1738 J. zyxwvuts Org. Chem. 1980,45, zyxwvut 1738-1748 zyxwv Topological Resonance Energies of Conjugated Ions, Radicals, and Ion Radicals’ Predrag IliE2 and Nenad TrinajstiE* The Rugjer BoBkoviE Institute, 41001 Zagreb, Croatia, Yugoslavia Received June 21, 1979 Topological resonance energy, TRE, defined as the topological contribution of ring closure with respect to a reference noncyclic structure, is applied to a set of 150 conjugated species. All of them are either closed-shell charged or open-shell neutral and charged species. The calculated TRE values were correlated with zyxw 88 experimental observations. It is shown that the TRE method is generally succes’sful in predicting the degree of aromaticity correlated with stability of conjugated ions, radicals, and ion radicals. Introduction Study of the chemistry of conjugated ions, radicals, and ion radicals has advanced in the last decade3+ owing to improvements in preparative techniques.’* However, the interest in preparation of such *-electronic species goes back into the last century (e.g., the preparation of tropy- lium bromidelo) although their true nature was not rec- ognized. The aromaticity (the intuitive but working con- cept for characterizing unsaturated organic mo1ecules)’l of ions and radicals, outside of monocyclic systems (an- nulenes and annular ions and radicals)12 which follow the Huckel rule,13until recently14could not be studied within the Hiickel theory.l5J6 Because of their definitions, the excellent aromaticity indexes Dewar resonance energy (DRE)” and resonance energy per A electron (REPE)ls zyxwvu can be used to predict the aromatic behavior of only closed- shell conjugated system^.'^ Dewar20has calculated the aromatic stabilization energies of several monocyclic ions and radicals by using the MmDO/3 theory. Unfortunately, MIND0/3 is not a simple method to use.21 Thus, people interested in novel aromatic ions and radicals, and not (1) This work is supported in part by (a) the self-managing Authority for Scientific Research of“ Croatia, (b) National Science Foundation Grant No. F6F006-Y, and (c) the Republic Assembly for Scientific Work of Bosnia and Herzegovina. (2) Faculty of Natural Sciences and Mathematics, The University in Sarajevo, 71000 Stuajevo, Bosnia and Herzegovina, Yugoslavia. (3) See, for example, the series of collective volumes and monographs “Reactive Intermediates in Organic Chemistry”, G. A. Olah, Ed., Wiley, New York, 1968. (4) P. J. Garratt and M. V. Sargent, Adu. Org. Chem., 1, 1 (1969). (5) N. S. Isaacs, “Reactive Intermediates in Organic Chemistry”, G. A. Olah, Ed., Wiley, New York, 1974. (6) D. Lewis and D. Peters, “Facts and Theories of Aromaticity”, Macmillan, London, 1975. (7) G. R. Stevenson, M. Colon, I. Ocasio, J. G. Concepcih, and A. McB. Block, J. Phys. Chem., 79, 1685 (1975). (8) G. A. Olah, J. S. zyxwvutsrqp Staral, G. Liang, L. A. Paquette, W. P. Melega, and M. J. Carmody, J. Am. Chem. SOC., 100,3349 (1978). (9) T. Bally, E. Haselbach, Z. Lanyiova, and P. Baertachi, Helu. Chim. Acta, 61, 2488 (1978). (10) G. Merling, Ber. Dtsch. Chem. Ges., 24, 3108 (1891). (11) E.g., “Aromaticity”, Special Publication No. 21, The Chemical Society, London, 1967. (12) P. J. Garratt, “Aromaticity”, McGraw-Hill, New York, 1971. (13) E. Hiickel, Z. Phys., 76,628 (1932). (14) I. Gutman, M. Milun and N. TrinajstiE, Math. Chem., 1, 171 (1975). (15) A. Streitwieser, Jr., “Molecular Orbital Theory for Organic Chemists”, Wiley, New York, 