Entropies of Organolithium Aggregation Based on Measured

Article pubs.acs.org/Organometallics

Entropies of Organolithium Aggregation Based on Measured Microsolvation Numbers Rudolf Knorr,* Thomas Menke, and Kathrin Ferchland Department Chemie, Ludwig-Maximilians-Universität München, Butenandtstrasse 5−13 (Haus F), 81377 München, Germany S Supporting Information *

ABSTRACT: The recent measurement (J. Am. Chem. Soc. 2008, 130, 14179−14188) of the microsolvation numbers of monodentate, nonchelating ethereal donor ligands coordinating to the monomers and dimers of two sterically shielded C(aryl)−Li compounds permits the determination of well-founded dimerization enthalpies (ΔH0) and entropies (ΔS0) from properly formulated equilibrium constants, which must include the concentrations of the free donor ligands. The monomers are found to dimerize endothermically (ΔH0 > 0) in [D8]toluene solution in the presence of the donor tBuOMe or THF, but only slightly exothermically (ΔH0 = −0.5 kcal per mol of dimer) with the donor Et2O. The dimerization entropies ΔS0 (in cal mol−1 K−1) with the respective equivalents of released donor ligands are 7.2 and 11.0 (with 2 equiv of tBuOMe in the two cases), 6.1 (with 2 Et2O), and 34.1 (with 4 THF). It is shown that the improper omission of microsolvation from the equilibrium constant (a usual practice when the ligand numbers are not known) can lead to “contaminated” aggregation entropies ΔSψ, which may deviate considerably from the “true” entropies ΔS0. A method is provided for estimating the required microsolvation numbers from 13C/Li NMR coupling constants 1JC,Li for less congested organolithium types whose coordinated and free donor ligands cannot be distinguished by NMR integration.

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INTRODUCTION

KMD =

Reversible aggregations of polar organometallic compounds are often accompanied by the endothermic release of monodentate (nonchelating) donor ligands Don (THF, Et2O, etc.) from the metallic center. This increase of the number of independent particles can result in a positive aggregation entropy (ΔS0), which may carry information about the number of donor ligands involved (microsolvation). This entropic bias tends to favor aggregations at higher temperatures, while the endothermicity implies that aggregations will become less favored on cooling, and the practically important consequences1 were often emphasized: Working at lower temperatures will increase the population of the smaller aggregates (which are often the more reactive ones) and may also suppress unwelcome sidereactions. Clearly, the detailed knowledge of the thermodynamics and kinetics of aggregation equilibria can assist quantitative reactivity studies. It can be of interest, therefore, to determine reliable thermodynamic parameters (including ΔS0 values) for the quantification of aggregation equilibria, and we wish to point out the problems that arise, using the simple example of a dimerizing organolithium monomer A1Li1 in eq 1 (where A = carbanion). The concentration [free Don] of the uncoordinated (free) portion of the donor ligand will codetermine the equilibrium (eq 2) unless dM = dD, where dM and dD are the microsolvation numbers per Li center of the monomeric (M) and dimeric (D) species A1Li1 and A2Li2, respectively.2

Kψ =

[A1Li1]2

[free Don](2dM − 2dD) (2)

[D] = KMD[free Don]−(2dM − 2dD) [M]2

(3)

ΔG 0 = ΔH 0 − T ΔS 0 = −RT ln KMD = −RT ln K ψ − RT(2dM − 2dD)ln[free Don] R ln K ψ = − =−

ΔGψ T

=−

ΔHψ T

(4)

+ ΔSψ

ΔH 0 + ΔS 0 − R(2dM − 2dD)ln[free Don] T

(5)

With few exceptions, the degree of such changes (dM − dD in eq 1) of microsolvation was generally unknown, so that the proper inclusion of [free Don] in the equilibrium constants (KMD in eq 2, for example) was not possible. Therefore, and because solvation data from X-ray diffraction analyses of crystalline organolithium compounds are not necessarily valid for equilibria in solution, there was often no other choice than to ignore the mathematical role of [free Don] in eq 2. Common practice4 is to use equilibrium pseudoconstants Kψ that depend on [free Don], as formulated in eq 3 for the example depicted in eqs 1 and 2. Such a use of Kψ in place of KMD would produce erroneous free enthalpies of reaction, ΔGψ = −RT ln Kψ = ΔHψ − TΔSψ (where R = 1.986 cal mol−1 K−1 is 3

