the intermolecular amidoalkylation reaction is a very useful carbon  carbon bondforming process in organic chemistry.1 it has been widely applied to the stereocontrolled functionalization of nitrogen heterocycles , as the reaction of the cyclic nacyliminium ion intermediates , generated in  situ , is usually highly diastereoselective.2 the possibility of using a broad variety of nucleophiles3 confers upon the reaction a very wide scope , and it has been employed in natural product and pharmaceutical syntheses.4 in recent years , the enantioselective amidoalkylation reaction using organocatalysis has emerged as a powerful method for the synthesis of enantioenriched compounds possessing tertiary or quaternary stereogenic centers.5 the most important developments in this area have focused on enantioselective friedel 
craftstype reactions.6 in particular , a number of reports have addressed the application of chiral hydrogenbond donors ( ureas and thioureas)7 and chiral brnsted acids ( cbas ) ( binolderived phosphoric acids)8 to the asymmetric intermolecular amidoalkylation reaction9 of nucleophiles , mainly electronrich heteroaromatics such as indoles and pyrroles10 with cyclic nacyliminium ions .
however , limitations remain on the applicability for tertiary nacyliminium ions ( i.e. ketonederived iminium ions ) , which can lead to synthetically important derivatives with chiral quaternary carbon centers , presumably owing to the low reactivity of ketimines and the more difficult control of facial selectivity.11 in this context , we have reported12 the first example of an enantioselective amidoalkylation of indoles with bicyclic hydroxylactams for the generation of a quaternary stereocenter in the preparation of 12  bsubstituted isoindoloisoquinolines ( ee up to 95  % ) by using binolderived brnsted acids . the amidoalkylation reaction occurs through the formation of a chiral phosphate / bicyclic quaternary nacyliminium ion pair . there was experimental evidence to propose that hydrogenbonding interactions of the phosphateionpaired intermediate to the indole nh could potentially be involved .
hence , the binolderived phosphoric acid would be acting as a bifunctional catalyst,13 interacting also with the nucleophile .
more recently , the same methodology has been applied by li and coworkers14 to the functionalization and preparation of isoindolocarbolines , generally with high enantioselectivities ( up to>99  % ee ) .
the potential of this type of hydroxylactam in stereochemical control has previously been demonstrated in transfer hydrogenation15 and alkenylation16 reactions . in the latter case ,
the presence of a hydroxyl group in the nucleophile , an ohydroxystyrene , was crucial for the generation of a hydrogen bond with the chiral phosphoric acid catalyst . in a similar way , in the asymmetric organocatalytic azafriedel  crafts reaction of ketimines with naphthols / phenols catalyzed by quininesquaramide catalysts , the formation of a hydrogen bond between the phenolic oh and the tertiary amine moiety of catalyst is proposed to explain the stereochemical outcome of the reaction.17 on the other hand , a chiral phosphoric acidcatalyzed enantioselective alkylation of enamides with indolyl methanols18 and 3hydroxyoxindoles19 has been reported , and its utility demonstrated in the total synthesis of ( )folicanthine . in this context , we decided to evaluate enamides 2 with a free nh group in the enantioselective amidoalkylation reaction with bicyclic hydroxylactams 1 derived from phthalimides , using chiral phosphoric acids as brnsted acid catalysts ( scheme  1 ) .
this would allow the enantioselective formation of a quaternary stereocenter at the c1 position of the tetrahydroisoquinoline unit of the isoindoloisoquinoline skeleton .
it should be pointed out that tetrahydroisoquinoline is a privileged heterocyclic core present in many biologically active natural products and pharmaceutical drugs.20 for example , c1 indol3yl substituted 1,2,3,4tetrahydroisoquinoline isa2011b ( figure  1 ) was found to have a potent inhibitory effect on proliferation in various types of aggressive cancer cell lines ( for the treatment of advanced prostate cancer).21 the isoindole motif is also a crucial structure in a number of molecules with pharmaceutical properties,22 such as ( s)pazinaclone or ( s)pagoclone , and c(3)substituted isoindolinones that are central nervous system ( cns ) active drug candidates.23 therefore , the development of new synthetic methods for the asymmetric synthesis of these heterocycles continues to be an intensely investigated field.24 besides , alkaloids with the isoindolo[2,1a]isoquinoline skeleton , such as hirsutine , jamtine , and nuevamine,25 combine the structural features of both skeletons and also display a wide spectrum of biological activities .
in fact , isoindoloisoquinolinone crr271 has been reported to inhibit parp1 activity and protect cells against oxidative dna damage , which could be implemented in the treatment of inflammatory diseases.26 
  catalytic enantioselective intermolecular amidoalkylation reactions
on the basis of our previous report , we initiated this study by evaluating the reaction of hydroxylactam 1  a with enamide 2  a to obtain enantioenriched 3  aa ( table  1 ) .
phosphoric acids 4  a  e and ntriflylphosphoramides 5  a  h were tested at room temperature in thf.12 significant differences in both reactivity and enantioselectivity were observed .
phosphoric acid 4  a was the most reactive , affording 3  aa in good yield ( 70  % ) after 24  h , but with no enantioselectivity ( table  1 , entry  1 ) . 
