Resurrection of Neutral Tris-homoaromaticity Frank Stahl,†,‡ Paul von Rague´ Schleyer,*,†,‡ Haijun Jiao,† Henry F. Schaefer III,‡ Kuo-Hsiang Chen,§ and Norman L. Allinger§ Institut fu¨ r Organische Chemie, Friedrich-Alexander-Universita¨ t Erlangen-Nu¨ rnberg, Henkestrasse 42, 91054 Erlangen, Germany, Center for Computational Quantum Chemistry, Computational Chemistry Annex, University of Georgia, 1004 Cedar Street, Athens, Georgia, 30602-2525, and Computational Center for Molecular Structure and Design, Department of Chemistry, University of Georgia, 1004 Cedar Street, Athens, Georgia, 30602-2525
[email protected] Received December 8, 2001
Neutral in-plane tris-homoaromaticity is evaluated in tris(bismethano)benzene (15) and modifications of this parent structure in which the π-orbitals might interact in the plane established by the unsaturated carbon atoms (in-plane conjugation). On the basis of magnetic susceptibility exaltation, nucleus-independent shift (NICS), and aromatic stabilization energy (ASE, evaluated via homodesmotic and isodesmic equations using B3LYP/6-311+G** + ZPVE energies, as well as by MM3 and MM4 force field computations), we identified triene 17, a triply bridged analogue of 15, as the system where homoaromaticity is most effective. The NICS(total) in the center of 17 is -30.1 ppm and the diatropic π-contribution is -18.0 ppm. This structure possesses more than one-third of the aromatic stabilization of benzene and is the best candidate for neutral tris-homoaromaticity ever proposed. The previously described tris-(bismethano)-benzene (15) also shows homoaromaticity but to a smaller extent compared to 17. Structure 18, which is closely related to 17, also is significantly homoaromatic but, as evaluated by MM3, strain partially counteracts the stabilizing effects from homoconjugation. Such a counteracting increase in strain largely cancels or even overwhelms the stabilization from homoconjugation in all other species considered in this study. 1. Introduction How many lives does homoaromaticity in neutral hydrocarbons have? During controversial discussions of the existence of neutral tris-homoaromaticity, dramatic pronouncements such as “the final nail to the coffin of neutral homoaromaticity”1 and “to ring the death knell”2 were employed in efforts to bury the concept once and for all. But no matter how compelling the arguments were, newer experimental and theoretical results would reanimate the lively dispute. Each new method employed to probe this intriguing phenomenon whose “very existence is a matter of a few kilocalories”3 seemed to lead to a different conclusion. R. V. Williams, in the latest review states,4 “There remains a dearth of neutral homoaromatics... . Recent studies continue to dispute the homoaromaticity of cycloheptatriene (1), although this reviewer is now convinced that 1 is marginally homoaromatic.” The ingenious concept of extended delocalization through a saturated linkage, later named homoaromaticity, dates back to the beginning of the last century: †
Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnberg. Computational Chemistry Annex, University of Georgia. Department of Chemistry, University of Georgia. (1) Holder, A. J. Comput. Chem. 1993, 14, 251. (2) Paquette, L. A.; Snow, R. A.; Muthard, J. L.; Cynkowski, T. J. Am. Chem. Soc. 1979, 101, 6991-6996. (3) Haddon, R. C. J. Org. Chem. 1979, 44, 3608-3616. (4) Williams, R. V. Chem. Rev. 2001, 101, 1185-1204. ‡ §
in 1901, Thiele5 reported the weaker acidity of cycloheptatriene (1, tropilidene, synthesized earlier by Willsta¨tter, Figure 1)6 compared to cyclopentadiene, both of which have CH2s “directly attached to two double bonds”.5 Thiele suggested that a partial interaction between the two unsaturated carbon atoms linked to the CH2 moiety, forming a benzene-like delocalized system, was responsible. As a consequence, the “energy of the methylene carbon would not be large enough to make the methylene protons as reactive as in cyclopentadiene”.5 In 1956, Doering7 speculated that 1 has a planar, “pseudo-aromatic” structure that permits 1,6-interaction. In the same year, Roberts and Applequist8 noticed that the cyclobutenyl cation 2 “appears to have a special stabilization which might be due to inductive and hyperconjugative effects of the 4-methylene group although a more attractive explanation is that the geometry of the small ring permits a substantial 1,3-π-bonding giving a cation which resembles the cyclopropenyl cation 3 (Figure 1)”. The term “homoaromaticity” was later coined by Winstein9-12 in conjunction with the “tris-homo-cyclopro(5) Thiele, J. Liebigs Ann. Chem. 1901, 319, 226-230. (6) Willsta¨tter, R. Liebigs Ann. Chem. 1900, 317, 204-217. (7) Doering, W. v. E.; Laber, G.; Vonderwahl, R.; Chamberlain, N. F.; Williams, R. B. J. Am. Chem. Soc. 1956, 78, 5448. (8) Applequist, D. A.; Roberts, J. D. J. Am. Chem. Soc. 1956, 78, 4012-4022. (9) Winstein, S.; Sonnenberg, J.; De Vries, L. J. Am. Chem. Soc. 1959, 81, 6523-6524.
10.1021/jo016358a CCC: $22.00 © 2002 American Chemical Society
Published on Web 08/28/2002
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FIGURE 1. Homoaromatic molecules reported in the literature.
penium ion” (the 3-bicyclo[3.1.0]hexyl cation, 4), and this field has gained widespread attention ever since. Numerous review articles are devoted to this topic.4,13-21 The homoaromaticity nomenclature (mono, bis, tris, etc.) is defined only by the number of interruptions to delocalization, whereas the size of the saturated linkage is not considered; i.e., all structures depicted in Figure 2 are candidates for tris-homoaromaticity as, in all cases, three saturated linkages, though of different carbon-chain lengths, connect the double bonds.13 (10) Winstein, S. J. Am. Chem. Soc. 1959, 81, 6524-6525. (11) Winstein, S.; Sonnenberg, J. J. Am. Chem. Soc. 1961, 83, 32353244. (12) Winstein, S.; Sonnenberg, J. J. Am. Chem. Soc. 1961, 83, 32443251. (13) Winstein, S. Chem. Soc. Spec. Publ. 1967, 21, 5. (14) Winstein, S. Q. Rev. Chem. Soc. 1969, 23, 1411. Reprinted in Carbonium Ions; Olah, G. A., Schleyer, P. v. R., Eds.; Wiley-Interscience: New York, 1972; Vol. III, p 965. (15) Story, P. R.; Clark, B. C., Jr. In Carbonium Ions; Olah, G. A., Schleyer, P. v. R., Eds.; Wiley-Interscience: New York, 1972; Vol. III, p 1007. (16) Warner, P. In Topics in Nonbenzenoid Aromatic Chemistry; Nozoe, T., Breslow, R., Hafner, K., Ito, S., Murata, I., Eds.; Hirokawa Publishing Co.: Tokyo, 1977; Vol. II, p 283. (17) Paquette, L. A. Angew. Chem., Int. Ed. Engl. 1978, 17, 106117; Angew. Chem. 1978, 90, 114-125. (18) Childs, R. F. Acc. Chem. Res. 1984, 17, 347. (19) Williams, R. V.; Kurtz, H. A. Adv. Phys. Org. Chem. 1994, 29, 273-331. (20) Cremer, D.; Childs, R. F.; Kraka, E. In The Chemistry of the Cyclopropyl Group; Rappoport, Z., Ed.; Wiley & Sons: Chichester, UK, 1995; Vol. 2, p 339. (21) Childs, R. F.; Cremer, D.; Elia, G. In The Chemistry of the Cyclopropyl Group; Rappoport, Z., Ed.; Wiley & Sons: Chichester, UK, 1995; Vol. 2, p 411.
