nucleophilic additions to conformationally 
 biased cyclohexanones 
 can provide two stereoisomeric alcohol products via reaction at the 
  axial  or the  equatorial  face of the 
 carbonyl ( figure 1 ) . the factors controlling 
 selectivities have been studied and debated for roughly three - quarters 
 of a century . the facial selectivity of 
 addition is influenced by the size of the nucleophilic reagent : small 
 nucleophiles tend to add to the axial face , whereas bulky nucleophiles 
 preferentially attack the equatorial face . for example , nabh4 and lialh4 both deliver hydride to the axial face of 4-tert - butylcyclohexanone ( 1 ) , giving an equatorial alcohol 
 as the major product , whereas bulky hydride reagents such as lihbbu3 ( l - selectride ) preferentially yield the axial alcohol via equatorial hydride 
 delivery ( figure 1 ) . the observed preferential addition 
 of bulky reagents to the equatorial 
 face is generally attributed to steric factors : the axial face is 
 more hindered than equatorial due to 1,3-diaxial interactions with 
 the incoming nucleophile . historically , conversely , dauben attributed the axial preference 
 observed with smaller reagents to  product development control  , 
 reflecting the greater stability of the resulting equatorial alcohol . a more widely accepted model based on torsional strain was first proposed 
 by felkin and later supported computationally by anh and eisenstein . anh model posits 
 that the transition state ( ts ) for addition to the equatorial face 
 of a cyclohexanone chair involves torsional strain greater than that 
 of axial attack ; that is , there are more eclipsing interactions during 
 equatorial attack compared to axial ( figure 2 ) . the stereoelectronic basis of these facial preferences has been 
 studied extensively through computational methods by houk and others using 
 small hydride reagents ( lih , nabh4 , lialh4 ) 
 as computationally affordable systems . although other models have 
 been proposed , including cieplak s model that emphasizes overlap 
 between an antiperiplanar  orbital and the developing  * 
 orbital , theoretical studies using small 
 hydride reagents overall support the torsional 
 strain model . increased eclipsed interactions ( torsional strain ) in 
 equatorial 
 face attack of hydrides to carbonyl compounds . this general trend in facial selectivity does not hold , however , 
 for some six - membered cyclic ketones . cis-2,6-disubstituted n - acylpiperidones ( e.g. , compounds 2 and 3 in scheme 1 ) have been studied extensively 
 by the comins group and others . for 2 and 3 , hydride addition from the equatorial face is favored even 
 when a small hydride reagent ( nabh4 ) is used ( scheme 1 , eqs 1 and 2 ) . indeed , the axial face of this class 
 of substrates should be particularly hindered due to the axial 2,6-substituents , 
 forced into this conformation by a strain with the n - substituent . surprisingly , however , the more conformationally 
 restricted bridged analogues ( tropinones , e.g. , compound 4 ) undergo favored axial attack by small hydride reagents despite 
 the steric hindrance imposed by the bridge ( eqs 3 and 4 ) . low energy twist - boat conformations of piperidones have 
 been observed 
 in solution by nmr spectroscopy and in the solid state by x - ray diffraction . we wondered if these twist - boat conformers might 
 be relevant to the transition states of reactions of these compounds . 
