deprotonation typically takes place exclusively at the  carbon atom to yield carbanions that can be considered acrolein acyl carbanion equivalents .
the presence of the allene function in the products of nucleophilic addition of carbanions such as 1 and 2 confers reactivity due to the strain inherent in the allene , which is often advantageous for synthetic applications .
our interest in 1 was initially as a reagent for the annulation of ketones to hydroxy 1,4-benzoquinones .
subsequently , we discovered that 1 and 2 were exceptionally useful reagents for the allene ether version of the nazarov cyclization .
[ 2f , 4 ] lithioallene 2 was the first reagent we developed for the chiral auxiliary controlled asymmetric nazarov cyclization .
early on we had observed that the nucleophilicity of 2 was greatly attenuated compared to 1 , and we attributed this to the presence in 2 of multiple ether functions that could effectively chelate lithium ion leading to unreactive aggregated species .
consistent with this hypothesis , we found that the nucleophilicity of 2 and of related species was restored by the addition of up to two equivalents of lithium chloride to the reaction mixture , an observation that is consistent with the known lithium chloride - induced disaggregation of carbanions .
this simple expedient addressed the immediate problem successfully , but it also raised questions regarding the solution phase structure of lithioallenes like 2
. a better understanding of the solution structure of these species would be useful for determining the origins of stereochemical induction in the nazarov cyclization .
all geometry optimizations , frequency calculations , and nmr chemical shift calculations were performed with the gaussian 03 program .
geometry optimizations were performed at the b3lyp/6 - 31+g(d ) level of theory , followed by frequency calculations at the same level .
free energy corrections were calculated at 200 k and 298.15 k from the frequency calculations and added to the electronic energies at each level of theory , in order to obtain approximate free energies of each species .
solvent effects were modeled by placing explicit tetrahydrofuran ( thf ) ligands on the lithium atoms .
generally , two or three ligands per lithium are used for a monomer , one or two for a dimer , and one ligand per lithium for a higher aggregate . in some cases ,
special care is taken to ensure consistent handling of standard states.[9 , 10 ] specifically , a correction term rtln(crt
/ p ) must be added per mole of each species in the reaction under consideration , which represents the change in free energy involved in compressing the system from standard pressure p ( or a concentration of p/rt ) used in gas - phase calculations to the standard concentration of c=1 mol l commonly used for solutions .
this term is numerically equal to + 1.1119 kcal mol at 200 k and + 1.8900 kcal mol at 298.15 k. while it cancels from both sides when the net change in the number of moles due to reaction n=0 , it is a non - negligible correction in cases where n0 .
yet another correction is required for cases where a thf ligand dissociates , as in eq .
since the concentration of pure thf is different from the standard concentration c , it was evaluated from its molar volume at 1 atm and 200 k or 273.15 k using the empirical expression provided by govender et al . , and incorporated into the second term of eq .
this correction to g amounts to 1.0273 and 1.4883 kcal mol per thf at 200 and 298.15 k , respectively .
this approach to modeling solvation effects on organolithium compounds has been used in other studies,[1217 ] and has been found to give results in agreement with available experimental evidence .
isotropic c nmr chemical shifts were calculated at the b3lyp/6 - 31+g(d ) level of theory .
chemical shift calculations were performed on the mp2-optimized geometry for each species and for tetramethylsilane ( tms ) , and the chemical shifts of each carbon atom relative to tms were obtained by subtraction .
we have previously reported that in the absence of lithium chloride , 1-methoxyallenyllithium exists as a dimer 
the optimized thf - solvated structures of two isomeric dimers and the tetramer are shown in figure 1 . in order to examine the tendency of this compound to form mixed aggregates with lithium chloride in the absence of the influence of solvents , the gas - phase free energies of mixed aggregate formation were calculated at the b3lyp/6 - 31+g(d ) and mp2/6 - 31+g(d ) levels of theory .
the optimized geometries of the gas - phase mixed aggregates are shown in figure 2 .
the calculated free energies of mixed dimer and mixed trimer formation are listed in table 1 , and those of mixed tetramer formation are in table 2 .
comparison of the two tables shows that the formation of higher mixed aggregates is most energetically favorable in the gas phase .
this is consistent with previously published studies.[1922 ] the free energies of gas - phase mixed aggregate formation calculated by the b3lyp and mp2 methods are in good agreement , generally within 12 kcal mole of each other .
although the gas - phase calculations are valuable for comparison of different computational methods and for predicting the structures and aggregation states in non - polar solvents , the negligible solubility of lithium chloride in those solvents makes it unlikely that these mixed aggregates will be observed in solution .
we therefore turned our attention to the thf - solvated structures and free energies of mixed aggregate formation .
optimized geometries of thf - solvated 1-methoxyallenyllithium homo - aggregates . reproduced ( adapted ) with permission from ref . .
grey : carbon ; white : hydrogen ; red : oxygen ; violet : lithium .
mp2-optimized gas - phase geometries of 1-methoxyallenyllithium ( aln ) mixed aggregates with lithium chloride .