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Homoaromaticity is firmly established in cationic22-26 and, more recently, in anionic27-31 systems where delocalization of charge is an additional driving force. The neutral32-34 and radical hydrocarbon counterparts remain controversial,4,17-19,35-37 although isoelectronic neutral (22) Olah, G. A.; Rasul, G.; Prakash, G. K. S. J. Org. Chem. 2000, 65, 5956-5959. (23) Exner, K.; Gescheidt, G.; Grossmann, B.; Heinze, J.; Bednarek, P.; Bally, T.; Prinzbach, H. Tetrahedron Lett. 2000, 41, 9595-9600. (24) Weiler, A.; Quennet, E.; Keller, M.; Exner, K.; Prinzbach, H. Tetrahedron Lett. 2000, 41, 4763-4767. (25) Exner, K.; Grossmann, B.; Gescheidt, G.; Heinze, J.; Keller, M.; Bally, T.; Bednarek, P.; Prinzbach, H. Angew. Chem., Int. Ed. 2000, 39, 1455-1458; Angew. Chem. 2000, 112, 1514-1517. (26) Exner, K.; Prinzbach, H.; Gescheidt, G.; Grossmann, B.; Heinze, J. J. Am. Chem. Soc. 1999, 121, 1964-1965. (27) Exner, K.; Hunkler, D.; Gescheidt, G.; Prinzbach, H. Angew. Chem., Int. Ed. 1998, 37, 1910-1913; Angew. Chem. 1998, 110, 20132016. (28) Exner, K.; Cullmann, O.; Voegtle, M.; Prinzbach, H.; Grossmann, B.; Heinze, J.; Liesum, L.; Bachmann, R.; Schweiger, A.; Gescheidt, G. J. Am. Chem. Soc. 2000, 122, 10650-10660. (29) Hofmann, M.; Scheschkewitz, D.; Ghaffari, A.; Geiseler, G.; Massa, W.; Schaefer, H. F.; Berndt, A. J. Mol. Model. 2000, 6, 257271. (30) Scheschkewitz, D.; Ghaffari, A.; Amseis, P.; Unverzagt, M.; Subramanian, G.; Hofmann, M.; Schleyer, P. V.; Schaefer, H. F.; Geiseler, G.; Massa, W.; Berndt, A. Angew. Chem., Int. Ed. 2000, 39, 1272-1275; Angew. Chem. 2000, 112, 1329-1332. (31) Lo¨sslein, W.; Pritzkow, H.; Schleyer, P. v. R.; Schmitz, L. R.; Siebert, W. Angew. Chem., Int. Ed. 2000, 39, 1276-1278; Angew. Chem. 2000, 112, 1333-1335. (32) Jiao, H.; Nagelkerke, R.; Kurtz, H. A.; Williams, R. V.; Borden, W. T.; Schleyer, P. v. R. J. Am. Chem. Soc. 1997, 119, 5921-5929. (33) Williams, R. V.; Gadgil, V. R.; Luger, P.; Koritsanszky, T.; Weber, M. J. Org. Chem. 1999, 64, 1180-1190. (34) Williams, R. V.; Gadgil, V. R.; Chauhan, K.; Jackman, L. M.; Fernandes, E. J. Org. Chem. 1998, 63, 3302-3309.
Resurrection of Neutral Tris-homoaromaticity
FIGURE 2. Molecules discussed as neutral tris-homoaromatics in the literature.
boron analogues of the carbocations are well accepted. Freeman extended the compounds considered for homoaromaticity recently by including carbenes.38,39 His density functional theory (DFT) studies reveal homoaromatic stabilization for the singlet states in his model compounds such as 7-carbenanorbornene (6c). The corresponding carbocation (6) was recognized as exceptionally stable and described as “homoallylic” by Winstein and co-workers as early as 1955.40,41 Isoelectronic and isolobal substitution of CH+ fragments in well-known homoaromatic cations such as 4 and 6 by BH (5 and 6b, respectively) led to some examples for neutral (hetero)-homoaromaticity.22,29,42-44 An undeniably beautiful example for three-dimensional, cationic homoaromaticity is the intriguing 1,3-dehydro-5,7-adamantanediyl dication 7 in which the four p orbitals of the four bridgehead carbons overlap inward in the cage in a tetrahedral fashion.42,45 Olah et al. also theoretically (35) McEwen, A. B.; Schleyer, P. v. R. J. Org. Chem. 1986, 51, 43574368. (36) Balaban, A. R.; Banciu, M.; Ciorba, V. Annulenes, Benzo-, Hetero-, Homo-derivatives and their Valence Isomers; CRC Press Inc.: Boca Raton, FL, 1987. (37) Cremer, D.; Kraka, E.; Slee, T. S.; Bader, R. F. W.; Lau, C. D. H.; Nguyen-Dang, T. T.; MacDougall, P. J. J. Am. Chem. Soc. 1983, 105, 5069-5075. (38) Freeman, P. K. J. Am. Chem. Soc. 1999, 120, 1019-1020. (39) Freeman, P. K.; Pugh, J. K. J. Org. Chem. 2000, 65, 61076111. (40) Winstein, S.; Shatavsky, M.; Norton, C.; Woodward, R. B. J. Am. Chem. Soc. 1955, 77, 4183-4184. (41) Winstein, S.; Ordronneau, C. J. Am. Chem. Soc. 1960, 82, 20842085. (42) Fokin, A. A.; Kiran, B.; Bremer, M.; Yang, X.; Jiao, H.; Schleyer, P. v. R.; Schreiner, P. R. Chem. Eur. J. 2000, 6, 1615-1628. (43) Schulman, J. M.; Disch, R. L.; Schleyer, P. v. R.; Buehl, M.; Bremer, M.; Koch, W. J. Am. Chem. Soc. 1992, 114, 7897-7901. (44) Fagan, P. J.; Nugent, W. A.; Calabrese, J. C. J. Am. Chem. Soc. 1994, 116, 1880-1889. (45) Bremer, M.; Schleyer, P. V.; Schotz, K.; Kausch, M.; Schindler, M. Angew. Chem., Int. Ed. Engl. 1987, 26, 761-763; Angew. Chem. 1987, 99, 795-799.
investigated isoelectronic analogues of this structure such as 8 and found evidence for neutral, three-dimensional (hetero)-homoaromaticity.22 Another related field of active pursuit is the search for a homoaromatic semibullvalene 9.33,34,46 This research is stimulated by the undoubtedly homoaromatic transition state 9-TS32 of the degenerate Cope rearrangement (Figure 1) of semibullvalene, which requires very little activation energy (∆G298 ) 6.2 kcal/ mol).47,48 In a sequel of experimental and theoretical studies, “tris-homo-benzene” (cis,cis,cis-1,4,7-cyclononatriene, 10),49-53 cis,cis,cis-1,5,9-cyclododecatriene (11),54 triquinacene (12),1,55-65 and C16-hexaquinacene (13)2,66,67 have been proposed as neutral tris-homoaromatics (Figure 2). (46) Williams, R. V. Eur. J. Org. Chem. 2001, 227-2235. (47) Cheng, A. K.; Anet, F. A. L.; Mioduski, J.; Meinwald, J. J. Am. Chem. Soc. 1974, 96, 2887-2891. (48) Moskau, D.; Aydin, R.; Leber, W.; Gu¨nther, H.; Quast, H.; Martin, H.-D.; Hassenru¨ck, K.; Miller, L. S.; Grohmann, K. Chem. Ber. 1989, 122, 925. (49) Radlick, P.; Winstein, S. J. Am. Chem. Soc. 1963, 85, 344345. (50) Untch, K. G. J. Am. Chem. Soc. 1963, 85, 345-346. (51) Roth, W. R. Liebigs Ann. Chem. 1964, 671, 10. (52) Roth, W. R.; Bang, W. B.; Goebel, P.; Sass, R. L.; Turner, R. B.; Yu, A. P. J. Am. Chem. Soc. 1964, 86, 3178-3179. (53) Bischof, P.; Gleiter, R.; Heilbronner, E. Helv. Chim. Acta 1970, 53, 1425-1434. (54) Untch, K. G.; Martin, D. J. J. Am. Chem. Soc. 1965, 87, 35183520. (55) Woodward, R. B.; Fukunaga, T.; Kelly, R. C. J. Am. Chem. Soc. 1964, 86, 3162-3164. (56) Bunzli, J. C.; Frost, D. C.; Weiler, L. Tetrahedron Lett. 1973, 14, 1159-1162. (57) Bischof, P.; Bosse, D.; Gleiter, R.; Kukla, M. J.; de Meijere, A. Chem. Ber. 1975, 108, 1218-1223. (58) Stevens, E. D.; Kramer, J. D.; Paquette, L. A. J. Org. Chem. 1976, 41, 2266-2269. (59) Liebman, J. F.; Paquette, L. A.; Peterson, J. R.; Rogers, D. W. J. Am. Chem. Soc. 1986, 108, 8267-8268. (60) Schulman, J. M.; Miller, M. A.; Disch, R. L. J. Mol. Struct. (THEOCHEM) 1988, 169, 563-568. (61) Miller, M. A.; Schulman, J. M.; Disch, R. L. J. Am. Chem. Soc. 1988, 110, 7681-7684.