 
on the contrary , no reaction was observed with 4  b after 72  h ( table  1 , entry  2 ) .
the best enantioselectivity was observed when 4  d was used , although the yield was poor ( table  1 , entry  4 ) .
ntriflylphosphoramides are known to have an increased acidity , and may lead to the formation of tighter ion pairs.27 indeed , 5  a  h proved to be more reactive , affording significantly higher yields and reducing the reaction time to 5  h in most cases ( table  1 , entries  613 ) .
the reaction time was extended , with no significant improvement in enantioselectivity ( table  1 , entry  9 ) .
it is important to note the different performances of catalysts 4  d and 5  d , which have the same substitution pattern on the aromatic backbones .
although 5  d was more reactive , an unexpected drop in the enantioselectivity ( 49 vs. 4  % ) was observed .
highly hindered ( r)vapolderived phosphoric acid 6 
 28 or multidentate disulfonimide 7 
 29 afforded good reactivity , but low enantioselectivity ( entries  15 and 16 ) , whereas taddolderived phosphoric acid 8 
 30 was not reactive ( entry  17 ) .
a subsequent optimization of the reaction conditions was carried out by using catalyst 4  d , which had afforded the highest ee ( 49  % ) .
both the reactivity and the enantioselectivity were improved when the reaction was performed at 40  c ( table  2 , entry  1 ) . besides , this enantioselectivity could be improved through a single crystallization to 84  % ee .
the use of an excess ( 3  equiv ) of 2  a significantly lowered the yield and enantioselectivity ( entry  2 ) , probably owing to selfcondensation of the enamide,31 whereas the use of molecular sieves to remove the water formed in the reaction did not improve the results ( entry  3 ) . at higher temperature ,
the results were similar , but the reaction time was reduced ( entry  4 ) .
the change of the solvent to dioxane afforded 3  aa with similar enantioselectivity , but lower yield ( entry  5 ) .
the best yield was obtained when the reaction was performed in dichloromethane at reflux ( 95  % , entry  7 ) .
in related chiral phosphoric acidcatalyzed reactions , it has been shown that the formation of ion pairs is favored in ch2cl2 over thf , although it was found that the degree of ionpair formation does not correlate with the enantioselectivity.32 the use of toluene provided similar results to those obtained in thf ( entry  9 ) , and again further increase of the temperature was detrimental ( entry  10 ) .
thus , enamides 2  b  d were prepared33 and reacted with hydroxylactam 1  a by using phosphoric acid 4  d or triflamide 5  c as catalysts in thf ( table  3 ) .
the electronic nature of the aromatic ring had a strong influence on the reactivity , as no reaction was observed with 2  b ( entry  1 ) , whereas a good yield was obtained with electronrich 2  c , although with no increase in the enantiomeric purity ( entry  2 ) .
the effect of the acyl terminus of the enamide was also checked , but the corresponding benzamide 2  d did not improve the enantioselectivity when using 4  d or 5  c ( table  3 , entries  4 and 5 vs. table  2 , entry  9 and table  1 , entry  8) . 
 
[ b ]  determined by chiral stationary phase hplc . [ c ]  3  equiv of 2  a were used .
[ b ]  determined by chiral stationary phase hplc . [ c ]  no reaction .
thus , the absolute configuration was unambiguously assigned by singlecrystal xray analysis of 3  aa as r ( see the supporting information).34 
  the formation of the r isomer in the reaction of 1  a with enamides is in consonance with our previous results for the amidoalkylation of indoles.12 thus , the sense of induction would be explained by the formation of an nacyliminium intermediate / chiral conjugatebase ion pair,35 as depicted in figure  2 .
thus , the chiral ion pair would be generated by protonation of the hydroxylactam . according to previously reported models,36
the acyliminium intermediate would be oriented avoiding the steric interactions with the catalyst 3 and 3substituents ( r ) . on the other hand ,
a hydrogen bond with the enamide nh moiety could be proposed , which would orient the phenyl ring away from the catalyst , favoring the si attack of the nucleophile . 
