one 
 century after its discovery , the 
 -sigmatropic rearrangement of allyl vinyl ethers ( i.e. , the claisen 
 rearrangement ) continues to be extensively investigated and applied 
 in the synthesis of natural products and complex organic molecules . many efforts have been devoted to develop small molecule and biocatalysts 
 for this synthetically powerful reaction . attractive 
 noncovalent interactions are responsible for much of the rate accelerations 
 and stereoselectivities observed in enzyme catalysis , and active site 
 residues can stabilize the transition state by electrostatic and noncovalent 
 interactions . a variety of dual hydrogen - bond 
 donor organocatalysts such as ureas , thio - ureas , guanidinium groups , 
 and bis - imidazoliums have been reported in the literature for claisen 
 rearrangements . some biological catalysts have also been identified , and de novo computational design strategies for 
 developing an aromatic claisen biocatalyst have been carried out . we are developing a new approach to the development 
 of organocatalysts called  spiroligozymes  wherein we 
 use transition state modeling to identify constellations of reactive 
 functional groups and then build those functional groups onto a spiroligomer 
 scaffold to see if they can act as organocatalysts . in this manuscript , we describe the design and synthesis 
 of a series of bis - amino acid monomers fused to amino acids through 
 diketopiperazines , that accelerate the claisen rearrangement of 1,1-dimethylallyl 
 coumarin . this paper reports the successful mimicry of the catalytic 
 dyad of bacterial ketosteroid isomerase ( ksi ) in a small spiroligozyme 
 and the catalysis of an aromatic claisen rearrangement of a 1,1-dimethylallyl 
 coumarin . aromatic claisen rearrangements are typically performed 
 in the 
 temperature range of 180225 c , and proceed through a concerted pericyclic pathway followed by a 
 keto / enol tautomerization that restores aromaticity . the cyclic transition 
 state of the claisen rearrangement is key for understanding a number 
 of phenomena . these include the effect of solvent on the rate of the 
 reaction , substituent effects , and stereoselectivity . there is one well - established enzyme - catalyzed claisen rearrangement , 
 the chorismate to prephenate transformation catalyzed by chorismate 
 mutase . the claisen rearrangement of o - prenylated tyrosines in a prenyltransferase 
 from the truf enzyme family has also been proposed , and catalytic antibodies have been developed for the chorismate 
 to prephenate conversion . considerable acceleration 
 of the claisen rearrangement can be achieved 
 by employing hydrogen - bonding solvents , especially water . in 1987 , carpenter and co - workers first reported the acceleration 
 of the claisen rearrangement of chorismic acid and related compounds 
 in aqueous media . the rate of the aromatic 
 claisen rearrangement of allyl naphthyl ether was also increased in 
 aqueous suspensions relative to other organic solvents such as toluene , 
 dimethylformamide , acetonitrile , and methanol . sharpless reported  on - water  catalysis of 
 a diels  alder reaction and aromatic claisen rearrangement . several examples from his lab illustrated the substantial rate acceleration 
 of the reactions when insoluble reactants were stirred in aqueous 
 suspension . catalysis has prompted several 
 computational studies to unravel the origin of the rate acceleration 
 in water and hydrogen - bonding solvents . it was found that the aqueous 
 acceleration of the claisen rearrangement is due to a greater stabilization 
 of the transition state by specific interactions with first shell 
 solvent molecules . jorgensen and co - workers computationally studied 
 the acceleration of the claisen rearrangement in water . the model 
 consisted of two explicit water molecules around the core heteroatom 
 of the allyl vinyl ether . curran 
 et al . discovered that dual hydrogen - bonding catalysts such 
 as ureas and thioureas accelerate the claisen rearrangement and measured 
 modest rate accelerations using nmr experiments . in addition , protonated catalysts including those based 
 on guanidinium , quinolinium thioamide , and ammonium structures 
 were also studied . the latter positively charged catalysts tend to 
 activate electrophiles more strongly than the neutral compounds . jacobsen and co - workers have developed diphenylguanadinium 
 salts as stereoselective claisen rearrangement catalysts for a variety 
 of substituted allyl vinyl ethers and -ketoester derivatives . the mechanism by which the guanidinium catalysts promote the claisen 
 rearrangement was also studied both experimentally and theoretically . the catalysis is mainly achieved by stabilization of the developing 
 negative charge on the oxallyl fragment , and by a secondary attractive 
 interaction between the -system of the catalyst and the partially 
 positive allyl cation fragment . kozlowski 
 and co - workers designed a bisamidinium catalyst salt able to catalyze 
 the claisen rearrangement through a two - point hydrogen bonding stabilization 