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Although the interpretations of the individual investigations differ, the final conclusion is that all of these examples, 10-13, are not homoaromatic. The σ-trishomobenzene analogues of 10, 11, and 12, 10-SAT, 11SAT, and 12-SAT, respectively, (Figure 2) have also been studied, but no evidence for cyclic electron delocalization has been reported.19,68-70 The latter σ-tris-homobenzenes isomerize to the corresponding π-tris-homobenzenes via tris-homoaromatic transition states 10-TS, 11-TS, and 12-TS. McEwen and Schleyer35 employed in 1986 a resourceful approach to evaluate neutral tris-homoaromaticity in the five experimentally known compounds 10-14 (Figure 2) and in five new molecules, including tris(bismethano)benzene 15, theoretically. McEwen and Schleyer used the MM2 force field,71 which separates the molecule mathematically into a σ-skeleton and a p atomic orbital (AO) system and treats these more or less independently. A variable-electronegativity SCF (VESCF) calculation on the p AOs provides the force constants to be used in the force field calculation.72 The normal VESCF cycle recognizes only bonded interactions; therefore, molecular structures are determined by exclusion of nonbonded pp interactions (i.e., homoconjugative interactions are not included). In a consecutive calculation, such nonbonded pp interactions (NBI) are specifically included by allowing the respective resonance integrals β to be nonzero. Favorable homoconjugation is reflected by negative differences in the total electronic energy derived from the two different calculations (∆Eel ) Eel(MMP2, NBI) - Eel(MMP2)). Two different heats of formation, ∆Hf, are obtained by treating the molecule first as a delocalized system (∆Hf(NBI)) and then separately as a system with localized double bonds (∆Hf) (∆∆Hf ) ∆Hf(NBI) - (∆Hf)). The difference ∆Eel - ∆∆Hf represents the change in strain energy, ∆Estrain (∆Estrain > 0 means an increase), between the localized and the delocalized (allow NBI) structure. In all of the molecules studied by McEwen and Schleyer, the increase in strain overrode the gain of homoaromatic stabilization. The largest value (5.41 kcal/ mol) for homoconjugative stabilization (∆Eel) was computed for 15 (Figures 2 and 4). Indeed, Schleyer and Jiao73 revisited this topic later (using ab initio methods) and concluded that 15 is homoaromatic on the basis of (62) Dewar, M. J. S.; Holder, A. J. J. Am. Chem. Soc. 1989, 111, 5384-5387. (63) Storer, J. W.; Houk, K. N. J. Am. Chem. Soc. 1992, 114, 11651168. (64) Verevkin, S. P.; Beckhaus, H.-D.; Ruchardt, C.; Haag, R.; Kozhushkov, S. I.; Zywietz, T.; de Meijere, A.; Jiao, H.; Schleyer, P. v. R. J. Am. Chem. Soc. 1998, 120, 11130-11135. (65) Rogers, D. W.; McLafferty, F. J. J. Phys. Chem. A 2000, 104, 9356-9361. (66) Paquette, L. A.; Snow, R. A.; Muthard, J. L.; Cynkowski, T. J. Am. Chem. Soc. 1978, 100, 1600-1602. (67) Christoph, G. G.; Muthard, J. L.; Paquette, L. A.; Boehm, M. C.; Gleiter, R. J. Am. Chem. Soc. 1978, 100, 7782-7784. (68) Rucker, C.; Muller-Botticher, H.; Braschwitz, W. D.; Prinzbach, H.; Reifenstahl, U.; Irngartinger, H. Liebigs Ann./Recl 1997, 967989. (69) McMullen, G.; Lutterbeck, M.; Fritz, H.; Prinzbach, H.; Kruger, C. Isr. J. Chem. 1982, 22, 19-26. (70) de Meijere, A. In Cage Hydrocarbons; Olah, G. A., Ed.; WileyInterscience: New York, 1990. (71) Kao, J.; Allinger, N. L. J. Am. Chem. Soc. 1977, 99, 975. (72) Allinger, N. L.; Tai, J. C. J. Am. Chem. Soc. 1965, 87, 20812097. (73) Schleyer, P. v. R.; Jiao, H. Pure Appl. Chem. 1996, 68, 209218.
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FIGURE 3. Optimized geometry (B3LYP/6-311+G**) of the transition state for the trimerization of ethylene.
FIGURE 4. Sketched and optimized structures of triene species 15-17.
computed magnetic susceptibility exaltation. This system is the centerpiece of the present paper. Houk et al.74 pointed out that in the trimerization of acetylene, the homoconjugative interactions among the three neutral proximal closed-shell π-systems are actually destabilizing. According to their early computations,
Resurrection of Neutral Tris-homoaromaticity
the activation barrier of 80 kcal/mol at HF/STO-3G for this thermally allowed synchronous pericyclic process is due to 60 kcal/mol for the distortion of the three acetylenes and 20 kcal/mol for the repulsive electronic interactions between the π-orbitals in the ring plane. This π repulsion was later confirmed by Bach75 and interpreted as being a significant impediment to the chance of uncovering neutral homoaromaticity. Schleyer and Jiao disagreed76 and demonstrated that although the interactions between the in-plane π-orbitals might be repulsive (estimated to be about 15 kcal/mol at B3LYP/6311+G**), the transition state can still be aromatic. This repulsive interaction is much reduced relative to that expected for a nonaromatic model transition state. The “energy of concert”77 can be approximated roughly by the energy of the biradical acetylene triplet state, which is 96.0 kcal/mol higher in energy compared to singlet acetylene. Indeed, the transition state was found by Schleyer and Jiao to be aromatic with a magnetic susceptibility exaltation of Λ ) -14.6 ppm-cgs (benzene value: -13.4 ppm-cgs) and a total nucleus independent chemical shift (NICS) of -24.1 ppm.76 The authors further explored dissected NICS (see also the methods section of this article) for different structures along the HF/6-31G* intrinsic reaction coordinate: the diamagnetic NICS(total) was shown to have a maximum at the transition state geometry. Whereas the change in diamagnetic NICS(π) is small during the beginning of the reaction, it varies considerably only past the transition state. The σ-components (σ-bonds and in-plane π-orbitals), in contrast, are highly diamagnetic at the transition state but become strongly paramagnetic in the product benzene.78 Hence, the electrons in the transition state for the trimerization of acetylene are cyclically delocalized, mainly in the plane of the carbon atoms but also, to a minor extent, in the perpendicular set of π-orbitals. If this transition state fulfills the requirements for being homoaromatic, the realization of neutral tris-homoaromaticity as a viable minimum depends on the proper embedding of the π-system into a well constructed σ-framework! The present paper extends the earlier studies of McEwen and Schleyer35 and of Jiao and Schleyer,76 employing higher levels of theory and reporting new σ-skeletons in which neutral tris-homoconjugation is shown to be effective.
