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Tri- and Tetraprotonated Ethane (C2H93+ and C2H104+) Containing Five- and Six-Coordinate Carbons Golam Rasul,* G. K. Surya Prakash, and George A. Olah Loker Hydrocarbon Research Institute and Department of Chemistry, UniVersity of Southern California, UniVersity Park, Los Angeles, California 90089-1661 ReceiVed: September 15, 2010; ReVised Manuscript ReceiVed: October 6, 2010
Triprotonated ethane (C2H93+) 4 and tetraprotonated ethane (C2H104+) 6 were found by ab initio MP2/ccpVTZ calculations as viable energy minima. Their structure has three and four two-electron three-center (2e-3c) bonds, respectively. In contrast, calculations showed no minimum-energy structure on the potential energy surface of pentaprotonated ethane (C2H115+). Charge-charge repulsion may approach its limit in this case. Sufficient stabilization of polycations by Schmidbaur-type auration with (C6H5)3PAu, an isolobal analogue of H+, should be possible for the preparation of the polyaurate derivatives of poly protonated ethane allowing their structural study. SCHEME 1
Introduction CH5+ is considered the parent of nonclassical carbocations because it contains a five-coordinate carbon atom (Scheme 1).1 Kekule’s2 four valent classical bond theory is unable to explain bonding in higher coordinate carbocations. These require the involvement of two-electron three-center (2e-3c) bonds as suggested by Olah.3 Such bonding is key to the σ-bond reactivity of saturated hydrocarbons in strong acids. Ab initio studies reconfirmed4 the preferred global minimum Cs symmetrical structure5 with a 2e-3c bond as suggested originally by Olah, Klopman, et al.6 Assumed facile bond-to-bond (polytopal) rearrangements were later confirmed by high-level calculations by Schleyer et al.,5a which showed CH5+ to be highly fluxional. The structure of the CH62+ dication containing two 2e-3c (carbonium type) bonds was calculationally studied by Olah et al (Scheme 1).7 We have also reported that even the parent seven-coordinate carbotrication, triprotonated methane (CH73+), is an energy minimum with three 2e-3c bonding interactions (Scheme 1).8 Diprotonated ethane (C2H82+) was studied7a by Lammertsma et al. The HF/6-31G* calculated structure (C2 symmetry) contains two pentacoordinated carbons with a 2e-3c bonding interactions on each. This further demonstrates the general importance of 2e-3c interactions in protonated alkanes. Formation of protonated di- and polycations in superacid solutions was also found by Olah, not only in case of saturated hydrocarbons but also in case of varied heteroatom derivatives (Lewis bases) containing nonbonding electron pairs.9 Such protonation or protosolvation in the limiting case can lead to either gitonic (in which the positive charge bearing centers are adjacent or geminal) or distonic (in which the positive charge bearing centers are separated by at least one carbon) onium dications. By using gold(I) organometallic ligand (LAu+) as isolobal substitute for H+, Schmidbaur et al. have prepared cationic trigonal bipyramidal10 and dicationic octahedral11 gold complexes containing five- and six-coordinate carbons. Such complexes were characterized by X-ray structural analysis (Scheme 2). They represent isolobal analogues of CH5+ and CH62+, respectively. * Corresponding author.
SCHEME 2
The significant metal-metal bonding occurring in these gold complexes renders them remarkably stable isolable crystalline salts. They have greatly contributed to our knowledge of highercoordinate carbocations. In continuation of our study of CH5+ and higher protonated alkanes, we have now extended our investigations to tri- and tetraprotonated ethanes by using highlevel ab initio calculations. Calculations Geometry optimizations, frequency calculations, and natural bond orbital (NBO) analysis were carried out with the Gaussian 09 program.12 The geometry optimizations were performed at the ab initio MP2/cc-pVTZ level. Vibrational frequencies at the MP2/cc-pVTZ//MP2/cc-pVTZ level were used to characterize stationary points as minima (number of imaginary frequency (NIMAG) ) 0) or transition states (NIMAG ) 1) and to evaluate zero-point vibrational energies (ZPE), which were scaled by a factor of 0.95.13 For improved energy, calculations were carried out by using the accurate W1BD method14 as implemented in Gaussian 09 program.12 Atomic charges at the MP2/cc-pVTZ//MP2/cc-pVTZ level were obtained by using the NBO analysis15 method.
10.1021/jp108820r 2010 American Chemical Society Published on Web 10/21/2010
C2H93+ and C2H104+ Containing Five- and Six-Coordinate Carbons
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Figure 2. MP2/cc-pVTZ calculated transition states of 7-9.
TABLE 1: Total Energies (au), ZPE,a and Relative Energies (kcal/mol)
Figure 1. MP2/cc-pVTZ structures and NBO charges (given in parentheses) of dications 1-6.
