the idea of exploiting 
 organolithium mixed aggregates to control 
 organolithium reactivity and selectivity lurked for several decades , but it moved to center stage in the early 1980s 
 largely owing to contributions of seebach and co - workers . in a dramatic application of aggregate - based 
 stereocontrol , the process group at merck has shown that 2 equiv each 
 of lithium cyclopropylacetylide 1 and lithium 
 ephedrate 2b effect the 1,2-addition in eq 1 in 98% enantioselectivity . synthesis 
 of more than 50  000 kg of reverse transcriptase inhibitor efavirenz 
 ( sustiva , stocrin ) using this protocol quashed any doubt about the 
 practicality of stoichiometric amino alkoxide auxiliaries . subsequently , dupont pharmaceuticals prepared 
 more than 2000 kg of a second - generation reverse transcriptase inhibitor 
 using a seemingly analogous 1,2-addition of lithium acetylide 1 to quinazolinone 4 with an extraordinary 99.5% 
 enantioselectivity ( eq 2 ) . in this case , 
 however , optimal selectivity was obtained using a 3:1 mixture of norcarane - derived 
 amino alkoxide 3a and 1.1 a cornell  merck collaboration traced the high enantioselectivity 
 in eq 1 to the reaction of substrate with 2:2 
 ( roli)2(rli)2 mixed tetramer 5 . a subsequent cornell dupont 
 collaboration attributed the enantioselectivity in eq 2 to the external 
 attack of acetylide on 3:1 ( roli)3(substrate)1 mixed tetramer 6 . in both 
 reactions , aging the reaction near ambient temperature before addition 
 at low temperature was key to attaining high selectivity . during these structural and mechanistic studies , the problem emanated 
 from the difficulties associated with characterizing o - lithiated species 
 in solution , wherein high symmetry and lack of o  li coupling 
 preclude direct nmr spectroscopic analysis . arnett and co - workers have previously reported a crystal structure 
 of the pseudoephedrate stereoisomer of 2a displaying 
 an s4-symmetric tetrameric core , but their 
 efforts to determine the solution structure were less conclusive . considerable inroads have now been made 
 toward characterizing the 
 structures of o - lithiated species in solution . using a combination of li nmr spectroscopy , 
 the method of continuous variations ( mcv ) , and density functional theory computations , we show herein that amino alkoxides 2a , b and 3a , b form exclusively unsolvated homotetramers 7a , b and 8a , b . several intraaggregate exchanges are shown 
 to be remarkably slow . in conjunction with li n double - labeling studies , the application of mcv is extended 
 to distinguish lithium hexamethyldisilazide - lithium amino 
 alkoxide dimers 11 and the corresponding ladders 12(16)a structural ambiguity 
 arising from opaque o  li linkages that has dogged us for many 
 years . lithium alkoxides 2a , b and 3a , b were 
 generated in toluene by treating the 
 corresponding alcohols with 1.0 equiv of labeled lithium 
 hexamethyldisilazide ( [ li]lihmds ) . to facilitate the narrative , we note at the 
 outset that the data support cubic tetramers 7a , b and 8a , b bearing s4-symmetric cores . low - temperature li nmr spectroscopy of all four alkoxides 
 reveals two resonances ( 1:1 ) that coalesce above 20 c 
 to afford a single sharp resonance above 0 c consistent with 
 a single aggregate containing two magnetically inequivalent lithium 
 nuclei . note that cubic tetramers 7a , b and 8a , b would show such a pair , whereas tetramers 9a , b and 10a , b with d2d - symmetric cores would each display a single li resonance . the coalescence temperature in toluene ( approximately 20 c 
 for all four alkoxides ) is higher than that in neat thf ( tcoalesc  35 c ) , suggesting that 
 thf assists the exchange . we attribute these behaviors to a degenerate 
 rearrangement of the chelates about the cubic tetramer frameworks 
 of 7a , b and 8a , b ( eq 3).3 despite the thf dependence on the rate of chelate 
 exchange , we conclude that thf is coordinated only transiently based 
 on a simple and powerful diagnostic probe as follows . pyridine strongly coordinates lithium nuclei and shifts li resonances markedly ( 0.5 to > 1.0 ppm ) downfield even 
 in 
 neat thf solutions . amino alkoxides 2a , b and 3a , b showed no measurable change in chemical shift 
 in solutions of 1.2 m pyridine / toluene compared with that in thf / toluene 
 or toluene solutions , demonstrating that the chelates occupy all available 
 coordination sites . the assignment of 7a is consistent 
 with a crystal 
 structure by arnett and co - workers . the 
 assignment of 7b was corroborated by an x - ray crystal 