 of the negatively charged ether oxygen in the transition state . the most prominent biological example of 
 a claisen rearrangement 
 is the enzyme chorismate mutase , which 
 catalyzes the claisen rearrangement of chorismate to prephenate more 
 than a million - fold relative to the uncatalyzed process . hilvert and co - workers have also studied the 
 enzyme catalyzed cope rearrangement of carbachorismate to carbaprephenate 
 in the enzyme bacillus subtilis chorismate 
 mutase ( bscm ) . they showed that a positively 
 charged residue at position 88 or 90 is essential for stabilization 
 of the transition state of the enzymatic chorismate rearrangement . borden and houk studied models for this rearrangement 
 and tested different theozymes to determine the effect of different 
 side chains in chorismate mutase . bertran 
 et al . performed a qm / mm study where two different transition states 
 were located for the chorismate conversion to prephenate . it was found 
 that the enzyme stabilizes one of the transition states ( ts ) by means 
 of hydrogen bonding interactions , while the other ts located , corresponded 
 to the preferred one in vacuum and in water . they found that aqueous solution and bscm active site environments 
 reduce the free energy barriers more than in the gas phase for both 
 reactions . the catalytic effect was mainly attributed to the enhanced 
 electrostatic stabilization of the transition state relative to the 
 starting substrate in the claisen rearrangement . very recently , lynf , a prenyltransferase from the 
 truf enzyme family , 
 was characterized . this enzyme performs 
 o - prenylation of tyrosine , serine , and threonine in cyclic peptides . it was found that at physiological temperature and in aqueous buffer , 
 o - prenylated tyrosine derivatives undergo spontaneous claisen rearrangements . in recent years , novel enzyme catalysts for the kemp elimination , retro - aldol , and 
 diels  alder reactions have been 
 designed , making use of the so - called  inside - out  approach . the first step of this protocol involves quantum mechanical calculations 
 of the ideal arrangement of catalytic groups around the transition 
 state of a reaction ; these computed complexes are called theozymes 
 ( short for theoretical enzymes ) . theozymes serve as models 
 for active site structures and for the prediction of activation barriers 
 relative to the uncatalyzed reaction in aqueous solution . the arrangement 
 of functional groups in the theozyme geometry is then incorporated 
 into protein scaffolds from the protein data bank using the computational package rosettamatch . the active sites of the generated proteins are 
 then minimized and repacked , and amino acids in the vicinity of the 
 active site are mutated to stabilize the ideal transition state geometry . the inside - out approach has been satisfactorily applied in the above - mentioned 
 cases ( kemp elimination , retro - aldol , and diels  alder reaction ) , 
 but it has some important limitations . up until now , most active designed 
 enzymes still perform quite poorly in comparison with the natural 
 existing enzymes ( i.e. , natural enzymes have average kcat / kuncat of 10 , whereas artificial enzymes developed through computational 
 modeling and directed evolution have kcat / kuncat values that range from 10 to 10 ) . in part , this is due to the difficulty of designing a protein with 
 the same ideal geometry of functional groups present in the theozyme . the design and testing of small - molecule  enzyme mimics  
 has been a tempting but frustrating target for organic chemists , and occasional success has been reported . we conceived the melding of the inside - out 
 approach with our recent successes in spiroligozyme syntheses to mount 
 catalytic groups from theozymes on a spiroligomer scaffold . spiroligomers are shape - programmable macromolecules 
 constructed by assembling stereochemically pure , cyclic , functionalized 
 bis - amino acids through pairs of amide bonds to create rigidified 
 scaffolds that present functional groups in controlled three - dimensional 
 constellations by virtue of the sequence , shape , and stereochemistry 
 inherent in each chiral building block . previously , spiroligomers 
 have been utilized as catalysts for the aldol reaction and transesterification 
 reaction . we now report a combined computational and 
 experimental approach to use spiroligozymes as catalysts for the aromatic 
 claisen rearrangement . bacterial 
 ketosteroid isomerase ( ksi ) is heavily utilized as a model system 
 for investigating fundamental aspects of enzyme catalysis . its natural function is the isomerization 
 of the position of a double bond in steroids . the mechanism involves 
 a general base that deprotonates the steroid forming a dienolate , 
 which is stabilized via hydrogen bonding with a tyrosine-16 residue 
 and a protonated aspartic acid-104 residue ( see figure 1a ) . the hydrogen bonding catalytic dyad was considered 
 a promising modality for the stabilization of the growing negative 
 charge in the transition state of the claisen rearrangement ( figure 1 ) . it was proposed by gerlt and gassman that the 
