8c were both favoured over VCPR, whereas Sustmann and co-workers bis-aryl VCP 51 was correctly predicted to undergo VCPR. 35 The calculated DG ‡ VCPR value of 31.0 AE 0.5 kcal mol À1 for 51 is within error of the reported experimental activation energy of 32.8 AE 1.6 kcal mol À1 (corrected to 298 K). Our temperature prediction suggests that the rearrangement could give full conversion aer 17 hours at 130 C, 70 C lower than the reported conditions (reaction time of 1.5 hours). Diuoro-VCP 52 could only undergo VCPR and a calculated DG ‡ VCPR value of 28.7 kcal mol À1 was very similar to phenyl-VCP 1a and predicted to rearrange at the same temperature of 100 C. These results strongly suggest that the Ni-catalyst present during the reaction of 52 at 140 C does not facilitate VCPR, a factor that was not obvious from experimental observations. 17h

Conclusion
A low cost computational assessment (UB3LYP/6-31G*) of substituent effects on the VCPR of diuorinated vinylcyclopropanes was used to guide the synthesis of a test set of novel diuorocyclopropanes. The VCPR system examined is most unusual in that reactions involving open shell singlets and triplet species are concurrent with a more classically concerted pericyclic rearrangement, posing a signicant challenge to available computational methods.
Radical stabilising groups, specically heteroarenes, were found to lower calculated free energies of activation more when bound directly to the cyclopropane instead of to the alkene, consistent with the open shell singlet mechanism for VCPR, and bringing about rearrangements at room temperature in some cases. The most reactive systems based on heteroarenes, underwent rearrangements at unexpectedly low temperatures, through competing VCPR and aromatic-vinylcyclopropane rearrangements to give access to both novel diuorocyclopentenes and uorinated benzocycloheptadienes, respectively. Optimised rearrangement temperatures for Fig. 7 Prediction plot of the difference between corrected DG ‡ VCPR (UB3LYP/6-31G* or UM05-2X/6-31+G*) and corrected DG ‡ [3,3] (B3LYP/6-31G* or M06-2X/6-31G*, respectively) for synthesised VCP. Colour used to represent the correct (green) or incorrect (red) predictions compared with experimental observations. Fig. 8 Correlation between corrected DG ‡ UM052X values (kcal mol À1 ) for VCPR and the optimised reaction temperatures (K) which gave 100% conversion of VCP. Error in DG ‡ UM052X values ¼ AE0.5 kcal mol À1 . Error in temperature ¼ AE5 K. Fig. 9 Testing the predictive capability of electronic structure models against compounds which undergo selective VCPR or [3,3]-rearrangement (simplified computational models were used for 50 (Ts replaced with Ms) and 52 (TBS replaced with TMS)). Free energies of activation (DG ‡ ) calculated on Gaussian'09 using UB3LYP/6-31G* (gas phase, 298 K) and quoted in kcal mol À1 . Predicted temperature derived from the straight line equation y ¼ 0.0721x + 2.0341 from a plot of corrected DG ‡ B3LYP against VCPR rearrangement temperatures (see ESI †).
isolated precursors showed a good trend with calculated activation energies, allowing estimates of rearrangement temperatures to be made before synthesis. Comparison of predictions made by electronic structure calculations with experimental activation energies for piperonyl 22a and literature examples showed that the (U)M05-2X/6-31+G* method remained the most accurate for assessing VCPR, but M06-2X/6-31G* calculations were better for the aromatic-vinylcyclopropane rearrangement. No single method stood out overall but the consistency in error observed with (U)B3LYP/6-31G* calculations for both pathways, meant that it came closest to a universal method for dealing with the reaction manifold. There was no simple relationship between the amount of HF-exchange and the accuracy of the predictions. The selectively for rearrangement pathways could be predicted accurately using electronic structure calculations, either with the Minnesota functionals or lower cost DFT methods ((U)B3LYP/6-31G*). The computational design model developed was tested against literature compounds and was found to predict observed experimental results correctly.
The ability to determine whether a VCP molecule will rearrange thermally at a synthetically useful temperature, and to predict which pathway it will take, is an extremely powerful development, and shows that effective triage of synthetic chemistry programmes is not only effective, but also practicable by non-specialists.