Theoretical Approach for the Equilibrium Structures and Relative Energies of C₇H₇⁺ Isomers and the Transition States between o-, m-, and p-Tolyl Cations

The equilibrium structures for the ground and transition states of $C_7H_7^+$ isomers have been investigated using sophisticated ab initio quantum mechanical techniques with various basis sets. The structures of tropyrium and benzyl cations have been fully optimized at the DZP CCSD(T) levels of theory. And the structures of o-, m-and p-tolyl cations are optimized fully up to the DZ CCSD(T) levels of theory. The geometries for the transition states between three isomers of tolyl cations have been optimized up to DZP CISD level of theory. The SCF harmonic vibrational frequencies for tropylium, benzyl, and three isomers of tolyl cations are all real numbers, which confirm the potential minima and each unique imaginary vibrational frequencies for TS1 and TS2 confirm the true transition states. The relative energy of the benzyl cation with respect to the tropyrium cation is predicted to be 28.5 kJ/mol and is in good agreement with the previous theoretical predictions. The 0 K heats of formation, ${\Delta}H^{\circ}_{f0}$, have been predicted to be 890, 1095, 1101, and 1110 kJ/mol for tropylium, ortho-, meta-, and para-tolyl cations by taking the experimental value of 919 kJ/mol for the benzyl cation as the base level. The relative stability between tolyl cations is in the order of ortho