 
we next studied the use of indolederived hydroxylactam 1  b in the reaction with enamide 2  a ( scheme  2 ) .
the reaction of hydroxylactam 1  b under chiral phosphoric acid catalysis with different nucleophiles has been described previously.14 , 15 , 16 we thought that the chiral phosphoric acid may act as a bifunctional catalyst , coordinating not only to the enamide but also to the indole nh.37 indeed , when hydroxylactam 1  b was treated with enamide 2  a and phosphoric acid 4  d in thf at room temperature , the reaction was much faster , leading to a good yield of carboline 3  ba in just 5  h. unfortunately , the enantioselectivity was in the same range to that observed for 1  a. similar results were obtained when a catalyst with the opposite configuration [ ( s)4  d ] was used in dioxane.38 
  to check if the interaction of the enamide with the catalyst is really determinant , related reactions of hydroxylactams 1  a and 1  b were carried out using enol ethers 9  a and 9  b as nucleophiles ( table  4 ) . 
 
reaction with enol ethers 9  a and 9  b. [ a ]  yield of isolated product .
[ b ]  determined by chiral stationary phase hplc . [ c ]  no reaction .
[ d ]  ( s ) 
 4  d was used as the catalyst .
enol ether 9  a was unreactive towards 1  a in thf and provided a very low conversion in dichloromethane ( table  4 , entries  1 and 2 ) .
in contrast , 1  b reacted with 9  a ( table  4 , entry  3 ) , but the reaction was slower and less efficient than the reaction with the corresponding enamide 2  a , as depicted in scheme  2 , though with the same degree of enantioselectivity ( 51  % ee ) .
when enol ether 9  b was used , 3  bb was obtained with good enantioselectivity in toluene ( 86  % ee ) , though with a low conversion .
these results show that , although coordination with the catalyst seems to be crucial for reactivity , there is not a direct effect on the enantioselectivity .
as noted above , the enantioselectivity is especially sensitive to the nature of the nucleophile and the catalyst , as well as the experimental conditions . as shown , the introduction of a chlorine atom into the aromatic ring of acetamide 2  b precluded the reaction , whereas the use of benzamide 2  d reduced the enantioselectivity as compared to the acetamides .
unfortunately , the optimal catalyst for 2  a led to poor enantioselectivities with the other enamides or enol ethers , and no obvious trends to improve the performance of these nucleophiles were qualitatively observed . the general catalytic cycle for this type of amidoalkylation reaction
is now reasonably well established ; however , the key catalyst features and experimental conditions responsible for enantioselection remain challenging .
thus , although there are detailed studies of the chiral phosphoric acidcatalyzed reduction of ketimines,39 the origin of the stereochemical outcome in the carbon  carbon bondforming reaction of ketimine has scarcely been investigated.39b in fact , it was not until very recently that the friedel  crafts reaction of 2methoxyfuran with aliphatic ketimines was studied theoretically by using dft calculations to assess the key factors governing the stereoselectivity .
thus , terada and coworkers40 analyzed the plausible transition states of the stereodetermining cc bondforming step , proposing that enantioselectivity stems from the formation of the hydrogenbond network among the triad of components ( catalyst , substrate , and nucleophile ) .
although computational chemistry has helped us to understand the mechanism of these amidoalkylation reactions , understanding how the different parameters affect its stereochemical outcome is still difficult to rationalize .
this is one of the underlying challenges in the field of asymmetric catalysis : to design or choose the adequate catalyst or experimental conditions for a given reaction type without engaging in a longterm , empirical investigation .
therefore , we sought to use chemoinformatic tools to predict the enantioselectivity of this type of intermolecular amidoalkylation reaction .
we decided to use quantitative structure  reactivity relationship ( qsrr ) methods.41 at this point , the pioneering work of sigman and coworkers42 should be pointed out , who demonstrated that a qsrr model between steric parameters of chiral ligand substituents and enantiomeric ratios of the products could be established . since then
, methodologies based on qsrr modeling have been applied to predict the enantioselectivity of different types of reactions , such as allylation43 and propargylation44 of carbonyl compounds , dehydrogenative hecktype45 reactions , asymmetric coppercatalyzed cyclopropanation of alkenes,46 and the henry reaction.47 recently , a dataintensive approach has also been reported for mechanistic elucidation applied to chiral anion catalysis in intramolecular dehydrogenative cn coupling.48 in this case , catalyst 
substrate association involves weak , noncovalent interactions similar to those involved in the amidoalkylation reactions .
we have previously developed a ptqspr approach , which combines perturbation theory ( pt ) and qsrr ideas , to correlate and predict different outputs ( activity , property ) in complex molecular systems ( metabolic reactions),49 nanoparticles,50 and so forth .
the method has also been extended to predict the enantioselectivity and/or yield of intramolecular carbolithiation51 and heck  heck cascade reactions.52 in some cases , the developed ptqsrr models use trace operators , like spectral moments , or eigenvalues of chemical structure matrices , like bond adjacency matrix , as the inputs.51 , 53 now , we intend to use this correlative ptqsrr approach to predict the effect of the structures of the substrate , nucleophile , and catalyst , as well as the experimental conditions , on the enantioselectivity of intermolecular amidoalkylation reactions .
