本論文藉由理論計算的方法，在UB3LYP/6-31G(d)的計算層級下對各穩定點的結構做幾何優選，探討取代基對於α-sulfenyl-, α-sulfinyl-, and α-sulfonyl-5-(R)-5-hexenyl radicals以及2,5-hexadienyl radicals分子內環化反應的影響，以下將分為兩部分進行討論:

第一部分:
α-sulfinyl-5-hexenyl radicals在形成環狀產物時顯示了高位向選擇性，其生成五員環與六員環的產物比例為94.0/6.0，而在α-sulfenyl-, and α-sulfonyl-5-hexenyl radicals中環化形成六員環的比例較高。相反的，在C5接上甲基後產物則變成六員環，而其他的取代基如拉電子基的CN、NO2或者是推電子基的NH2等反應的主產物也是形成六員環，其中當反應物為α-sulfonyl-5-amine-5-hexenyl radicals時，經由計算後得到六員環的比例為100，為選擇性最高的反應物。

第二部分:
當不同種類的取代基如CN、NO2、CH3、NH2以及tert-butyl等取代在2,5-hexadienyl radicals的C1、C5以及C6位置上時，其對於分子內環化反應有不同效應的影響。當推電子基在C1上時，自由基的SOMO軌域能量會上升，進而增加與LUMO軌域之間的作用力，相反的拉電子基則會使SOMO軌域能量下降，進而增加與HOMO軌域之間的作用力。而上述的兩種作用力使得反應的活化能降低了0.9〜10.2 kcal/mol，使反應速率增加了3〜2.7 × 107倍。相似的作用力也發生在C6的位置，而反應的活化能降低了0.2-4.8 kcal/mol，反應速率則增加了2〜2800倍。而當取代基接在C5時則因為立障效應使產物變為六員環。最後，我們嘗試將雙取代基取代在C1以及C6的位置，並討論capto-dative effect對環化反應的影響，結果顯示拉電子基雙取代使活化能下降的較多。

We carried out the DFT calculation of intramolecular cyclization reaction of α-sulfenyl-, α-sulfinyl-, α-sulfonyl-5-(R)-5-hexenyl radicals and 2,5-hexadienyl radicals by density functional theory. All of the local minimum structures are optimized with 6-31G(d) basis set at the levels of UB3LYP. There are two sections rendered here.

Section 1:
The α-sulfinyl-5-hexenyl radical exhibits unexpected regioselectivity (94.0:6.0) via the 5-exo mode, whereas the α-sulfenyl- and α-sulfonyl-5-hexenyl radicals show increasing branching ratios of the 6-endo product. In contrast, the cyclization of the α-sulfur-based 5-methyl-substituted counterparts yields essentially the 6-endo products in all cases; in particular, the α-SO2-5-CH3-5-hexenyl radical gives high regioselectivity (98.8:1.2) via the 6-endo mode. Several other 5-substituted moieties, including the electron-withdrawing – CN and NO2 – or electron-donating substituents – NH2 – also proceed preferentially to 6-endo closure. The α-sulfonyl- 5-amine-5-hexenyl radical is calculated to proceed exclusively the 6-endo product, a demonstration of the high synthetic value of the reaction.

Section 2:
Various substituents – CN, NO2, CH3, NH2, and tert-butyl – at various positions – C1, C5 and C6 – were considered in the calculations. An electron-donating substituent on the C1 position raises the radical SOMO energies to increase the interaction with the alkene LUMO, whereas an electron-withdrawing counterpart lowers the SOMO and increases the interaction with the alkene HOMO. Both interactions decrease the activation energies, by 0.9 to 10.2 kcal/mol, and increase the rate of reaction rate, from 3 to 2.7 × 107 times. Similar results were obtained for the substituents at the C6 position, and the activation energies for the intramolecular cyclization were decreased by 0.2 - 4.8 kcal/mol and the reaction rate increased from 2 to 2800 times. The substituent at the C5 position favors the formation of a 6-endo product because of a steric effect. The effects of disubstituents at both C1 and C6 positions were also investigated; the results showed that the electron-withdrawing groups decrease most effectively the activation energies. The so-called captodative effect was also investigated.