Results and Discussion Tri- and tetraprotonated ethane results by successive protonation of ethane (C2H6) 1 leading from protonated (C2H7+) 2 and diprotonated (C2H82+) ethane 3 to triprotonated (C2H93+) 4 and 5 and tetraprotonated ethane (C2H104+) 6 (Figure 1). These structures were calculated at the MP2/cc-pVTZ level (Figure 1). Transition states 7, 8, and 9 for deprotonation of 3, 4, and 6, respectively, were also computed at the same MP2/cc-pVTZ level (Figure 2). Calculated energies are given in Table 1. As mentioned in the introduction, diprotonated ethane (C2H82+) was first theoretically investigated by Lammertsma et al.7a who found that a C2 symmetrical structure (Scheme 3) is minimum at the HF/6-31G* level. Later, Olah et al.16 showed that both C2 symmetrical structure and C2h structure 3 are the minima at the MP2/6-31G** level on the potential energy surface (PES). In fact, 2 is less stable than 3 by only 0.4 kcal/mol. The two 2e-3c bonds of the C2 symmetrical structure are almost perpendicular to each other, whereas they have an anti orientation in 3. At the MP2/cc-pVTZ level, the Cs symmetric form 4 and C2 symmetric form 5 were found to be energy minima for triprotonated ethane C2H93+. At the MP2/cc-pVTZ//MP2/ccpVTZ + ZPE level, the structure 4 was computed to be 6.0 kcal/mol more stable than the structure 5. By using W1BD theory,14 this energy difference reduces to only 2.3 kcal/mol. Structure 4 resembling a complex between +CH2CH2+ and
1 2 3 4 5 6 7 8 9
MP2/cc-pvtz
ZPE
rel. energyb
W1BD
rel. energyc
-79.62990 -79.85353 -79.86119 -79.57876 -79.56730 -79.10441 -79.74492 -79.55160 -79.09666
45.1 49.1 51.9 52.6 51.4 49.6 48.6 50.3 49.7
138.3 2.0 0.0 177.9 183.9 472.5 69.7 192.6 477.5
-79.76916 -79.98763 -79.99071 -79.70672 -79.70298 -79.23511 -79.88116 -79.68444 -79.22834
139.0 1.9 0.0 178.2 180.5 474.1 68.7 192.1 478.3
a ZPE at MP2/cc-pvtz//MP2/cc-pvtz scaled by a factor of 0.96. Relative energy at MP2/cc-pVTZ//MP2/cc-pVTZ + ZPE level. c Relative energy based on computed W1BD energies. b
SCHEME 3
three hydrogen molecules results in the formation of three 2e-3c bonds (Figure 1). Thus, the structure contains both fiveand six-coordinate carbons. Charge-charge repulsion is substantial in such a small trication. However, the bonding interactions of trication 4 are strong enough to counter charge-charge repulsion. The NBO charge calculations (Figure 1) show that the hydrogen atoms of 4 bear the positive charges. The C-H bond distances of 2e-3c interections are in the range of 1.195-1.253 Å. These are slightly longer than that found in the 2e-3c C-H bonds (1.188 Å) of diprotonated ethane 3 at the same theoretical level. The calculated H-H distances in the 2e-3c interections of 4 are 1.058 and 1.085 Å. These are also slightly longer than that found in the 2e-3 H-H bond of 3. On the other hand, the
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Rasul et al. SCHEME 4
Figure 3. PES of protonated ethane calculated by W1BD method.