the model predicts the enantiomeric excess ee(%)nr of a new reaction ( nr ) by comparison to a reaction of a reference ( rr ) with known enantiomeric excess ee(%)rr that involves a set of molecules ( mq ) , which play different roles ( substrate , catalyst , etc . )
our goal is to find a useful tool to rationalize the enantioselectivity in this and related processes and to orient the catalyst choice .
in this way , trends to improve the experimental results could be found . to accomplish this ,
this dataset included the abovedescribed reactions and literature data for related reactions with different types of substrates ( cyclic and bicyclic hydroxylactams ) , nucleophiles ( enamides , indoles , etc . ) , and chiral catalysts ( phosphoric acids , phosphoramides , etc . ) under different experimental conditions.12 , 15 , 18 , 19 , 54 the molecular descriptors v(mq ) used to quantify the chemical structure of all the molecules involved in the reaction were calculated with the software dragon.55 these molecular descriptors were the absolute eigenvalues of the matrix of topological distance weighted with atomic polarizabilities v(mq)=aeigpq . to find the qsrr model , a multivariate linear regression ( mlr ) analysis
was performed with the software statistica,56 combining forward stepwise and standard procedures of variable selections ( see the supporting information ) .
then , we initiated the study with the training and validation of the new ptqsrr model for the enantioselectivity of the reactions under study .
we found a model useful to predict the efficiency of the new reaction ee(%)new , given the expected value of efficiency ee(%)expected=<ee(%)>new for any new reaction in the solvent used and the values of the perturbation terms .
the equation of this model is the correlation function shown in [ equation  ( 1)]:(1)ee%new=0.558333 + 0.316901g0newee%new-0.000699g0newg4new+0.132149g0newysubvsub-0.001459g0newyprodvprod-0.011935g0newycatvcat-0.136922g0newynucvnuc-0.000373g0newysolvvsolvn=38419_r=0.93_f=36394.0_p<0.005 
  all of the variables of the model ( table  5 ) are statistically significant , according to student test ( see values of t and the plevel in table  6 ) .
a notable feature of this model is its ability to predict a high number of perturbations in intermolecular amidoalkylation reactions ( n=38  419 ) with high goodnessoffit r=0.93 ( 86.5  % of variance of data explained ) .
the model was validated with an external validation series of a large dataset of perturbations in intermolecular amidoalkylation reactions ( n=12  806 ) .
notably , the goodnessoffit for the external validation series was also high r=0.93 ( table  6 ) .
the chemical data associated with this ptqsrr model , as well as the observed and predicted values of ee(% ) , are listed in the supporting information .
the new ptqsrr model reported here allows both the computational screening of a very large set of reactions with different substrates , nucleophiles , and catalysts and the scanning of experimental conditions ( solvents , temperature , etc.).57 
  definition of all the terms used in the model . 
 
[ a ]  dragon variables ( v ) v 
 q = v(q)nrv(q)rr , with q = substrate ( sub ) , product ( prod ) ,  etc .
[ i ]  fisher ratio . to illustrate the practical use of the model in our experimental problem ,
thus , computational screening of the effect of structural changes of the nucleophiles and catalysts on the enantioselectivity of amidoalkylation reactions was carried out .
first , bicyclic hydroxylactam 1  a was selected as the model substrate under the optimized experimental conditions , that is , thf as the solvent , 40  c , and 96  h ( table  2 ) . as the training set ( data points used for model development ) was limited to a series of enamides , an expanded library of computationally designed enamides and carbamates bearing steric and electronic variations at the nitrogen atom and the aromatic ring was built .
it was hypothesized that both positions may contribute synergistically to the selectivity of the system , either by changing the acidity of the nh hydrogen atom and/or the alkene nucleophilicity , which likely modulates the early or late nature of the corresponding transition states involved in the selectivitydetermining step ( see figure  2 ) . regarding the catalyst ,
a series of chiral brnsted acids with strong acidic functionalities , such as binolderived phosphoric acids , phosphoramides , and so on , were also computationally designed . in addition , the chiral binol framework has been modified , as it has been shown to be crucial in improving the catalyst performance ( figure  3 ) . 
