Evaluating the Viability of Successive Ring‐Expansions Based on Amino Acid and Hydroxyacid Side‐Chain Insertion

Abstract The outcome of ring‐expansion reactions based on amino/hydroxyacid side‐chain insertion is strongly dependent on ring size. This manuscript, which builds upon our previous work on Successive Ring Expansion (SuRE) methods, details efforts to better define the scope and limitations of these reactions on lactam and β‐ketoester ring systems with respect to ring size and additional functionality. The synthetic results provide clear guidelines as to which substrate classes are more likely to be successful and are supported by computational results, using a density functional theory (DFT) approach. Calculating the relative Gibbs free energies of the three isomeric species that are formed reversibly during ring expansion enables the viability of new synthetic reactions to be correctly predicted in most cases. The new synthetic and computational results are expected to support the design of new lactam‐ and β‐ketoester‐based ring‐expansion reactions.


Introduction
Rearrangements that allow ring-enlarged products to be prepared from smaller cyclic systemsh ave much utility in synthetic chemistry. [1,2] Ring expansions are particularly useful for the synthesis of medium-sized rings (8-to 11-membered) and macrocycles (12 + membered), as alternatives to directe nd-to-end cyclisations. [3] End-to-endc yclisations can be difficult and unpredictable processes due to competing intermolecular coupling and other side reactions, and they often necessitate the use of impractical high-dilution (or pseudo-high-dilution) conditions. [4] In contrast,h igh dilution can often be avoidedc ompletely in well-designed ring-expansions ystems. [1,2,5] Side-chain insertion ring-expansionr eactions (Scheme 1a) are au seful sub-class of ring expansion, as the requisite precursors are generally straightforwardt op repare. Various methods in which the ring expansion is accompanied by concomi-tant CÀO, CÀNa nd CÀCb ond formation are known, and this topic has been recently reviewed. [1a] Amongst this class of reaction, our group has developed as eries side-chain insertionring expansion processest hat can be performed iteratively.T hese methods, which we have termed" Successive Ring Expansion" (SuRE) reactions, [5] enable the controlled, iterative insertion of amino acido rh ydroxyacid-derived linear sequences into cyclic b-ketoesters (4!6,S cheme 1b) [5a,b] or lactams ( 7!9,S cheme 1c). [5c,d] In our experience, the most important factor in determining the outcome of new ring-expansion reactions of the types summarised in Scheme 1b and ci sr ing size. This is welld emonstrated by the outcomeso fo ur published lactone-forming ring expansions of imides of the form 10 (Scheme 2). [5d] Thus, for both a-a nd b-hydroxyacid derived linear fragments (3-and 4-atom ring expansions, respectively), there is ac lear point at which ring expansion "switches on"; the reactions work for startingm aterials with rings that are eight-memberedo rm ore for three-atom expansions (m = 1) and rings that are six-membered or more for four-atom expansions (m = 2). The analogous reactions fail for smaller ring variants.W eh ave previously postulated that these reactionsa re under thermodynamic control, andh ence that the reaction outcomes dependo nt he relative Gibbs free energies of the three isomeric forms that the substrate must pass through for ring expansion to occur.T his idea is supported by calculations performed at the DFT/B3LYP/ 6-31G* level of theory; [5d, 6-8] thus, five-membered ring-open form imide 12 RO (RO = ring-opened) was calculated to be significantly lower in Gibbs free energy than its isomeric ringclosed (12 RC ,R C= ring-closed) and ring-expandedf orms (12 RE , RE = ring-expanded), andt his was replicated in the synthetic results,w ithi mide 12 RO being isolated in 99 %y ield following hydrogenolysis of the parent benzyl protected imide (10, where n = 2, m = 1). Conversely, in the case of the analogous eight-membered starting material (10,w here n = 5, m = 1), the ring-expanded form 13 RE wasc alculated to be the most stable isomer,a nd upon testing the reaction, 13 RE was isolated in 89 %y ield, meaning that the calculations again were in line with the synthetic results.
These calculations,w hich drew inspiration from as imilara pproach used by [2d] were done primarily to validate our ideas about the reactions being under thermodynamic control. In this work, we have explored the validity of using calculations of this type predictively.A sw econtinue to developt his research programme, having ar eliable predictive tool to inform the likelihood of new SuRE variants working before committing to labour-intensive synthetic effortsw ill be of value. The utility of this approachi sd emonstrated herein;i n total, 52 new ring-expansion reactions have been attempted, with 48 successfully furnishing the desired ring-expanded product. Our DFT/B3LYP/6-31G*m ethod correctlyp redicted the reaction outcome in almosta ll cases, and compared favourably when benchmarked against other alternative methods, including those that model solvation and dispersioni nteractions.T hus,w eb elieve that this widelya vailableD FT/B3LYP/ 6-31G* approach will be useful to help assess the viability of new ring-expansion reactions before committing to synthetic efforts.