trication 5 is a hydrogen-bridged structure. Each of the carbon in 5 is five-coordinated, involving a 2e-3c bond. We considered the possible deprotonation path for ion 4. By using W1BD theory,14 dissociation of 4 into C2H82+ 3 and H+ is calculated to be exothermic by 178.2 kcal/mol. The transition structure, 8, for the deprotonation process was located. The transition structure 8 lies 14.9 kcal/mol higher in energy than structure 4. It, therefore, has a substantial energy barrier for deprotonation. MP2/cc-pVTZ optimization shows that the propeller-shaped C2 symmetrical structure 6 is the only minimum on the PES of tetraprotonated ethane C2H104+ (Figure 1). Structure 6 contains two six-coordinate carbons. The structure formally resembles a complex between a tetrapositive acetylene 2+CHCH2+ with four hydrogen molecules resulting in the formation of four 2e3c bonds. The C-H bond distances of 6 (range 1.257-1.257 Å) are slightly longer than those found in similar 2e-3c C-H bonds (range 1.195-1.253 Å) of 4. The nature of two 2e-3c bonds on each of the carbon is slightly different. One of the 2e-3c interaction has a H-H bond distance of 1.183 Å, and the other has a distance of 1.217 Å. The calculated central C-C bond length of 6 (1.652 Å) is considerably longer than the corresponding C-C bond length of 4 (1.575 Å) as a result of strong charge-charge repulsion. However, the bonding interactions of tetracation 6 are strong enough to counter this strong charge-charge repulsion. Dissociation of 6 into C2H93+ 4 and H+ was calculated to be exothermic by 295.9 kcal/mol. The transition structure for the dissociation (9) lies just 4.2 kcal/mol higher in energy than structure 6. This shows that the tetracation 6, if formed, will dissociate spontaneously into C2H93+ 4 and H+. PES of protonated ethane calculated by W1BD method is depicted in Figure 3. We also searched for any minimum-energy structures of pentaprotonated ethane, C2H115+. At the MP2/cc-pVTZ level, no minimum could be found on the PES structure of C2H115+ (including a structure with five 2e-3c bonds as shown in Scheme 4). Thus, in C2H115+, charge-charge repulsion may have reached its prohibitive limit. Conclusion The present study at the MP2/cc-pVTZ level shows that triprotonated (C2H93+) 4 and tetraprotonated ethane (C2H104+) 6 are energy minima, although their deprotonations are highly exothermic. The calculated structure of the trication 4 contains a five- and a six-coordinate carbons with three 2e-3c bonds. Dissociation of 4 into C2H82+ 3 and H+ is calculated to be
exothermic by 178.2 kcal/mol. However, dissociation has a substantial energy barrier of 14.9 kcal/mol. On the other hand, tetraprotonated ethane C2H104+ 6 contains two six-coordinate carbons and has four 2e-3c bonds. Similar dissociation of 6 is highly exothermic by 295.9 kcal/mol and has a low energy barrier of 4.2 kcal/mol. This shows that the tetracation 6 is both kinetically and thermodynamically highly unstable. Although experimental verification of tri- and tetraprotonated ethane will be extremely difficult, better stabilization of some of these polycations by Schmidbaur-type auration6 with (C6H5)3PAu ligands, an isolobal analogue of H+, should be possible. Some of these species could also be formed experimentally by generating polycations, for example, the polycation of acetylene by Auger-electron emission embedded in H2. Pentaprotonated ethane (C2H115+) remains even computationally elusive because charge-charge repulsions appear to have reached a prohibitive limit. Acknowledgment. This paper is dedicated to Professor Paul von Rague´ Schleyer, a doyen of computational chemistry on the occasion of his 80th birthday. Support of our work by the Loker Hydrocarbon Research Instititue is gratefully acknowledged. References and Notes (1) Olah, G. A.; Prakash, G. K. S.; Williams, R. E.; Field, L. D.; Wade, K.; Hypercarbon Chemistry; John Wiley & Sons: New York, 1987. (2) Kekule, F. A. Ann. 1858, 106, 129. Kekule, F. A. Z. Chem. 1867, 3, 217. (3) Olah, G. A.; Chemical ReactiVity and Reaction Paths; Klopman, G., Ed.; Wiley: London, 1974. (4) Marx, D.; Parrinello, M. Nature 1995, 375, 216. (5) See also recent discussions on CH5+ structures based on highlevel ab initio calculations. (a) Schreiner, P. R.; Kim, S.-J.; Schaefer, H. F.; Schleyer, P. V. R. J. Chem. Phys. 1993, 99, 3716. (b) Scuseria, G. E. Nature 1993, 366, 512. (c) White, E. T.; Tang, J.; Oka, T. Science 1999, 284, 135. (6) Olah, G. A.; Klopman, G.; Schlosberg, R. H. J. Am. Chem. Soc. 1969, 91, 3261. Olah, G. A.; Schlosberg, R. H. J. Am. Chem. Soc. 1968, 90, 2726. (7) (a) Lammertsma, K.; Olah, G. A.; Barzaghi, M.; Simonetta, M. J. Am. Chem. Soc. 1982, 104, 6851. (b) Lammertsma, K.; Barzaghi, M.; Olah, G. A.; Pople, J. A.; Schleyer, P. V. R.; Simonetta, M. J. Am. Chem. Soc. 1983, 105, 5258. (8) Olah, G. A.; Rasul, G. J. Am. Chem. Soc. 1996, 118, 8503. (9) Olah, G. A. Angew. Chem., Int. Ed. Engl. 1993, 32, 767. (10) Scherbaum, F.; Grohmann, A.; Mu¨ller, G.; Schmidbaur, H. Angew. Chem., Int. Ed. Engl. 1989, 28, 463. (11) Scherbaum, F.; Grohmann, A.; Huber, B.; Kru¨ger, C.; Schmidbaur, H. Angew. Chem., Int. Ed. Engl. 1988, 27, 1544. (12) 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.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, 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,
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