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Kinetic and Equilibrium Lithium Acidities of Arenes: Theory and Experiment† Andrew Streitwieser,* Kamesh Shah, Julius R. Reyes, Xingyue Zhang, Nicole R. Davis, and Eric C. Wu Department of Chemistry, UniVersity of California-Berkeley, Berkeley, California 94720-1460 ReceiVed: February 27, 2010; ReVised Manuscript ReceiVed: May 03, 2010
Kinetic acidities of arenes, ArH, measured some time ago by hydrogen isotope exchange kinetics with lithium cyclohexylamide (LiCHA) in cyclohexylamine (CHA) show a wide range of reactivities that involve several electronic mechanisms. These experimental reactivities give an excellent Brønsted correlation with equilibrium lithium ion pair acidities (pK(Li)) derived as shown recently from computations of ArLi · 2E (E ) dimethyl ether). The various electronic mechanisms are well modeled by ab initio HF calculations with modest basis sets. Additional calculations using NH3 as a model for CHA further characterize the TS of the exchange reactions. The slopes of Brønsted correlations of ion pair systems can vary depending on the nature of the ion pairs. Lithium acidity is defined by the lithium-hydrogen exchange equilibrium in eq 1. K
RH + R′-Li+)R-Li+ + R′H
(1)
Over the years we have measured a number of such equilibria in THF with the results expressed as pK(Li) relative to fluorene taken as a standard and assigned its pK in DMSO1 (22.90 per hydrogen). We showed recently that a number of these pK(Li) for contact ion pair lithium salts are well modeled by Hartree-Fock calculations with two or three ethers coordinated to lithium.2 Because many of the systems used are rather large we used dimethyl ether as our computational model for THF. In this paper we inquire whether comparable models are effective for corresponding kinetic acidities. Several decades ago we measured the hydrogen isotope exchange reactions of a number of deuteriated and tritiated arenes with lithium cyclohexylamide (LiCHA) in cyclohexylamine (CHA), eq 2.3-6 CHA
ArD(T) + LiNHC6H11 98 (ArLi) f ArH
(2)
The compounds measured and their relative exchange rates are summarized in Table 1 and are shown for convenience in Figure 1. At least three different interaction mechanisms are involved with these reactivities as illustrated in Figure 2. For normal arenes the aryl anion lone pair is closer to the nucleus of a distant π-center than to the electron density of its pz-orbital, giving a net electrostatic attraction (Figure 2a).3 Alternatively, Figure 2a can be regarded as a simple diagram of the electrostatic interactive of the aryl lone pair with a distant quadrupole. Thus, the reactivities of larger polycyclic arenes are greater because they have more such π-centers.7 The R-type positions of the two biphenylenes shown are much more reactive than normal arenes. This higher reactivity was rationalized previously6 on †
Part of the “Klaus Ruedenberg Festschrift”. * To whom correspondence should be addressed. E-mail: astreit@ berkeley.edu.
the basis that small-membered rings require more p-character in the ring orbitals, leaving more s-character for the exocyclic orbital (Figure 2b). This orbital is now effectively more electronegative and enhances the acidity of an attached C-H group. The third interaction, Figure 2c, is the normal electrostatic effect of a substituent dipole. We now inquire how well these disparate electronic effects are modeled by ab initio calculations at a modest theory level. For each position shown in Figure 1 we computed the energy and zero point energy (ZPE) for structures optimized at the HF 6-31+g(d) level of ArH and ArLi · 2E (E ) dimethyl ether) to obtain ∆(E + ZPE) for eq 3.8 Using the correlation established previously, eq 4,2 these energies were converted to the corresponding pK(Li) numbers. The ∆(E + ZPE) energies and the derived pK(Li) are included in Table 1. All of the optimized structures and energies are summarized in Table S1 (Supporting Information). All of these systems are minima on the potential energy surface (PES); all frequencies are real. All calculations were done with Gaussian039 or Gaussian09.10
ArH + PhLi · 2E ) ArLi · 2E + PhH
(3)