 structure of 5a showing the s4-symmetric cubic tetramer core ( figure 1 ; supporting information ) . assignment of 2a , b and 3a , b as tetramers 7a , b and 8a , b relied critically on mcv . in this experiment , the high symmetries of the lithium alkoxides 
 are disrupted by forming ensembles of homo- and heteroaggregates ( eq 4 ) . the number and symmetries of 
 the heteroaggregates and the dependence of the distribution on the 
 mole fraction ( xa or xb ) attest to the structures of 
 the homoaggregates , an and bn . in most previous applications of mcv , cubic tetramers appear as 
 a series of five homo- and heteroaggregates with the characteristic 
 resonance counts illustrated in chart 1.4 characterization of the alkoxides as tetramers using mcv 
 is illustrated 
 with 2a and 2b emblematically . mixtures 
 of 2a and 2b in a 1:1 ratio in toluene or 
 thf give intractable nmr spectra at low temperature . the complexity 
 inherent to ensembles is exacerbated by the stereochemistry of chelation 
 ( discussed in detail below ) . on warming , however , the overlapping 
 resonances coalesce to afford a sharp five - peak ensemble at + 60 c 
 consistent with a tetramer ensemble  a4 , a3b1 , a2b2 , a1b3 , and b4with each stoichiometry 
 appearing as a single resonance ( figure 2 ) . 
 the apparent intraaggregate li li exchange is well - precedented and has been useful in characterizing o - lithiated 
 species , but it is usually significantly more facile . the aggregates 
 were monitored in the high temperature limit with varying proportions 
 of 2a and 2b and fixed total alkoxide concentration . the relative integrations of the five distinct aggregates are plotted 
 versus measured mole fractions ( xa or xb ) of the two components in figure 3 . the number of aggregates and quality of the fit confirm the tetramer 
 assignment . in conjunction with the symmetry of the homoaggregates 
 at low temperature and solvent - independent chemical shift , mcv completes 
 the assignment of alkoxides 2a and 2b as 
 solvent - free tetramers 7a and 7b . li nmr spectrum of a 1:1 mixture of lithium ephedrates 2a and 2b in toluene recorded at + 60 c . job plot showing the relative integrations of tetrameric homo- 
 and heteroaggregates versus measured mole fractions of 2a ( xa ) for 0.10 m mixtures of lithium ephedrates [ li]2a ( a ) and [ li]2b ( b ) in toluene at + 60 c . studies of norcarane - derived alkoxides 3a and 3b afforded results fully analogous to those of 2a and 2b in every respect , supporting unsolvated cubic 
 tetramers 8a and 8b . relatively minor quantitative 
 differences include slightly faster chelate exchanges and slightly 
 slower intraaggregate li  li site exchanges . the stereochemical 
 preference for s4 rather than d2d cubic 
 cores was examined using density functional theory computations at 
 the b3lyp level of theory with the 6 - 31g(d ) pople basis set . free energies were calculated from an mp2-derived 
 single - point energy [ 6 - 31g(d ) basis set ] and a b3lyp - derived thermal 
 correction [ 6 - 31g(d ) ] at 195 k and 1 atm . the 21 kcal / mol preference 
 for the s4 form in 7b ( eq 5 ) is fully consistent with the experimental data . although we often use computations only qualitatively , this difference 
 is very large for isodesmic stereoisomers . computations of a sterically less congested variant 
 in which the phenyl and methyl moieties along the backbone of ephedrate 2a were omitted show a reduced but still sizable 7 kcal / mol 
 preference for the s4 core ( eq 6).5 during 
 the studies described above , we detected lithium alkoxide  lihmds 
 mixed aggregates that formed quantitatively with 1.0 equiv of excess 
 lihmds . for example , lithium ephedrate 2a with a 1.0 equiv excess of [ li , n]lihmds displays two li doublets in a 1:1 ratio ( jli  n = 1.0 hz ) and a single resonance 
 appearing as a quintet in the n nmr spectrum ( figure 4 ) . the data are consistent with the basic mixed 
 dimer subunits 11a , b or the corresponding ladder 12a . once again , the spectroscopically opaque li li nmr spectrum recorded on a 1:1 mixture of [ li , n]lihmds ( 0.10 m ) and lithium amino alkoxides 2a ( 0.10 m total concentration ) in toluene cosolvent at 30 
 c . mixtures of lithium ephedrates 2a and 2b in toluene at varying proportions but 
 constant lithium alkoxide 
 titer in the presence of 1.0 equiv of excess lihmds afford li spectra showing the two original resonance pairs along with additional 
 resonances consistent with mixed ladder 12c ( figure 5 ) . the downfield ensemble is not well resolved , 
 yet the upfield resonances clearly show 12a and 12b along with two resonances ( 1:1 ) attributed to mixed ladder 12c . we suspect that the well - resolved upfield resonances 
 correspond to those bearing the dialkylamino chelates . maintaining 