 
then , this large library of nucleophiles and catalysts was evaluated with the developed ptqsrr model for the above amidoalkylation reaction .
a selection of the simulation of the enantioselectivity on a set of 212  catalysts versus 88  nucleophiles is depicted in figure  4 by using an image with gradient color , which is related to higher ( green ) or lower ( red ) ee(% ) , in order to achieve the best visual result . 
  selected
ee(% ) predicted for intermolecular amidoalkylation reaction.58 
  according to the model , the best results would be expected with obenzyl carbamates 2  o  q , instead of their acetamide counterparts , under the above indicated experimental conditions , with almost all catalysts tested . besides , the predictions indicated that high enantioselectivities would be obtained if these types of carbamates had an electrondonor substituent ( och3 , nhcoch3 ) in the para position , whereas the presence of a chlorine atom would lead to a decrease in the predicted ee(% ) , in agreement with our experimental results .
interestingly , the screening revealed that the best ee(% ) would be obtained by employing chiral brnsted acids 1315 and incorporating a sterically demanding h8binaphthyl moiety instead of the unsaturated analogues , in particular , phosphoramides ( ro)2ponhso2c8h17 
 14  e  h with the bulkiest aromatic substituents in the binol framework ( figure  4 ) . on the other hand ,
the use of atom stochastic moments enables backprojection of the model onto the enantioselectivity,59 that is , a map projecting the contribution of each atom or group of atoms to the enantioselectivity can be drawn .
the backprojection map of the catalytic activity of the biphenylsubstituted phosphoramide 14  h is depicted in table  7 , showing how the different electronic and steric variations on the catalyst affect the predicted ee(% ) values .
thus , the presence of the substituted biphenyl system on the binol framework is crucial to obtain high levels of enantioselectivity .
backprojection map analysis of the catalytic activity of the biphenyl substituted phosphoramide 14  h. another important application of the developed model lies with its potential to predict the enantioselectivity outcomes of new hydroxylactam substrates . to define the substrate scope , acetamide 2  a was selected as the nucleophile and a similar study of substrates versus catalysts was carried out . as in the previous case
then , the library was expanded with the computationally designed chiral brnsted acids and a series of hydroxylactams ( cyclic and bicyclic cores with different substitution patterns ) .
next , the ee(% ) values were predicted with the model for the standard amidoalkylation reaction conditions ( thf as the solvent , 40  c , 96  h ) of these new hydroxylactams . as an example
, table  8 shows the backprojection map analysis of the enantioselectivity for substrates 1  a and 1  c. the model predicts that benzofused hydroxylactams would lead to lower ee(% ) values in the amidoalkylation reactions . besides
, the substituents on the aromatic ring of the isoquinoline moiety seem to play an important role . 
 
backprojection map analysis of the enantioselectivity of substrates 1  a and 1  c. in view of these results , we decided to study the effect of physicochemical parameters of substituents in different positions ( ortho , para , and meta ) of the benzene rings , both on the isoquinoline and isoindole moieties , on the enantioselectivity .
for this purpose , one of the reactions that provided a higher ee(% ) in our experimental study ( table  2 , entry  1 ) was selected as the reaction of reference .
then , different derivatives of the substrate introducing both electrondonating and electronwithdrawing substituents in those positions were computationally created .
next , the eigenvalues of these derivatives were calculated and introduced into equation  ( 1 ) to predict the new ee(% ) values . finally , a simple linear regression analysis of the ee(% ) versus different constants of the substituents was carried out .
specifically , the hammett parameters (  
 p 
  and  
 p ) to measure electronic effects with and without the creation of electrostatic charge in the center of reaction60 were selected .
in addition , the charton constants ( )61 to measure steric effects on ortho positions were used .
the hammet constants did not show significant correlations with the ee(% ) values ( see the supporting information ) .
in contrast , the  values showed a significant negative correlation r 
 = 0.89 p<0.05 with ee(% ) in different positions of both rings , as shown in figure  5 , which indicates that the steric hindrance of the substituents of the substrate would hinder the arrangement of the substrate in the chiral pocket of the catalyst .
these predictions are in agreement with the proposed model ( see figure  2).62 
  predicted ee(% ) versus charton parameter values .
we have previously developed a ptqspr approach , which combines perturbation theory ( pt ) and qsrr ideas , to correlate and predict different outputs ( activity , property ) in complex molecular systems ( metabolic reactions),49 nanoparticles,50 and so forth .
the method has also been extended to predict the enantioselectivity and/or yield of intramolecular carbolithiation51 and heck  heck cascade reactions.52 in some cases , the developed ptqsrr models use trace operators , like spectral moments , or eigenvalues of chemical structure matrices , like bond adjacency matrix , as the inputs.51 , 53 now , we intend to use this correlative ptqsrr approach to predict the effect of the structures of the substrate , nucleophile , and catalyst , as well as the experimental conditions , on the enantioselectivity of intermolecular amidoalkylation reactions .