2 A1Li1&dM Don ⇄ A 2Li 2&2dD Don + (2dM − 2dD)Don

Received: October 4, 2012 Published: January 9, 2013

(1) © 2013 American Chemical Society

[A 2Li 2]

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equilibria of our system (Scheme 1) in [D8]toluene solution as simple examples with measured microsolvation numbers.

the universal gas constant), in lieu of the proper results (namely, ΔG0) to be expected from eq 4. In particular, the differential immobilization (that is, dM − dD) of portions of Don at the monomer and dimer fractions may bring about a temperature dependence of [free Don] in eqs 2 and 4 in cases of a temperature-dependent D/M concentration ratio even if the total [Don] is held constant. Thus, the omission of [free Don] and its temperature dependence by using Kψ values may result in erroneous pseudoenthalpies ΔHψ and pseudoentropies ΔS ψ in eq 5 (which is derived from eq 4 through rearrangement). In the special case of a large excess of the free donor over the organolithium substrate, [free Don] ≈ total [Don] would be almost5 independent of the temperature; it can then be recognized from eqs 4 and 5 that d ln KMD/dT = ΔH0/ (RT2) ≈ d ln Kψ/dT = ΔHψ/(RT2), so that ΔHψ ≈ ΔH0, whereby eq 5 simplifies to ΔSψ ≈ ΔS0 − R(2dM − 2dD)ln[free Don]. In other words, ΔSψ can be a “contaminated” kind of entropy and may be more negative or more positive than ΔS0, depending on the sign of the contaminating term R ln[free Don]. In the donor solvent THF,6 for example, ΔSψ would then be too negative by an entropy equivalent of ca. 21 cal K−1 per mol of dimer in the case of the release of four THF molecules, as encountered further below with dM = 3 and dD =

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RESULTS AND DISCUSSION Syntheses and properties of the two 2-(α-aryl-α-lithiomethylidene)-1,1,3,3-tetramethylindans 1a and 1b were previously10 described. The 1H and 13C NMR chemical shift values δ are characteristic9 of the monomeric (1aM and 1bM) and dimeric (1aD and 1bD) forms below the M/D coalescence temperatures (mostly around −10 °C), so that simple integration of the pairwise corresponding 1M and 1D signals can provide the integral fractions yM = [1M]/[1] for 1M and yD = 2[1D]/[1] for 1D, where the concentration [1] = [1M] + 2[1D] gives the employed sum of “monomeric” units (“per Li”) as present in 1M and 1D together, because these are the units counted by NMR integrations.12 With yD = 1 − yM and dD = 1, the dimerization constant KMD of eq 2 takes the form of eqs 6a and 6b, where the known total donor concentration [Don] is diminished by the portions coordinated at Li in 1M&dMDon and 1D&2dDDon. KMD = 0.5yD [1](yM [1])−2 × ([Don] − dMyM [1] − dDyD [1])(2dM − 2dD)

Scheme 1

(6a)

= 0.5(1 − yM )[1](yM [1])−2 × {[Don] − dMyM [1] − (1 − yM )[1]}(2dM − 2) yM = (δcoal − δ D)(δM − δ D)−1

(6b) (7)

The integral fractions yM and yD can no longer be obtained by integration when the M/D interconversion rates become rapid on the NMR time scale above ca. −5 °C: As illustrated in Figure 1 for three of the 16 M/D pairs of 13C nuclei in 1a (Scheme 1), the coalesced shift values (δcoal) depend now on the equilibrium composition (yM), so that yM can be determined by eq 7, provided that the chemical shift values δM and δD are known above the coalescence temperatures; Figure 1 shows that the linear extrapolations of δM and δD appear to be sufficiently reliable.13 By these two analytical methods, yM could be measured between the temperature extrema denoted as “low T/high T” in Table 1. The best yM value at a particular temperature was obtained as an average over the primary data from suitable signal pairs that were chosen from the 16 types of 13C and nine types of 1H nuclei. The yM values were then used for computing KMD (eq 6b), whose temperature dependence (eq 4) yielded the thermodynamic parameters ΔH0 and ΔS0 with low statistical errors (Table 1) because of the very broad range of experimental temperatures.13 Notice that these parameters refer to the equilibrium formulation of eq 1 and are therefore defined per dimer (that is, for two “monomeric” units). Back-calculation (eq 4) at any other temperatures from these ΔH0 and ΔS0 data gave KMD values, which predicted yM (eqs 6) and finally (eq 7) theoretical temperature dependencies of δcoal; these are shown as short lines between the extrapolated M and D lines on the high-temperature side of Figure 1 and agree reasonably well with the observed δcoal values. Suitable samples of 1a for equilibrium measurements were prepared in NMR tubes from solutions of the crystalline, unsolvated trimer9 in [D8]toluene at ambient temperature under a cover of dry argon gas. Addition of the donor tBuOMe (only 0.96 equivalent, 0.46 M) generated the disolvated dimer