 formation of short , strong hydrogen bonds ( sshb , also called low - barrier 
 hydrogen bonds lbhb ) between the ksi oxyanion hole and the reaction 
 intermediate stabilizes the transition state of the reaction . there has been an intense debate about the role of sshbs in enzyme 
 catalysis . we designed a series of 
 bioinspired spiroligozyme catalysts that display a carboxylic acid 
 and a phenol on a spiroligomer backbone that resembles the hydrogen 
 bonding catalytic dyad of ksi ( see figure 1b ) . the use of a phenol and carboxylic acid is a stark departure 
 from the currently utilized organocatalysts for the claisen rearrangement , 
 which generally rely on n  h hydrogen - bond donors . the optimized 
 theozyme for the aromatic claisen rearrangement using the ksi catalytic 
 dyad ( i.e. , asp / tyr ; see figure 1b ) suggests 
 that a 10-fold acceleration with respect to the background 
 reaction could be achieved ( at m06 - 2x/6 - 311+g(d , p)//m06 - 2x/6 - 31g(d ) 
 and in cpcm implicit solvation for ch2cl2 with 
  = 4 ) . selection of the scaffold to tether the catalytic 
 residues was 
 accomplished by matching carboxylic acid / phenol functionalized amber 
 94 minimized spiroligomer structural 
 motifs that we have synthetic access to against the crystal structure 
 data for kis as shown in figure 1a ( pdb code 3owu ) . a scaffold previously used for studying electron transfer 
 in water was selected as a starting point for further optimization . the scaffold features a single bis - amino acid 
 building block with one functional group introduced via a 2,5-dioxopiperazine 
 ( dkp ) ring and the other introduced via amide linkage at the pyrrolidine 
 nitrogen forming a well - defined cleft between the two catalytic residues . ( a ) molecular 
 model overlay of the active site of ksi ( pdb code 3owu(1 ) ) with the spiroligomer mimetic bpc8 . ksi is 
 displayed as a rainbow ribbon with y16 and d103 shown in gray . the spirocyclic catalyst bpc8 is displayed as dark green and is overlaid matching the oxygens 
 of the catalytic residues . ( a ) hmba resin ( 1.1 
 equiv ) , msnt ( 2 equiv ) , nmi 
 ( 2 equiv ) , dcm ( 0.1 m ) ; ( b ) 33% hbr in acoh / dcm ( 1:1 , 0.1 m ) ; ( c ) 
 benzoic acid derivative ( 3 equiv ) , hatu ( 3 equiv ) , dipea ( 6 equiv ) , 
 nmp ( 0.2 m ) ; ( d ) substituted amine ( 6 equiv ) , pyaop ( 3 equiv ) , nmp 
 ( 0.2 m ) ; ( e ) 20% piperidine in dmf ( 0.1 m ) ; ( f ) n - boc - amino acid ( 3 
 equiv ) , hatu ( 3 equiv ) , dipea ( 6 equiv ) , nmp ( 0.2 m ) ; ( g ) tfa / dcm 
 ( 1:1 , 0.1 m ) ; ( h ) 10% dipea in mecn ( 0.05 m ) . a series of molecules of this scaffold type were synthesized using 
 solid phase synthesis on hmba resin ( scheme 1 ) . the bis - amino acid1 was attached to hmba resin with msnt and 
 nmi in dcm . the benzyl carbamate and tert - butyl ester 
 were then removed by treatment with 33% hbr in acoh as a 1:1 volumetric 
 mixture with dcm . the c-2 carboxylic acid was converted 
 to an amide using pyaop and the amine r3r4nh 
 in nmp to form the resin bound intermediate 2 . the phenylalanine 
 derivative was then introduced using hatu and dipea in nmp to produce 
 intermediate 3 . the tert - butyl carbamate , 
 ester , and ether were removed with treatment with a 1:1 volumetric 
 mixture of tfa and dcm . the dkp was closed and subsequent cleavage 
 from the resin was affected with a 10% solution of dipea in mecn . purification with c18 reverse phase hplc yielded the pure 
 catalysts bpc110 in 6070% isolated yields 
 ( table 1 ) . the series of catalysts bpc110 and controls 
 were tested for acceleration of the aromatic claisen rearrangement 
 of the 1,1-dimethylallyl coumarin substrate 4 . catalyst 
 was added at 20 mol % relative to the substrate 4 at 
 0.2 m in dichloroethane . the reaction vessels were sealed and stirred 
 magnetically at 60 c for 84 h. high - density polypropylene vessels 
 had to be used because untreated glass vessels lead to decomposition 
 of the reagent , presumably catalyzed by trace acid . percent conversions were obtained by comparison 
 of the area contributions from the product 5 and starting 
 material peaks . rate constants were determined by fitting the concentration 
 of product with respect to time using a first - order kinetics model . table 1 lists relative rate constants for the 
 catalysts as well as benzoic acid and diphenylguanidinium barf catalyst . the compound bpc1 displayed 
 a 11-fold rate enhancement 
 relative to the background reaction ( entries 12 ) . bpc1 was designed to display a terephthalic acid and a tyrosine in order 
 to project a carboxylic acid and a phenol alcohol toward each other . molecular modeling suggested that this would direct the terephthalic 
 acid and phenol toward each other so that they could both simultaneously 
 act as hydrogen bond donors to a single ether oxygen atom . this close 
 approach of these two hydrogen - bonding groups is promoted by the stereochemistry 
 of the spirofused pyrrolidine and diketopiperazine ring onto which 
 the groups are mounted ( figure 1a ) . this close 
 approach is analogous to the close approach that is achieved when 
 a pyrene and a para - dimethylaniline group are displayed 
