The bond lengths and SCF screened potentials of bicyclo- .
[4.2.0]octa-1,3,5,7-tetraene (1), bicyclo[6.2.0]deca-1,3,5,7,9-pentane (2),
cyclobuta[l,2:3,4]dicyclopentene (3), cyclopenta[3,4]cyclobuta[l,2]cycloheptene
(4), benzo[3,4]cyclobuta[l,2]cyclooctene (5), cyclobuta[
1,2, :3,4Jdicycloheptene (6), and cyclobuta[l,2 :3,4]dicyclooctene (7)
were calculated by using the SCF screened potential MO CI method.
From the bond lengths and the characteristics of the screened
potentials, it is concluded that molecules 1, 2, 3, 4, 6, and 7 are
polyolefinic and molecule 5 has both aromatic and polyolefinic
characters

Hiroyuki Yamaguchi

Kunihiko Ninomiya

Masateru Ogata

English

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CROATICA CHEMICA ACTA CCA-1254 CCACAA 53 (4) 675-685 (1980) YU ISSN 0011-1643 UDC 539.19:547.64 Conference Paper The Position Dependence of the SCF Screened Potential in Several Nonbenzenoid Hydrocarbons Containing a Four-Membered Ring* Hiroyuki Yamaguchi, Kunihiko Ninomiya, and Masateru Ogata Contribution from the Department of Chemistry, Faculty of Science, Kumamoto University, Kumamoto 860, Japan Received September 3, 1979 The bond lengths and SCF screened potentials of bicyclo- . [4.2.0]octa-1,3,5,7-tetraene (1), bicyclo[6.2.0]deca-1,3,5,7,9-pentane (2), cyclobuta[l,2:3,4]dicyclopentene (3), cyclopenta[3,4]cyclobuta[l,2]-cycloheptene (4), benzo[3,4]cyclobuta[l,2]cyclooctene (5), cyclobuta-[1,2, :3,4Jdicycloheptene (6), and cyclobuta[l,2 :3,4]dicyclooctene (7) were calculated by using the SCF screened potential MO CI method. From the bond lengths and the characteristics of the screened potentials, it is concluded that molecules 1, 2, 3, 4, 6, and 7 are polyolefinic and molecule 5 has both aromatic and polyolefinic characters. INTRODUCTION Cyclobutadiene has recently become the center of reawakened interest1- 5 since Lin and Krantz6 provided the first physical evidence for the structure (the object of an intensive search since Kekule's abortive attempt 108 years ago7). Very recently, Masamune et al.8 have concluded from the infrared spectra of cyclobutadiene and its derivatives that the cyclobutadiene ring in the ground state is not square but very likely rectangular. The aromatic characteristics of nonbenzenoid aromatic hydrocarbons con-taining a four-membered ring such as bicyclo[4.2.0]octa-1,3,5,7-tetraene (1), bicyclo[6.2.0]deca-1,3,5,7,9-pentaene (2), cyclobuta[l,2 :3,4]dicyclopentene (3), cy-clopenta[3,4]cyclobuta[l,2]cycloheptene ( 4), benzo[3,4 ]cyclobu ta[l,2]cyclooctene (5), cyclobuta[l,2:3,4]dicycloheptene (6), and cyclobuta[l,2:3,4]dicyclooctene (7) have long been of interest from both theoretical and synthetical points of view. Many attempts to synthesize these hydrocarbons (1-7) have been made hitherto.9- 12 Molecule 1 has detected as a reactive intermediate.11 Molecules 2, 3, 4, 5, 6, and 7 have not yet been synthesized. Based on Dewar's definition of aromaticity,13 many theoretical investigations about the aromatic chara-cteristics of 1, 3, 4, and 6 have been carried out.14- 18 Recently, Koyanagi and Yamaguchi19 have pointed out that the position dependence of the SCF screened potential reflects sensitively the local beha-viors of :rt-electrons and becomes a theoretical aromaticity criterion. * Presented in part at the International IUPAC Symposium on Aromaticity, held in Dubrovnik, Croatia, Yugoslavia, September 3- 5, 1979. 