1. For comparison, the more precise evaluation of RT ln[free THF] for eq 5 in ref 5 would correspond to an entropic equivalent of −20.9 (±0.9) cal mol−1 K−1 for the release of four THF ligands. Understandably, there is a strong demand for improving our knowledge of microsolvation numbers, as witnessed by many quantum-chemical calculations and various attempts7,8 through diffusion-ordered NMR spectroscopy. In our experimental model system9 (1a,b in Scheme 1),10 steric congestion impedes the exchange of coordinated, monodentate, nonchelating ethereal donor ligands to such a degree that the microsolvation numbers d could be measured directly through integration of the NMR signals: The monomers 1aM and 1bM carry two tBuOMe (tert-butyl methyl ether, dM = 2), two Et2O (dM = 2), or three THF ligands (dM = 3), while their dimers 1aD and 1bD are always disolvated (dD = 1).11 On the basis of the measured d values, we discovered9 the more general empirical relationship d = L(1JC,Li n)−1 − a, where the sensitivity factor L is ca. 42 Hz for the 6Li isotope in Scheme 1, 1JC,Li is the scalar one-bond 13C−Li spin−spin coupling constant, n is the number of Li cations bound directly to the inspected carbanionic center, and a is the number of carbanionic centers bound directly to a Li cation, so that n = a = 1 for our monomers 1M in Scheme 1 and n = a = 2 for our dimers 1D. We will now quantify the dimerization 469

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Scheme 2

microsolvation numbers dM = 2 and dD = 1 (entry 3 of Table 1), the analogous Δpt = 1 results in the similar dimerization entropy of ΔS0 = 6.1 cal mol−1 K−1. The much more positive ΔS0 value in entry 4 is a consequence of the established11 microsolvation numbers dM = 3 and dD = 1 for THF: The particle balance Δpt in Table 1 is now three because five particles (Scheme 2b: 1D plus four liberated THF) are formed from two monomers, which results in ΔS0 = 34.1 cal mol−1 K−1 (entry 4), that is, on average 11.4 entropy units per independent particle, in reasonable agreement with the above ΔS0 values for Don = tBuOMe and Et2O. The bimolecular processes in Scheme 2a might formally be envisioned as beginning with the cleavage of two secondcoordinating16 ligands Don from two molecules of 1M&2Don, leaving two hypothetical monosolvated monomers (1M&1Don), which stick to the more strongly bound firstcoordinating16 donor ligands; the latter two fragments would unite to give the dimer 1D&2Don through formation of two new A−Li “bonds”.17 In a simplifying interpretation of the ΔH0 value, the two new A−Li bonds in the dimer appear to be weaker by ΔH0 = 3.5 kcal mol−1 than the two bonds connecting two Li with two second-coordinating16 Don in 1M&2Don.18 The inferior donor quality of Et2O is illustrated by the very weakly exothermic dimerization (ΔH0 = −0.5 kcal mol−1), which results from KMD values (Table S214) that were found to diminish only slightly with increasing temperatures. Loosely speaking, the two bonds connecting two Li with two secondcoordinating16 Et2O donors (Scheme 2a) in 1aM&2Et2O appear weaker by −ΔH0 than the two new A−Li bonds18 in 1aD&2Et2O. The low solubility of the p-SiMe3 analogue 1bD&2Et2O in [D8]toluene prevented an analysis of a corresponding equilibrium. A monomer 1M&3THF must lose the second- and the thirdcoordinating16 of its three THF ligands (Scheme 2b) on dimerization: Four of these Li−oxygen coordinative bonds

Figure 1. Three examples of the temperature dependence of chemical shifts δM, δD, and (coalesced) δcoal of 1aM and 1aD coordinating with the donor tBuOMe in [D8]toluene. Concentrations: filled symbols, [1] = 0.13−0.28 M, [tBuOMe] = 0.80 M; open symbols, [1] = 0.28 M, [tBuOMe] = 1.41 M; “I”, [1] = 0.45 M, [tBuOMe] = 0.70 M; “X”, [1] ≤ 0.48 M, [tBuOMe] = 0.46 M.

