10952
J. Phys. Chem. 1996, 100, 10952-10955
Computational Study of the Thermochemistry of C5H5+ Isomers: Which C5H5+ Isomer Is the Most Stable? Mikhail N. Glukhovtsev,*,1a Robert D. Bach,1a and Sergei Laiter1b Department of Chemistry, Wayne State UniVersity, Detroit, Michigan 48202, and Laboratory for Molecular Modeling, School of Pharmacy, UniVersity of North Carolina, Chapel Hill, North Carolina 27599 ReceiVed: April 17, 1996X
G2, G2(MP2), and G2(B3LYP/MP2/CC) calculations show the vinylcyclopropenyl cation 3 to be the lowest energy of the C5H5+ isomers. The calculated energy difference between the cyclopentadienyl cation 2 and the vinylcyclopropenyl cation 3 is very small (11.9 and 13.1 kJ mol-1 at G2 and G2(B3LYP/MP2/CC) levels, respectively), and higher level corrections used in G2, G2(MP2), and G2(B3LYP/MP2/CC) theories have a crucial effect upon it. Calculations using G2 theory without higher level corrections indicate that the cyclopentadienyl cation 2 is 0.2 kJ mol-1 more stable than the vinylcyclopropenyl cation 3. The calculated ∆Hf298 values for 2 and 3 are 1090.6 and 1081.1 kJ mol-1, respectively. The disagreement of the calculated G2 ∆Hf298(2) and ∆Hf298(3) values with the experimental estimates of 1052 and 1012 kJ mol-1 leads to the suggestion that these experimental estimates need to be reexamined. The calculated electron affinity for the cation 2 (8.41 eV using G2 theory) is in excellent agreement with the experimental value of 8.41 eV. Calculations of the ∆Hf298 value for the nonclassical pyramidal structure (4) of (CH)5+ lead to the value of 1145.3 kJ mol-1.
1. Introduction The cyclopropenyl cation (1) has been suggested to be a principal precursor in the formation of soot in fuel-rich flames.2 This process involves the reaction of the cyclopropenyl cation with acetylene (eq 1) as an initial step of the mechanism that leads to the formation of successively larger cations and eventually soot particles. To understand the mechanism of reaction 1, it is important to determine what structures are the most stable isomers of C3H3+ and C5H5+.
cyclopropenyl cation (1) + acetylene f C5H5+ (3) (1) Although the available experimental data undoubtedly indicate that the cyclopropenyl cation is the lowest energy C3H3+ isomer and that its enthalpy of formation (∆Hf298 ) 1075 kJ mol-1) is apparently well established,3 both experimental and theoretical data on the relative energies of the C5H5+ species remain controversial.3-6 Experimental3 and computational4-6 data show that the cyclopentadienyl cation 2 having the triplet ground state7 and the vinylcyclopropenyl cation 3 are the lowest energy isomers of C5H5+. Which of these two isomers has a lower energy is still an open question. Lias et al. in their compendium on ion thermochemistry3 give ∆Hf298 values of 1052 and 1012 kJ mol-1 for 2 and 3, respectively. Calculations at the MP2/6-31G(d,p)//HF/6-31G(d) level4 predict ∆Hf298 ) 1062.3 kJ mol-1 for 3 and suggest that cation 3 is 94.0 kJ mol-1 lower in energy than triplet 2. In contrast, higher level calculations5 at the QCISD(T)/6-31G(d,p)//MP2/6-31G(d) level have indicated that the triplet cyclopentadienyl cation 2 has 8.4 kJ mol-1 lower energy than the vinylcyclopropenyl cation 3. The relative stability of the four-π electron antiaromatic cyclic triplet (CH)5+ ion 2 and its isomer 3, which contains an aromatic cyclopropenyl fragment but is destabilized, however, by the strain of the three-membered ring, is also important in discussions of energetic effects of aromaticity and antiaromaticity.6 X
Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)01134-3 CCC: $12.00