pK(Li) ) 37.68 ( 0.49 + (0.538 ( 0.014) (∆E + ZPE) (4) A plot of the log relative rate versus the computed pK(Li) is shown in Figure 3. This plot is a type of Brønsted11 correlation, but it differs from the usual such plot because it compares an experimental kinetic acidity with a theoretical equilibrium acidity.12 The correlation is quite good. The most serious deviation is that of the ortho-position of biphenyl for which the experimental steric hindrance with the adjacent phenyl group is clearly greater than that of the model. The ortho-biphenyl position is anomalous in all of the comparisons to be discussed and will not be considered further. Some of the scatter found with the other points might well come from experimental errors. The experimental reactivities of the fluorobenzenes and trifluoromethylbenzene are at a lower temperature (25 °C) than the other results (50 °C). Some of the experiments are exchange rates with tritium, and some of the kD/kT ratios measured do
10.1021/jp101791e 2010 American Chemical Society Published on Web 05/12/2010
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TABLE 1: Relative Rates of Exchange Reactions of ArD or ArT with LiCHA in CHA at 50 °C (Except Where Indicated) Together with ∆(E + ZPE) for Equation 3 at HF 6-31+g(d) and the Corresponding pK(THF, Li) Derived from Equation 4a Aryl-H
Rel Rate
∆(E + ZPE) kcal mol-1, eq 3
pK(THF, Li), eq 4
∆(E + ZPE) ArLi · 3NH3, kcal mol-1
∆E‡ TS, kcal mol-1
phenyl 1-naphthyl 2-naphthyl 9-phenanthryl 1-anthracenyl 9-anthracenyl 1-pyrenyl 2-pyrenyl 4-pyrenyl 1-biphenylenyl 2-biphenylenyl 5-benzo[b]biphenylenyl 2-biphenylyl 3-biphenylyl 4-biphenylyl 2-fluorophenyl 3-fluorophenyl 4-fluorophenyl 3-(trifluoromethyl)phenyl
1 6.5 4.1 17.9 10.9 45 24.9 20.9 31.3 490 6.2 2000 1.2 3.7 2.3 630 000 107 11 580
0 -2.353 -1.401 -3.183 -2.108 -4.372 -3.289 -2.211 -3.716 -5.631 -1.376 -7.228 -3.072 -1.069 -0.969 -10.629 -3.678 -1.990 -5.248
37.68 36.44 36.94 36.00 35.99 35.37 35.94 36.51 35.72 34.71 36.95 33.86 32.07 37.12 37.17 32.07 35.74 36.63 34.91
0 -2.295 -1.599 -2.961 -3.152 -2.887 -2.821 -2.332 -3.478 -6.298 -1.463 -7.333 -2.542 -1.119 -1.026 -11.747 -3.917 -1.869 -5.566
0 -2.065 -1.055 -2.866 -2.640 -4.199 -2.664 -1.513 -3.256 -4.662 -0.966 -6.318 1.140 -0.260 -0.528 -7.774 -2.886 -1.305 -4.118
a
The fifth column gives the relative energies for forming the products of eq 5, and the sixth column gives the relative TS energies at HF 6-31+G(d,p) in kcal mol-1.
ization or solvent hydrogen bonds so that the substituent is closer to the center of charge in the TS than in the reactant.21-23 This situation does not apply in the present case, and we would expect the slope to lie in the normal range of 0-1. In the traditional view, the slope close to unity in Figure 3 would imply that reaction is almost complete at the TS. In this example, however, ion pairs in two different solvents are involved and we will show that this situation can lead to another limitation in the interpretation of the Brønsted slope. In a further extension of the theory we considered another model in which ammonia is used as a computational model for
Figure 1. Relative exchange rates for reactions of ArD or ArT with LiCHA in CHA (eq 2).
Figure 2. Interaction mechanisms for aryl anions: (a) net electrostatic attraction to distant π-center; (b) exocyclic orbital in a small ring has extra s-character; (c) electrostatic interaction with substituent dipole.
vary significantly.3,4 Other errors are involved in extrapolating measured relative rates to benzene as the standard. One unusual feature of Figure 3 is the slope of close to unity. The magnitude of a Brønsted slope has long been considered to be a measure of the position of the transition state along the reaction coordinate;13-15 this result also derives from Marcuslike treatments of the reaction in terms of intersecting parabolas or similar figures.16-19 There are also well-known cases of Brønsted slopes outside the “normal” range of 0-1.20 These cases generally involve more complex functions with delocal-
Figure 3. Brønsted plot of experimental relative exchange rates in Figure 1 with theoretical pK(Li). Blue circles are normal polycyclic aryl positions; red squares are the biphenylene positions adjacent to the four-membered ring; green squares are the fluorine-containing benzenes. The blue circle farthest from the line is 2-biphenyl and is not included in the correlation. The regression line shown is: log rel. rate ) (36.91 ( 1.83) - (0.984 ( 0.051)pK; R2 ) 0.96.