2. Computational Methods All structures were optimized sequentially with 6-31G* and 6-311+G** basis sets79 employing Becke’s80 three-parameter hybrid functional in conjunction with the correlation functional of Lee, Yang, and Parr81 (B3LYP) as implemented in Gaussian 98.82 Frequency calculations were carried out at B3LYP/6-31G* (74) Houk, K. N.; Gandour, R. W.; Strozier, R. W.; Rondan, N. G.; Paquette, L. A. J. Am. Chem. Soc. 1979, 101, 6797-6802. (75) Bach, R. D.; Wolber, G. J.; Schlegel, H. B. J. Am. Chem. Soc. 1985, 107, 2837-2841. (76) Jiao, H.; Schleyer, P. v. R. J. Phys. Org. Chem. 1998, 11, 655662. (77) Doering, W. v. E.; Roth, W. R.; Breuckmann, R.; Figge, L.; Lennartz, H.-W.; Fessner, W.-D.; Prinzbach, H. Chem. Ber. 1988, 121, 1-9. (78) Schleyer, P. v. R.; Manoharan, M.; Wang, Z.-X.; Jiao, H.; Puchta, R.; Hommes, N. J. R. v. E. Org. Lett. 2001, 3, 2465-2468. (79) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley-Interscience: New York, 1986. (80) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652.
to characterize the optimized structures as energy minima and to obtain the zero-point vibrational energy (ZPVE) corrections. The latter were used unscaled to correct the B3LYP/6-311+G** energies. The restricted B3LYP/6-311+G** wavefunctions for all triene structures studied were tested to be stable.83-85 Magnetic susceptibilities (χ) were computed using the CSGT method86,87 at B3LYP/6-311+G**//B3LYP/6-311+G**. In addition, we computed NICS88 and 1H NMR chemical shifts at HF/6-31G*//B3LYP/6-31G*, B3LYP/6-31G*//B3LYP/6-31G*, and B3LYP/6-31G*//B3LYP/6-311+G** using the GIAO method. For conversion of the calculated shieldings into 1H NMR chemical shifts, we chose benzene (1H NMR δ 7.27 ppm) as the reference compound. Further refinement of NICS, “dissected NICS”,78,89 can be achieved by separating the contributions of the different bonds to the NICS total value. Such dissection is only possible with the IGLO method in which, unlike GIAO, the gauge origins are included in localized orbitals. Dissected NICS calculations were carried out at the SOS-DFPT-IGLO level using the Perdew-Wang-91 exchange correlation functional and the IGLO-III (TZ2P) basis set as implemented in the deMon NMR module.90,91 The program uses the Pipek-Mezey localization procedure,92 which separates multiple bonds into σ- and π-components.
3. Evaluation of Resonance Energies Resonance energies are not directly measurable quantities; hence, they are based on energy differences. Due to the necessity of choosing a reference system, the definition of resonance energy is ambiguous as the chosen references are arbitrary. For example, to evaluate the aromatic stabilization energy (ASE) for benzene, one has to model a hypothetical cyclohexatriene with noninteracting localized double bonds. Schleyer and Jiao proposed the following homodesmotic equation, which gives an ASE for benzene of about 35 kcal/mol:73,93
Dewar examined the energies of linear polyenes and defined those as references for cyclic molecules. On the basis of s-trans-butadiene, the “Dewar resonance energy” (DRE)94 of benzene is on the order of 20 kcal/mol. (81) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785-789. (82) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.;Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (83) Seeger, R.; Pople, J. A. J. Chem. Phys. 1977, 66, 3045-3050. (84) Bauernschmitt, R.; Ahlrichs, R. J. Chem. Phys. 1996, 104, 9047-9052. (85) Dehareng, D.; Dive, G. J. Comput. Chem. 2000, 21, 483-504. (86) Keith, T. A.; Bader, R. F. W. Chem. Phys. Lett. 1993, 210, 223231. (87) Cheeseman, J. R.; Trucks, G. W.; Keith, T. A.; Frisch, M. J. J. Chem. Phys. 1996, 104, 5497-5509. (88) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; van Eikema Hommes, N. J. R. J. Am. Chem. Soc. 1996, 118, 6317-6318. (89) Schleyer, P. v. R.; Jiao, H.; Hommes, N. J. R. v. E.; Malkin, V. G.; Malkina, O. L. J. Am. Chem. Soc. 1997, 119, 12669-12670. (90) Malkin, V. G.; Malkina, O. L.; Casida, M. E.; Salahub, D. R. J. Am. Chem. Soc. 1994, 116, 5898-5908.
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Stahl et al.
Although widely quoted, these DREs are unsatisfactory since no s-trans conformations (which are lower in energy than s-cis conformations) are present in benzene. The choice of the “best” reference system and homodesmotic equation is disputed in the literature; a new isomerization method gives ASE ) 33 kcal/mol93b in agreement with the value from eq 1.93 In this work we employed different ways of calculating resonance energies. Resonance energies were evaluated by different isodesmic and homodesmotic equations based on our density functional theory computations. Additionally, in analogy to the earlier study by McEwen and Schleyer35 (summarized in the Introduction), we computed resonance energies using both MM395-97 and MM498,99 as well as heats of formations using MM3. (There is currently no provision for calculating heats of formation with MM4 for compounds with four-membered rings.) There are several methods, involving different approximations, for determining resonance energies in molecular mechanics calculations. The conceptually simplest procedure used here is to handle the delocalized electronic system in two different ways in separate calculations, as localized or as delocalized. With MM3, one can calculate the heat of formation using both these treatments. Any resonance energy is revealed as a lowering of the heat of formation of the delocalized molecule relative to that of the localized molecule. MM3 computations were carried out on compounds 15-20 using this method; the results are listed in Table 6. The heats of formation of these molecules are always more negative when treated as a conjugated system. The energy difference, which varies rather little (from 5.2 to 5.8 kcal/mol), is taken as the aromatic stabilization energy. Note that the values found are appreciable, about 1/3 of the value for benzene computed by the same method. A somewhat more complicated calculation, which appears to provide a better approximation, can be carried out with either MM3 or MM4; both were used here for the same set of compounds. This method is based on the σ-π separation treatment inherent in the molecular mechanics scheme when a delocalized system is computed. This works directly for planar molecules. Nonplanar molecules can also be handled by “flattening” the molecule (removing the direction cosine terms), invoking the now valid σ-π separation as usual, calculating the bond orders and dependent properties, and then switching over to the regular molecular mechanics computation that allows the molecule to relax. (91) Malkin, V. G.; Malkina, O. L.; Eriksson, L. A.; Salahub, D. R. In Density Functional Calculations; Seminario, J. M., Politzer, P., Eds.; Elsevier: Amsterdam, 1995; Vol. 1. (92) Pipek, J.; Mezey, P. G. J. Chem. Phys. 1989, 90, 4916-4932. (93) (a) Schleyer, P. v. R.; Manoharan, M.; Jiao, H.; Stahl, F. Org. Lett. 2001, 3, 3233-3236. (b) Schleyer, P. v. R.; Pu¨hlhofer, F. Org. Lett. 2002, 4, 2873. (94) Schaad, L. J.; Hess, B. A. Chem. Rev. 2001, 101, 1465-1476. (95) Lii, J. H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 85768582. (96) Lii, J. H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 85668575. (97) Allinger, N. L.; Yuh, Y. H.; Lii, J. H. J. Am. Chem. Soc. 1989, 111, 8551-8566. (98) Allinger, N. L.; Chen, K. S.; Lii, J. H. J. Comput. Chem. 1996, 17, 642-668. (99) Nevins, N.; Lii, J. H.; Allinger, N. L. J. Comput. Chem. 1996, 17, 695-729.