In an attempt to readdress the above controversies, we carried out calculations of the triplet cyclopentadienyl cation 2 and the vinylcyclopropenyl cation 3 using various levels of theory, the highest among them are G2,8 G2(MP2),9 and G2(B3LYP/MP2/ CC)10 calculations. We also calculated the pyramidal isomer 4, which is of interest as a consequence of its three-dimensional aromaticity.6 This structure, a number of derivatives of which were synthesized,11 has been suggested12 to be an intermediate in carbon atom scrambling in C5H5+ prior to acetylene loss.13 The (CH)5+ cyclic C2V structures of the singlet state were found5 to be higher in energy than the vinylcyclopropenyl cation 3 and were not considered here. 2. Computational Methods G2 theory8 corresponds effectively to calculations at the QCISD(T)/6-311+G(3df,2p) level with zero-point vibrational energy (ZPE) and higher level corrections. The GAUSSIAN92 program14 was employed. Geometries were optimized at the MP2(full)/6-31G(d) level. To obtain theoretical enthalpies of reactions at 298 K, vibrational contributions to temperature corrections to the enthalpy15 were derived using harmonic frequencies computed at the HF/6-31G(d) level and scaled by 0.8929 according to the G2 scheme8 and using standard statistical thermodynamics formulas.15 All relative energies and reaction energies in this paper correspond to enthalpy changes (∆H) at 0 or 298 K as indicated. The G2(B3LYP/MP2/CC) scheme suggested by Bauschlicher and Partridge10 is a modification of the G2(MP2) approach in which geometry optimization and calculation of the vibrational frequencies are carried out at the B3LYP/6-31G(d) level16a (using the combined Becke © 1996 American Chemical Society
Thermochemistry of C5H5+
J. Phys. Chem., Vol. 100, No. 26, 1996 10953
TABLE 1: Calculated G2 Total Energies (hartrees) and Relative Energies (kJ mol-1) of C5H5+ Isomers 2, 3, and 4 as well as the Energy with Respect to Their Dissociation Products, Cyclopropenyl Cation (CH)3+ 1 and Acetylene G2 (0 K) cyclopentadienyl cation 2 D5h vinylcyclopropenyl cation 3, Cs pyramidal C5H5+ isomer 4, C4V cyclopropenyl cation 1, D3h + HCtCH
G2 (298 K)
-192.764 78 -192.759 61
Erela Erel (0 K) (298 K) 0
0
-192.769 32 -192.763 21 -11.9b
-9.5
-192.743 83 -192.738 77
55.0
54.7
-192.685 03c -192.677 22 209.4
216.3
a Calculations using G2(MP2) theory give almost the same relative energies, which are -11.8, 53.0, and 209.8 kJ mol-1, respectively. For the cyclopropenyl cation 1, Etot (G2(MP2)) ) -115.496 95 hartrees (-115.492 84 hartrees at 298 K). For acetylene, Etot (G2(MP2)) ) -77.184 08 hartrees (-77.180 38 hartrees at 298 K). b G2 energies calculated without ZPE corrections lead to the relative energy of -10.8 kJ mol-1 for the vinylcyclopropenyl cation 3. c G2 energies of the cyclopropenyl cation, (CH)3+ 1, and acetylene are -115.499 29 hartrees (-115.495 18 hartrees at 298 K) and -77.185 74 hartrees (-77.182 04 hartrees at 298 K), respectively.
hybrid functional16b and the Lee-Yang-Parr nonlocal correlation functional16c), and the single-point energy is calculated at the CCSD(T)/6-311G(d,p) level rather than calculated using the QCISD(T) approach. In the G2(B3LYP/MP2/CC) scheme10 the harmonic frequencies are scaled with 0.98 and the value A for the higher level correction is 0.004 51 hartrees (the value B is the same (0.000 19 hartrees)10 as in G2 theory8). Calculations were also carried out at the B3LYP/6-311+G(3df,2p)//B3LYP/ 6-311G(d,p) and BD(T)/6-311G(d,p)//B3LYP/6-311G(d,p) (Brueckner doubles, including a perturbation correction for triple excitations)17 levels. The theoretical enthalpy of formation for vinylcyclopropenyl cation 3 was derived in three different ways: (1) from the G2 atomization energies and the experimental enthalpies of formation for the corresponding atoms, which were taken from ref 3; (2) and (3) from the G2 enthalpies of reactions 1 and 2 using experimental enthalpies of formation of the corresponding molecules, taken from ref 3.