 in place of the terephthalic acid and phenol . the c-2 amide was modified to primary and tertiary amides ( entries 
 3 and 4 ) to create the catalysts bpc2 and bpc3 which are more soluble in dichloroethane , and this does not effect 
 the catalytic rate , suggesting that the c2 amide is not involved in 
 hydrogen bond stabilization of the transition state . the cooperativity 
 of the two hydrogen bond donor groups was probed by altering the stereochemistry 
 of the bicyclic backbone to create bpc4 , which modeling 
 suggests would pull the two donors away from each other ( entry 5)and 
 the activity of bpc4 drops to 2-fold above background , 
 which is similar to the activity of benzoic acid alone ( entry 7 ) . the cooperativity was further probed by removing the phenol alcohol 
 using phenylalanine in place of tyrosine to form bpc5 ( entry 6 ) and its activity is equivalent to bpc4 and 
 benzoic acid . altering the substitution of the carboxylic acid on 
 the benzoic acid derivative to meta ( bpc6 ) and ortho 
 ( bpc7 ) leads to less well - aligned hydrogen bond donor 
 groups by modeling and leads to lower activity catalysts ( entries 
 8 and 9 ) . swapping the positions of the alcohol and the carboxylic 
 acid ( bpc8 ) brings the carboxylic acid and phenol alcohol 
 in better alignment to simultaneously donate two hydrogen bonds to 
 a single oxygen and increased the relative rate to 30-fold over background 
 ( entry 10 ) . altering the position of the alcohol on the benzoic acid 
 derivative to meta ( bpc9 ) and ortho ( bpc10 ) also leads to less - well - aligned hydrogen bond donor groups by modeling 
 and led to less active catalysts ( entries 11 and 12 ) . diphenyl guanidinium 
 barf ( dpgb ; entry 13 ) is a prototype of a series of asymmetric catalysts 
 of the claisen rearrangement developed by the jacobsen group . under these reaction conditions , dpgb generated 
 the product 5 with a krel of 14 ; however , concomitant with product formation , significant 
 amounts of side products were formed , as observed by analytical reverse 
 phase c18 hplc analysis during the course of the reaction . 
 among these side products , the free coumarin was observed , indicating 
 that the guanidinium catalyst is effective , under these reaction conditions , 
 at breaking the ether linkage between the coumarin oxygen and allylic 
 carbon , possibly by acting as a bronsted acid . modeling suggests 
 that the diketopiperazine ring of the bpc scaffold 
 exists in a boat - like conformation . the boat conformation and the 
 rotamer preferences of the functional groups could be altered through 
 n - alkylation of the amide nitrogens within the diketopiperazine ring , 
 and this could alter the presentation of the phenol and carboxylic 
 acid groups and change their catalytic activity . dichloroethane solutions 
 of bpc110 are cloudy at room temperature , although 
 clear at 60 c , which we attributed to diketopiperazine - tape 
 formation at room temperature . n - alkylation 
 could also improve the solubility of the catalysts in the dichloroethane 
 solvent because it would disrupt hydrogen - bonded tape - formation . we 
 created three n - alkylated versions of bpc8 , the mono 
 n - benzylated catalysts bpc11 and bpc12 , 
 and the di - n - benzylated catalyst bpc13 . unlike bpc110 , these new catalysts were completely soluble 
 in dichloroethane at 40 mm at room temperature , as well as at 60 c , 
 under the reaction conditions . in order to synthesize these , 
 an alternative solid phase synthesis 
 had to be devised to assemble the tetra- and penta - substituted dkp 
 rings shown in scheme 2 . the bis - amino acid 
 derivative6 was attached 
 to an isobutyl amine modified formyl resin via hatu promoted acylation . the pyrollidine alloc group was removed using palladium catalyst in 
 the presence of a scavenger and then acylated with the t - butyl - protected 4-hydroxy benzoic acid . the c-4 amino acid protecting 
 group was then removed followed by reductive alkylation to the c-4 
 nitrogen with benzaldehyde to form 7 . treatment of 
 the resin with neat tfa was used to cleave the intermediate from the 
 resin , which led to spontaneous diketopiperazine formation and concomitant 
 removal of all protecting groups . purification with reverse phase 
 hplc yielded the pure catalysts in 7580% yields relative to 
 solid support loading . ( a ) substituted amino resin ( 1 equiv ) , hatu ( 1 
 equiv ) , dipea ( 2 equiv ) , nmp ( 0.2 m ) ; ( b ) ( p(ph3)4)pd(0 ) ( 0.3 equiv ) , bh3:dma ( 6 equiv ) , dcm ( 0.1 m ) ; ( c ) 
 benzoic acid derivative ( 3 equiv ) , hatu ( 3 equiv ) , dipea ( 6 equiv ) , 
 nmp ( 0.2 m ) ; ( d ) 20% piperidine in dmf ( 0.1 m ) ; ( e ) phcho ( 2 equiv ) ; 
 nah3bcn ( 2 equiv ) ; dmf ( 0.1 m ) ; ( f ) boc - amino acid ( 3 equiv ) ; 
 hatu ( 3 equiv ) , dipea ( 6 equiv ) ; nmp ( 0.2 m ) ; ( g ) tfa . kinetic studies of catalysts bpc1 , bpc8 , and bpc1113 are shown in figure 2 . improvement in catalytic rate was observed over 
 the course 
 of each catalyst generation with bpc13 ( krel = 58 ) providing the largest rate enhancement relative 
 to the background reaction . claisen rearrangement product formation as a 