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Initially, variable electronegativity (VESCF)100,101 π-system electronic calculations are carried out. This is a selfconsistent field method that allows the ionization potential computed at an atom to change in response to variations in the electron density. Such calculations give bond orders between bonded atoms. From these data, the necessary stretching force constants and bond lengths are deduced so that molecular mechanics calculations may be carried out. For the present cases, where one wishes to evaluate resonance energy involving nonbonded atoms, MM calculations are first performed in the usual fashion to give an electronic energy. Then, maintaining the same geometry, one omits the specific resonance integrals between the nonbonded (homoconjugated) atoms and repeats the computation.102 When the specific integrals have insignificantly small values, the electronic energy is the same whether or not they are included. Since the geometries are the same, the steric energies also are the same. Hence, the resonance energy would be zero. However, when these nonbonded resonance integrals have nonzero values, the electronic energy changes in the direction that stabilizes the system. Hence, the resonance energy in this approximation is just the electronic energy obtained in the fully delocalized approximation minus the energy obtained when the explicit nonbonded integrals of interest are set to zero. The ∆Eel values obtained in that fashion with MM3 and MM4 also are displayed in Table 6. Still another approximation is possible. The bond orders from the VESCF calculation are used to obtain molecular mechanics bond parameters only between bonded atoms. Hence, the omission of these integrals between nonbonded atoms has no direct effect on the molecular mechanics calculation. There is, however, an indirect effect. The omission of those integrals (unless they have negligible values) results in overall changes in the electronic system, which then causes bond order changes that affect the molecular mechanics parameters. Thus, the steric energy of the molecule (overall energy apart from the π-electronic energy) changes slightly. One method of evaluation employs the total (electronic plus steric) energies; these also are included in Table 6. 4. Results and Discussion 4.1 Trimerization of Ethylene as a Model for Trishomoaromaticity. How can three CdC double bonds be held together by saturated linkages in a sufficiently close proximity so that homoconjugation becomes effective? As a starting structure for this search, we chose Schleyer et al.’s35,73 “in-plane” benzene analogue (15, Figure 4) where the three CdC double bonds are connected by four-membered rings with the π-orbitals in the plane established by the six sp2 carbon atoms. (100) Brown, R. D.; Heffernen, N. L. Australian J. Chem. 1959, 12, 319. (101) Allinger, N. L.; Li, F. B.; Yan, L. Q.; Tai, J. C. J. Comput. Chem. 1990, 11, 868-895. (102) This method differs from that described earlier,35 which was used in MM2. The MM2 SCF calculations date from the precomputer days, when it was expedient to omit calculation of all the small (nonbonded) resonance integrals in the system and just set them equal to zero. One could add any such integrals of interest specifically to a case at hand. As all these integrals are included automatically in the MM3 scheme, specific integrals are deleted in special cases.
Resurrection of Neutral Tris-homoaromaticity TABLE 1. NICS Values, GIAO-B3LYP/6-31G*//B3LYP/ 6-311+G** and IGLO-SOS-DFPT-PW91/III//B3LYP/ 6-311+G**, Computed at the Geometric Center of the Carbon Atoms and at Points along the Threefold Rotational z-Axis for the D3-symmetric Transition State of the Trimerization of Ethylene (3-C2H4-TS) method
NICS
0.0 Å
0.5 Å
1.0 Å
1.5 Å
2.0 Å
GIAO IGLO
total total πCC σCC σCH
-26.1 -26.0 -15.0 -2.4 -8.4
-22.2 -22.3 -13.2 -1.8 -7.2
-14.8 -15.1 -9.6 -0.9 -4.5
-8.8 -9.3 -6.3 0.0 -2.4
-5.3 -5.1 -5.2 +0.3 -1.2
Cyclic trienes are the most promising candidates to be considered as neutral tris-homoaromatics. Hence, the trimerization of ethylene103 (Figure 3) is the most appropriate model. Although the transition structure is not quite planar (D3 instead of D3h), nonbonded π-interactions occur toward the center of the six carbon atoms. The second, perpendicular set of π-orbitals involved in the trimerization of acetylene (see Introduction) are not present. The optimized geometry for this D3-symmetric transition state (3-C2H4-TS) is depicted in Figure 3. The existence of a diatropic ring current in this transition state is indicated by NICS (NICS(π) ) -15.0 ppm in the center, Table 1). We also computed a diamagnetic susceptibility exaltation of Λ ) -38.4 ppm-cgs with respect to three isolated ethylenes. Hence, this transition state is quite aromatic on the basis of computed magnetic properties. The homoconjugative distance in 3-C2H4-TS, 2.205 Å (Figure 3), is rather long. This indicates that minimizing the separation between the unsaturated carbon atoms is certainly crucial but not the sole discriminator for the existence or nonexistence of neutral in-plane tris-homoaromaticity. 4.2 Potential Energy Surface of the C-C Bond Stretching in Ethane. The empirical C-C bond energy from thermochemical data104 for ethane is 82.8 kcal/mol (via atomization energies, ∆Hat298K, and assuming that the CH bond energies are identical to methane). The computed C2H6 f 2CH3 dissociation energy at UBSB3LYP/6-311+G** is 91.7 kcal/mol (88.2 ( 2.0 kcal/mol via experimental heats of formation).104 Note that the dissociation energy equals the bond energy only in diatomics. In polyatomic molecules, the dissociation energy also involves structural and electronic relaxation in the products (relaxation energy).105 Taking this into account, several theoretical procedures have been developed to assess the intrinsic bond energy of different bonds with some success.105-108 A carbon-carbon distance of about 2.2 Å as in 3-C2H4TS is typical for pericyclic transition states76,103 and led us to carry out a simple but particularly instructive investigation. We performed a relaxed scan for the stretching of the C-C bond in ethane (Scheme 1, Table (103) Houk, K. N.; Li, Y.; Evanseck, J. D. Angew. Chem., Int. Ed. Engl. 1992, 31, 682-708; Angew. Chem. 1992, 104, 711-739. (104) Cox, J. O.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: New York, 1970. (105) Exner, K.; Schleyer, P. v. R. J. Phys. Chem. A 2001, 105, 34073416. (106) Ehrhardt, C.; Ahlrichs, R. Theor. Chim. Acta 1985, 68, 231245. (107) Barone, V.; Fliszar, S. Int. J. Quantum Chem. 1995, 55, 469476. (108) Grimme, S. J. Am. Chem. Soc. 1996, 118, 1529-1534.
2)109 at the UBS-B3LYP/6-311+G** level (UBS ) unrestricted broken spin; here spatial and spin symmetries are destroyed by mixing the frontier orbitals; hence, the two electrons of the breaking bond can be accommodated in two different orbitals). The structure with the C-C bond elongated to 2.2 Å is only 47.5 kcal/mol higher in energy compared to the equilibrium structure with a C-C bond length of 1.531 Å at (UBS)-B3LYP/6-311+G**. Hence, almost half of the total bond energy is still present at this long distance! Provided that the p orbitals comprising the through space CC bond are pointing at each other, there is substantial bonding at 2.5 Å and even larger separations. 4.3 Geometries and NICS for the Triene Species 15-17. All tricoordinate carbon atoms in molecules 1517 represented in Figure 4 are pyramidalized. In the trimerization of ethylene (3-C2H4-TS), the hydrogens are twisted to the outside of the ring (pyramidalization angle ) 27.1°, Figure 3). The diatropic ring current, which is present, is reflected in the NICS values (Table 1) and by the computed diamagnetic susceptibility exaltation of Λ ) -38.4 ppm-cgs with respect to three isolated ethylenes. The pyramidalization angle for the neutral in-plane trishomoaromatic 15 (Figure 4) is larger (32.3°), and the larger p orbital lobes are bent away from optimal π-interaction. NICS, nevertheless, remains quite negative (-24.2 ppm at GIAO-B3LYP/6-31G*/B3LYP/6-311+G**, Table 3). Hence, the less favorable pyramidalization seems to be compensated by the short nonbonded distance (1.873 Å) between the unsaturated carbon atoms. The strategy of connecting the methylene groups of the four-membered rings to close the open faces of the parent structure 15 and create a molecular cage, 16 (Figure 4), appears to result in a less favorable situation. The C-C double bonds are shorter; the through-space distances are longer, and the pyramidalization angle is increased drastically (53.5°). The small NICS(0) (-2.9 ppm at GIAO-B3LYP/6-31G*/B3LYP/6-311+G**, Table 3) suggests the absence of a diatropic ring current in this structure. A different approach is more favorable: connecting the methylene units (CH2) of each four-membered ring with a C2 linkage, 17 (Figure 4), results in a smaller pyramidalization angle (24.8°) than that in 15 (32.3°) and a remarkably short “homoconjugative” distance of only 1.781 Å. We computed a large negative NICS (-30.5 ppm at GIAO-B3LYP/6-31G*/B3LYP/6-311+G**, Table 3) for this structure. NICS and, more generally, the shieldings of all magnetically active nuclei are the sum of different effects. Dissected NICS computations employing IGLO allow the evaluation of the localized orbital contributions from C-H and C-C single bonds as well as from the σ- and the π-components of multiple bonds. In benzene, the NICS(total) in the center (-8.8 ppm) is the result of diamagnetic contributions from the π-bonds (-20.7 ppm) and local paramagnetic contributions from the σ-bonds (+14.0 ppm).78,89 The C-H bonds also participate. For 15 and 17, we computed large negative NICS(total) values at all levels of theory employed; in contrast, 16 gives uniformly small values (Table 3). The good match of the different NICS computations agrees with previous (109) Lorant, F.; Behar, F.; Goddard, W. A., III; Tang, Y. J. Phys. Chem. A 2001, 105, 7896-7904.