the model predicts the enantiomeric excess ee(%)nr of a new reaction ( nr ) by comparison to a reaction of a reference ( rr ) with known enantiomeric excess ee(%)rr that involves a set of molecules ( mq ) , which play different roles ( substrate , catalyst , etc . )
our goal is to find a useful tool to rationalize the enantioselectivity in this and related processes and to orient the catalyst choice . in this way , trends to improve the experimental results could be found . to accomplish this ,
this dataset included the abovedescribed reactions and literature data for related reactions with different types of substrates ( cyclic and bicyclic hydroxylactams ) , nucleophiles ( enamides , indoles , etc . ) , and chiral catalysts ( phosphoric acids , phosphoramides , etc . ) under different experimental conditions.12 , 15 , 18 , 19 , 54 the molecular descriptors v(mq ) used to quantify the chemical structure of all the molecules involved in the reaction were calculated with the software dragon.55 these molecular descriptors were the absolute eigenvalues of the matrix of topological distance weighted with atomic polarizabilities v(mq)=aeigpq . to find the qsrr model , a multivariate linear regression ( mlr ) analysis
was performed with the software statistica,56 combining forward stepwise and standard procedures of variable selections ( see the supporting information ) .
then , we initiated the study with the training and validation of the new ptqsrr model for the enantioselectivity of the reactions under study .
we found a model useful to predict the efficiency of the new reaction ee(%)new , given the expected value of efficiency ee(%)expected=<ee(%)>new for any new reaction in the solvent used and the values of the perturbation terms .
the equation of this model is the correlation function shown in [ equation  ( 1)]:(1)ee%new=0.558333 + 0.316901g0newee%new-0.000699g0newg4new+0.132149g0newysubvsub-0.001459g0newyprodvprod-0.011935g0newycatvcat-0.136922g0newynucvnuc-0.000373g0newysolvvsolvn=38419_r=0.93_f=36394.0_p<0.005 
  all of the variables of the model ( table  5 ) are statistically significant , according to student test ( see values of t and the plevel in table  6 ) .
a notable feature of this model is its ability to predict a high number of perturbations in intermolecular amidoalkylation reactions ( n=38  419 ) with high goodnessoffit r=0.93 ( 86.5  % of variance of data explained ) .
the model was validated with an external validation series of a large dataset of perturbations in intermolecular amidoalkylation reactions ( n=12  806 ) .
notably , the goodnessoffit for the external validation series was also high r=0.93 ( table  6 ) .
the chemical data associated with this ptqsrr model , as well as the observed and predicted values of ee(% ) , are listed in the supporting information .
the new ptqsrr model reported here allows both the computational screening of a very large set of reactions with different substrates , nucleophiles , and catalysts and the scanning of experimental conditions ( solvents , temperature , etc.).57 
  definition of all the terms used in the model . 
 
[ a ]  dragon variables ( v ) v 
 q = v(q)nrv(q)rr , with q = substrate ( sub ) , product ( prod ) ,  etc .
[ i ]  fisher ratio . to illustrate the practical use of the model in our experimental problem ,
thus , computational screening of the effect of structural changes of the nucleophiles and catalysts on the enantioselectivity of amidoalkylation reactions was carried out .
first , bicyclic hydroxylactam 1  a was selected as the model substrate under the optimized experimental conditions , that is , thf as the solvent , 40  c , and 96  h ( table  2 ) . as the training set ( data points used for model development ) was limited to a series of enamides , an expanded library of computationally designed enamides and carbamates bearing steric and electronic variations at the nitrogen atom and the aromatic ring was built .
it was hypothesized that both positions may contribute synergistically to the selectivity of the system , either by changing the acidity of the nh hydrogen atom and/or the alkene nucleophilicity , which likely modulates the early or late nature of the corresponding transition states involved in the selectivitydetermining step ( see figure  2 ) . regarding the catalyst ,
a series of chiral brnsted acids with strong acidic functionalities , such as binolderived phosphoric acids , phosphoramides , and so on , were also computationally designed . in addition , the chiral binol framework has been modified , as it has been shown to be crucial in improving the catalyst performance ( figure  3 ) . 
 
then , this large library of nucleophiles and catalysts was evaluated with the developed ptqsrr model for the above amidoalkylation reaction .
a selection of the simulation of the enantioselectivity on a set of 212  catalysts versus 88  nucleophiles is depicted in figure  4 by using an image with gradient color , which is related to higher ( green ) or lower ( red ) ee(% ) , in order to achieve the best visual result . 
  selected
ee(% ) predicted for intermolecular amidoalkylation reaction.58 
  according to the model , the best results would be expected with obenzyl carbamates 2  o  q , instead of their acetamide counterparts , under the above indicated experimental conditions , with almost all catalysts tested .
besides , the predictions indicated that high enantioselectivities would be obtained if these types of carbamates had an electrondonor substituent ( och3 , nhcoch3 ) in the para position , whereas the presence of a chlorine atom would lead to a decrease in the predicted ee(% ) , in agreement with our experimental results .