Results and Discussion
We startedb ye xamining the ring expansion of simple lactams with sarcosined erivative 15.W eh ad alreadys hown that this acid chloride is compatiblew itho ur standard lactam ring expansionm ethod ( 14!16,S cheme 3a), but prior to this work, 13-membered lactam 14 was the smallest aliphatic lactam on which we have reported as uccessful ring expansion with any linear a-amino acid chloride.
Prior to doing the synthetic chemistry,w er an DFT calculations based on the methodu sed in our earlier study.T os ummarise this method, each of the three components of the equilibria derivingf rom five-to eight-membered ring imide precursors 17 RO -20 RO were optimised at the DFT/B3LYP/6-31G* level of theoryi nv acuum. [6][7][8] Conformational searches of the optimised structures were performed at the Molecular Mechanics Force Field level. All the generated structures were retained, and their energies werec alculated using DFT/B3LYP/6-31G*. The lowest energy geometry in each case was selected, fully optimised and determined to be minimab yt he absence of negative vibrational modes, in vacuum using DFT/B3LYP/6-31G*. In each case, the relative free energies of the imide (17 RO -20 RO ), ring-closed (17 RC -20 RC ), and ring-expanded (17 RE -20 RE )i somers were calculated, with DG rel values quoted in kcal mol À1 (Scheme 3b). More information about the choice of this methoda nd method effects are included later in the manuscript; [7] until then, the discussion will focus on the synthetic aspects and DFT/B3LYP/6-31G* calculations.
In the five-t os even-membered series,t he imide isomers 17 RO -19 RO were calculated to be the most stable, thus suggesting that ring expansion is unlikely to proceed in thesee xamples. This prediction was verifiedb ys ynthetic results;t hus, none of the ring-expanded products 17 RO -19 RO were obtained when attempts were made to prepare them using the standard conditions, with no tractable products isolated from these reactions (17 RO -19 RO, Scheme 3c). Conversely, the ringexpanded isomer 20 RE was calculated to be the lowesti nf ree energy in the eight-membered ring series,a nd this again was borne out in the synthetic results, with 20 RE isolated in 82 % yield. Thus, the use of an eight-membered ring starting material (or larger) appearst ob et he 'switch on' point fort his series, as it was for the analogous lactone systemsi nS cheme 2. This is supported by the highy ielding( 66-94 %) ring expansions of 9-12-membered lactam systems to form products 21 RE -24 RE under the standard conditions.
Medicinal interest in medium-sized rings and macrocycles has increased significantly in the last decade, [9] and the reaction variant described in Scheme 3a ppears to be well suited for use in the preparation of peptoid-containing macrocycles, [10] as long as the startingl actami sa ne ight-membered ring or larger.T hus, to better demonstrate its potentialu tility, we went on to investigate the range of N-substituents that can be tolerated on the linear unit 26,w ith these resultss ummarised in Scheme4.I nt otal, 24 new ring-expansion reactions of this type have been performed, to make 27 a-y (27 k was described previously) [5c] using various functionalised amino acid-derived linear fragments (26). Most of the reactionsp roceeded in high yield (the yield quoted is for the full N-acylation/protecting group cleavage/rearrangement sequence) under the standard reaction conditions, significantly expanding the range and diversity of amino acid derivatives that have been demonstrated in the SuRE methodt odate.
All the new SuRE reactions presented in Scheme 4w orked (at least to some degree), although there wereafew outliers that were lower yielding (e.g.,f uran-derivative 27 v). In these cases,w eb elieve that the lower yield is not caused by an inherentd ifference in the thermodynamics of the ring expansion equilibrium (i.e.,the relative free energies of the analogous isomers 27 v RO , 27 v RC and 27 v RE are in line with those for the methyl analogue 20,s ee SI for full details) [11] but can be explained by substrate-dependent side reactions or problems with the preceding N-acylations tep. For example, in the case of furan derivative 27 v,the lower yield is largely due to incomplete N-acylation( step i),w hich in turn is likely to be ac onsequenceo ft he relative instability of the acid-sensitive furan motif. Unexpected side reactions/degradation also cannot be ruled out during the ring-expansion reaction (step ii)i nc ases where more reactivef unctionalg roups are involved.