grey : carbon ; white : hydrogen ; red : oxygen ; violet : lithium ; green : chlorine .
free energies of gas - phase mixed dimer and mixed trimer formation of 1-methoxyallenyllithium with lithium chloride free energies of gas - phase mixed tetramer formation of 1-methoxyallenyllithium with lithium chloride dimeric lithium compounds can be solvated by one or two thf ligands per lithium , while steric constraints generally limit solvation to one thf per lithium in higher aggregates . to determine which solvation state should be used for calculations involving the dimers , the free energies of tetrasolvated dimers of 1-methoxyallenyllithium , lithium chloride , and the mixed dimer were calculated from the disolvated dimers , as shown in eq .
free energies of solvation of 1-methoxyallenyllithium  lithium chloride dimers and a 1:1 mixed dimer with lithium chloride we have previously shown that the b3lyp/6 - 31+g(d ) method predicts the disolvate to be too stable , while the mp2 calculations with the same basis set predict the tetrasolvated form to be too stable , relative to higher level calculations . due to the anion - like character of these organolithium species , the diffuse functions on the heavy atoms are necessary to adequately describe the bonding , but little advantage was gained by using even larger basis sets .
taking an average of the b3lyp and mp2 solvation free energies leads to the conclusion that the tetrasolvated form of each dimer was favored , and the tetrasolvates were used in subsequent calculations .
the free energies of mixed dimer and mixed trimer formation in thf solution were calculated from the solvated homo - dimers of 1-methoxyallenyllithium and lithium chloride , as shown in eq .
the free energies of thf - solvated mixed tetramer formation were also calculated from the 1-methoxyallenyllithium  lithium chloride mixed dimer , according to eq .
free energies of thf - solvated mixed dimer and mixed trimer formation of 1-methoxyallenyllithium with lithium chloride free energies of thf - solvated mixed tetramer formation of 1-methoxyallenyllithium with lithium chloride free energies of thf - solvated mixed tetramer formation from the mixed dimer mp2-optimized geometries of thf - solvated 1-methoxyallenyllithium mixed aggregates with lithium chloride .
grey : carbon ; white : hydrogen ; red : oxygen ; violet : lithium ; green : chlorine .
the data in tables 4 and 5 show a significant disagreement between the b3lyp and mp2-calculated free energies of mixed aggregate formation , with the former method predicting a greater tendency toward mixed aggregate formation .
the two methods differ in the inclusion of electron correlation , as b3lyp ( as well as other dft methods ) includes it implicitly , while mp2 is based on perturbation theory .
the mp2 calculations predict a modest tendency toward formation of the mixed dimer , with little tendency to form the mixed trimers .
the data in table 6 predicts mixed tetramers to form at the b3lyp level , but the mixed dimer was predicted to be favored at the mp2 level .
the calculations predict that mixed aggregates will be formed , but since neither computational method is perfect , it isnt possible to say for certain which mixed aggregates predominate from the free energies of formation alone .
table 7 shows the calculated c nmr chemical shifts for the 1-methoxyallenyllithium dimers , tetramer , and its mixed aggregates with lithium chloride .
the nmr spectrum of 1-methoxyallenyllithium without lithium chloride is shown in figure 4 a , and with 0.3 and 1.0 equivalent lithium chloride in figures 4 b and 4 c , respectively .
as we previously reported , c1 at about 154 ppm and c2 at about 193 ppm give the most information about the aggregation state .
the predominant species seen in figure 4 a is the 1-methoxyallenyllithium dimer 1 , with smaller amounts of the tetramer , resonating downfield of the dimer ( c1 ) and upfield of the dimer ( c2 ) .
the small peak upfield of the c2 dimer 1 peak is consistent with a small amount of the second dimer described previously . calculated c nmr chemical shifts ( b3lyp/6 - 31+g(d ) ) of thf - solvated 1-methoxyallenyllithium and its mixed aggregates with lithium chloride c nmr spectrum of 1-methoxyallenyllithium a ) without lithium chloride at 100 c .
c nmr ( 125.75 mhz , [ d8]thf ) : =194.34 , 154.03 ppm ; b ) with 0.3 equiv lithium chloride at 100 c .
c nmr ( 125.75 mhz , [ d8]thf ) : =194.23 , 153.84 ppm ; c ) with 1.0 equiv lithium chloride at 100 c .
c nmr ( 125.75 mhz , [ d8]thf ) : =194.23 , 153.73 ppm . the calculated chemical shifts of the 1-methoxyallenyllithium  lithium chloride mixed dimer are very close to those of the major homo - dimer from ref .  
the chemical shift of the mixed dimers c2 is calculated to be slightly upfield of that of dimer 1 , and a partially overlapping peak , slightly upfield of the homo - dimer , was observed with 0.3 equivalents of lithium chloride , shown in figure 4 b. the expansion of the region of the c2 peak clearly shows a second species .