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Stahl et al. SCHEME 1. Stretching of the C-C Bond in Ethane at UBS-B3LYP/6-311+G** (Dissociation Limit: 91.7 kcal/mol)
TABLE 2. Energy Profile of the C-C Bond Stretching in Ethane at (UBS)-B3LYP/6-311+G** C-C distance [Å]
E [hartree]
Erel [kcal/mol]
1.4 1.53 (equilibrium) 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
-79.84648 -79.85654 -79.85457 -79.84657 -79.83501 -79.82172 -79.80784 -79.79409 -79.78089 -79.76846 -79.75690 -79.74624 -79.73702 -79.73026 -79.72534 -79.72172 -79.71903
6.3 0.0 1.2 6.3 13.5 21.9 30.6 39.2 47.5 55.3 62.5 69.2 75.0 79.2 82.3 84.6 86.3
observations and documents the independence of NICS values from the level of theory employed for the NMR calculation and for the geometry optimization. The dissection reveals significantly larger π-contributions for 17 (-18.0 ppm in the center and -12.7 ppm at 1 Å, Table 3) compared to those for 15 and 16. Although the NICS(total) is smaller in 16 than that in 15, the π-bond contributions match well (-8.3 ppm for 15 and -7.5 ppm for 16 in the centers). The difference in NICS(total) between 15 and 16 arises from less diamagnetic contributions of the four-membered rings in 16 (-6.0 ppm for 16 vs -10.8 and -12.0 ppm for 15 and 17, respectively) and paramagnetic contributions of the additional C-C σ-bonds that connect the four-membered rings. Hence, both species sustain diatropic ring currents. Since the π-orbitals point directly toward the center where NICS is computed, one might expect local effects just from these π-electrons even in the absence of a diatropic ring current, cf. ref 110. To assess this effect, we computed NICS for individual ethylene fragments (fixed C-H bond length of 1.085 Å, Figure 5) with pyramidalization angles and C-C bond lengths constrained as in 15-17. Also, the distance of the NICS (110) Martin, N. H.; Brown, J. D.; Nance, K. H.; Schaefer, H. F., III; Schleyer, P. v. R.; Wang, Z.-X.; Woodcock, H. L. Org. Lett. 2001, 3, 3823-3826.
6606 J. Org. Chem., Vol. 67, No. 19, 2002
points to the C-C double bond being retained in these calculations. The π-bond contributions in all cases are small (Table 4). The sum for three such double bonds would still be well below the computed π-contributions for 15-17. The large π-contributions in 17, especially at points away from the center along the 3-fold axis, predict that this structure has a well tailored σ-skeleton for effective homoconjugation and should be the most promising candidate in this set. Note that NICS (π, 1 Å) for 17 also is larger than NICS (π, 0) for both 15 and 16. It is instructive to compare these results with those for triquinacene (12, Figure 2), whose homoaromaticity was “definitely disproved” only in 199864 after a long controversy (see Introduction). Negligible NICS of -1.6 ppm in the center of the six unsaturated carbon atoms in triquinacene and a magnetic susceptibility exaltation of only -0.6 ppm-cgs were reported in 199864 (also see refs 111 and 112). Dissected NICS reveals small values for both σ- and π-contributions of the double bonds (Table 3): the π-contributions of 12 even become paramagnetic at points away from the center, and the σ-contributions become diamagnetic. The chemical shifts of the endo-methylene hydrogen atoms of the four-membered rings pointing toward the 3-fold axis in 15 and 17 are computed to be 0.11 and 0.30 ppm, respectively. These upfield positions provide further evidence for the presence of diatropic ring currents in those systems. For comparison, a chemical shift of 3.34 ppm was computed for the exo-hydrogen atoms in 15. 4.4 Energies and Magnetic Susceptibility Exaltations of Triene Species 15-17. In addition to the geometric features and NICS values, magnetic susceptibility exaltations (Λ)113-115 and aromatic stabilization energies (ASE) provide corroborating data for neutral tris-homoaromaticity in the scrutinized hydrocarbons 15-17. We computed all hydrogenation products of 15(111) Mascal, M.; Lera, M.; Blake, A. J. J. Org. Chem. 2000, 65, 7253-7255. (112) Jiao, H. J.; Halet, J. F.; Gladysz, J. A. J. Org. Chem. 2001, 66, 3902-3905. (113) Pauling, L. J. Phys. Chem. 1936, 4, 673-677. (114) Dauben, H. P., Jr.; Wilson, J. D.; Laity, J. L. J. Am. Chem. Soc. 1969, 91, 1991-1998. (115) Dauben, H. P., Jr.; Wilson, J. D.; Laity, J. L. J. Am. Chem. Soc. 1968, 90, 811-813.
Resurrection of Neutral Tris-homoaromaticity TABLE 3. NICS Values Computed in the Center of the Three CdC Double Bonds and at 1 and 2 Å above the Ring along the Main Rotational Axis for the Neutral In-Plane Tris-homoaromatic Candidates 15-17 method GIAO
IGLO
HF/6-31G*// B3LYP/6-31G*
total
B3LYP/6-31G*// B3LYP/6-31G*
total
B3LYP/6-31G*// B3LYP/6-311+G**
total
SOS-PW91/TZ2P// B3LYP/6-31G*
total CdC (π) CdC (σ) cyclobutane rings
0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å
15
16a
17
-22.1 -11.7 -4.1 -21.5 -11.0 -3.9 -24.2 -12.3 -4.5 -21.3 -11.0 -3.7 -8.3 -4.9 -1.8 -2.4 -0.6 -0.2 -10.8 -6.0 -1.8
-5.3 -6.5
-34.2 -18.3 -6.8 -30.6 -15.8 -6.0 -30.5 -15.8 -6.0 -30.1 -15.8 -5.8 -18.0 -12.7 -5.7 +2.8 +3.1 +1.8 -12.0 -6.0 -2.4
-3.6 -4.5 -2.9 -4.2 -4.3 -4.5 -7.5 -3.1 +1.5 +2.7 -6.0 -0.8
triquinacene (12)
-1.6 -1.4 -0.8 -2.8 -2.4 -1.4 -1.2 +1.4 +1.2 +2.1 -0.8 -0.7
a NICS points higher than 1 Å are affected heavily by the atomic orbital of the carbon atom connecting the four-membered rings and the C-H bond. Dissected NICS at 1.5 Å totals +7.5 ppm with a contribution from the AO of this carbon of -1.4 and -7.0 ppm from the C-H bond. The NICS (2 Å) point is essentially located at the carbon atom.
FIGURE 5. Evaluation of NICS for bent ethylene with pyramidalization angle and CC bond length as in 15.