Next, we examined the ring expansions of cyclic b-ketoesters. These reactions weret he subjecto fo ur first two publications in this area, [5a,b] which focusedm ainly on the insertion of b-aminoa cid derived linear fragments;f or example, five-to eight-and 12-membered cyclic b-ketoesters (28)w ere all found to undergos mooth ring expansion (to form products of the type 30)u pon reaction under the reported conditions with b-alanine derived acid chloride 29 (Scheme 5a). [5a] DFT/B3LYP/ 6-31G* calculations were performed to measure the energies of the equilibrating isomers of the five-, six-, and 12-membered ring systems 31-33 as before.P leasingly,t he calculations suggest that the ring-expanded isomers are lowest in energy by a clear margin, suggesting that there is as trong thermodynamic driving force for ring expansion in this series (Scheme5b). To complete the synthetic series, we went on to perform the ring expansion of nine-to 11-membered b-ketoesters for the first time, with these new synthetic reactions proceeding well, affording lactams 34-36 (52-74%,S cheme 5c).
The hydroxyacid-based analogue of this cyclic b-ketoester ring expansion was less well developed, with the expansion of seven-membered 37 the only example of this type featured in our previous publications to have been performed on as imple cyclic b-ketoester (Scheme 6a). Given the importance of macrocyclic lactones in medicinal chemistry, [12] we decidedt ot est whether the scope of this variant could be expanded. As was done for the analogous amino acid system, DFT/B3LYP/6-31G* calculations were performed to measure the energies of the equilibrating isomers of the five-, six-, and 12-membered ring systems 40-42 (Scheme 6b), which again suggested that there is ac lear thermodynamic driving force for ring expansion. Pleasingly, the corresponding synthetic experiments all worked well, with five-to eight-membered b-ketoesters undergoing Cacylation,h ydrogenolysis and ring expansion to give ring-expandedl actones 39, 40 RE , 41 RE and 43 all in comparable yields (Scheme 6c). In as mall change to the published conditions showni nS cheme 6a,w ef ound that performing the hydrogenolysis in ethyl acetate (rather than methanol)a nd then stirring with triethylamine in chloroform led to superior reaction yields.T he main reason the isolated yields are in the 50-60% range (and not higher) is due to loss of material during the Cacylation step (especially the work-up, during whicht he magnesium salts can cause problems with phase separation) and these results are in line with typical yields in our previous papers. [5a,b] We then went on to test otherl actam-based ring expansion systemsw ith additional functionality present in the starting lactams. Hydroxyacid and amino acid derivatives 38 and 46 were used to exemplify the syntheticr eactions, and in the calculations for 46,asimplifiedN -methyl (rathert han N-benzyl) derivativew as used (i.e.,f rom 47)a st his significantly reduced the computational time butw as found to have very little impact on thec alculations. [13] Thus,w es tarted by examining lactamsc ontaining a-heteroatoms( 52, 55, 58 and 60)w ith amino acid and hydroxyacid derivatives 38 and 46.T he analogous heteroatom-free variants of these reactions had been tested in our earlier work (Scheme 7a)a nd were shown to be high yielding. Therefore, based purely on our chemical intu- ition at this stage, we did not expect to see much variation upon switching to these new systems. However,s tartingf rom six-membered lactam 52,am uch lower isolated yield (41 %) of the ring-expandedp roduct 53 RE was obtained in the amino acid series, while the ring-expanded lactone 54 RE was isolated as an inseparablem ixture with its ring-opened imide form 54 RO .T he calculations give clues as to why these reactions did not proceed well;f or example, the ring-opened andr ing-expanded isomers 53 RO and 53 RE werec alculated to have very similar Gibbs free energies, thus suggestingt hat both may be formed in this reaction, although only the relatively non-polar product 53 RE was isolated after chromatography,i nm odest yield. Compounds 54 RO and 54 RE were also calculated to be similar in free energy and in this case am ixture of products was isolated. Conversely,u ponm ovingt os even-membered startingm aterial 55,aclear preference for the ring-expanded isomer was predicted by the calculations, which manifested in much improved synthetic yields for the desired ring-expanded isomers(70 and 75 %for 56 RE and 57 RE respectively).
In contrastt oo xygen-containing 52 and 55,s ulfur-containing lactams 58 and 60 both performed well in the synthetic ring-expansion reactions with 46; [14] ring-expanded products 59 RE and 61 RE were each formedi ng ood yield. This was again mirrored in the calculations, with 59 RE and 61 RE calculated to be the lowest energy isomersi ne ach case by clear margins. The differencei nr eactivity between 52 and 58,w hich is presumably ar esult of some relatively subtle stereoelectronic effects and/ord ifferences in bond lengths, is not something that we would have predicted without the calculations.