 to study this possibility experimentally , we compared the reactivity 
 of piperidone 3 and its tropinone analogue 5 toward k - selectride . notably , although the former substrate can 
 access a twist - boat conformation , the latter can not due to geometrical 
 constraints . based on the results of a competition experiment ( scheme 2 ) , the rate of reduction of tropinone 5 with k - selectride is about 3-fold slower than that of piperidone 3 ; however , both processes are completely selective toward 
 formation of the axial alcohol ( equatorial attack of hydride ) . this 
 result , in combination with the contrasting stereoselectivity of these 
 two classes of substrates with nonbulky hydrides ( scheme 1 , eqs 3 and 4 ) , encouraged 
 us to computationally explore the hypothesis that a twist - boat transition 
 state could in fact be contributing significantly to the reaction 
 of cis-2,6-disubstituted n - acylpiperidones . we have undertaken a computational 
 study of the factors influencing 
 the differences in reactivity and facial selectivity of reduction 
 of these two structurally similar piperidone and tropinone substrate 
 classes . we have analyzed the roles of the six - membered ring conformation 
 and the size of the nucleophile on stereoselectivities . the contributions 
 of both steric repulsion and torsional strain to the activation energy 
 upon hydride addition , factors that have been found to be particularly 
 relevant in cyclic ketones , were analyzed . our calculations indicate that , although a chair conformation experiences 
 greater torsional strain during attack at the equatorial face by a 
 small hydride , attack at the two faces of a twist - boat do not necessarily 
 follow the same trend . additionally , with very bulky hydride reagents , 
 the difference in torsional strain during attack at the axial vs equatorial 
 face of a chair is nearly negligible due to a late transition state . figure 3 depicts 
 the substrates and hydride 
 reagents used in our computational studies . while 4-tert - butylcyclohexanone ( 1 ) is a well - studied conformationally 
 biased cyclic ketone , chosen as a baseline , n - methoxycarbonyl - cis-2,6-dimethylpiperidone ( 6 ) and n - methoxycarbonyltropinone ( 7 ) were selected 
 as piperidone and tropinone model substrates . lithium aluminum hydride ( lah ) 
 is the small hydride model . for 
 a bulky hydride , we mimicked the reactivity of l - selectride ( lithium 
 tri - sec - butylborohydride ) using a computationally 
 affordable surrogate ( l - selectride is conformationally and stereochemically 
 very complex , with thousands of low energy conformers ) . we initially tested libhme3 as a 
 bulky hydride model but were unable to reproduce the experimental 
 selectivities using this relatively simple trialkylborohydride . however , 
 a more sterically demanding hydride , lithium triisopropylborohydride 
 ( ltbh ) was found to satisfactorily reproduce the experimental selectivities 
 of l - selectride , albeit at greater computational cost than libhme3 due to the large conformational space of ltbh . figure 4 depicts the calculated 
 geometries of the most stable 
 chair ( 1ch , 6ch , and 7ch ) and twist - boat ( 1 tb and 6 tb ) conformations of the cyclic ketone 
 substrates . newman projections sighting down the ring carbon  carbonyl 
 carbon bond are also provided . because of an internal plane of symmetry 
 in the chair conformations , the two possible newman projections are 
 enantiomeric ( e.g. , sighting down the c2c1 bond of 1ch provides the mirror image of sighting 
 down c6c1 ) . conversely , two different newman projections are 
 given for 1 tb and 6 tb , as the twist - boat conformations of these 
 substrates lack a plane or axis of symmetry . in the ground state , 1 adopts a chair conformation ( 1ch ) that is more stable than the minimum energy twist - boat conformation 
 ( 1 tb , in which c1 and c4 are 
 at the bow and stern ) by 3.2 kcal mol ( figure 4a ) . conformations of cyclic ketone substrates calculated at 
 the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) 
 level . gibbs free energies ( g ) are referenced 
 to the lowest energy conformer , when applicable , and are given in 
 kcal mol ; angles are given in degrees . both chair and twist boat conformations were also 
 located for piperidone 6 ( figure 4b ) . previous studies on 
 cis-2,6-disubstituted n - acylpiperidones have indicated 
 that the chair conformation with equatorial 2- and 6-substituents 
 is unstable . the resulting a - strain between the 2,6-diequatorial and the n - substituents disfavors 