1aD&2tBuOMe quantitatively,13 as expected from the measured9 microsolvation numbers dM = 2 and dD = 1; the monomer 1aM&2tBuOMe grew in with additional amounts of tBuOMe. The fast dimerization reactions of both 1aM and 1bM are endothermic, with ΔH0 = +3.5 kcal mol−1 in entries 1 and 2 of Table 1, which implies that the equilibrium constants KMD, listed in Tables S1 (1a)14 and S4 (1b),14 grow with increasing temperatures. This energetic preference of the monomers 1a,bM&2Don is counterbalanced by the dimerization entropy: The positive ΔS0 values (entries 1 and 2), which favor the dimers upon heating, result partially through the formation (Scheme 2a) of three product particles (namely, 1D plus 2dM − 2dD = 2 released Don ligands) from two monomeric particles, which contributes the entropy increments of 11.0 (entry 1) and 7.2 (entry 2) cal mol−1 K−1 on average for a balance of one independent particle (Δpt = 1 in Table 1).15 For Et2O as the donor ligand with the same measured9

Table 1. Microsolvation Numbers dM and dD, Thermodynamic Parametersa ΔH0 (kcal mol−1) and ΔS0 (cal mol−1 K−1), and Auxiliary Data for the Dimerization of Monomers 1aM and 1bM in [D8]Toluene entry

1

p-R

Don

2dMb

2dDb

1 2 3 4

a b a a

H SiMe3 H H

tBuOMe tBuOMe Et2O THF

4 4 4 6

2 2 2 2

ΔH0 3.5 3.4 −0.5 8.8

(±0.4) (±0.2) (±0.2) (±0.6)

ΔS0 11.0 7.2 6.1 34.1

(±1.6) (±0.9) (±0.8) (±2.2)

low T/high Tc

ΔDond

Δpte

−92/+70 −96/−20 −85/+25 −94/+75

2 2 2 4

1 1 1 3

a

Defined per dimer (or per two monomers). bMeasured microsolvation numbers of 1a and 1b10 from ref 9. cLow and high temperature limits (°C) of the measurements. dNumber of free donor molecules released on dimerization. eBalance of independent particles (starting particles subtracted from products). 470

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together are stronger by ΔH0 = 8.8 kcal mol−1 than the two new A−Li bonds18 in 1D&2THF. Subtraction of the thermodynamic data and the microsolvation interactions14 for the ligand tBuOMe in entry 1 from those for THF in entry 4 can provide an assessment of the thermodynamic role of the third-coordinating16 THF ligand in 1M&3THF: With the proviso of some positive or negative (perhaps partially canceling) correction terms,14 the entropic effect should be roughly (34 − 11)/2 = +11 cal mol−1 K−1, and the enthalpic effect roughly (8.8 − 3.5)/2 = +2.7 kcal mol−1. Similar magnitudes of ca. 10 cal mol−1 K−1 are known19,20 for the entropy changes of melting crystals of moderately sized molecules (relative mass 100−300), which suggests that the mobility and flexibility of donor ligands released from Li+ may on the whole resemble those properties of the particles in a liquefying solid. In cyclopentane as the solvent in place of [D8]toluene, the dimerization of 1aM&3THF was found to have an equilibrium constant of KMD = 4.1 (±2.1) mol3 L−3 at 25 °C, which resembles that in [D8]toluene (Table S3); however, analyses at lower temperatures were not possible because of the lower solubility. The interconversion rates of our 1M/1D models are slow on our NMR time scales below the coalescence temperatures TC of roughly −5 °C for 1a with tBuOMe (Figure 1), +5 °C for 1a with Et2O, −40 °C for 1a with THF, and −20 °C for 1b with tBuOMe. These data correspond to crudely estimated free activation enthalpies ΔG‡(2 M → D) in the range of 11 to 14 kcal mol−1. Inspection of Scheme 1 leads one to expect that the deaggregating rupture of two of the four A−Li “bonds” in 1D (Schemes 2a,b) implies loss of magnetic coherence between the separating nuclei, so that the 1JC,Li NMR splitting should vanish with rates similar to those of the M/D interconversion (or faster, that is, at lower TC, if more efficient mechanisms of Li exchange operate). Our experimental observations14 are consistent with these expectations.