TABLE 4. NICS (IGLO-SOS-DFPT/IGLO-III) Computed for Ethylene Fragments with Pyramidalization Angles and C-C Bond Lengths Analogous to 15-17 total σ π
0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å
C2H4 as in 15
C2H4 as in 16
C2H4 as in 17
-4.8 -1.5 -0.1 -2.0 -0.3 +0.3 -0.5 -0.4 -0.3
-4.3 -1.0 +0.2 -2.1 -0.2 +0.4 -0.5 -0.4 -0.3
-5.5 -1.7 -0.2 -2.2 -0.4 +0.3 -0.6 -0.4 -0.3
17 in order to employ isodesmic eq 2 to evaluate both magnetic susceptibility exaltations and ASEs (X ) 15, 16, or 17).
X + trihydro-X f dihydro-X + monohydro-X
(2)
The energies of eq 2 applied to C12H12 (15), C14H8 (16), and C18H18 (17) and their hydrogenation products (trihydro-X indicates the fully hydrogenated species, dihydro-X the species with two double bonds hydrogenated, and monohydro-X the species with only one double bond hydrogenated) are essentially zero (Table 5). This suggests that all three molecules are NOT homoaromatic. (The same equation applied to benzene and its respective hydrogenation products gives an ASE of 35.8 kcal/mol at UB3LYP/6-311+G** + B3LYP/6-31G* ZPVE; see also
eq 1 in Section 3.) However, the magnetic susceptibility exaltations of 15-17 (Table 5), also evaluated according to eq 1, suggest a different conclusion: the exaltations are diamagnetic for 15 (-40.4 ppm-cgs), 16 (-8.9 ppmcgs), and 17 (-56.3 ppm-cgs). By definition, the magnetic susceptibility exaltation (Λ) is given as the difference between the actually measured or computed magnetic susceptibility (χΜ) and the quantity estimated from an increment scheme (χΜ′).114-116 The values thus derived are in close agreement (Λ(15) ) -37.6 ppm-cgs, Λ(16) ) +6.9 ppm-cgs, Λ(17) ) -59.9 ppm-cgs) with those derived by isodesmic eq 2. What is the reason for the difference in the results of the energetic and the magnetic susceptibility exaltation evaluations? The problem is that 15-17 are highly strained. Strain results from the four-membered rings, from the pyramidalization of the C-C double bonds, and possibly from repulsive interactions of the proximal π-systems. The optimized geometries of the partially hydrogenated species of 15-17 (Figure 6) show clearly that the geometries of 15 and 17 are more flexible and the strain is relieved upon hydrogenation. This strain relief counteracts the ASE effect when eq 1 is employed. The σ-framework of 16 is too rigid, so the tricoordinate carbon atoms cannot reduce their large pyramidalization angles significantly. We suggest two alternative equations to take these special geometric features into account. First we only use the triene species and the fully hydrogenated analogues of 15-17 to propose the following isodesmic equation (X ) 15, 16, or 17).
X + 3 ethane f perhydro-X + 3 ethylene
(3)
As there should be less strain in the perhydro-X compound than in X, eq 3 should be exothermic if X is not stabilized by homoaromaticity. But the computed (116) Dauben, H. P., Jr.; Wilson, J. D.; Laity, J. L. In Nonbenzenoid Aromatics; Snyder, J. P., Ed.; Academic Press: New York, 1971; Vol. 2, pp 167-206.
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Stahl et al. TABLE 5. Aromatic Stabilization Energies (ASEs) and Diamagnetic Susceptibility Exaltations (Λ) Evaluated According to Different Homodesmotic and Isodesmic Equations
computed magnetic susceptibility (χΜ) [ppm-cgs] C12H12 (15) C14H8 (16) C18H18 (17) benzene a
-122.5 -81.5 -194.5
diamagneti susceptibility exaltation (Λ) via increment scheme115,116
diamagnetic susceptibility exaltation (Λ) according to eq 2 [ppm-cgs]
-37.6 +6.9 -59.9 -13.7
-40.4 -8.9 -56.3
ASE according to eq 2 [kcal/mol]
ASE according to eq 3 [kcal/mol]
-1.5 +1.6 +1.1 +35.8
+3.1 -97.5 +38.4 +55.1
ASE according to eqs 4a,b [kcal/mol] +14.2 +27.3 +60.7a
According to eq 4.
FIGURE 6. Optimized geometries (B3LYP/6-31G*) of the hydrogenation products of trienes 15-17.
enthalpies (∆HR(298 K)) for eq 3 are endothermic for 15 (+3.1 kcal/mol) and 17 (+38.4 kcal/mol) and are only 6608 J. Org. Chem., Vol. 67, No. 19, 2002
dramatically exothermic for 16 (-97.5 kcal/mol). Hence, analogous to the evaluated magnetic susceptibility ex-
Resurrection of Neutral Tris-homoaromaticity
altations, 15 and 17 appear to be stabilized effectively, while 16 is unfavorable. To compensate for the effects of strain to a large extent, we constructed an artificial reference system by “cutting” one four-membered ring and the two attached double bonds out of the structure of 15. We then replaced the methylene carbon atoms of the next four-membered rings attached to the double bonds by hydrogen atoms, retaining the angles as in the optimized structure of 15. We only optimized the bond lengths of the C-C double bonds and the terminal C-H bonds in this reference compound. Consequently, we also computed an ethylene reference structure with the same pyramidalization angles found in 15. We applied the same construction scheme to provide a reference for 17.
TABLE 6. Energies Computed with MM3 and MM4 MM3 ∆∆Hf s-trans-butadiene benzene 15 16 17 18 19 20
0.0 17.8 5.8 5.2 5.8 5.7 5.6 5.8
∆Eel
4.5 2.8 5.6 4.5 4.5 4.7
These results can be compared with ASEs derived from MM3 and MM4 force field computations (see Computational Methods). As heats of formation for structures with small rings cannot be computed with MM4, no correction for strain can be applied to the “pure” electronic resonance energies. All energies evaluated by MM3 and MM4 are given in Table 6. For 15, an increase in strain (∆Estrain) is indicated by a 1.3 kcal/mol difference between ∆∆Hf and ∆Eel. As this does not overcome the stabilization from homoconjugation completely, the net ASE is 3.2 kcal/mol. Structure 16, which we ruled out as homoaromatic despite NICS evidence for some diatropic ring current, shows a stabilization energy of about 2.8 kcal/mol. This is effectively counterbalanced by a strain increase of 2.4 kcal/mol. Molecule 17, which we termed
∆Estrain
1.3 2.4 0.2 1.2 1.2 1.1
ASE
∆Eel
17.8 3.2 0.4 5.4 3.3 3.3 3.6
-0.2 18.1 6.0 4.3 7.2 6.4 6.0 6.6
TABLE 7. Comparison of the Aromatic Stabilization Energies [kcal/mol] Evaluated by Means of Eqs 4a and 4b and the MM3 Molecular Mechanics Approach ASE according to eq 4a,b benzene reference according to eq 5 percentage of the benzene ASE ASE according to MM3 benzene reference percentage of the benzene ASE
Using the two homodesmotic equations 4a and 4b, we obtained ASEs for 15 of -14.2 kcal/mol and -27.3 kcal/ mol for 17. Equations 4a and 4b should be largely independent of strain and therefore are expected to provide reliable ASE estimates for 15 and 17. One can also design an analogous eq 5 for benzene where s-cisbutadiene is removed by eliminating two adjacent carbon atoms with their directly bound hydrogens. We only add two hydrogen atoms to the terminal carbons of this C2vsymmetric s-cis-butadiene thus derived in a benzene-like geometry. We proceed in the same way with the ethylene fragment, add two hydrogen atoms, and compute the energy for these artificial references both in benzene-like geometries. For benzene, the computed ASE is -60.7 kcal/mol using eq 5. Though this is certainly not the best way to estimate the ASE of benzene, it is useful to calibrate the ASEs we derived for 15 and 17 by eqs 4a and 4b. Thus, the ASE of -27.3 kcal/mol for 17 (eq 4a) estimates a stabilization due to homoaromaticity for 17 of 45% of the ASE for benzene, and 15, with an ASE of -14.2 kcal/mol (eq 4b), benefits from 23% of the benzene stabilization.