 such a conformation , and instead these substituents exist in an axial 
 ( or pseudoaxial ) orientation in conformation 6ch . indeed , our calculations show that the energy penalty 
 for placing these two groups equatorial is 6.1 kcal mol relative to 6ch ( see supporting information ) . despite the greater 
 intrinsic stability of chair conformations , 6ch has a disadvantageous 1,3-diaxial interaction between 
 the two axial methyl substituents , which is alleviated in 6 tb ( the distances between the proximal hydrogens 
 of the two methyl groups in 6ch and 6 tb are 2.19 and 2.76  , 
 respectively ) . the calculated geometry of the most stable 6 tb very closely matches that predicted by 
 the nmr studies of venkatraj et al . , in which c6 ( the ring carbon 
 syn to the carbonyl of the n - acyl group ) and c3 are 
 at the bow and stern positions . the twist - boat 
 conformation of 6 is predicted to be only 0.5 kcal mol higher in energy than 6ch , suggesting the coexistence of both isomers in solution . as 
 described above , previous experimental and computational studies have 
 indicated that similar piperidones ( albeit bearing bulkier 2- and 
 6-substituents ) exist predominantly in a twist - boat conformation in 
 solution and in the solid state . the six - membered ring of tropinone 7 is locked into 
 a chair conformation ( figure 4c ) . the bridging 
 ch2ch2 cinches the chair together 
 on one side , making the nitrogen flap more folded in 7ch , with a flap angle ( out - of - plane dihedral 
 angle ) of 115 compared to 138 in 6ch (  , figure 4d ) . conversely , 
 the carbonyl flap on the opposite side of 7ch is more flattened , with a flap angle of 146 
 (  , figure 4d ) , compared to 131 
 in 6ch and 137 in 1ch . the lowest energy reactant species 
 for the reduction of cyclic ketones 1 , 6 , and 7 by lah are prereaction coordination complexes 
 that are stabilized by 10.9 to 12.3 kcal mol with respect to the separated reactants ( see , for example , figure 5a ) . substrate geometries are not significantly distorted 
 by formation of the coordination complexes , and the energy differences 
 between chair and twist - boat conformations ( for 1 and 6 ) are very nearly conserved ( figure 5b ) . thus , all of the calculated activation barriers reported herein 
 are measured from the lowest - energy prereaction coordination complexes . although the most realistic representation of the lithium counterion 
 would likely include coordinated solvent ( thf ) molecules , we were 
 unable to obtain optimized geometries of all the transition states 
 needed to account for stereoselectivity using explicit solvent . however , 
 significant computational precedent exists for successfully reproducing 
 experimental selectivities of hydride reductions involving nonexplicitly 
 solvated lithium species . ( a ) example of formation 
 of the reactant complex with lah , shown 
 for 1ch . ( b ) comparison of the 
 gibbs free energies ( g ) of chair and twist - boat 
 conformations of free ketones 1 , 6 , and 7 and their prereaction complexes with lah . optimized structures 
 were calculated at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) 
 level . gibbs free energies ( g ) are referenced 
 to the lowest energy free ketone conformation and are given in kcal 
 mol . because neither face of a twist - boat experiences nucleophilic 
 attack 
 via a true axial or equatorial trajectory , attack on the twist - boat 
 face that corresponds to the axial face of the analogous chair will 
 be herein be referred to as  pro - axial  attack or attack 
 at the  pro - axial face  ( the term  pro - equatorial  
 will also be used ) . these terms refer to the orientation of the added 
 nucleophile in the product ( i.e. , the axial or equatorial orientation 
 of the hydride ) and not of the hydroxyl . the torsional strain associated 
 with the transition states herein is represented graphically by newman 
 projections and described numerically by the parameter  , which 
 corresponds to the average deviation from 60 of the 12 dihedral 
 angles of both newman projections involving the carbonyl carbon ( figure 6 ) . it should be noted that due to the intrinsic 
 conformational differences between chair and twist - boat conformations , 
 there is a certain amount of eclipsing already associated with the 
 twist - boats . hence , the ranges of  values for these two ring 
 conformers are different , and these parameters should only be compared 
 between attack at the axial and equatorial faces of the same ring 
 conformation , not across different conformations . it should be also 
 noted that , depending on the position of the ts in the reaction coordinate , 