676 H. YAMAGUCHI ET AL. d) co ·3 OD 2 3 4 y 0=6 * 00 Lz 5 6 7 Figure 1. Numbering of atoms and choice of axes. Carbon atoms are numbered consecutively, starting with the starred atom and proceeding clockwise along the periphery. The aim of this paper is to add, in view of these circumstances, to the understanding of the aromatic characteristics of these molecuels (1-7) through an attempt to calculate bond lengths and screened potentials using a SCF screened potential MO CI method.20-2s METHOD OF CALCULATION A procedure that combines the SCF screened potential with the variable bond-length techniques is used in the Pariser-Parr-Pople SCF MO CI method.24•2·; At each step of the SCF calculation, the new bond lengths are obtained from the corresponding bond orders.26 The screened potential is evaluated by using the bare potential obtained from the new bond lengths. The bare potential is calculated using the Mataga-Nishimoto formula.27 This screened potential is used in the calculation of the next SCF step. The calculation is repeated until self-consistency is reached. As the starting geometrical structures for iterative calculation, we adopt various distorted structures in which bond lengths are distorted, so that the set of displacement vectors may form a basis for an irreducible representation of the full symmetry group. If self-consistency is achieved at two or more different nuclear arrangements, the total energies should be compared with each other in order to determine which one is most favorable. The total energy is assumed to be the sum of the n:-electron energy and the a-electron energy.19All the singly-excited states are considered in the calculation of the RPA polarization part. RESULTS AND DISCUSSION Molecular-symmetry Groups and Bond Distances. The symmetry groups and bond lengths corresponding to the most stable nuclear configurations for 1, 2, 3, 4, 5, 6, and 7 are shown in Table I. In molecules 3, 4, 6, and 7, two different self-consistent nuclear arrange-ments, one belonging to the full symmetry group of a molecule and the other belonging to a reduced symmetry group, were obtained. In molecule 3, for example, the starting bond distortions, belonging to Ag, B2g, and B1u represen-molecule (symmetry) 4 (C,;) SCF SCREENED POTENTIAL TABLE I Predicted Symmetry Groups and Bond Lengths bond bond length molecule bond A (symmetry) 1-2 1.370 10-11 1-6 1.433 11-12 1-8 1.491 2-3 1.429 5 (C2v) 1-2 3-4 1.370 1-14 7-8 1.342 2-3 5-6 1-2 1.354 5-14 1-8 1.487 6-7 1-10 1.460 6-13 2-3 1.464 7-8 3-4 1.351 8-9 4-5 1.465 9-10 9-10 1.358 6 (C2v) 1-2 1-2 1.454 1-14 1-10 1.358 2-3 2-3 1.357 3-4 3-4 1.454 4-5 4-5 1.370 5-6 4-10 1.476 6-7 9-10 1.465 6-14 13-14 1-2 1.363 1-12 1.444 7 (C2v) 1-2 2-3 1.445 1-16 3-4 1.367 2-3 4-5 1.471\ 3-4 4-12 1.452 7-8 5-6 1.368 7-16 5-11 1.451 8-9 6-7 1.442 8-15 7-8 1.365 9-10 8-9 1.442 10-11 9-10 1.365 11-12 677 bond length A 1.443 1.393 1.393 1.402 1.400 1.467 1.408 1.353 1.484 1.468 1.349 1.469 1.456 1.358 1.355 1.456 1.356 1.455 1.374 1.468 1.471 1.461 1.357 1.352 1.463 1.455 1.486 1.471 1.374 1.348 1.472 1.347 tations, all converge into the unique self-consistent set of bond lengths belonging to point group D2h , and those belonging to B3u converge into the set of bond lengths belonging to point group C2v· The stabilization energies which favor the lower-symmetry nuclear arrangements for 3, 4, 6, and 7 a,re pre-dicted to be 0.62, 2.38, 5.27, and 1.83 kcal moi-1, respectively. In these molecules, there are marked double-bond fixations in the periphery. It can be concluded that molecules 3, 4, and 6 are derived from 5-(2,4-cyclopentadien-1-ylidene)-'l,3-cyclopentadiene, 7-(2,4-cyclopentadiene-1-ylidene) ~ 1,3,5-cycloheptatriene, and 7-(2,4, 6-cyclohepta trien-1-y lidene )-1,35-cycloheptatriene respectively, by intra-molecular union28 between positions separated by three bonds.16 The calcu-lated bond lengths indicate that molecule 7 is made up of two 1,3,5,7-cyclo-octatetraene molecules. The above results for 3, 4, and 6 are almost the same as the results obtained by using the bare potential SCF MO CI method.1s,29,so 678 H. YAMAGUCHI E T AL. On the other hand, in molecules 1, 2, and 5, self-consistency was achieved only for the fully-symmetrical nuclear arrangement belonging to point group C2v· Molecules 1 and 2 show in a greater or lesser degree a double-bond fixation in the peripheral carbon skeleton. The calculated bond lengths indicate that molecules 1 and 2 are composed of a vinyl molecule and 1,3,5-cyclohexa-triene and 1,3,5,7-cyc1ooctatetraene, respectively. In