MM4
15
17
14.2 60.7 23% 3.2 17.8 18%
27.3 60.7 45% 5.4 17.8 30%
the “best tailored” system for effective homoconjugation, has the largest stabilization energy (5.4 kcal/mol) of all species studied, and most importantly, strain increase does not overcome this aromatic stabilization. Hence, our conclusion based on density functional studies of magnetic susceptibilities, NICS, and energetic considerations is consistent with MM3 force field computations. For a relative quantification (Table 7) of the stabilization energies derived by MM3, the Dewar RE for benzene, calculated from MM3 heats of formation, is 17.8 kcal/ mol. Hence, an ASE of 5.4 kcal/mol for 17 is 30% of the benzene value and, therefore, in reasonable agreement with our DFT evaluations described above (45%). The strain-corrected ASE for 15 via MM3 is 3.2 kcal/mol and therefore 18% of the benzene value, which is in good agreement with our DFT results (23%). 4.5 Additional Candidates. Having validated the applicability of NICS to distinguish neutral in-plane trishomoaromatics from nonhomoaromatics, we examined some additional homoaromatic candidates (Figure 7). Structure 20 is similar to 17 (Figure 4), but the linkages attached to the tetravalent carbon atoms of the fourmembered rings are extended by an additional methylene (CH2) unit. While the C-C double-bond distance compared to that in 17 is essentially unchanged (1.384 vs 1.383 Å), the through-space distance is increased (1.816 Å in 20 vs 1.781 Å in 17). The pyramidalization angle, 29.3°, also is larger (24.8° in 17). These geometric features suggest diminished homoaromatic character compared to 17 but an increase compared to 15. Our NICS results indeed reflect this expectation: the GIAONICS (Table 8) are slightly smaller than that in 17 (Table 2) but significantly larger than that in 15. The decisive π-contributions of the C-C double bonds in the center are essentially equal to those in 17. The computed diamagnetic susceptibility exaltation with reference to an increment value114,116 is -36.3 ppm-cgs (Table 9). Hence, we conclude that 20 also sustains a diatropic ring current. According to resonance energy evaluations by MM3, the ASE (3.6 kcal/mol, Table 6) in 20 is dampened by an increase in strain between the localized and the J. Org. Chem, Vol. 67, No. 19, 2002 6609
Stahl et al.
FIGURE 7. Optimized geometries (B3LYP/6-311+G**) of the neutral in-plane tris-homoaromaticity candidates 18-20.
delocalized structure. Hence, 20 should be homoaromatic but is slightly inferior to our best candidate 17. In structures 18 and 19, three-membered rings were introduced to connect the saturated carbon atoms of the four-membered rings. The optimized geometries (Figure 7) of both species have short C-C double bonds, 1.364 and 1.357 Å, and rather long through-space distances of 1.884 and 1.893 Å, respectively. The pyramidalization angles, 34.2 and 37.1°, respectively, also are large. Cyclopropane units exhibit unusual magnetic properties and therefore have substantial effects32,117-119 on NICS and the diamagnetic susceptibility, as they are σ-aro(117) Sawicka, D.; Houk, K. N. J. Mol. Model. 2000, 6, 158-165. (118) Sauers, R. R. Tetrahedron 1998, 54, 337-348. (119) Bettinger, H. F.; Pak, C.; Schleyer, P. v. R.; Schaefer, H. F., III. J. Chem. Soc., Perkin Trans. 2 1999, 2377-2381.
6610 J. Org. Chem., Vol. 67, No. 19, 2002
matic themselves.105 Dissected NICS (Table 8) reveals only small effects from the cyclopropane moieties in 18 and 19 in the center of the ring but an increasing influence at points above the ring (-1.2 ppm in the center of 18 but -20.7 ppm at 2 Å above the ring). The π-contributions are comparable in both 18 and 19 to those in 15 (Table 3). The diamagnetic susceptibilities are computed to be -50.7 and -56.2 ppm-cgs, respectively (Table 9). Hence, we conclude that 18 and 19 exhibit cyclic electron delocalization but only to a small extent. The evaluated stabilization energies at MM3 (Table 6) for 18 and 19, 3.3 and 3.3 kcal/mol, respectively, also are in the same range as that for 15 (3.2 kcal/mol) but are much smaller than that for 17 (5.4 kcal/mol). Note that these MM3 values are smaller than those derived from other evaluation methods.
Resurrection of Neutral Tris-homoaromaticity TABLE 8. NICS for Neutral In-Plane Tris-homoaromaticity Candidates 18-20 method GIAO-B3LYP/6-31G*// B3LYP/6-311+G**
total
IGLO-SOS-PW91/TZ2P//B3LYP/6-311+G**
total CdC (π) CdC (σ) cyclobutane rings cyclopropane ring C-C bond between cyclopropane and cyclobutane moieties
0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å 0.0 Å 1.0 Å 2.0 Å
18a
19b
20
-26.7 -18.1 (-13.7) -35.0 (-4.7) -26.3 -18.3 (-13.9) -34.6 (-4.5) -7.2 -3.6 (-4.2) -0.9 (-1.5) -4.0 -2.1 (-1.5) -0.9 (-0.6) -13.8 -7.8 (-7.8) -1.8 (-2.9) -1.2 -3.6 -20.7 +1.1
-27.3 -17.7 -34.8 -27.0 -18.0 -34.4 -6.6 -4.5 -2.1 -3.6 -0.7 +0.6 -14.4 -8.4 -1.8 -0.9 -3.0 -20.7 +1.2
-28.1 -14.8 -5.8 -28.6 -15.3 -5.8 -18.0 -12.0 -5.7 +2.1 +3.0 +1.8 -14.4 -6.9 -1.6
+1.5 -3.6
+1.5 -3.9
a NICS were computed along the threefold axis; values computed toward the three-membered ring are given first, and values determined along the other direction are given in parentheses. The center of the cyclopropane moiety is at 2.4 Å. b NICS were computed along the threefold axis. Due to the point symmetry of the molecule, NICS was computed only in one direction and the cyclopropane contributions are only those of the ring in this direction. Also, only three C-C single bonds connecting the cyclopropane and cyclobutane moieties were taken into account. The center of the three-membered ring is at 2.4 Å along the threefold axis.
TABLE 9. Computed Magnetic Susceptibilities (CSGT-B3LYP/6-311+G**) for 18-20 as Well as Exaltations with Reference to Increment Values114,116
18 19 20
computed magnetic susceptibility χM [ppm-cgs]
magnetic susceptibility exaltation Λ [ppm-cgs]
-154.6 -179.1 -204.5
-50.7 -56.2 -36.3
5. Conclusions Numerous candidates for neutral tris-homoaromaticity in hydrocarbons proposed in the past have stimulated lively and controversial discussions. Following earlier work by McEwen and Schleyer35 as well as Jiao and Schleyer,73 we designed refined σ-frameworks in which the long-disputed in-plane neutral tris-homoaromaticity finally is firmly established. All magnetic and energetic criteria agree that 17 is the best σ-framework for the realization of neutral tris-homoaromaticity in hydrocarbons. It has large negative NICS values (with π-contributions of -18.0 and -12.7 ppm in the center and at 1 Å above the ring, respectively), a diamagnetic susceptibility
exaltation Λ ) -56.3 ppm-cgs, and more than one-third of the aromatic stabilization energy of benzene. Structure 15 also is homoaromatic, with a diamagnetic susceptibility exaltation Λ ) -40.4 ppm-cgs and about 20% of the benzene stabilization. The cage, 16, however, sustains a weak diatropic ring current, but its unfavorable σ-skeleton overrides any stabilization and is therefore not a promising candidate for the realization of neutral trishomoaromaticity. Among the second set of molecules investigated (1820), 20 exhibits the largest dissected NICS π-contributions and is closely related to 17. Dissected NICS for 18 and 19 indicates weak diatropic ring currents in these structures, and the resonance energies computed with MM3 and MM4 are comparable to that for 15. Though 17 appears to be the most promising trishomoaromatic candidate, 15 might be easier to synthesize. We encourage experimental investigation. Supporting Information Available: Tables of energies and structures. This material is available free of charge via the Internet at http://pubs.acs.org. JO016358A
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