 the range of values for  can change significantly due to the 
 greater sp character of the carbonyl carbon in late and 
 more distorted ts . measurement of torsional strain (  ) in the ts of 
 hydride 
 addition to cyclic ketones . the transition structures obtained for addition of lah to 
 both 
 faces of the different conformations of ketones 1 , 6 , and 7 are provided in figures 79 . consistent with experimental 
 selectivity trends,1ch was found to favor attack at the axial face 
 by lah , rather than the equatorial face , by 1.1 kcal mol ( corresponding to an 86:14 ratio of axial : equatorial addition products 
 at 25 c ) . the analysis of the geometries of the transition states 
 for attack at the axial and equatorial faces ( 1ch - ts - lahax and 1ch - ts - laheq , figure 7 ) revealed features 
 consistent with the previously described models in which attack on the equatorial face experiences greater 
 torsional strain compared to axial face attack . although the corresponding 
  equatorial  and  axial  transition states 
 are located at similar points on the reaction coordinate ( the forming 
 c  h and breaking al  h bond lengths are 1.66 and 1.71 
  , respectively , for both transition structures ) , addition to 
 the equatorial face of 1ch involves 
 slightly greater eclipsing interactions (  = 12 for axial 
 face attack vs 14 for equatorial face attack ) . moreover , addition 
 to the chair equatorial face requires greater distortion of the ring 
 dihedral angle relative to the geometry of the reactant 1ch ( dihedral angle c  c  c  c 
 = 40 and 60 for 1ch - ts - lahax and 1ch - ts - laheq , respectively , compared to 48 for 1ch ) . these results illustrate how changes 
 in geometry occurring in the ts region can sometimes have opposing 
 effects : the expansion of a single dihedral angle to optimal values 
 of a c(sp)c(sp ) bond can be detrimental 
 if it implies a great distortion from the reactant structure . the 
 delicate balance between these stabilizing / destabilizing geometric 
 features ultimately results in the overall relative energies of competing 
 pathways . lowest energy transition structures for the addition of lah to 
 ( a ) the axial face of chair 1ch , ( b ) the equatorial face of chair 1ch , ( c ) the pro - axial face of twist - boat 1 tb , and ( d ) the pro - equatorial face of twist - boat 
 1 tb . optimized structures were calculated 
 at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) level . activation 
 gibbs free energies ( g ) 
 are referenced to the lowest energy prereaction coordination complex 
 and are given in kcal mol ; distances are given 
 in angstroms and angles in degrees . the twist - boat transition states for 1 ( figure 7c and 7d ) are slightly later 
 ( the forming c  h bond length is 1.60  for 1tb - ts - lah and 1.66  for 1ch - ts - lah ) and , consequently , 
 higher in energy than the chair transition states for both pro - axial 
 and pro - equatorial hydride addition . this difference in position on 
 the reaction coordinate contributes to amplifying the intrinsic preference 
 for the chair conformation in the transition state ( gtwist - chair = 6.2 
 and 4.7 kcal mol for pro - axial and pro - equatorial 
 addition , respectively ) with respect to the initial reactant ( gtwist - chair = 2.8 kcal mol ) . the increased destabilization of the twist - boat relative to the 
 chair can also be attributed , at least in part , to a greater difference 
 in torsional strain between the two transition states . h 
 = 8 ) to transition state , especially for axial attack ( o  c  c  h 
 of 1ch - ts - lahax = 45 ) , albeit with an 8 compression 
 in the c  c  c  c angle . in contrast , the twist - boat 
 transition states maintain an eclipsed arrangement ( the smaller o  c  c  h 
 angle = 4 in 1 tb , compared 
 to 611 in 1tb - ts - lah ) . notably , neither face of the twist boat is strongly 
 preferred for hydride addition by lah due to similar torsional strain 
 occurring in both approaches , as represented by very similar  
 values . in fact , pro - equatorial attack on the twist boat is slightly 
 favored over pro - axial attack by 0.4 kcal mol ( figure 7c and 7d ) . this weak preference 
 for pro - equatorial attack in the twist boat is opposite to the preference 
 for axial attack on 1ch and alludes 
 to the possibility that stable twist - boat conformations can alter 
 the usual stereoselectivity . consistent with literature reports , the equatorial face of piperidone 6 is predicted to 
 be more reactive than the axial face toward lah by at least 1 kcal 
 mol ( figure 8) . the predicted 