scarce and the usually employed solvent mixtures of Me2O, Et2O, and THF with lower freezing points would be unsuited for simple analyses of donor coordination. (Me2O alone as a solvent appears to be suitable4,26 below −141 °C.)27 In this situation, a habit of ignoring microsolvation and using pseudoconstants Kψ (easily recognized if their units are reported) to quantify aggregation equilibria can furnish erroneous thermodynamic parameters ΔHψ and ΔSψ, of which especially the “contaminated” entropy ΔSψ may differ considerably from the “true” ΔS0 value.15 Nevertheless, Kψ values encode product/source ratios that may be utilized under closely equal conditions (such as the same [free Don] in eq 3), while ΔHψ can provide the temperature dependence of a series of such Kψ data under those conditions. However, the respective ΔSψ values are contaminated by the temperatureindependent part of R ln Kψ (eq 5) and hence may be used only in this sense rather than for a direct interpretation of entropy values, which is reserved for ΔS0. Corresponding considerations apply to organometallic ion-pair equilibria or to the reversible recombinations of SN1 ion pairs to their covalent isomers,28 although the deviations are probably less spectacular. The novel9 alternative possibility of estimating microsolvation numbers d from 13 C/6Li (better than from 13 C/7Li)29 NMR spin−spin coupling constants 1JC,Li via d = L(1JC,Li n)−1 − a (as explained in the Introduction) provides a tool for determining d values indirectly along the following lines. The coordination with n 6Li nuclei can be read at sufficiently low temperatures from the multiplicity and intensity of the 13C NMR splitting pattern of the carbanionic center, namely, a 1:1:1 triplet for n = 1 or a 1:2:3:2:1 quintet for n = 2, and so on. The magnitude of 1JC,Li serves to identify the aggregational and “fluxional” states9 of the equilibrium components; at this stage, it is normally easy to deduce a correct a value. The requisite sensitivity parameter L may be chosen from a suitable (structurally related) example30 in the published collection.31 As confirmed in that collection,32 microsolvation numbers for monomeric tBuCH2Li (dM = 3) and its dimer (dD = 2) in the solvent THF had been guessed33 correctly; the reported33 dimerization entropy ΔS0 = +11.4 cal mol−1 K−1 per dimer contains contributions of the release of two-third-coordinating THF ligands from two monomers and of dimerization of the two formally remaining fragments.

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CONCLUSIONS The availability and application of reliable microsolvation numbers for monodentate ethereal donor ligands, as exemplified here with 1a and 1b, can raise the quality of thermodynamic analyses of C−Li aggregation to a level comparable with that of N−Li compounds with properly formulated21−23 dimerization equilibria. We have attained reasonably accurate thermodynamic parameters through extension of the analytical scope (column “low T/high T” in Table 1) from direct integration of the separate monomeric and dimeric components to far above the NMR coalescence temperatures. Our dimerization entropy of 1a with THF in [D8]toluene (ΔS0 = 34.1 cal mol−1 K−1 in entry 4 of Table 1) is practically equal to ΔS0 = 33.8 cal mol−1 K−1 for the dimerization of monomeric 2-(lithiomethylidene)-1,1,3,3-tetramethylindan24,25 (that is, 1a without the α-phenyl substituent) in THF as the solvent. Approximately 11 cal mol−1 K−1 of the total entropy change might be attributed to the release of the third-coordinating16 THF ligand. We have used here the simple example of an organolithium dimerization to draw attention to the general importance of knowing microsolvation numbers for the determination and interpretation of entropies of aggregation for mechanistic purposes. At present, however, microsolvation by monodentate (nonchelating) ethereal donor ligands cannot yet be determined directly for most C−Li species because suitable liquid media for NMR measurements at far below −110 °C are