1961. (16) E. Heilbronner and H. Bock, “The HMO-Model and Its Appli- cation, 1. Basis and Manipulation”, Wiley, New York, 1976 (translation from German). (17) M. J. S. Dewar, “The Molecular Orbital Theory of Organic Chemistry”, McGraw-Hill, New York, 1969. (18) B. A. Hess, Jr., and L. J. Schaad, J. Am. Chem. SOC., 93, 305 (1971). (19) B. A. Hess, Jr., private communication (Oct 1978). Hess and Schaad succeeded in defining the reference structure for ions and radicals within the framework of the DRE concept. (20) M. J. S. Dewar, Pure Appl. Chem., 44, 767 (1975). (21) R. C. Bingham, .MI. J. S. Dewar, and D. H. Lo, J. Am. Chem. SOC., 97, 1285 (1975). familiar with the MO theories of higher level, have lacked a simple working MO method for predicting the aromatic stability of ions and radicals in spite of several currently available methods that work for classical conjugated molecules.18~22-30 Recently such a method was developed independently by the Zagreb g ro~p~~1~~-~~ and by Aihara*% by using very different ways of r e a ~ o n i n g . ~ ~ In essence, this method is based on the fundamental idea40s41 of using an acyclic polyene zyxwv as a reference structure, suggested by Dewar42 and independently by Breslow and MohacsP and elaborated by Hess and Schaad18”4*45 within the Hiickel scheme. The latter authors have shown how the Huckel model with proper reference structures is satisfactory for predicting aromatic stability even for heterocycles&-@containing (22) J. Kruszewski and T. M. Krygowski, Tetrahedron Lett., 319 (23) G. G. Hall, Int. J. Math. Educ. Sci. Technol., 4, 223 (1973). (24) W. C. Herndon, J. Am. Chem. SOC., 95, 2404 (1973). (25) C. F. Wilcox, Jr., Croat. Chem. Acta, 47,87 (1975). (26) P. George, M. Trachtman, C. W. Bock, and A. M. Brett, Theor. (27) R. Swinborne-Sheldrake, W. C. Herndon, and I. Gutman, Theor. (28) M. RandiE, Tetrahedron, 33, 1905 (1977). (29) M. RandiE, J. Am. Chem. SOC., 99, 444 (1977). (1970). Chim. Acta, 38, 121 (1975). Chim. Acta, 755 (1975). (30) J. P. Gastmans, D. F. Gastmans, and M. H. Mendes Ferrez, Tetrahedron, 33, 2205 (1977). (31) I. Gutman and N. Trinajstit., Acta Chim. Acad. Sci. Hung., 91, (32) I. Gutman, M. Milun, and N. TrinajstiE, Croat. Chem. Acta, 48, (33) M. Milun, Ph.D. Thesis, University of Zagreb, 1976. (34) I. Gutman, M. Milun, and N. TrinajstiE, J. Am. Chem. SOC., 99, (35) N. Trinajstit, Int. J. Quantum Chem., Sll, 469 (1977). (36) J.4. Aihara, J. Am. Chem. SOC., 98, 2750 (1976). (37) J.-i. Aihara, J. Org. Chem., 41, 2488 (1976). (38) J.-i. Aihara, J. Am. Chem. SOC., 98, 6840 (1976). (39) A. Graovac, I. Gutman, and N. TrinajstiE, “Topological Approach to the Chemistry of Conjugated Molecules”, Lecture Notes in Chemistry, No. 4, Springer-Verlag, Berlin, 1977. 203 (1976). 87 (1976). 1692 (1977). (40) N. C. Baird, J. Chem. Ed., 48, 509 (1971). (41) 1. Gutman, M. Milun, and N. TrinajstiE, Chem. Phys. Lett., 23, (42) Reference 17, Chapters V and IX. (43) R. Breslow and E. Mohacsi, J. Am. Chem. SOC., 85, 431 (1963). (44) B. A. Hess, Jr., and L. J. Schaad, J. Am. Chem. SOC., 93, 2413 (45) B. A. Hess, Jr., and L. J. Schaad, J. Org. Chem., 36, 3418 (1971). 284 (1973). (1971). (46) B. A. Hem, Jr., L. J. Schaad, and C. W. Holyoke, Jr., Tetrahedron, 28, 3657 (1972). (47) B. A. Hess, Jr., and L. J. Schaad, J. Am. Chem. SOC., 95, 3907 (48) B. A. Hess, Jr., L. J. Schaad, and C. W. Holyoke, Tetrahedron, (1973). 31, 295 (1975). 0022-3263/80/1945-1738$01.00/0 0 1980 American Chemical Society