 the total concentration of excess lihmds at 0.10 m and the total alkoxide 
 titer at 0.10 m while varying proportions ( mole fractions ) of the 
 two alkoxides afforded a mole fraction - dependent distribution consistent 
 with ladders 12a , 12b , and 12c . the resulting job plot is illustrated in figure 6 . the resonance counts and quality of the fit confirm the 
 1:1 association of two mixed dimeric subunits and the overall ladder 
 motif . li nmr spectra 
 recorded on mixtures of [ li]lihmds ( 0.10 m ) and lithium 
 amino alkoxides 2a and 2b ( 0.10 m total 
 concentration ) in toluene cosolvent at 30 
 c : ( a ) 0.10 m [ li]2b ; ( b ) 0.080 m [ li]2b and 0.020 m [ li]2a ; ( c ) 0.050 m [ li]2b and 0.050 m [ li]2a ; ( d ) 0.020 m [ li]2b and 
 0.080 m [ li]2a ; and ( e ) 0.10 m [ li]2a . job plot showing the relative integrations of mixed ladders 12a ( a2 ) , 12b ( b2 ) , and 12c ( ab ) versus measured mole fractions of 2b  lihmds 
 ( xb ) in mixtures containing 
 0.10 total amino alkoxide and 0.10 m lihmds at 30 c . synthetically 
 important lithium amino alkoxides pose an interesting 
 challenge for structural organolithium chemists . arnett and co - workers 
 have shown that crystalline pseudoephedrate stereoisomer of 2a is a cubic tetramer analogous to 9a , but their 
 efforts to determine the solution structure were less conclusive . messy li nmr spectra cast doubt on the colligative measurements , 
 which are notoriously sensitive to impurities . we previously studied amino alkoxides 2a and 3a using nmr spectroscopy and gleaned no useful information . the current paper describes how a combination of li 
 nmr spectroscopy and mcv allowed us to characterize 2a , b and 3a , b as stereochemically pure cubic tetramers 7a , b and 8a , b . computational studies suggest 
 that the s4-symmetric cubic core is inherently 
 more stable than the d2d core , a preference that is amplified by the substituents along the 
 chelate backbone ( eqs 4 and 5 ) . during these studies , we made a number of observations 
 and achieved some tactical developments in mcv that call for further 
 elaboration . in the low temperature limit , all four homoaggregates 
 display two 
 distinct resonances that , with warming , coalesce into a single resonance 
 owing to facile degenerate isomerizations of the chelates ( eq 3 ) . although this observation proved critical to complete 
 the structural assignments , it foreshadowed severe technical problems 
 with the use of mcv . in typical applications of mcv to characterize 
 tetramer ensembles ( eq 4 ) , we would observe 
 three heteroaggregates of stoichiometries3:1 , 2:2 , and 1:3displaying 
 resonance counts and integrations reflecting the symmetries ( chart 1 ) . the amino alkoxides , 
 by contrast , show a markedly increased resonance count arising from 
 stereochemical complexity ( chart 2 ) . the 3:1 and 1:3 
 heterotetramers exist as two distinct diastereomers each displaying eight resonances total . two c2-symmetric diastereomers displaying two resonances each 
 and two c1-symmetric diastereomers containing 
 four discrete lithium resonances each . thus , the tetramer ensemble 
 in the slow exchange limit would include 32 resonances in total . it 
 is not shocking , therefore , that ensembles generated from 2a/2b or 3a/3b pairings are intractable in the low temperature 
 limit . two general classes of intraaggregate exchanges would , 
 in principle , 
 simplify the spectra . chelate  chelate exchange ( eq 3 ) without further deepseated adjustments within the 
 cubic core would reduce the complexity of chart 2 to the simpler distribution depicted in chart 1 and lower the li resonance count from 32 to 8 . intraaggregate 
 exchange of all li nuclei within each 
 aggregate would lead to further symmetrization , causing the five - aggregate 
 ensemble to appear as five discrete li singlets . in practice , 
 warming the samples appeared to elicit rapid chelate exchange , but 
 we could not readily observe all eight resonances at a single temperature 
 owing to differential exchange rates of the different aggregates . warming of the samples to 6070 c , however , elicited 
 the hoped - for rapid intraaggregate li  li site exchanges . we 
 have examined structures in the limit of rapid intraaggregate exchange 
 before , but the temperatures required for vicinal 
 amino alkoxides are remarkably high . ensembles generated from lithium alkoxides and 
 related o - lithiated species of differing aggregation states resist 
 heteroaggregation , affording no heteroaggregates whatsoever or an 
 ensemble of homo- and heteroaggregates that deviates significantly 
 from statistical data . the most compelling 
 assignments stem from structurally related roli / roli pairs . 