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EXPERIMENTAL SECTION

Equipment and Data Collection. Reference 9 provides all details of the preparation of 1a and 1b,10 the NMR equipment (1H NMR at 400 MHz, 13C NMR at 100.6 MHz), and the spectroscopic techniques used here. Temperatures were determined before and after measurements of the sample tubes, using calibrated NMR tubes (5 mm) filled with methanol or ethylene glycol which have temperature-dependent proton NMR shift differences. To circumvent 13C NMR relaxation problems, dimerization equilibria were analyzed through measurements of separate integral ratios of pairwise corresponding 13CH signals for M and D on one hand and of pairwise corresponding signals of nonprotonated 13C nuclei on the other hand. When these ratios were similar to those determined from 1H NMR signals, the reliable values were averaged and then used to calculate the yM values and to estimate their errors (Tables S5−S12). These errors propagate through KMD (eq 2 and Tables S1−S4) into ΔH0 and ΔS0 (eq 4 and Table 1). Our thermodynamic results are based on the usual standard state concentrations (1 M). Natural logarithms (ln) are understood to be calculated with the dimensionless magnitudes of the employed quantities. 471

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(15) As a further example of the consequences of omitting microsolvation by setting dM = dD in eq 6a, the experimental yM (and yD) values (Table S4)14 for 1bM (and 1bD), as obtained with [1b] = 0.056 M and [tBuOMe] = 0.17 M in [D8]toluene, would erroneously furnish ΔHψ = 2.8 (±0.1) kcal mol−1 and ΔSψ = 15.2 (±0.6) cal mol−1 K−1 per dimer, to be compared with the correct ΔH0 = 3.4 and ΔS0 = 7.2 in entry 2 of Table 1. (Due to [tBuOMe] < 1, ln[free tBuOMe] in eq 5 is negative here, so that ΔSψ is much too positive.) (16) An impression of successively decreasing Li−ligand bond energies may be gained from calculations of the sequential microsolvation steps at the (hypothetical) monomeric methyllithium, as reported by: Abbotto, A.; Streitwieser, A.; Schleyer, P. von R. J. Am. Chem. Soc. 1997, 119, 11255−11268, last paragraph on p 11257 therein. (17) The strong electric C−Li dipole moment of a monomer will be practically cancelled in the corresponding dimer (see Scheme 1 or 2); this was considered to be the major (thermodynamic) driving force promoting aggregation in a weakly polar ethereal solvent, as remarked by: Reich, H. J.; Goldenberg, W. S.; Gudmundsson, B. Ö .; Sanders, A. W.; Kulicke, K. J.; Simon, K.; Guzei, I. A. J. Am. Chem. Soc. 2001, 123, 8067−8079, on p 8077. (18) Including adjustments concerning the changing energetic quality of two Li−Don bonds, repulsive interactions, changing molecular electric dipole moments,17 and electrostriction of the solvent. Notice that the A−Li “bonds” drawn in the dimers are mainly electrostatic interactions rather than two-electron bonds. (19) Page, M. I.; Jencks, W. P. Proc. Natl. Acad. Sci. U. S. A. 1971, 68, 1678−1683. (20) Searle, M. S.; Williams, D. H. J. Am. Chem. Soc. 1992, 114, 10690−10697. (21) Lucht, B. L.; Collum, D. B. J. Am. Chem. Soc. 1995, 117, 9863− 9874, Table 3 therein. (22) Hilmersson, G.; Davidsson, Ö . J. Org. Chem. 1995, 60, 7660− 7669, on p 7665. (23) Lucht, B. L.; Collum, D. B. Acc. Chem. Res. 1999, 32, 1035− 1042. (24) This is compound S3 in Table S1 of the Supporting Information of ref 9; it has also dM = 3 and dD = 1 according to entries 63 and 64 therein. (25) To compare the values per mol of dimer, we have doubled the ΔS0 value found by: Knorr, R.; Freudenreich, J.; Polborn, K.; Nöth, H.; Linti, G. Tetrahedron 1994, 50, 5845−5860, on p 5852. (26) Goldstein, M. J.; Wenzel, T. T. Helv. Chim. Acta 1984, 67, 2029−2036. (27) 15N-Labeled nitrogen donor ligands are appropriate for determining microsolvation numbers through the 6Li NMR multiplicity pattern of 1J(15N,6Li) coupling. Because of their high ligand exchange rates, however, such monodentate nitrogen ligands are apparently unsuited23 for an analysis of the role of free donors in aggregation equilibria. For an example and further references, see: Waldmüller, D.; Kotsatos, B. J.; Nichols, M. A.; Williard, P. G. J. Am. Chem. Soc. 1997, 119, 5479−5480. (28) (a) Feigel, M.; Kessler, H. Chem. Ber. 1978, 111, 1659−1669. (b) Kessler, H.; Feigel, M. Acc. Chem. Res. 1982, 15, 2−8. (29) Fraenkel, G.; Fraenkel, A. M.; Geckle, M. J.; Schloss, F. J. Am. Chem. Soc. 1979, 101, 4745−4747. (30) Listed together with the pertinent citations in Tables 2, S1, and S2 of ref 9. (31) A further alternative for identifying the states of aggregation (but not the “fluxional” state9 and probably not the d value) of aryllithium species would make deliberate use of the 13C-ipso chemical shifts of phenyllithium reported by: Reich, H. J.; Green, D. P.; Medina, M. A.; Goldenberg, W. S.; Gudmundsson, B. Ö .; Dykstra, R. R.; Phillips, N. H. J. Am. Chem. Soc. 1998, 120, 7201−7210, Figure 13 therein. (32) Entries 38 and 43 in Table S1 of ref 9. (33) Fraenkel, G.; Chow, A.; Winchester, W. R. J. Am. Chem. Soc. 1990, 112, 6190−6198.

ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S4 of temperature-dependent equilibrium constants and appertaining concentrations; delineation of the ΔH0 and ΔS0 contributions of the third-coordinating THF ligand; Tables S5−S12 of temperature-dependent integral fractions yM and chemical shifts δ. This material is available free of charge via the Internet at http://pubs.acs.org. R Related Articles *

Sterically Congested Molecules, 26. For Part 25, see: Knorr, R.; Böhrer, G.; Schubert, B.; Böhrer, P. Chem.−Eur. J. 2012, 18, 7506−7515.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is dedicated to Professor Hendrik Zipse on the occasion of his 50th birthday and in recognition of his successful efforts to introduce the first-named author to the techniques of ab initio computation. We thank Professor Herbert Mayr for his support, the Deutsche Forschungsgemeinschaft for the initial resources, and a reviewer for his very thoughtful comments.

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REFERENCES

(1) As explained for the dimerization of dimeric n-butyllithium by: Seebach, D.; Hässig, R.; Gabriel, J. Helv. Chim. Acta 1983, 66, 308− 337, on p 320 therein. (2) “&” in eq 1 symbolizes coordinative bonds between the oxygen atom of the donor and the lithium cation. (3) For a short list of pioneering discoveries of discrete NMR signals for lithium-coordinated donor ligands, see: Reich, H. J.; Kulicke, K. J. J. Am. Chem. Soc. 1996, 118, 273−274. (4) (a) Heinzer, J.; Oth, J. F. M.; Seebach, D. Helv. Chim. Acta 1985, 68, 1848−1862, Tables 4−6 and Appendix E therein. (b) Jackman, L. M.; Smith, B. D. J. Am. Chem. Soc. 1988, 110, 3829−3835, footnote 21 therein. (5) Pratt, L. M.; Truhlar, D. G.; Cramer, C. J.; Kass, S. R.; Thompson, J. D.; Xidos, J. D. J. Org. Chem. 2007, 72, 2962−2966, on p 2964. (6) The concentration of THF as the solvent is ca. 14 M at ca. −90 °C according to: (a) Metz, D. J.; Glines, A. J. Phys. Chem. 1967, 71, 1158. (b) Bauer, W.; Seebach, D. Helv. Chim. Acta 1984, 67, 1972− 1988, footnote 10 on p 1978 therein. (7) García-Á lvarez, P.; Mulvey, R. E.; Parkinson, J. A. Angew. Chem. 2011, 123, 9842−9845; Angew. Chem., Int. Ed. 2011, 50, 9668−9671. (8) Li, D.; Keresztes, I.; Hopson, R.; Williard, P. G. Acc. Chem. Res. 2009, 42, 270−280. (9) Knorr, R.; Menke, T.; Ferchland, K.; Mehlstäubl, J.; Stephenson, D. S. J. Am. Chem. Soc. 2008, 130, 14179−14188. (10) These compounds correspond to 8 and 12 in ref 9. (11) See Table 1 in ref 9. (12) A partial 13C NMR spectrum, recorded at −82 °C, was displayed in Figure 7 of ref 9. (13) Given the presence of at least one equivalent of the donor ligands, the chemical shift data δ of 1aM and 1aD provided no evidence for perceptible amounts of other species according to pp S27−S33 in the Supporting Information for ref 9. Therefore, the microsolvation numbers did not change perceptibly over the investigated temperature ranges. (14) See the Supporting Information. 472

dx.doi.org/10.1021/om3009348 | Organometallics 2013, 32, 468−472