interestingly , the screening revealed that the best ee(% ) would be obtained by employing chiral brnsted acids 1315 and incorporating a sterically demanding h8binaphthyl moiety instead of the unsaturated analogues , in particular , phosphoramides ( ro)2ponhso2c8h17 
 14  e  h with the bulkiest aromatic substituents in the binol framework ( figure  4 ) . on the other hand ,
the use of atom stochastic moments enables backprojection of the model onto the enantioselectivity,59 that is , a map projecting the contribution of each atom or group of atoms to the enantioselectivity can be drawn .
the backprojection map of the catalytic activity of the biphenylsubstituted phosphoramide 14  h is depicted in table  7 , showing how the different electronic and steric variations on the catalyst affect the predicted ee(% ) values .
thus , the presence of the substituted biphenyl system on the binol framework is crucial to obtain high levels of enantioselectivity .
backprojection map analysis of the catalytic activity of the biphenyl substituted phosphoramide 14  h. another important application of the developed model lies with its potential to predict the enantioselectivity outcomes of new hydroxylactam substrates . to define the substrate scope , acetamide 2  a was selected as the nucleophile and a similar study of substrates versus catalysts was carried out . as in the previous case , we first selected a series of wellknown substrates and catalysts from the literature .
then , the library was expanded with the computationally designed chiral brnsted acids and a series of hydroxylactams ( cyclic and bicyclic cores with different substitution patterns ) .
next , the ee(% ) values were predicted with the model for the standard amidoalkylation reaction conditions ( thf as the solvent , 40  c , 96  h ) of these new hydroxylactams . as an example
, table  8 shows the backprojection map analysis of the enantioselectivity for substrates 1  a and 1  c. the model predicts that benzofused hydroxylactams would lead to lower ee(% ) values in the amidoalkylation reactions . besides
, the substituents on the aromatic ring of the isoquinoline moiety seem to play an important role . 
 
backprojection map analysis of the enantioselectivity of substrates 1  a and 1  c. in view of these results , we decided to study the effect of physicochemical parameters of substituents in different positions ( ortho , para , and meta ) of the benzene rings , both on the isoquinoline and isoindole moieties , on the enantioselectivity .
for this purpose , one of the reactions that provided a higher ee(% ) in our experimental study ( table  2 , entry  1 ) was selected as the reaction of reference .
then , different derivatives of the substrate introducing both electrondonating and electronwithdrawing substituents in those positions were computationally created .
next , the eigenvalues of these derivatives were calculated and introduced into equation  ( 1 ) to predict the new ee(% ) values . finally , a simple linear regression analysis of the ee(% ) versus different constants of the substituents was carried out . specifically , the hammett parameters (  
 p 
  and  
 p ) to measure electronic effects with and without the creation of electrostatic charge in the center of reaction60 were selected . in addition , the charton constants ( )61 to measure steric effects on ortho positions were used .
the hammet constants did not show significant correlations with the ee(% ) values ( see the supporting information ) .
in contrast , the  values showed a significant negative correlation r 
 = 0.89 p<0.05 with ee(% ) in different positions of both rings , as shown in figure  5 , which indicates that the steric hindrance of the substituents of the substrate would hinder the arrangement of the substrate in the chiral pocket of the catalyst .
these predictions are in agreement with the proposed model ( see figure  2).62 
  predicted ee(% ) versus charton parameter values .
enantioselective amidoalkylation reaction of enamides with bicyclic hydroxylactams catalyzed by chiral binolderived phosphoric acids allows the introduction of new functionality ( an acylmethyl group ) in the new generated quaternary stereocenter at the c1 position of the tetrahydroisoquinoline unit of the isoindoloisoquinoline skeleton . to achieve reasonable levels of enantioselectivity , either the enamides used as nucleophiles or the substrates
should have a free nh group , which would indicate that hydrogenbonding interactions of the phosphate ionpaired intermediate to the nh bonds could potentially be involved .
as the understanding of how the different parameters affect the stereochemical outcomes of these reactions is still difficult to rationalize , a correlative ptqsrr model has been developed to find trends that improve the experiment without engaging in a longterm empirical investigation .
the qsrr model predicts the effect of the substituents on the aromatic rings of the enamides or hydroxylactams , as well as the substitution pattern of the catalysts .
for example , a relationship between steric parameters ( charton parameters ) of substrate substituents and enantiomeric ratios of the products could be established . besides , the best ee would be expected with obenzyl carbamates with an electrondonor substituent ( och3 , nhcoch3 ) in the para position , with chiral phosphoramides incorporating a sterically demanding h8binaphthyl moiety , in particular , ( ro)2ponhso2c8h17 
 14  e  h with the bulkiest aromatic substituents in the binol framework .
therefore , the developed model is expected to be useful as a reference tool to choose the adequate catalyst or experimental conditions for enantioselective amidoalkylation reactions .