 at the outset , however , we thought that pairing structurally very 
 different alkoxides would be required to obtain sufficient resolution 
 in the li nmr spectra . nonetheless , the 2a/2b and 3a/3b pairs differing 
 marginally at the dialkylamino appendages provide convincing 
 results . more heterogeneous pairings 
 of lithium ephedrate and norcarane - derived lithium alkoxides2/3 pairs  also appeared to provide tetramer 
 ensembles , but rapid intraaggregate exchange demanded very high ( > 80 
 c ) temperatures . mounting evidence suggests that cubic 
 tetramers of enolates and 
 related o - lithiated species are far more robust ( less dynamic ) than 
 we ever suspected . the effects of aging ( warming  cooling 
 cycles ) and catalytically active lithium salts on aggregate equilibrations 
 may profoundly influence stereo- and regiochemical outcomes . both 
 chelate  chelate and li  li site exchanges are observed 
 at lower temperatures in thf than in toluene , indicating a role of 
 thf despite apparent lack of solvation . during the studies of 
 homoaggregates we detected lithium alkoxide ( lihmds does not form mixed aggregates 
 in thf . ) the connectivities obtained 
 from li n double - labeling studies 
 do not distinguish cyclic dimer 11 from ladder 12 , a distinction that has eluded us previously . we used mcv to reveal that mixtures of lihmds 
 and alkoxides afford mixed ladders ( 12a  c ) . the chirality of these mixed aggregates may also pique 
 curiosity among those interested in enantioselective reactions of 
 lithium amides . we have shown that cubic 
 tetramers are a dominant form of several 
 lithium amino alkoxides . this study and others suggest that such tetramers composed of o - lithiated species 
 are very robust . it is not difficult to imagine , therefore , that practitioners 
 using lithium enolates to achieve stereocontrolled carbon the importance of lithium amino alkoxides as auxiliaries in organolithium 
 chemistry has grown markedly in the absence of any structural insights 
 whatsoever . notably , structural studies of aggregates underlying 
 the merck chemistry ( eq 1 ) have played a direct role in the development of the protocols 
 subsequently used at dupont ( eq 2 ) . in this context , 
 we note a curious observation that may prove important . inserting 
 lithium salts into the cubic tetramers of 7a and 8a to form the mixed tetramers 5 and 6 central to merck s and dupont s enantioselective additions 
 requires disruption of the chelate orientations of the s4 core structure of homoaggregates 7a and 8a . we wonder : would mixed aggregates that allow three of 
 the four chelates in the s4 core to remain 
 intact ( eq 7 ) offer more generalized control 
 of the stereochemistry toluene , thf , and pyridine were 
 distilled from blue solutions containing sodium benzophenone ketyl . [ li]lihmds and [ li , n]lihmds 
 were prepared and recrystallized using modified literature protocols . air- and moisture - sensitive materials were manipulated 
 under argon using standard glovebox , vacuum line , schlenk , and syringe 
 techniques . nmr samples were prepared using protocols described previously.li nmr spectra were typically recorded 
 on a 500 or 600 mhz spectrometer with the delay between scans set 
 to > 5  t1 to ensure accurate integrations . chemical shifts 
 are 
 reported relative to a 0.30 m licl / meoh standard at 80 
 c .
lithium 
 ephedrates and norcarane - derived lithium amino alkoxides 
 used to effect highly enantioselective 1,2-additions on large scales 
 have been characterized in toluene and tetrahydrofuran . 
 the method 
 of continuous variations in conjunction with 6li nmr spectroscopy 
 reveals that the lithium amino alkoxides are tetrameric . in each case , 
 low - temperature 6li nmr spectra show stereoisomerically 
 pure homoaggregates displaying resonances consistent with an s4-symmetric cubic core rather than the alternative d2d core . 
 these assignments 
 are supported by density functional theory computations and conform 
 to x - ray crystal structures . 
 slow aggregate exchanges are discussed 
 in the context of amino alkoxides as chiral auxiliaries .