cyclopropenyl cation (1) + ethylene f C5H5+ (3) + H2 (2) The determination of the formation enthalpy from the atomization energy calculated using G2 theory may lead to an overestimated value in the case of species containing multiple bonds and having strong π electron delocalization. For example, the ∆Hf298 value for benzene calculated from the G2 atomatization energy is 18.4 kJ mol-1 larger18 than the experimental value. As for the cyclopropenyl cation 1, the difference between the G2 enthalpy of formation calculated from the G2 atomization energy (∆Hf298 ) 1080.8 kJ mol-1) and the experimental ∆Hf298 value (1075 kJ mol)3 is much smaller than that for benzene, we have derived an estimate of the ∆Hf298 (3) value from the G2 atomization energy. This estimate for the vinylcyclopropenyl cation 3 was corrected, however, using the ∆Hf298 values found from the enthalpies of reactions 1 and 2. The ∆Hf298(3) value averaged from these theoretical estimates was taken as the final estimate. 3. Results and Discussion Which C5H5+ Isomer Is the Most Stable: The Energy Difference between the Cyclopropenyl and Cyclopentadienyl Cations. Calculated G2 energies of the C5H5+ isomers are listed in Table 1. Geometries of 2, 3, and 4 optimized at the MP2/
Figure 1. Geometries of C5H5+ isomers 2-4 optimized at the MP2(full)/6-31G(d) and B3LYP/6-311G(d,p) (in parentheses) levels.
6-31G(d) and B3LYP/6-311G(d,p) levels are shown in Figure 1. It is notable that both approaches lead to almost the same geometries of these cations. G2, G2(MP2), and G2(B3LYP/MP2/CC) calculations show the vinylcyclopropenyl cation 3 to be the lowest energy isomer of C5H5+, albeit the energy difference between 2 and 3 is very small (11.9 and 13.1 kJ mol-1 at G2 and G2(B3LYP/MP2/ CC) levels, respectively). The data presented in Table 2 reveal that the higher level corrections used in these schemes play a crucial role in the calculations of the energy difference between the singlet 3 and cyclic triplet 2. The calculations at the MP2, BD(T), CCSD(T), and QCISD(T) levels as well as at the G2 and G2(MP2) levels without these corrections either favor triplet 2 or give almost the same energies for structures 2 and 3 (Table 2). The B3LYP/6-311+G(3d,2p)//B3LYP/ 6-311G(d,p) calculations lead to almost equal energies for 2 and 3. The possibility of serious deviations of G2 calculated atomization energies from experimental ones, which may be caused by a problem with the higher level correction,19 is exemplified by triplet molecules O2 and S2.8a,18a The atomization energies of these molecules calculated using G2 theory are 10.0 and 13.8 kJ mol-1, respectively, smaller than the experimental values. Therefore, one may expect that the
10954 J. Phys. Chem., Vol. 100, No. 26, 1996
Glukhovtsev et al.
TABLE 2: Relative Energies (kJ mol-1) of Cyclopentadienyl Cation (2) and Vinylcyclopropenyl Cation (3) Calculated at Various Computational Levelsa computational level
Erel
b
MP2/6-311G(d,p)//MP2/6-31G(d) MP2/6-311G(2df,p)//MP2/6-31G(d)b MP2/6-311+G(3df,2p)//MP2/6-31G(d)b MP4/6-311G(d,p)//MP2/6-31G(d)b MP4/6-311+G(d,p)//MP2/6-31G(d)b MP4/6-311G(2df,p)//MP2/6-31G(d)b QCISD(T)/6-311G(d,p)//MP2/6-31G(d)b B3LYP/6-311+G(3df,2p)//B3LYP/6-311G(d,p) + ZPE(B3LYP/6-311G(d,p))c CCSD(T)/6-311G(d,p)//B3LYP/6-31G(d) + ZPE(B3LYP/6-31G(d))d BD(T)/6-311G(d,p)//B3LYP/6-31G(d) + ZPE(B3LYP/6-31G(d))e G2(MP2)f G2 G2(B3LYP/MP2/CC)g
6.3 3.3 1.2 6.5 6.8 3.4 5.4 0.8
G2 theory experimental estimatesa difference between the theoretical and experimental values a
3.7 3.8 -11.8 (+0.3)h -11.9i (+0.2)h -13.1 (-1.8)h
b a In kJ mol-1. E rel ) Etot(3) - Etot(2). With ∆ZPE(HF/6-31G(d)) correction (-1.1 kJ mol-1, scaled). c Total energy of 3 at B3LYP/6311+G(3df,2p)//B3LYP/6-311G(d,p) is -193.226 14 hartrees. ZPE(B3LYP/6-311G(d,p)) for 3 is 209.1 kJ mol-1. d Scaled ∆ZPE(B3LYP/6-31G(d)) ) -3.6 kJ mol-1. e Total energy of 3 at BD(T)/6-311G(d,p)//B3LYP/6-31G(d,p) is -192.669 30 hartrees. f G2(MP2) energies of 2 and 3 are -192.760 95 and -192.765 46 hartrees, respectively. g G2(B3LYP/MP2/CC) energy of the vinylcyclopropenyl cation 3 is -192.759 31 hartrees (-192.702 91 hartrees without higher level correction). h The energy differences calculated for 2 and 3 using G2, G2(MP2), and G2(B3LYP/MP2/CC) theories without higher level corrections are given in parentheses. i The relative energy is -10.8 kJ mol-1 without ZPE corrections.