one type is the intensity factors g 
 q that accounts only for nonstructural intensity factors f 
 q ( temperature , time , solvent dipole , etc . ) in the new reaction .
we calculated the g 
 q as products of all factors considered to affect the molecules of class q 
 .
the second type of perturbation factor is the  
 qv(m 
 q ) terms .
consequently , they are the product of the switching functions  
 q = g 
 0new(g 
 qnew / g 
 qref ) used to quantify the changes on intensity factors and shifting functions v(m 

the five classes of molecules are , according to their different roles in the reaction , m 
 0=substrate ( sub ) , m 
 1=product ( prod ) , m 
 2=catalyst ( cat ) , m 
 3=nucleophile ( nuc ) , and m 
 4=solvent ( solv ) .
this second set of functions involves molecular descriptors of chemical structures calculated with the software dragon.55 the molecular descriptors used in this study were the absolute eigenvalues of the matrix of topological distance weighted with atomic polarizabilities v(mq)=ae 
 igpq .
the final formula of the model considered an initial term ee(%)expected , additive terms for the conditions of the new reaction , and multiplicative terms for the intensity factors and structural changes .
the formula of the model used is given in equation  ( 2):(2)ee%new = a0+a1g0newee%new+q=2q=6aqg0newgqnewq=1q=6aqqvmq 
  a solution of 12bhidroxyisoindoloisoquinolone 1  a ( 0.2  mmol ) , enamides 2  a  c ( 0.4  mmol ) and catalyst 4  d in dry thf ( 5  ml ) was stirred during 96  h at 40  c .
the reaction was quenched by addition of hcl ( 1  m , 1  ml ) and then satuarated nahco3 ( 1  ml ) .
the crude reaction mixture was purified by column chromatography ( alumina ) to afford the corresponding enantioenriched isoindolo[1,2a]isoquinolones 3  aa  ac .
one type is the intensity factors g 
 q that accounts only for nonstructural intensity factors f 
 q ( temperature , time , solvent dipole , etc . ) in the new reaction .
we calculated the g 
 q as products of all factors considered to affect the molecules of class q 
 .
the second type of perturbation factor is the  
 qv(m 
 q ) terms .
consequently , they are the product of the switching functions  
 q = g 
 0new(g 
 qnew / g 
 qref ) used to quantify the changes on intensity factors and shifting functions v(m 

the five classes of molecules are , according to their different roles in the reaction , m 
 0=substrate ( sub ) , m 
 1=product ( prod ) , m 
 2=catalyst ( cat ) , m 
 3=nucleophile ( nuc ) , and m 
 4=solvent ( solv ) .
this second set of functions involves molecular descriptors of chemical structures calculated with the software dragon.55 the molecular descriptors used in this study were the absolute eigenvalues of the matrix of topological distance weighted with atomic polarizabilities v(mq)=ae 
 igpq .
the final formula of the model considered an initial term ee(%)expected , additive terms for the conditions of the new reaction , and multiplicative terms for the intensity factors and structural changes .
the formula of the model used is given in equation  ( 2):(2)ee%new = a0+a1g0newee%new+q=2q=6aqg0newgqnewq=1q=6aqqvmq 

a solution of 12bhidroxyisoindoloisoquinolone 1  a ( 0.2  mmol ) , enamides 2  a  c ( 0.4  mmol ) and catalyst 4  d in dry thf ( 5  ml ) was stirred during 96  h at 40  c .
the reaction was quenched by addition of hcl ( 1  m , 1  ml ) and then satuarated nahco3 ( 1  ml ) .
the crude reaction mixture was purified by column chromatography ( alumina ) to afford the corresponding enantioenriched isoindolo[1,2a]isoquinolones 3  aa  ac .
as a service to our authors and readers , this journal provides supporting information supplied by the authors .
such materials are peer reviewed and may be reorganized for online delivery , but are not copyedited or typeset .
technical support issues arising from supporting information ( other than missing files ) should be addressed to the authors .
 abstractenamides with a free nh group have been evaluated as nucleophiles in chiral brnsted acidcatalyzed enantioselective amidoalkylation reactions of bicyclic hydroxylactams for the generation of quaternary stereocenters . 
 a quantitative structure  reactivity relationship ( qsrr ) method has been developed to find a useful tool to rationalize the enantioselectivity in this and related processes and to orient the catalyst choice . 
 this correlative perturbation theory ( pt)qsrr approach has been used to predict the effect of the structure of the substrate , nucleophile , and catalyst , as well as the experimental conditions , on the enantioselectivity . in this way , trends to improve the experimental results could be found without engaging in a longterm empirical investigation . 
Introduction
Results and Discussion
Predictive Study
Conclusions
Experimental Section
Model Development
General Procedure for the Synthesis of Enantioenriched Isoindolo[1,2
Supporting information