We also examined benzannulated, fluorinated and branched lactam startingm aterials 62, 65, 68 and 70,a nd as before, the predictive ability of the calculations was retained. Indeed, the ability to predictw hen reactions will fail completely is also important;f or example, the ring-opened imide isomer 64 RO was calculated to be the mosts table isomer in this series, and this was corroborated by the synthetic results.
In general, we have found that for systems in which the ring-expanded isomer is calculated to be the lowest in energy by more than 3kcal mol À1 ,then the reactions tend to work reliably.I nc ases where the free energy differencei sl esst han 3kcal mol À1 ,t he reaction outcomes are less predictable, often giving low yields of ring-expandedp roducts and/orm ixtures. The reactions to form ring-expandedp roducts 69 RE and 72 RE , which were isolated in modest 30 and 45 %y ields, respectively, are outliers in terms of yield, but the lower yields in these cases simply reflect the fact that the N-acylation step did not proceedt oc ompletion in either case. Indeed, an important caveat to keep in mind when using this DFT/B3LYP/6-31G* methodi st hat it only gives an indication of the chances of achieving af avourable equilibrium. It does not account for the efficiency of the synthetic steps that take place before the equilibrium, the possibility of off-equilibrium side reactions or other kinetic effects.
As all the ring-expanded products described in this manuscript werem ade using SuRE methods, they are all, in theory, potentialstarting materials for further ring-expansion reactions. Representativee xamples of products (73-77)t hat have been expanded for as econd time in our earlier work are shown in Figure 1, with the second linear fragment inserted highlighted in red. After undergoing one ring expansion, the rings should all be large enough that they are beyondt he "switch on" point for anyo ft he ring-expansion reaction types that we have studied and calculated (not withstandinga ny effects resultingf rom the additionally added functional groups) and shouldt herefore be thermodynamically favourable. This is corroborated by our work to datei nw hich several successful successive ring-expansionr eactions are reported.T his does not mean that performing additional iterations is always routine (e.g.,i ns ome cases, the acylation reactions can be more difficult on these more functionalised systems, sometimes requiring additional equivalents of acid chloride), [5c-d] but once acylation has been achieved, ring expansion is typicallys traightforward. Three new examples of doublyr ing-expanded products (78-80,s ee the Supporting Information for reaction conditions), based on new substrates made for the first time in this manuscript, have been performed anda re reported here for completeness.

Computational chemistry:M ethod evaluation
The DFT/B3LYP/6-31G* methodologyu sed has demonstrated, in both this and previous work, [5d] good successi np redicting the outcome of SuRE reactions. Calculations at the B3LYP/6-31G* level are relatively computationally efficient, but do not take into consideration effects such as solvation and dispersion. These additions are typically used to improvet he accuracy of such calculations, therefore, we decided to benchmark their effects,a long with ar ange of functionals, in ordert od etermineany potential method-effects in the calculations.
For this study general gradient approximation,G GA (BP86), hybrid (B3LYP and PBE0) andm eta-hybrid (M06 and M06-2X) functionals wereu sed. Solvation effects were applied using a PCM model with either dichloromethane or chloroform as relevant to simulatet he reaction conditions. The effects of dispersion are inherentlyt akeni nto consideration by the M06 and M06-2X functionals. [15] They were also applied using the Grimme'sD 3m ethod with Becke-Johnson damping [16] to a PBE0/def2-TZVPP single-point calculation, using the geometry and thermodynamic corrections from aB P86/SV(P) calculation; this method has been used successfully by our groups in previous projects, [17] and also testst he effect of al arget riple zeta basis set. [18]  Initially,awide range of methods werebenchmarked against structures 17-20,b yr eoptimising the structures from the B3LYP/6-31G* calculations and comparing the relative energies with the experimental outcomes (Table 1). Structures with which the ring-closed isomer has al arger energy than the ring-opened or ring-expanded isomers (17, 19 and 20), produced the most comparable results, with there being little differencew hen using GGA or hybrid functionals with the 6-31G* basis set.
Modellingt he effects of solvation also had little effect on the relative energy differences when using the hybrid B3LYP functional. Comparable resultsa re observed both with and withouts olventc orrections. However,t his does not extend to the BP86/SV(P) calculations, with more significant relative energy differences observed when compared to the standard B3LYP/6-31G* calculations, which appears to come from greater stabilisation of the ring-closed and ring-expanded isomers than the ring-opened when solventisi ncluded.