 stereoselectivity for this reaction , considering all feasible pathways , 
 is a 89:11 ratio of axial : equatorial alcohols at 25 c ( or 95:5 
 at 78 c ) . this equatorial preference is predicted for 
 both chair and twist - boat transition structures ( geq - ax = 0.8 
 and 2.0 kcal mol for 6ch - ts - lah and 6tb - ts - lah , respectively ) . in the 
 chair conformation , the destabilization of the ts for axial face attack 
 is likely caused by the steric hindrance with the 2,6-dimethyl substituents , 
 which translates into a longer forming c  h bond distance ( 1.75 
  vs 1.66  in the cyclohexanone ts ) . attack at the equatorial 
 face of the chair conformation also benefits from a slight mitigation 
 of the 1,3-diaxial interactions between the two methyl groups in the 
 transition state ( dh  h = 2.22  ) , 
 while axial attack does not provide any such relief ( dh  h = 2.18  , compared to 2.19  in the 
 reactant ) . these steric factors override the intrinsically greater 
 torsional strain generated in attack on the equatorial face . lowest energy 
 transition structures for the addition of lah to 
 ( a ) the axial face of chair 6ch , ( b ) the equatorial face of chair 6ch , ( c ) the pro - axial face of twist - boat 6 tb , and ( d ) the pro - equatorial face of twist - boat 
 6 tb . optimized structures were calculated 
 at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) level . activation 
 gibbs free energies ( g ) 
 are referenced to the lowest energy prereaction coordination complex 
 and are given in kcal mol ; distances are given 
 in angstroms and angles in degrees . consistent with our hypothesis that twist - boat transition 
 states 
 may be involved , pro - equatorial attack on the twist - boat conformation 
 of 6 is not only unusually stable but is even slightly 
 favored ( by 0.3 kcal mol ) over attack on the chair 
 conformation . in fact , 6tb - ts - laheq was calculated to be the 
 lowest energy pathway for the addition of lah to 6 . the 
 trajectory of hydride addition to the pro - axial face of 6 tb is remote from the 2,6-dimethyl substituents 
 ( dh  h = 3.85  in 6tb - ts - lahax ) . nevertheless , pro - equatorial attack on the twist - boat is 
 preferred , and is 5 kcal mol lower than 
 that of the twist - boat transition state of cyclohexanone 1 . consistent 
 with its experimentally observed reactivity , and contrary to its nonbridged analogue 6 , tropinone 7 is predicted to undergo preferential hydride attack by lah 
 at the axial face ( typical felkin  anh selectivity ) , although 
 with a lower stereoselectivity ( geq - ax = + 0.7 kcal mol , leading to a 85:15 ratio of equatorial : axial alcohols at 78 
 c ) . steric hindrance in the axial addition trajectory of 7ch - ts - lahax is slightly less important , since the alh4 approaches somewhat further away from the ethylene bridge in 7 than from the dimethyls of piperidone 6 . also , 
 the advantage of alleviating the 1,3-diaxial interactions described 
 for the equatorial attack in 6ch and both approaches in 6 tb does 
 not apply to 7ch , in which these 
 substituents are bridged . the geometric constraints imposed by the 
 bicyclic structure of 7ch preclude 
 relaxation of the torsional strain generated in the transition states , 
 as reflected by the activation barriers that are calculated to be 
 24 kcal mol higher for 7 than 
 for 6 and 1 and by the 712 
 increase in the  values for 7 with respect to 6 and 1 . in view of the different stereochemical 
 outcomes observed for the addition of lah to piperidone 6 and tropinone 7 , it can be concluded that relaxation 
 of 1,3-diaxial interactions , either by accessing twist - boat conformations 
 or by favoring equatorial addition trajectories , is the key factor 
 determining facial stereoselectivity in the reduction of this type 
 of system with small hydrides , overriding the contribution of other 
 steric factors . lowest energy transition structures for the addition of 
 lah to 
 ( a ) the axial face of 7ch , and 
 ( b ) the equatorial face of 7ch . optimized structures were calculated at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) 
 level . activation gibbs free energies ( g ) are referenced to the lowest energy prereaction coordination 
 complex and are given in kcal mol ; distances are 
 given in angstroms and angles in degrees . as observed 
 with lah , all three substrates studied form prereaction coordination 
 complexes with lithium triisopropylborohydride ( ltbh ) that are lower 
 in energy than the separated reactants ( see , for example , figure 10a ) . the activation energies reported here for reduction 