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Figure 4. The reaction complex, TS and product for reaction 5 with benzene at HF 6-31+G(d,p). Relative to the separated reactants, the energies (E + ZPE) are -9.416, 14.964, and -0.071 kcal mol-1, respectively.
cyclohexylamine. In the LiNH2 · 2NH3 reactant, Li is only 3-coordinate, but as it binds to C to form the ArLi · 3NH3 product, eq 5, it becomes 4-coordinate.
LiNH2 · 2NH3 + ArH f LiNH2 · 2NH3 · ArH f RC
Ar · · · H · · · NH2 · Li · 2NH3 f ArLi · 3NH3 TS
(5)
product
A simple amine would undoubtedly be a better computational model for cyclohexylamine than ammonia, but there would then be many conformations of three RNH2 ligands on lithium to be considered and computed. Accordingly, we thought it better to start with NH3 as a model to avoid such multiple conformations.24 The separated reactants in reaction 5 are shown going first to a reaction complex, RC, which then rearranges through the TS to form the product. These structures for the reaction with benzene are shown in Figure 4. Because of the changing bonding at H, the calculations were done with a larger basis set, 6-31+G(d,p) to include polarization functions at H. The hydrogen being transferred is only weakly bonded to both N and C. The NH bond length is 1.00 Å in the product compared to 1.27 Å in the TS; similarly, CH increases from 1.08 Å in benzene to 1.47 Å in the TS. The TS has, as expected, one imaginary frequency, but to show that it is indeed the TS for reaction 5 we carried out an intrinsic reaction coordinate (IRC) calculation using Gaussian09 with 80 structures in each direction from the TS using the default increment of 0.1 bohr. Figure 5 shows the electronic energy of each of these points along the reaction coordinate. The energies of the RC and the reaction product are also shown to indicate how far along the total reaction coordinate the IRC calculation has gone. The furthest structures at both ends of the IRC are shown in Figure 6. The two end structures closely resemble the reaction complex (RC) and the product in Figure 4, leaving no doubt that the TS has been correctly identified. One result of this IRC computation bears on the possible role of internal return in the reaction mechanism. “Internal return”25-28
Figure 5. IRC for the reaction of LiNH2 · 2NH3 with benzene showing 80 points on each side of the TS at HF 6-31+G(d,p).
in a hydrogen-isotope transfer process occurs when the rate of the proton-transfer back reaction is comparable to or greater than the exchange of the hydrogen isotope with bulk solvent. In this case, the isotope can return to give no net reaction, and the experimental rate constant for isotope exchange is less than that of the proton-transfer step itself. The phenomenon is most important for localized anions in which the proton-transfer product is strongly hydrogen-bonded and can return faster than solvent exchange, but its potential role must be considered in all proton-transfer studies. In the present case, the barrier shown for proton transfer in Figure 5 is much greater than that for rotation about a C-Li or Li-N bond. Thus, once the product ArLi · 3NH3 is formed, the hydrogens on the ligands effectively equilibrate and, combined with the primary isotope effect, the probability that the isotope will be in the return step is relatively small. This probability will be somewhat larger for a real 3RNH2 ligand (6 hydrogens) compared to our 3NH3 model (9 hydro-
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Figure 6. IRC extrema structures: reactant side (structure -80), left; product side (structure +80), right.
Figure 7. Comparison of the relative energies of formation of ArLi · 3NH3 with ArLi · 2E (expressed as pK(Li,THF). Blue circles are normal aromatic hydrocarbons, red squares are the R-biphenylene positions, and green squares are the fluorine-containing compounds. The regression line is y ) -76.592 ( 3.162 + (2.040 ( 0.088)x; R2 ) 0.969.