The effects of dispersion had the greatest impact on the expected outcomes of the experiments, with the M06, M06-2X and D3(BJ)-PBE0 calculations showingl ower relative energies for the ring-closed and ring-expanded isomers, predicting that ring expansions hould be comparatively more thermodynamically favourable in these examples, and in somec ases contradicting the experimentalr esults. We believe that due to the side chain present in the ring-opened structures being directed away from the ring, there are fewer stabilising interactions present than compared to the ring-closed or expanded isomers. As ac onsequence of these differentm olecule geometries, it appears that modellingt he dispersion interactions may result in the stability of the ring-expanded isomer being overpredicted when compared to the ring-opened form.T his alters the expected reaction outcomew here the B3LYP/6-31G* calculations predict these isomers to be similar in energy.
With dispersione ffects havingalarge effect on the relative energy differences and the predicted thermodynamic out- comes on these examples, the study was extended to include these effects to several other systems, using the M06-2X/6-31G* methodology.Ac omparison between this methoda nd B3LYP/6-31G* is presented in Table 2. As observed with structures 17-20 (Table1), the main difference between the two methods is that, when comparedt ot he ring-expanded form, the relative energies of the ring-closed forms are lower at the M06-2X/6-31G*l evel (D ave = À5.2 kcal mol À1 ), and ring-opened isomersi ncreased (D ave = 3.1 kcal mol À1 ). In most instances this doesn'tc hange the expected outcome of the reaction, however,w here there is as maller difference in the energy of the ring-opened and ring-expanded isomers (see 53, 63 and 64), this does result in ring expansion being predicted to be favourable. Notably in some examples the intermediate ringclosed isomer becomes lower in energy than the ring-opened, however,this does not seem to correlate to any observable differencei nh ow well the reaction proceeds experimentally (see 32, 40 and 69 for examples). Thus, for either method, both the B3LYP and M06-2X functionals correctlyp redicts the expected reactiono utcomes in the majority of cases,a lthough on average, it is the B3LYP methodt hat more closely correlates with the experimental findings, despite the fact that the M06-2X functional usually performsb etter for organic molecules due to the inclusion of dispersion corrections. [15,19] Therefore, we believe that these results clearly demonstrate that the B3LYP/6-31G* methodology is suitable as an aid forp redicting the outcomeo fS uRE reactions, balancing computational efficiency with good prediction of reaction outcome. The observation that ag reater than 3kcal mol À1 energy difference between ring-opened and ringexpanded isomers is needed to more confidently predict the outcomeo fther eaction, is based upon the inherent computational accuracyo ft hese calculations

Conclusions
In summary,w eh ave significantly expanded the scope of various classes of SuRE reaction, and have shown that the reaction outcomes can be predicted based on the relative Gibbs free energies of three isomeric speciesi ne quilibrium by using DFT calculations. [20] Useful conclusions can also be drawn from the significantly expanded synthetic scoping reactions and at otal of 48 new ring-expanded products are reported in this manuscript. In most cases, the isomer calculated to be lowest in energy wast he major product obtained in the corresponding synthetic results.
Of course,a ny computational predictivem ethodo ft his type will never be 100 %a ccurate, especially given how difficult it is to modelt he properties and conformations of relatively flexible systemsl ike macrocycles. [21] In view of this, the approximations involved in the calculations and the possibility that kinetic effects might prevent equilibrium being reached in some reaction systems, we do not recommend using the calculations to make quantitativep redictions on reaction yields or the Boltzmann distribution of the isomersi nt he presumed equilibria. The guideline that af ree energy difference of more than 3kcal mol À1 in favour of the ring-expanded isomer when using Table 2. Relative difference of Gibbs energies at 298 K. Solvent corrections were applied using aP CM model with either dichloromethaneo r chloroform as relevant for the M06-2X/6-31G* calculations. See the Supporting Information for absolute energies. Blue numbers denotest he most significant differences between the two methods > 3kcalmol À1 . D ave is defineda st he mean value of the energy at M06-2X/6-31G*energy at B3LYP/6-31G*.  the B3LYP/6-31G* methodology usually leads to as uccessful reactioni saq ualitative observation, that this was true in all such cases tested in which the preceding acylation step was efficient. It should not be considered ah ardr ule. However,a s ag uide to assessing the viability of new ring-expansion reactions before embarkingo ns ynthetic effort, we do believe that this DFT/B3LYP/6-31G* method,w hich is widely implemented across the vast majority of computational chemistry packages, has practical utility and will be useful in directing future synthetic efforts, in our group and others.