 function of time and 
 catalyst ( 0.2 m substrate in dichloroethane , 60 c , 0.02 m catalyst ) . the catalyst bpc1 was crystallized from water / acetonitrile 
 1:1 at room temperature and its crystal structure was determined ( figure 3 ) . in the crystal structure the tyrosine side chain 
 is observed to fold back over the diketopiperazine and pyrrolidine 
 rings in the conformation that was proposed for dual hydrogen bonded 
 catalysis . the terephthalic acid is rotated away from the tyrosine 
 in one of the two available amide rotamers . the preference of this 
 rotamer of the terephthalic acid in the crystal structure can be understood 
 in terms of crystal packing forces and an intermolecular hydrogen 
 bond between the amide carbonyl of the terephthalic acid and the tyrosine 
 alcohol of another molecule of bpc1 . the x - ray crystal 
 structure is very similar to the predicted conformation bpc1a in figure 4b . x - ray crystal structure 
 of bpc1 illustrates the proposed 
 catalytically active conformation of the tyrosine side chain and one 
 of the two possible amide rotamers of the terphthalic acid . this x - ray 
 observed conformation is very similar to bpc1a ( figure 4b ) , one of the lowest energy predicted structures 
 of bpc1 . we have explored the catalysis 
 by bpc1 , bpc8 , and bpc1113 using molecular dynamics ( md ) to explore the conformational space 
 of each catalyst and used quantum mechanics ( qm ) to evaluate transition 
 states . we performed a conformational analysis of bpc1 , bpc8 , and bpc1113 using the monte 
 carlo ( mcmm ) method and the opls - aa force field as implemented in 
 the macromodel computational package ( see si for a detailed description of the computational methods used ) . in each case , 20 or more lower energy conformers were further reoptimized 
 using the hybrid meta exchange - correlation dft functional m06 - 2x , which includes medium - range correlation , with 
 the standard 6 - 31g(d ) basis set . solvent effects 
 were included with the conductor - like polarizable continuum model 
 ( cpcm ) with dichloroethane as the solvent . m06 - 2x/6 - 31g(d ) energies indicated that the lowest energy conformer 
 for bpc8 is from 6.5 up to 18.6 kcal / mol more stable 
 than the rest of the computed conformers . the situation for bpc1 is slightly different as the lowest energy conformer 
 ( bpc1a ) is only 0.2 kcal / mol more stable than bpc1b , with the rest of the computed conformers being from 4 up to 15 
 kcal / mol higher in energy ( see figure 4 ) . bpc8 and bpc1b both present close approaching , 
 preorganized carboxylic acid and phenol groups for catalysis , while bpc1a has these two functional groups far separated ( see figure 4 ) . m06 - 2x/6 - 31g(d ) optimized structures for the lowest energy 
 conformers 
 for bpc8 , bpc1a , and bpc1b . m06 - 2x/6 - 311+g(d , p)//m06 - 2x/6 - 31g(d ) relative gibbs free energies 
 have been computed using the thermal corrections at m06 - 2x/6 - 31g(d ) 
 level ( grel are relative to bpc8(a ) which can be calculated given that bpc1 and bpc8 have the same number of atoms , all distances 
 are represented in  ) . m06 - 2x/6 - 31g(d ) optimized structures for the ( a ) theozyme with 
 the asp / glu and tyr motif and ( b ) the uncatalyzed reaction ( all distances 
 are represented in  ) . the optimized transition state structures with catalytic 
 conformations 
 of bpc8 , bpc1a , and bpc1b are 
 shown in figure 6 . the computed activation 
 barrier for the claisen rearrangement catalyzed by bpc8 is 28.1 kcal / mol with respect to isolated reactants ( i.e. , bpc8 and the coumarin reactant ) . as a reference , the computed 
 activation barrier in terms of free gibbs energy for the background 
 reaction is 30.0 kcal / mol at the m06 - 2x/6 - 311+g(d , p)//m06 - 2x/6 - 31g(d ) 
 level of theory in cpcm dichloroethane ( see figure 5 ) . the catalyzed reaction is bimolecular , and the rate of 
 rearrangement is considerably faster than the background , but there 
 is unfavorable entropy of association of the substrate and catalyst . the reactant complex between bpc8 and the 1,1-dimethylallyl 
 coumarin ether is 3.9 kcal / mol higher in gibbs free energy than isolated 
 reactants ; that is , the nearly 10 kcal / mol binding is counteracted 
 by ts for the bimolecular 
 association . in the transition state , both hydroxyl groups of bpc8 are stabilizing the partial negative charge on the ether 
 oxygen and are approximately 1.7  away ( see figure 6 ) . the breaking o c 
 and the forming c  c bond distances are 2.274 and 2.416  , 
 respectively . for bpc1a , the catalysis of the aromatic 
 claisen rearrangement could be assessed considering two different 
 approaches . instead , the hydroxyl group of the phenol is interacting 
 with a carbonyl group of the bis - peptide backbone ( see figures 4b and 6b ) . therefore , the bpc1a catalyzed reaction was studied using either the phenol 
 or the carboxylic group individually hydrogen bonded to the ether 
 oxygen of the coumarin transition state . this single hydrogen - bonding 
 ts has a computed gibbs free activation barrier of 30.9 kcal / mol relative 
 to isolated reactants , bpc1a and the coumarin ether . 