the peak corresponding to c1 was broadened from 53.8 hz to 60.1 hz at 1/2 height with 0.3 equivalents lithium chloride , suggesting that the peaks are not fully resolved . with 1.0 equivalent lithium chloride , shown in figure 4
c , the spectrum is consistent with a single major species , and the c1 peak was narrowed to 42.8 hz .
small peaks are visible in both spectra that may arise from small amounts of the 1-methoxyallenyllithium tetramer
. those peaks are also consistent with small amounts of higher mixed aggregates . from the relative peak sizes of c1 and c2 , the relaxation time of c1 decreases with increasing lithium chloride concentration .
this is further evidence of a change in the chemical environment about c1 . from comparison of the observed and calculated chemical shifts , mixed trimers and tetramers
thus , the predictions of the mp2 free energies of mixed aggregate formation appear to be more reliable than b3lyp for this particular system .
the calculated free energies of mixed aggregate formation at the b3lyp/6 - 31+g(d ) and mp2/6 - 31+g(d ) levels of theory predict 1-methoxyallenyllithium to form mixed aggregates with lithium chloride .
the two methods generated different predictions of which mixed aggregates will be formed , with the former favoring mixed trimers and tetramers in thf solution , and the latter favoring mixed dimers .
formation of the sterically unhindered mixed dimers is also consistent with the enhanced reactivity of these compounds in the presence of lithium chloride , as was described in the introduction .
the spectra are also consistent with some residual 1-methoxyallenyllithium tetramer , as well as small amounts of higher mixed aggregates
. although neither computational method is perfect , the mp2-calculated free energies are in better agreement with experiment than the b3lyp energies for this particular system .
the c nmr spectra in [ d8]thf were recorded on a varian unity inova 500 ( varian , palo alto , usa ) at 173 , 193 , 223 , and 243 k at 125.75 mhz with a 3 s delay between pulses . since
no new features were observed at the higher temperatures , only the spectra acquired at 173 k were reported .
preparation of 1-methoxyallenyllithium in [ d8]thf : an oven - dried nmr tube was charged with methoxyallene ( 50 mg , 0.71 mmol ) under nitrogen .
[ d8]thf ( 750 l ) was added by syringe through a septum , and the solution was cooled to 78 c . a 2.46 m solution of n - buli in hexanes ( 0.35 ml , 1.2 equiv ) was added , and the solution was left standing at 78 c for 15 min .
the total concentration of 1-methoxyallenyllithium was 0.65 m. the solution was then frozen in liquid nitrogen , and the nmr tube was flame - sealed .
preparation of 1-methoxyallenyllithium in [ d8]thf with 0.3 equiv of licl : an oven - dried nmr tube was charged with methoxyallene ( 39 mg , 0.56 mmol ) under nitrogen .
licl in [ d8]thf ( 0.38 ml of a solution of 17.2 mg in 0.95 ml ) was added by syringe through a septum , and the solution was cooled to 78 c
. a 2.76 m solution of n - buli in hexanes ( 0.24 ml , 1.2 equiv ) was added , and the solution was left standing at 78 c for 15 min . the total concentration of 1-methoxyallenyllithium was 0.90 m. the solution was then frozen in liquid nitrogen , and the nmr tube was flame - sealed .
preparation of 1-methoxyallenyllithium in [ d8]thf with 1.0 equiv of licl : an oven dried nmr tube was charged with methoxyallene ( 37 mg , 0.53 mmol ) under nitrogen .
licl in [ d8]thf ( 0.59 ml of a solution of 36 mg in 0.95 ml ) was added by syringe through a septum , and the solution was cooled to 78 c . a 2.76 m solution of n - buli in hexanes ( 0.25 ml , 1.3 equiv ) was added , and the solution was left standing at 78 c for 15 min .
the total concentration of 1-methoxyallenyllithium was 0.63 m. the solution was then frozen in liquid nitrogen , and the nmr tube was flame - sealed .
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 a combined computational and 13c nmr study was used to investigate the formation of mixed aggregates of 1-methoxyallenyllithium and lithium chloride in tetrahydrofuran ( thf ) solution . 
 the observed and calculated chemical shifts , as well as the calculated free energies of mixed aggregate formation ( mp2/6 - 31+g(d ) ) , are consistent with the formation of a mixed dimer as the major species in solution . 
 free energies of mixed dimer , trimer , and tetramer formation were calculated by using the b3lyp and mp2 methods and the 6 - 31+g(d ) basis set . 
 the two methods generated different predictions of which mixed aggregates will be formed , with b3lyp/6 - 31+g(d ) favoring mixed trimers and tetramers in thf solution , and mp2/6 - 31+g(d ) favoring mixed dimers . 
 formation of the sterically unhindered mixed dimers is also consistent with the enhanced reactivity of these compounds in the presence of lithium chloride . 
 the spectra are also consistent with some residual 1-methoxyallenyllithium tetramer , as well as small amounts of higher mixed aggregates 
 . although neither computational method is perfect , for this particular system , the calculated free energies derived using the mp2 method are in better agreement with experimental data than those derived using the b3lyp method . 
Introduction
Computational Methods
Results and Discussion
Conclusions
Experimental Section
Supporting Information