 with ltbh are also measured from the lowest - energy prereaction coordination 
 complexes . for 1 , the difference in energy between chair 
 and twist - boat conformations is essentially conserved upon formation 
 of the prereaction complex ( figure 10b ) . however , 
 for piperidone 6 , the twist - boat conformation is destabilized 
 relative to the chair upon formation of the prereaction complex ( gtwist - chair = 1.8 kcal mol for the prereaction complexes vs 0.5 kcal mol for the uncomplexed ketone conformations , respectively ) . ( a ) example 
 of formation of the reactant complex with ltbh , shown 
 for 1ch . ( b ) comparison of the 
 gibbs free energies ( g ) of chair and twist - boat 
 conformations of free ketones 1 , 6 , and 7 and their prereaction complexes with ltbh . optimized structures 
 were calculated at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) 
 level . gibbs free energies ( g ) are referenced 
 to the lowest energy free ketone conformation and are given in kcal 
 mol . the bulky hydride reagent is less reactive than the sterically 
 less - demanding reagent lah , as reflected by higher overall activation 
 barriers calculated for ltbh . the reactivity trend observed for the 
 three cyclic ketones toward lah is maintained for reduction with ltbh , 
 although the differences in the calculated activation energies are 
 smaller ( g = 24.7 , 24.9 , 
 and 25.3 kcal mol for 1 , 6 , and 7 , respectively ; figures 1113 ) . both the lithium and the potassium 
 salts of selectride are commonly used experimentally as a bulky hydride 
 reagents . therefore , we also investigated the reactivity of piperidone 6 and tropinone 7 toward potassium triisopropylborohydride 
 ( ktbh ) , in addition to ltbh . the corresponding calculated activation 
 energies indicate a somewhat greater reactivity of ktbh with respect 
 to ltbh ( g = 22.9 and 25.1 
 kcal mol for the reaction of ktbh with 6 and 7 , respectively ) . this 
 may be due to a weaker interaction between k and the incoming 
 hydride in the transition structure , as suggested by the computed 
 transition state geometries . the kinetic 
 preference for 6 vs 7 predicted by our calculations 
 is consistent with the results of the competition experiment described 
 in scheme 2 . due to the very similar chair 
 vs twist - boat selectivity trends calculated for ltbh and ktbh ( gtwist - chair = 2.8 
 and 2.6 kcal mol for the reaction of 6 with ltbh and ktbh , respectively ) , and to facilitate a more direct 
 comparison to lah a more detailed description of the reactivity of ktbh with 6 and 7 can be found in the supporting 
 information . in accordance with experimental results , the three substrates studied 
 are consistently 
 predicted to prefer attack at the equatorial face by the bulky hydride 
 reagent ltbh . despite the large number of conformers accessible for 
 each productive reaction pathway ( e.g. , 108 conformers representing 
 approach of ltbh to just one face of 6 ) , in all cases 
 reaction with ltbh proceeds through significantly later transition 
 states ( forming dc h = 1.381.45 
 with ltbh vs 1.661.75  with lah , figure 1113 ) . ltbh favors addition 
 to the equatorial face of 1ch by 3.7 kcal mol ( figure 11a and 11b ) . thus , 
 the surrounding dihedral angles in the chair ts are more staggered 
 than in the transition structures with lah . this feature is reflected 
 in the slightly smaller values of  for the chair ts with ltbh 
 (  = 1011 ) vs with lah (  = 1214 ) . furthermore , the difference in torsional strain between attack at 
 the axial and equatorial faces ( range of  values ) with ltbh 
 is smaller than with lah , rendering torsional strain less influential 
 on facial selectivity of these chair ts . only a small energy 
 difference is calculated between the transition 
 states for reaction at the two faces of the twist boat with ltbh ( geq - ax = + 0.6 kcal 
 mol ) . addition to either face of the twist boat 
 is prohibitively high in energy relative to the favored addition to 
 the equatorial face of 1ch ( gtwist - chair 6 
 kcal mol for pro - equatorial addition , figure 11d vs 11b ) . lowest energy transition 
 structures for the addition of ltbh to 
 ( a ) the axial face of chair 1ch , ( b ) the equatorial face of chair 1ch , ( c ) the pro - axial face of twist - boat 1 tb , and ( d ) the pro - equatorial face of twist - boat 
 1 tb . optimized structures were calculated 
 at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) level . activation 
 gibbs free energies ( g ) 
 are referenced to the lowest energy prereaction coordination complex 
 and are given in kcal mol ; distances are given 