 at the ts , the hydrogen bond distance between the ether oxygen and 
 the hydrogen of the phenol is 1.743  , and the c  o breaking 
 and c  c forming bond are 2.159 and 2.279  , respectively . the coumarin analogue is nicely -stacked to the benzoic acid 
 moiety ( the distance between the center of mass of the benzene rings 
 is approximately 3.3  ) . an enantiomer bound to the same catalyst 
 was also found , but was 0.2 kcal / mol higher in energy . the transition 
 state involving bpc1b , which has both hydroxyl groups 
 in a closer disposition , presents an activation barrier that is 0.5 
 kcal / mol higher than the previous ts for bpc1a ( the gibbs 
 free activation barrier compared to isolated reactants is 31.4 kcal / mol ; 
 see figure 6c ) . this slightly higher activation 
 barrier is mainly attributed to the fact that only the hydroxyl group 
 of the phenol moiety is stabilizing the negative charge of the ether 
 oxygen , and more importantly the favorable -stacking interaction 
 between the coumarin derivative and the benzoic acid moiety is lost 
 ( see figure 6c ) . in both bpc1a and bpc1b cases , m06 - 2x/6 - 311+g(d , p)//m06 - 2x/6 - 31g(d ) 
 optimized transition state 
 structures for the claisen rearrangement catalyzed by ( a ) bpc8 , ( b ) bpc1a , and ( c ) bpc1b in dichloroethane 
 using cpcm implicit solvation model . the uncatalyzed reaction has 
 a gibbs free activation barrier of 30.0 kcal / mol . we have also studied the more active catalysts bpc1113 . the conformational analysis and the subsequent optimization at 
 m06 - 2x/6 - 31g(d ) level indicated that the lowest energy conformers 
 for all three cases present the proper arrangement for catalysis with 
 the carboxyl and the phenol group in close proximity ( see figure 7 , figure s1 and si for 
 more details ) . m06 - 2x/6 - 31g(d ) optimized structures for the lowest energy 
 conformers 
 for ( a ) bpc11 , ( b ) bpc12 , and ( c ) bpc13 . we have studied the spiroligozyme catalyzed claisen 
 rearrangement 
 of the lowest energy conformers of the catalysts ( i.e. , 4 for bpc11 , 4 for bpc12 , and 4 for bpc13 ) . it should be emphasized here that the main differences between 
 the 4 different conformers studied for each case arise mainly from 
 different conformations of the benzyl and isopropyl substituents ( see figure s1 ) . the difference in energy between 
 the different conformers is less than 4 kcal / mol in all cases . we 
 calculated the energy of each catalyst bound to the substrate relative 
 to the energy of the lowest energy conformer of each unbound catalyst 
 and substrate . the energies are 8.7 , 6.9 , and 5.2 kcal / mol for bpc11 , bpc12 , and bpc13 , respectively 
 ( see figure s2 ) . for bpc11 the oh hydrogen bond ( 2.2  ) the oh in bpc11 is 
 also hydrogen bonded to the co of the carboxylic moiety ( 2.1  ) . 