1. Bennasar, M. L.; Juan, C.; Bosch, J. Chem. Commun. 2000, 2459- 2460.
2. Ellis, D. A.; Hart, D. J.; Zhao, L. Tetrahedron Lett. 2000, 41, 9357-9360.
3. Snider, B. B.; Buckman, B. O. J. Org. Chem. 1992, 57, 4883-4888.
4. Haney, B. P.; Curran, D. P. J. Org. Chem. 2000, 65, 2007-2013.
5. Beckwith, A. L. J.; Ingold, K. U. In Rearrangements in Ground and Excited States; de Mayo, P., Ed.; Academic: New York, 1980, pp 162-283.
6. (a) Beckwith, A. L. J. Tetrahedron 1981, 37, 3073 and references therein. (b) Beckwith, A. L. J.; Schiesser, C. H. Tetrahedron 1985, 41, 3925.
7. Surzur, J. M. In Reactive Intermediates; Abramovitch, R. A., Ed.; Plenum: New York, 1981; Vol. 2, Chapter 3.
8. Griller, D.; Ingold, K. U. Acc. Chem. Res. 1980,13, 317.
9. Jasperse, C. P.; Curran, D. P.; Fevig, T. L. Chem. Rev. 1991, 91, 1237-1286.
10. Heck, R. F.; Nolley, J. P., Jr. J. Am. Chem. Soc. 1968, 90, 5518.
11. Sonogashira K.; Tohda, Y.; Hagihara, N. Tetrahedron Lett. 1975, 4467.
12. (a) Gomberg, M. J. Am. Chem. Soc. 1900, 22, 757. (b) Gomberg, M. Chem. Ber. 1900, 33, 3150.
13. (a) Beckwith, A. L. J.; Meijs, G. F. J. Chem. Soc. Perkin Trans. 2 1979, 1535. (b) Beckwith, A. L. J.; Phillipou, G.; Serelis, A. K. Tetrahedron Lett. 1981, 22, 2811.
14. Spellmeyer, D. C.; Houk, K. N. J. Org. Chem. 1987, 52, 959-974.
15. Carey, F. A.; Sundberg, R. J. Advanced Organic Chemistry 4th Ed. Part A, 2000, Kluwer Academic/ Plenum Publishers, New York USA.
16. Korth, H, G.; Lommes, P.; and Sustmann, R. J. Am. Chem. Soc. 1984, 106, 663.
17. (a) Della, E. W.; Smith, P. A. J. Chem. Soc., Perkin Trans 1 2001, 445. (b) Della, E. W.; Smith, P. A. Tetrahedron Lett. 2001, 42, 481. (c) Della, E. W.; Smith, P. A. J. Org. Chem. 2000, 65, 6627. (d) Della, E. W.; Smith, P. A. J. Org. Chem. 1999, 64, 1798. (e) Della, E. W.; Knill, A. M.; Smith P. A. Chem. Commun. 1996, 14, 1637. (f) Della, E. W.; Knill, A. M. Tetrahedron Lett. 1996, 37, 5805. (g) Della, E. W.; Knill, A. M. J. Org. Chem. 1996, 61, 7529. (h) Della, E. W.; Knill, A. M. Aust. J. Chem. 1995, 48, 2047.
18. (a) Wilt, J. J. Org. Chem. 1981, 103, 5251; Tetrahedron 1985, 41, 3979. (b) Wilt, J. W.; Lustztyk, J.; Peeran, M.; Ingold, K. U. J. Am. Chem. Soc. 1988, 110, 281.
19. Pross, A. Theoretical and Physical Principles of Organic Reactivity, John Wiley & Sons: New Tork, 1995.
20. (a) Magnoli, D. E.; Murdoch, J. R. J. Am. Chem. Soc. 1981, 103, 7465. (b) Murdoch, J. R.; Magnoli, D. E. J. Am. Chem. Soc. 1982, 104, 3792. (c) Wolf, S.; Mitchell, J.; Schlegel, H. B. J. Am. Chem. Soc. 1981, 103, 7694.
21. (a) Murdoch, J. R. J. Am. Chem. Soc. 1983, 105, 2660. (b) Wolfe, S. Theoretical Aspects of Physical Organic Chemistry; John Wiley and Sons: New York, NY, 1992; pp 33-44. (c) Murdoch, J. R. J. Am. Chem. Soc. 1983, 105, 2159.