Figure 8. Brønsted plot of ∆E‡ vs ∆E for reaction 5. Blue circles are normal aromatic hydrocarbons, red squares are the R-biphenylene positions, and green squares are the fluorine-containing compounds. The outlying blue point is 9-anthracene. The regression line shown is: y ) (-0.280 ( 0.253) + (0.712 ( 0.058)x; R2 ) 0.905.
gens) but, together with the primary isotope effect (which is almost the same for the back reaction as for the forward reaction), will still amount to only a few percent even without exchange of a ligand amine with bulk solvent. The computed TS is neither reactant-like nor product-like and would be described as being roughly midway along the reaction coordinate. This position is given in Figure 5. Consequently, if the Brønsted slope were indicative of the position of the TS along the reaction coordinate, we would have expected a slope in the neighborhood of 0.5. To see why the actual slope is so much greater in Figure 3 we consider some further comparisons. The TS and reaction products were calculated for all of the positions shown in Figure 1. Note in all cases that the reaction product, ArLi · 3NH3, has one Li-N bond in the ring plane with the other NH3 groups above and below the plane. For several compounds, two isomeric structures are possible that differ by rotation of the Li · 3NH3 group by 60°. Only the more stable conformation was used. In general, the Li-NH3 group avoids a peri-position. For the 9-anthracene position symmetry requires that one Li-NH3 group eclipse a peri-position and might be responsible for the deviation of this point in the correlations to be discussed. The computational results of all of these compounds are presented in Supporting Information. The relative energies of the total reactions in eq 5, LiNH2 · 2NH3 + ArH f ArLi · 3NH3, are compared in Figure 7
with the pK(Li,THF) values derived from ArLi · 2E. The result is an excellent correlation whose slope of 2.04, however, is significantly higher than the conversion factor between pK and energy, 2.303RT (1.36 at 25 °C and 1.48 at 50 °C). The difference can be rationalized by the different ion pairs involved. The interaction mechanisms in Figure 2 apply to the free anions. The cation in an ion pair will have the opposite effect but of smaller magnitude because it is farther away. Ligands on the cation will have an additional effect depending on their number, orientation, and dipole moment. Thus, the Li · 2E group is expected to have a larger moderating effect on the anion interaction mechanisms than the Li · 3NH3 group. That is, the ArLi · 3NH3 scale will be expanded compared to the ArLi · 2E scale and result in a larger slope. This result adds interest to the purely theoretical Brønsted plot of ∆E‡ versus ∆E for reaction 5 because the TS has been shown by IRC to be on the route to the product, ArLi · 3NH3. This plot is shown in Figure 8. There is surprisingly more scatter in this theory-theory correlation but the regression line is sufficiently well described to show that the Brønsted slope of 0.71 is in the “normal” range, and moreover is a reasonable measure of the position of the TS along the reaction coordinate. Finally, we consider in Figure 9 the Brønsted plot of log k for the experimental kinetic acidity (eq 2) compared to the
Kinetic and Equilibrium Lithium Acidities of Arenes
Figure 9. Brønsted plot of the kinetic acidity in eq 2 vs the ∆E for formation of the reaction product, ArLi · 3NH3,, of eq 5. Blue circles are normal aromatic hydrocarbons, red squares are the R-biphenylene positions, and green squares are the fluorine-containing compounds. The regression line shown is: y ) (-0.044 ( 0.082) - (0.480 ( 0.019)x; R2 ) 0.977.
relative reaction energy, ∆E, of eq 5. The slope, corrected by 2.303RT, of 0.32 is at the low end of normal Brønsted slopes and suggests that the interaction mechanisms in Figure 2 are moderated compared to the theoretical model by dielectric solvation in the solvent used for the experimental exchange rates, cyclohexylamine. Conclusions Ab initio calculations at relatively modest theory levels can successfully model experimental reactivities in organolithium chemistry if the model lithium includes coordinated ligands. These theoretical models can give useful Brønsted-type plots relating experiment to theory, but care must be taken in interpreting the corresponding Brønsted slopes. The variations of these slopes can be rationalized by consideration of simple electrostatic effects of ion pairs. In particular, the experimental kinetic acidities of different types of arene hydrogens shown in Figure 1 are well modeled by such computations. Acknowledgment. This work was supported in part by a Dreyfus Senior Mentor grant. We also thank Dr. Kathleen Durkin and Dr. Jamin Krinsky of the Molecular Graphics and Computational Facility (supported in part by NSF grants CHE0233882 and CHE-0840505), College of Chemistry, UC Berkeley, for their assistance. Supporting Information Available: Tables of computational results, 97 pages. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Bordwell, F. G. Acc. Chem. Res. 1988, 21, 456–63. (2) Streitwieser, A.; Reyes, J. R.; Singhapricha, T.; Vu, S.; Shah, K. J. Org. Chem., in press. (3) Streitwieser, A., Jr.; Lawler, R. G. J. Am. Chem. Soc. 1965, 87, 5388–5394.