 in angstroms and angles in degrees . due to exceedingly large steric repulsions between ltbh and 
 the 
 substrate 2,6-substituents , only equatorial - face addition transition 
 structures could be located for the reaction of piperidone 6 ( figure 12 ) and tropinone 7 ( figure 13 ) with this bulky hydride 
 reagent . the energetic degeneracy predicted 
 for the pro - equatorial addition of lah to both the chair and twist - boat 
 conformations of 6 is not conserved with ltbh , for which 
 the twist - boat transition state is disfavored by 3 kcal mol due to a simultaneous reduction in the torsional 
 strain of 6ch - ts - ltbheq (  = 10 ) and increase in torsional 
 strain of 6tb - ts - ltbheq (  = 33 ) . taken together with 
 the results using lah , these studies show that twist - boat conformations 
 can be relevant for both reactivity and selectivity of cis-2,6-disubstituted 
 piperidones for reduction by small hydride reagents 
 but not with ltbh or , presumably , other bulky nucleophiles . lowest energy 
 transition structures for the addition of ltbh to 
 ( a ) the equatorial face of chair 6ch and ( b ) the pro - equatorial face of twist - boat 6 tb . optimized structures were calculated 
 at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) level . activation 
 gibbs free energies ( g ) 
 are referenced to the lowest energy prereaction coordination complex 
 and are given in kcal mol ; distances are given 
 in angstroms and angles in degrees . lowest energy transition structure for the addition of ltbh to 
 the equatorial face of 7ch . optimized 
 structures were calculated at the smd(thf)/b3lyp/6 - 311+g(2d , p)//b3lyp/6 - 31g(d , p ) 
 level . activation gibbs free energy ( g ) is referenced to the lowest energy prereaction coordination 
 complex and is given in kcal mol ; distances are 
 given in angstroms and angles in degrees . the computational results described in 
 this paper are consistent 
 with the felkin  anh model for predicting the facial selectivity 
 of the reaction of tert - butylcyclohexanone 1 and tropinone 7 with a small hydride reagent : 
 lah preferentially adds to the axial face of both 1 and 7 . an exception to this common trend is found in piperidone 6 , for which a twist - boat conformation is calculated to be 
 relevant to the transition state for addition of a small hydride reagent , 
 and pro - equatorial attack by lah is overall preferred . our results 
 indicate that pro - equatorial attack on a twist - boat ( i.e. , attack 
 at the face that would lead to an equatorial nucleophile in the chair 
 conformation of the product ) with a small nucleophile does not necessarily 
 incur more torsional strain than pro - axial attack . additionally , our 
 calculations show that the torsional strain developed during both 
 attack on the axial and equatorial faces of a chair depends also on 
 the nature of the incoming nucleophile . with a bulky hydride , the 
 degree of torsional strain experienced in the transition states for 
 attack at the equatorial and axial faces are similar , and selectivity 
 is dominated by steric effects . all synthetic reactions described 
 in this paper were performed using oven - dried glassware under an argon 
 or dry nitrogen atmosphere . thf , toluene , and diethyl ether were dried 
 by distillation from sodium / benzophenone . other reagents and solvents 
 were stored over molecular sieves under argon and used directly . radial 
 plc was performed using a model 7924 t chromatotron using thin layers 
 of silica gel the mass analyzer type used for 
 the hrms measurements was tof with electrospray as the ionization 
 method . chemical shifts are in  units ( ppm ) with tms ( 0.0 ppm ) used 
 as an internal standard for h nmr spectra and the cdcl3 absorption at 77.23 ppm for c nmr . to cubrsme2 ( 177 mg , 0.86 
 mmol ) in dms ( 4 ml ) at 78 c the reaction mixture was allowed to 
 warm to 30 c over 30 min and then cooled to 78 
 c . a solution of n-(phenoxycarbonyl)-2-methyl-2,3-dihydropyridone 
 ( 100 mg , 0.43 mmol ) in 0.5 ml of dms was added via syringe . the mixture 
 was stirred at 78 c for 3 h and then at 42 c 
 for 30 min . the cooling bath was removed and saturated aqueous nh4cl ( 0.5 ml ) was added followed by anhydrous na2so4 ( 8 g ) . after stirring for 2 h , purification 
 by radial plc ( sio2 , 1020% etoac / hexanes ) afforded 
 91 mg ( 85% ) of 3 as a clear oil ( product contains 7% 
 of the trans isomer ) . ir ( neat ) 2974 , 1710 , 1336 , 1204 cm ; h nmr ( 300 mhz , cdcl3 )  7.36 ( m , 
 2h ) , 7.2 ( m , 1h ) , 7.11 ( d , 2h , j = 8.4 hz ) , 4.90 
 ( m , 2h ) , 2.79 ( dd , 2h , j = 7.6 , 15.1 hz ) , 2.38 ( dd 