• Ab initio;
• $C_7H_7^+$;
• Tolyl;
• Benzyl;
• Tropylium

1. Lin, C. Y.; Dunbar, R. C. J. Phys. Chem. 1994, 98, 1369 https://doi.org/10.1021/j100056a001
2. Dunbar, R. C.; Honovich, J. P.; Asamoto, B. J. Phys. Chem. 1988, 92, 6935 https://doi.org/10.1021/j100335a019
3. Dunbar, R. C.; Lifshitz, C. J. Chem. Phys. 1991, 94, 3542 https://doi.org/10.1063/1.459776
4. Lifshitz, C.; Levin, I.; Kababia, S.; Dunbar, R. C. J. Phys. Chem. 1991, 95, 1667 https://doi.org/10.1021/j100157a032
5. Shin, S. K.; Han, S. J.; Kim, B. Int. J. Mass Spectrom. Ion Processes 1996, 158, 345 https://doi.org/10.1016/S0168-1176(96)04463-1
6. Kim, B.; Shin, S. K. J. Chem. Phys. 1997, 106, 1411 https://doi.org/10.1063/1.473289
7. Choe, J. C.; Kim, M. S. Int. J. Mass Spectrom. Ion Processes 1991, 107, 103 https://doi.org/10.1016/0168-1176(91)85076-X
8. Cho, Y. S.; Kim, M. S.; Choe, J. C. Int. J. Mass Spectrom. Ion Processes 1995, 145, 187 https://doi.org/10.1016/0168-1176(95)04228-D
9. Olesik, S.; Baer, T.; Morrow, J. C.; Ridal, J. J.; Buschek, J.; Holmes, J. L. Org. Mass Spectrom. 1989, 24, 1008 https://doi.org/10.1002/oms.1210241107
10. Jackson, J.-A.; Lias, S. G.; Ausloos, P. J. Am. Chem. Soc. 1977, 99, 7515 https://doi.org/10.1021/ja00465a020
11. McLafferty, F. W.; Bockhoff, F. M. Org. Mass Spectrom. 1979, 14, 181 https://doi.org/10.1002/oms.1210140402
12. Lifshitz, C. Acc. Chem. Soc. 1994, 27, 138 https://doi.org/10.1021/ar00041a004
13. McLafferty, F. W.; Bockhoff, F. M. J. Am. Chem. Soc. 1979, 101, 1783 https://doi.org/10.1021/ja00501a024
14. Baer, T.; Morrow, J. C.; Shao, J. D.; Olesik, S. J. Am. Chem. Soc. 1988, 110, 5633 https://doi.org/10.1021/ja00225a008
15. Morgenthaler, L. N.; Eyler, J. R. Int. J. Mass Spectrom. Ion Processes 1981, 31, 153
16. Traeger, J. C.; Kompe, B. M. Int. J. Mass Spectrom. Ion Processes 1990, 101, 111 https://doi.org/10.1016/0168-1176(90)87004-Z
17. Houle, F. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1978, 100, 3293
18. Mcmillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493 https://doi.org/10.1146/annurev.pc.33.100182.002425
19. Eiden, G. C.; Lu, K.-T.; Badenhoop, J.; Weinhold, F.; Weisshaar, J. C. J. Chem. Phys. 1996, 104, 8886 https://doi.org/10.1063/1.471624
20. Dunbar, R. C. J. Am. Chem. Soc. 1973, 95, 472 https://doi.org/10.1021/ja00783a028
21. Cone, C.; Dewar, J. S.; Landman, D. J. Am. Chem. Soc. 1977, 99, 372 https://doi.org/10.1021/ja00444a011
22. Nicolaides, A.; Radom, L. J. Am. Chem. Soc. 1994, 116, 9769 https://doi.org/10.1021/ja00100a060
23. Shin, S. K. Chem, Phys. Lett. 1997, 280, 260 https://doi.org/10.1016/S0009-2614(97)01145-7
24. Ignatyev, I. S.; Sundius, T. Chem. Phys. Lett. 2000, 326, 101 https://doi.org/10.1016/S0009-2614(00)00767-3
25. Huzinaga, S. J. Chem. Phys. 1965, 42, 1293 https://doi.org/10.1063/1.1696113
26. Dunning, T. H. J. Chem. Phys. 1970, 53, 2823 https://doi.org/10.1063/1.1674408
27. Dunning, T. H. J. Chem. Phys. 1971, 55, 716 https://doi.org/10.1063/1.1676139
28. Yamaguchi, Y.; Osamura, Y.; Goddard, J. D.; Schaefer, H. F. A New Dimension to Quantum Chemistry: Analytic Derivative Methods in Ab initio Molecular Electronic structure Theory; Oxford University Press: New York, 1994
29. Brooks, B. R.; Laidig, W. D.; Sate, P.; Goddard, J. D.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1980, 72, 4652 https://doi.org/10.1063/1.439707
30. Scheiner, A. C.; Scuseria, G. E.; Rice, J. E.; Lee, T. J.; Schaefer, H. F. J. Chem. Phys. 1987, 87, 5361 https://doi.org/10.1063/1.453655
31. Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1982, 77, 5647 https://doi.org/10.1063/1.443771
32. Janssen, C. L.; Seidl, E. T.; Scuseria, G. E.; Hamilton, T. P.; Yamaguchi, Y.; Remington, R. B.; Xie, Y.; Vacek, G.; Sherrill, C. D.; Crawford, T. D.; Fermann, J. T.; Allen, W. D.; Brocks, B. R.; Fitzgerald, G. B.; Fox, D. J.; Gaw, J. F.; Handy, N. C.; Laidig, W. D.; Lee, T. J.; Pitzer, R. M.; Rice, J. E.; Saxe, P.; Scheiner, A. C.; Schaefer, H. F. PSI 2.0.8; PSITECH Inc.: Watkinssvills, GA. U.S.A., 1994
33. Cabana, A.; Bachand, J.; Giguere, J. Can. J. Phys. 1974, 52, 1949 https://doi.org/10.1139/p74-256
34. Grev, R. S.; Janssen, C. L.; Schaefer, H. F. J. Chem. Phys. 1991, 95, 5128 https://doi.org/10.1063/1.461680
35. Klots, C. J. Phys. Chem. 1992, 96, 1733 https://doi.org/10.1021/j100183a044

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10. On the Benzylium/Tropylium Ion Dichotomy: Electronic Absorption Spectra in Neon Matrices vol.123, pp.13, 2002, https://doi.org/10.1002/ange.201008036
11. On the Benzylium/Tropylium Ion Dichotomy: Electronic Absorption Spectra in Neon Matrices vol.50, pp.13, 2002, https://doi.org/10.1002/anie.201008036
12. Exploration of minima on the C 7 H 7 + $_{\boldsymbol {7}} \text{H}_{\boldsymbol {7}}^{\boldsymbol {+} }$ surface: Structural, stability- and charge-related considerations vol.126, pp.4, 2002, https://doi.org/10.1007/s12039-014-0646-4