J. Phys. Chem. A, Vol. 114, No. 33, 2010 8797 (4) Streitwieser, A.; Lawler, R. G.; Perrin, C. J. Am. Chem. Soc. 1965, 87, 5383–5388. (5) Streitwieser, A., Jr.; Mares, F. J. Am. Chem. Soc. 1968, 90, 644– 648. (6) Streitwieser, A., Jr.; Ziegler, G. R.; Mowery, P. C.; Lewis, A.; Lawler, R. G. J. Am. Chem. Soc. 1968, 90, 1357–1358. (7) Reference 3 noted a correlation between the kinetic acidity and a field effect function, Σ1/rj, in which rj is the distance between the reacting carbon and each remaining aromatic carbon. (8) One reviewer inquired why we did not use B3LYP, a commonly used hybrid DFT method. There are now several dozen DFT methods used by different authors. All are essentially semi-empirical methods containing parameters whose values are usually established with a training set of molecules. In all such methods one must take care in applying the particular DFT method outside the range of training molecules used. Hartree-Fock methods do not have arbitrary parameters and, although in their simplest form cannot be used for weak covalent bonds or open shells, do work well for electrostatic interactions of closed shells such as the coordinated lithium compounds dealt with in this paper. (9) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, J., T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q. G.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03; Gaussian, Inc.: Pittsburgh PA., 2003. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; , J. A. Montgomery, J.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd; J. J. Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Normand; J. Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Cossi, J. M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adam, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels; A. D. Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski; J. Fox, D. J. Gaussian09; Gaussian, Inc.: Wallingford CT, 2009. (11) Anslyn, E. V.; Dougherty, D. A. Modern Physical Organic Chemistry, University Science Books: Herndon, VA, 2006. (12) For an example of a comparison of kinetic acidities and theory see Schlosser, M.; Marzi, E.; Cottet, F.; Buker, H. H.; Nibbering, N. M. M. Chem.sEur. J. 2001, 7, 3511–3516. (13) Leffler, J. E. Science 1953, 117, 340–341. (14) Leffler, J. E.; Grunwald, E. Rates and Equilibria of Organic Reactions; Wiley: New York, 1963. (15) Murdoch, J. R. J. Am. Chem. Soc. 1972, 94, 4410–4418. (16) Bell, R. P. J. C. S. Faraday Trans. 2 1976, 2088–2094. (17) Cohen, A.; Marcus, R. A. J. Phys. Chem. 1968, 78, 4249–4256. (18) Koeppl, G. W.; Kresge, A. J. J. C. S. Chem. Comm. 1973, 371– 373. (19) Marcus, R. A. J. Phys. Chem. 1968, 72, 891–899. (20) Pross, A. J. Org. Chem. 1984, 49, 1811–1818. (21) Kresge, A. J. Chem. Soc. ReV. 1973, 475–503. (22) Marcus, R. A. J. Am. Chem. Soc. 1969, 91, 7224–7225. (23) Ponec, R. Collect. Czech. Chem. Commun. 2004, 69, 2121–2133. (24) The use of NH3 as a computational model for an amine should not be confused with the real ammonia, a more polar solvent in which significant dissociation to free ions is expected compared to an amine such as cyclohexylamine. (25) Cram, D. J. Fundamentals of Carbanion Chemistry; Academic Press: New York, 1965. (26) Koch, H. F. Acc. Chem. Res. 1984, 17, 137–144. (27) Koch, H. F. In Isotope Effects in Chemistry and Biology; Kohen, A., Limbach, H.-H., Eds.; Taylor & Francis: Boca Raton, 2005, p 465474. (28) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry; 3rd ed.; Narper & Row, Pubishers: New York, 1987.
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