 the hydrogen bond length for cooh to the substrate is progressively 
 decreased from bpc11 to bpc13 . bpc13 has similar hydrogen bond lengths for both oh and cooh , so the reactant 
 complex for bpc13 presents a closer arrangement to the 
 ts structure ( figure 10 ) , which presents hydrogen 
 bond distances of ca . molecular dynamics ( md ) simulations 
 using amber11 and a 10  truncated 
 octahedral box with explicit 
 chloroform molecules ( see si for further 
 details ) were performed in order to determine the relative free energies 
 of catalytic and noncatalytic conformers of the catalyst . in figure 8 , the average distances between both oxygen atoms 
 of the phenol and benzoic acid moieties of the spiroligozymes ( dist 
 ooh  ooh ) along the 1 s md simulation 
 are represented . in figure 9 , the histograms 
 for the ooh the standard deviation is also shown using a shaded area and has been 
 computed every 20 ps . for each catalyst analyzed in this way ( i.e. , bpc8 and bpc1113 ) , 250 superimposed md 
 snapshots have also been included where both the open and closed conformations 
 have been marked using two different colors . the ideal arrangement 
 for catalysis is substantially altered along the simulation for bpc8 , bpc11 , and bpc13 catalysts 
 ( see figures 8 and 10 ) . the distance between 
 the hydroxyl groups of both the phenol and benzoic acid moieties ( d(ooh  ooh ) ) along the md trajectory 
 for bpc8 and bpc1113 are 5.86  
 2.87 , 5.16  2.61 , 4.39  0.88 , and 4.68  1.80  , 
 respectively . these distances are substantially longer than the optimized 
 qm value of 2.84  , especially for bpc8 and bpc11 cases . the higher distance and deviation found for bpc8 and bpc11 is due to a conformational change 
 that leads to an arrangement where both benzoic acid and phenol moieties 
 are not interacting ( see snapshots in figure 8 , and histograms in figure 9 ) . interestingly , 
 in most cases more than 100 ns of simulation is needed to observe 
 the latter conformational change ( see plots in figure 8) . md simulations indicate that the correct arrangement for 
 catalysis is present 68.5% of the simulation time for bpc8 . in this suitable arrangement , the averaged ooh  ooh distance is 4.41  0.79  , which is still substantially 
 longer than the qm value of 2.84  . the distance between hydroxyl 
 groups is less than 4  14.5% of the simulation time . the introduction 
 of a benzyl substituent on the amide backbone leads to a substantial 
 improvement . bpc11 the arrangement stays close to the qm value ( i.e. , less 
 than 3  ) 55.5% of the time . bpc13 , 
 which has benzyl substituents on both amide backbone nitrogens , adopts 
 the correct arrangement ca . ooh distance for the bpc13 suitable arrangement for catalysis is 4.41  0.79 
  ; the ooh the md simulations performed on the 
 free catalysts have shown that the ideal arrangement for catalysis 
 is substantially modified , especially in the case of bpc8 . in the case of bpc11 , bpc12 , and bpc13 , those conformers with the suitable arrangement for 
 catalysis present averaged ooh these simulations indicate the fraction 
 of conformers that have the catalytic groups properly preorganized 
 for catalysis . representation of 250 superimposed md snapshots for ( a ) bpc8 ( magenta ) , ( b ) bpc11 ( cyan ) , ( c ) bpc12 ( purple ) , and ( d ) bpc13 ( gold ) . the plots monitoring 
 the ooh  ooh distance along the 1 s 
 md trajectory for these catalysts are also included . the mean ( dark 
 line ) and standard deviation of the ooh  ooh distance is represented using a shaded area ( width is 1 std dev ) 
 and have been calculated every 10 steps of the simulation ( i.e. , 20 
 ps ) ( all distances are expressed in  ) . ooh distance 
 during the 1 s md trajectory for ( a ) bpc8 ( magenta ) , 
 ( b ) bpc11 ( cyan ) , ( c ) bpc12 ( purple ) , and 
 ( d ) bpc13 ( gold ) . we have also computed the gibbs 
 free activation energies for the 
 spiroligozyme catalyzed claisen rearrangement involving bpc11 , bpc12 , and bpc13 . in figure 10 , the m06 - 2x/6 - 31g(d ) optimized transition state 
 structures for the lowest activation barrier with each catalyst are 
 shown . the computed activation barriers for bpc11 , bpc12 , and bpc13 are 28.8 , 29.1 , and 25.7 kcal / mol 
 referred to the reactants : the isolated spiroligozyme , each in their 
 lowest energy conformer , and the coumarin ether . minor differences 
 are observed among the computed activation barriers , especially in 
 the case of bpc11 and bpc12 . as mentioned 
 earlier for bpc1 and bpc8 , the optimized 79 kcal / mol higher in gibbs - free 
 energy than isolated reactants in the case of bpc11 and bpc12 , and ca . the breaking o  c and the forming c  c bond distances 
 are approximately 2.260 and 2.390  ( see figure 10 ) . the hydrogen bonds formed between the ether oxygen and 
 the phenol and benzoic acid moieties to stabilize the partial negative 
 charge are 1.710 and 1.692 , and 1.734 and 1.640  in bpc11 and bpc12 , respectively . interestingly , bpc13 presents slightly shorter hydrogen bond distances of 1.620 and 1.718 
  . the computed activation barriers for the uncatalyzed 
 and bpc1 , bpc8 , and bpc1113 catalyzed 
 claisen rearrangements at 333 k are 30.0 , 30.9 , 28.1 , 28.8 , 29.1 , 
 and 25.7 kcal / mol , respectively . md simulations have shown that bpc8 and bpc1113 adopt the appropriate 
 conformation for catalysis ( the hydroxyl distance is less than 4  ) 
 14.5% , 55.5% , 32.1% , and 31.9% of the simulation time , respectively . the latter fraction of conformers ( f ) in the catalytic 
 conformation must be used to estimate the experimental rate constant 
 ( kcat = fkcat , computed ) . this leads to a computed kcat / kuncat of ca . 3 and 210 for bpc8 and bpc13 with respect to the background reaction , 
 respectively . we calculated quantum mechanical distortion energies 
 by removing the substrate from each transition state structure and 
 carrying out a single - point energy calculation at this geometry and 
 subtracting the minimum energy conformation of each catalyst . the 
 distortion energies were 6.8 , 5.1 , 8.8 , and 3.6 kcal / mol for bpc8 , bpc11 , bpc12 , and bpc13 , respectively . the lower activation barrier observed for bpc13 is attributed to the lower distortion energy needed to distort the 
 catalyst to adopt the ts geometry . m06 - 2x/6 - 311+g(d , p)//m06 - 2x/6 - 31g(d ) 
 optimized transition state 
 structures for the claisen rearrangement catalyzed by ( a ) bpc11 , ( b ) bpc12 , and ( c ) bpc13 in dichloroethane 
 using cpcm implicit solvation model . the uncatalyzed reaction has 
 a gibbs free activation barrier of 30.0 kcal / mol . all distances are 
 represented in  . using transition state theory we calculated the gexpt values from the relative 
 rate enhancements and plotted them against the gcalc values ( table 2 ) . the calculations correctly predict that bcp13 will be the most active catalyst , that bpc8 , bpc11 , and bcp12 will have intermediate 
 activity , and that bpc1 will have the lowest activity . 