TABLE 3: Calculated G2 Enthalpy of Formation (∆Hf) of Vinylcyclopropenyl Cation (3) (in kJ mol-1)a from the atomization energy from the G2 enthalpy of reaction 1 b from the G2 enthalpy of reaction 2 d averaged ∆Hf298 value
TABLE 4: Calculated G2 and Experimental Enthalpies of Formation (∆Hf) of Cyclopentadienyl Cation (2) and Vinylcyclopropenyl Cation (3) and the Energy Difference between 2 and 3 (in kJ mol-1)
∆Hf0
∆Hf298
1097.7
1089.1 1077.2c 1076.9e 1081.1
a The experimental estimate3 of ∆Hf298 (3) is 1012 kJ mol-1. b The enthalpy of reaction 1 calculated at the G2 level is -225.8 kJ mol-1 at 298 K. c Using the experimental ∆Hf298 values of the cyclopropenyl cation (1075 kJ mol-1) and acetylene (228.0 kJ mol-1) taken from ref 3. d The enthalpy of reaction 2 calculated at the G2 level is -53.7 and -50.3 kJ mol-1 at 0 and 298 K, respectively. e Using the experimental ∆Hf298 value of ethylene (52.2 kJ mol-1) taken from ref 3.
atomization energy of the triplet cyclopentadienyl cation 2 calculated using G2 theory can be underestimated as well. Thus, we can conclude that C5H5+ isomers 2 and 3 are very close in energy but a precise estimate of their energy difference requires very high-level calculations. Enthalpies of Formation of C5H5+ Isomers 2, 3, and 4. Experimental estimates3 of the enthalpies of formation of 2 and 3 are 1052 and 1012 kJ mol-1, showing the energy difference of 40 kJ mol-1 in favor of 3. This value is considerably larger than the calculated relative energy of the triplet 2. In order to ascertain the origin of this disagreement between the experimental and theoretical values, we calculated the enthalpy of formation of the vinylcyclopropenyl cation 3 using the G2 atomization energy of 3 and the enthalpies of reactions 1 and 2 as described above. The ∆Hf298(3) value averaged from these three theoretical estimates (Table 3) is 1081.8 kJ mol-1. This value is larger than the experimental estimates3,20 of 1012 and 1000 ( 21 kJ mol-1 (Table 4). The disagreements between theoretical and experimental estimates of the ∆Hf298(3) value and the energy difference for isomers 2 and 3 with the G2
∆Hf298(2)
∆Hf298(3)
∆∆Hf298(3 - 2)
1090.6 1052 39
1081.1 1012 69
-9.5 -40 30
The experimental ∆Hf298 values were taken from ref 3.