 2h , j = 2.1 , 15.0 hz ) , 1.38 ( d , 6h , j = 7.0 hz ) ; c nmr ( 75 mhz , cdcl3 )  
 207.9 , 154.0 , 151.4 , 129.6 , 125.7 , 121.9 , 49.5 , 45.5 , 23.2 ; hrms calcd 
 for c14h17no3 [ ( m + h ) ] 248.1281 , found 248.1275 . to a solution of piperidone 3 in thf ( 2 ml ) at 78 c was added k - selectride ( 1 m / thf , 
 0.33 ml , 0.33 mmol ) , and the mixture was stirred at 78 c 
 for 1 h. anhydrous acetone ( 0.3 ml ) was added , and stirring was continued 
 for 5 min . the cooling bath was removed , saturated nh4cl 
 ( 0.5 ml ) added , and the mixture stirred at rt for 1 h. etoac ( 15 ml ) 
 and dry na2so4 ( 3 g ) were added . after 
 stirring for 1 h , filtration and concentration gave the crude product . purification by radial plc ( sio2 , etoac / hexanes ) afforded 
 63 mg ( 84% ) of alcohol 3a as a white solid , mp 127128 
 c ( 10% etoac / hexanes ) . ir ( neat ) 3466 , 2967 , 1710 , 1688 ; h nmr ( 300 mhz , cdcl3 )  7.33 ( t , 2h , j = 8.4 hz ) , 7.19 ( t , 1h , j = 8.4 hz ) , 
 7.1 ( d , 2h , j = 8.4 hz ) , 4.46 ( m , 2h ) , 4.0 ( m , 1h ) , 
 2.28 ( s , 1h ) , 2.06 ( m , 2h ) , 1.62 ( m , 2h ) , 1.46 ( d , 6h , j = 6.6 hz ) ; c nmr ( 75 mhz , cdcl3 )  
 154.3 , 151.6 , 129.5 , 125.4 , 122.0 , 65.1 , 46.8 , 37.1 , 24.0 ; hrms calcd 
 for c14h19no3 [ ( m + h ) ] 250.1438 , found 250.1433 . to a 50/50 mixture of piperidones 3 ( 0.12 mmol ) and 5 ( 0.12 mmol ) in thf ( 3 ml ) 
 at 74 c was added k - selectide ( 1 m / thf , 0.12 ml , 0.12 
 mmol ) dropwise . anhydrous acetone ( 0.2 ml ) was added , and stirring was continued 
 for 5 min . the cooling bath was removed , saturated aqueous nh4cl ( 0.5 ml ) added , and the mixture stirred for 1 h at room 
 temperature . etoac ( 10 ml ) and anhydrous na2so4 ( 4 g ) were added . after stirring for 1 h analysis by hplc and nmr showed 
 that the ketones 3 and 5 were reduced in 
 a ratio of 75:25 ( see supporting information ) . all geometry optimizations were 
 carried out with the b3lyp hybrid functional and 6 - 31g(d , p ) basis set . single - point energy calculations 
 were performed on the optimized geometries using the 6 - 311+g(2d , p ) 
 basis set . the meta - hybrid m06 - 2x functional 
 was also tested for both geometry optimization and single - point energy 
 calculations , using the same basis sets described above . similar results 
 were obtained with both methods , although the b3lyp functional showed 
 a better agreement with experimental results . the theoretical ratio 
 of reaction products was obtained through the gibbs free energy of 
 the different transition states ( g ) using a maxwell  boltzmann distribution at the appropriate 
 temperature . the nature of the stationary points 
 was determined in each case according to the appropriate number of 
 negative eigenvalues of the hessian matrix from the frequency calculations . scaled frequencies were not considered , because significant errors 
 in the calculated thermodynamic properties are not found at this theoretical 
 level . mass - weighted intrinsic reaction coordinate 
 ( irc ) calculations were carried out using the gonzalez and schlegel 
 scheme to ensure that the tss indeed connect the 
 appropriate reactants and products . bulk solvent effects were considered 
 implicitly by performing single - point energy calculations on the gas - phase 
 optimized geometries , through the smd polarizable continuum model 
 of cramer and truhlar as implemented 
 in gaussian 09 . the parameters for tetrahydrofuran were used to calculate 
 solvation free energies ( gsolv ) . cartesian coordinates , electronic energies , entropies , enthalpies , 
 gibbs free energies , and lowest frequencies of the different conformations 
 of all structures are available as supporting 
 information .
the role of twist - boat 
 conformers of cyclohexanones in hydride 
 reductions was explored . 
 the hydride reductions of a cis-2,6-disubstituted n - acylpiperidone , an n - acyltropinone , and tert - butylcyclohexanone by lithium aluminum hydride and 
 by a bulky borohydride reagent were investigated computationally and 
 compared to experiment . 
 our results indicate that in certain cases , 
 factors such as substrate conformation , nucleophile bulkiness , and 
 remote steric features can affect stereoselectivity in ways that are 
 difficult to predict by the general felkin  anh model . in particular , 
 we have calculated that a twist - boat conformation is relevant to the 
 reactivity and facial selectivity of hydride reduction of cis-2,6-disubstituted n - acylpiperidones with a small hydride reagent ( lialh4 ) but not with a bulky hydride ( lithium triisopropylborohydride ) .