 a linear fit of the two sets of values has a slope of 4.0 , and so 
 while the calculations predict the trend of activity , they predict 
 higher activity of the catalysts than is observed . the calculations 
 of reaction rates are based upon separated reactants in solution as 
 the reference . since hydrogen bonding groups , especially carboxylic 
 acids , are known to form observable complexes with ca . 380 m 
 dissociation constants in non - hydrogen - bonding solvents ( carboxylic 
 acid dimers ) , the catalysts and substrates 
 are expected to form stabilized hydrogen bonding complexes in solution , 
 thus increasing the activation barriers as compared to the calculations 
 reported here . from figures 6 and 10 . we have developed a series of dual hydrogen - bond 
 donor catalysts 
 for the aromatic claisen rearrangement modeled on the active site 
 of ketosteroid isomerase . these catalysts are designed to present 
 a carboxylic acid and a phenol alcohol that each simultaneously donate 
 one hydrogen bond donor to a single ether oxygen of the 1,1-dimethylallyl 
 coumarin substrate to stabilize the developing negative charge on 
 the ether oxygen in the transition state of the claisen rearrangement . the catalysts provide increasing reactivity as they better organize 
 their hydrogen bonding groups and more closely approximate the functional 
 group display observed in ketosteroid isomerase and as they are better 
 able to stabilize the transition state as determined by transition 
 state modeling . the first designed catalyst bpc1 accelerates 
 the reaction 11-fold relative to background , while the best catalyst , bpc13 , accelerates the reaction 58-fold . the combined qm and 
 md computational study of these systems established that bpc13 gives a higher acceleration of the reaction due to an optimal disposition 
 of the hydroxyl groups of both the phenol and benzoic acid moieties 
 in both the ts and the reactant complex . this optimal arrangement 
 is induced by the benzyl substituents of the amide backbone , which 
 limit the movement of the benzoic acid and phenol moieties . md simulations 
 have determined that this arrangement is better conserved in the case 
 of bpc13 and bpc11 . the higher efficiency 
 of bpc13 compared to bpc8 , bpc11 , and bpc12 is due to the combination of a lower activation 
 barrier due to a lower distortion energy , and a better preorganization 
 of bpc13 , which maintains both hydrogen donors in close 
 proximity ca . comparison of the experimentally determined activation barrier lowering 
 to calculated values demonstrates that calculations overestimate the 
 catalytic power of the two hydrogen bond catalysis by 4-fold : this 
 is most likely due to our lack of understanding and the difficulty 
 modeling how solvation and self - association affect the energies of 
 the ground states and transition states . these catalysts represent 
 the first examples of synthetic claisen 
 rearrangement catalysts that utilize o  h hydrogen bond donors 
 as found in the ketosteroid isomerase enzyme rather than n h 
 hydrogen bond donors observed in urea- , thiourea- , guanidinium- , and 
 bisimidazolium - based catalysts of the claisen rearrangement .
a series 
 of hydrogen - bonding catalysts have been designed for the 
 aromatic claisen rearrangement of a 1,1-dimethylallyl coumarin . 
 these 
 catalysts were designed as mimics of the two - point hydrogen - bonding 
 interaction present in ketosteroid isomerase that has been proposed 
 to stabilize a developing negative charge on the ether oxygen in the 
 migration of the double bond.1 two hydrogen 
 bond donating groups , a phenol alcohol and a carboxylic acid , were 
 grafted onto a conformationally restrained spirocyclic scaffold , and 
 together they enhance the rate of the claisen rearrangement by a factor 
 of 58 over the background reaction . 
 theoretical calculations correctly 
 predict the most active catalyst and suggest that both preorganization 
 and favorable interactions with the transition state of the reaction 
 are responsible for the observed rate enhancement .