calculated value prompt us to suggest that the experimental ∆Hf298(3) value3 is not accurate and needs to be corrected. The enthalpy of formation of the cyclopentadienyl cation 2 calculated from the G2 energy difference between 2 and 3 (Table 1) is 1090.6 kJ mol-1 at 298 K. This value differs from the experimental estimate3,13 of 1052 kJ mol-1. However, the G2 calculated electron affinity of the cyclopentadienyl cation 2 (8.41 eV; G2 energy of cyclopentadienyl radical is -193.074 01 hartrees) is in excellent agreement with the experimental value of 8.41 eV.3 Therefore, we can conclude that the experimental estimate for ∆Hf298(2) also needs reappraisal. Stabilization of the nonclassical pyramidal structure 4 was discussed by Stohrer and Hoffmann.21 We found that this structure is 55.0 kJ mol-1 higher in energy than the cyclopentadienyl cation 2 (Table 1) at the G2 level. Calculations of the ∆Hf298(4) value using the energy difference between 3 and 4 and the G2 enthalpy of formation of 3 lead to the value of 1145.3 kJ mol.-1 Acknowledgment. Computer time for this study was made available by the National Center for Supercomputing Applications (Urbana, Illinois). We thank the referee for helpful comments. M.N.G. also thanks Dr. Nico J. R. van Eikema Hommes for making the “Molecule” program available, which was used for drawing the structures in Figure 1. References and Notes (1) (a) Wayne State University. (b) University of North Carolina. (2) (a) Harris, S. J.; Weiner, A. M. Annu. ReV. Phys. Chem. 1985, 36, 31. (b) Calcote, H. F.; Gill, R. J. In Soot Formation in Combustion; Bockhorn, H., Ed., Springer: Berlin, 1994; p 471. (3) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data Suppl. 1 1988, 17. (4) Feng, J.; Leszczynski, J.; Weiner, B.; Zerner, M. C. J. Am. Chem. Soc. 1989, 111, 4648. (5) Glukhovtsev, M. N.; Reindl, B.; Schleyer, P. v. R. MendeleeV Commun. 1993, 100. (6) (a) Glukovtsev, M. N., Simkin, B.; Minkin, V. I. Russian Chem. ReV. (Engl. Transl.) 1985, 54, 54. (b) Minkin, V. I.; Glukhovtsev, M. N.; Simkin, B. Ya. Aromaticity and Antiaromaticity. Electronic and Structural Aspects; Wiley: New York, 1994. (7) Saunder, M.; Berger, R.; Jaffe, A.; McBride, J. M.; O’Neil, J.; Breslow, R.; Hoffman, J. M.; Perchonek, C.; Wasserman, E.; Hutton, R. S.; Kuck, V. J. J. Am. Chem. Soc. 1973, 95, 3017. (8) (a) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (b) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1995. 103, 4192. (9) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1993, 98, 1293. (10) Bauschlicher, C. W.; Partridge, H. J. Chem. Phys. 1995, 103, 1788. (11) Olah, G.; Prakash, G. K.; Williams, R. E.; Field, L. D.; Weid, K. Hypercarbon Chemistry; Wiley: New York, 1987. (12) Schwarz, H.; Thies, H.; Franke, W. In Ionic Process in the Gas Phase; Ferreira, M. A. A., Ed.; Reidel: New York, 1984; p 267. (13) Davidson, R. A.; Skell, P. S. J. Am. Chem. Soc. 1973, 95, 6843. (14) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
Thermochemistry of C5H5+ J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN-92; Gaussian Inc.: Pittsburgh, PA, 1992. (15) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab. Initio Molecular Orbital Theory; Wiley: New York, 1986. (16) (a) Stevens, P. J.; Devlin, F. J.; Chablowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 80, 11623. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (c) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B41, 785. (17) Handy, N. C.; Pople, J. A.; Head-Gordon, M.; Raghavachari, K.; Trucks, G. W. Chem. Phys. Lett. 1989, 164, 185.
J. Phys. Chem., Vol. 100, No. 26, 1996 10955 (18) (a) Nicolaides, A.; Radom, L. J. Phys. Chem. 1994, 98, 3092. (b) Glukhovtsev, M. N.; Laiter, S. Theor. Chim. Acta 1995, 92, 327. (19) Raghavachari, K.; Curtiss, L. A. In Modern Electronic Structure Theory; Yarkony, D. R. Ed.; World Scientific: Singapore, 1995; p 991. (20) McCrey, D. A.; Freiser, B. S. J. Am. Chem. Soc. 1978, 100, 2902. (21) Stohrer, W. D.; Hoffmann, R. J. Am. Chem. Soc. 1972, 94, 1661.
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