22. Gaussian 03, Revision C.02, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; and Pople, J. A.; Gaussian, Inc., Wallingford CT, 2004.
23. Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154.
24. (a) Janoschek, R.; Rossi, M. J. Int. J. Chem. Kinet. 2002, 34, 550-560. (b) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1999, 110, 4703. (c) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J. Chem. Phys. 1999, 110, 7650. (d) Janoschek, R.; Rossi, M. Int. J. Chem. Kin. 2002, 34, 550-560.
25. Beckwith, A. L. J.; Moad, G. J. Chem. Soc., Chem. Commun. 1974, 472.
26. Della, E. W.; Graney S. D. J. Org. Chem. 2004, 69, 3824-3835.
27. Della, E. W.; Graney S. D. Org. Lett. 2002, 4, 4065-5067.
28. Fleming, I. Frontier Orbitals and Organic Chemical Reactions; Wiley: London, UK, 1976.
29. Hansch, C.; Leo, A.; Taft, R. W. Chem. Rev. 1991, 91, 165; record the following values: SO2 (σI = 0.53), SO (σI = 0.52), and S (σI = 0.23).
30. Ke, B.-W.; Lin, C.-H.; Tsai, Y.-M. Tetrahedron. 1997, 53, 7805 and refs 2-4 therein.
31. Park, S. U.; Chung, S. K.; Newcomb, M. J. Am. Chem. Soc. 1986, 108, 240-244.
32. Giese, B. Angew. Chem., Int. Ed. Engl. 1983, 22, 753-764.
33. (a) Hehre, W. J.; Radom, L.; Schleyer, P. V. R.; Pople, J. A. Ab initio Molecular Orbital Theory: John Wiley & Sons: New Tork, 1986. (b) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry, McGraw-Hill: New York, 1989.
34. Jensen, F. Introduction to Computational Chemistry; Wiley publishing, 1999.
35. (a) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (b) Lee, C.; Wang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (c) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
36. (a) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B 864. (b) Kohn, W.; Sham, L. J. Phys. Rev. 1965, A1133. (c) Becke, A. D. J. Chem. Phys. 1992, 96, 2155. (d) Becke, A. D. J. Chem. Phys. 1992, 97, 9173. (e) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: Oxford UK 1989.
37. Cramer, C. J. Essentials of Computational Chemistry 2th Ed; John Wiley & Sons: New Tork, 2004.
38. Duncan, W. T.; Bell, R. L.; and Truong, T. N. J. Comput. Chem. 1998, 19, 1039.
39. (a)Anglada, J. M.; Domingo, V. M. J. Phys. Chem. A. 2005, 109, 10786. (b) Zhang,W.; Du, B. J. Mol. Struct. (THEOCHEM), 2006, 760, 131.
40. (a) Miehlich, B. ; Savin, A. ; Stoll, H. ; Preuss, H. Chem. Phys. Lett. 1989, 157, 200. (b) Wong, N. B.; Cheung, Y. S.; Wu, D. Y.; Ren, Y.; Wang, X.; Tian, A. M.; Li, W. A. J. Mol. Struct. (THEOCHEM) 2000, 507, 153. (c) Aubauer, C.; Klapotke, T. M.; Schulz, A. J. Mol. Strust. (THEOCHEM) 2001, 543, 285. (d) Reed, A. E.; Curtiss, L. A.; and Weinhold, F. Chem. Rev. 1988, 88, 899.