molecule 5, it is predicted that the bond lengths of the six-membered ring are almost the same as those in the free benzene molecule and there are marked double-bond fixations in the other region of the periphery. It is considered that molecule 5 is made up of benzene and 1,3,5,7-cyclooctatetraene. Position Dependence of SCF Screened Potential. The carbon atoms in 1,3,5-hexatriene are numbered as in Figure 2. Terasaka et al.21 divided the SCF screened potentials V into the following groups: Vw Vw V1 3 , ••• ; V221 V23 , V241 • •• ; •• •• In Figure 2, the SCF screened potentials in each group are 8 7 ,_ -s--! ~ 1:5-<!J -0 a.. 4 -0 8 0 I 2 4 6 ~1 3 5 8 0 0 0 0 I I I I 2 3 4 5 Number Figure 2. The SCF screened potentials in 1,3,5-hexatriene plotted against the number (for the meaning of the number, see the text). · plotted against a number that indicates the kinds of screened potential, that is, 0: one-center potentials Vm V2 2 , Va3 , ••• ; 1: the nearest two-center potentials V12, V23 , V34 , ••• ; etc. Figure 2 shows that there are two kinds of numbers: tha:t is, at an even number, one kind of screened potential exists, while at an odd number there exist two kinds of screened potentials.21 The screened potentials of 1, 2, 3, 4, 5, 6, and 7 are shown in Figure 3, 4, 5, 6, 7, 8, and 9, respectively. The position dependence of the SCF screened potential in the six-membered ring of 1 shows trends similar to those of the polyene. Figures 4(a), 7(b), and 9(a) indicate that the characteristics of the screened potentials of the eigth-membered ring of 2, 5, and 7 are almost the same as SCF SCREENED POTENTIAL 679 9,.. (a) 9,.. (b) () () 8 [_o 8'"" a:·"~~ .... ,.----.7 7 > ~ 0 ]6 8 6 c. (\) -0 0...5 ... 8 5 0 8 0 0 0 4 4 0 I I 0 2 3 0 2 Number Number Figure 3. The SCF screened potentials in bicyclo[4.2.0]octa-1,3,5,7-tetraene plotted against the number (for the meaning of the number, see the text); (a) the 6-membered ring, (b) the 4-membered ring. 9 (a) 9 (b) 0 8 ... 811 r--, , .... .7 r··o r a,, .. J L--~ ', ,, '--···' ~6 g 6 (\) 0 0 0..5 5 § 0 0 4 § 0 4 8 a 0 3 3 ... I 0 2 3 4 0 2 Number Number Figure 4. The SCF screened potentials in bicyclo[6.2.0]deca-l,3,5,7,9-pentaene plotted against the number (for the meaning of the number, see the text); (a) the 8-membered ring, (b) the 4-membered ring. 680 H. YAMAGUCHI ET AL. (a) () (b) 8 ,'"-~ .... -u 8'~ /~-u--~\ <' : \."" __ J--- ' , '-- .... ..,,' 7- 7-~6- 0 6>-~ 0 0 -;ij ~5 ... <!> 5 0 6 0 g CL 0 4 .... Q 4-3 ... 3 I I 0 2 0 2 Number Number Figure 5. The SCF screened potentials in cyclobuta[l,2:3,4]-dicyclopentene plotted against the number (for the meaning of the number, see the text); (a) the 5-membered ring, (b) the 4-membered ring. 8 7 --4 -3 -0 (a) o--T'.~\ .I ' -1. / ...... , § 8 § 0 I 1 2 Number 8 )-r 7~ 6 >-5 .... 8 4-0 8 3-3 0 (b) ,,-· --, ·n--) C:, ' ........... , ,, ..... J 0 8 8 I 1 2 Number 8<). ll ~' I -6-5-4-3'-0 (c) /------)---o ( I \ J--'-. .. __ ,' 8 8 8 I I 1 2 Number Figure 6. The SCF screened potentials in cyclopenta[3,4]-cyclobuta[l,2Jcycloheptene plotted against the number (for the meaning of the number, see the text); (a) the 7-membered ring, (b) the 4-membered ring, (c) the 5-membered ring. 9 8 B 7 ... I-3 .. 0 (a) ,r···. 0 I ·.,. ... . . l, )-··-'---·'# 8 0 2 Number SCF SCREENED POTENTIAL 9 (b) ) 8> 0 .. -.. --r 1 7 ... .. .t ) ..... _, s.- 8 5 94 0 8 0 0 3- 8 . 3 0 2 3 Number 681 9. (c) 0 80 , .......... a·····-. 7 . . . . \~ __ _,,'' ...... _,,,, .. 6 5 0 4 8 0 8 3 .. I I 4 0 1 2 Number Figure 7. The SCF screened potentials In benzo[3,4]cyclobuta[l,2]cyclooctene plotted against the number (for the meaning of the number, see the text); (a) the 6-membered ring, (b) the a-membered ring, (c) the 4-membered ring. (a) (b) ') 8 I) 7 7 a 6 0 5'" 8 4.- 0 0 § e e 3 3 ... I I I 0 1 2 3 0 1 2 Number Number Figure 8. The SCF screened potentials in cyclobuta[l,2:3,4]-dicycloheptene plotted against the number (for the meaning of the number, see the text); (a) the 7-membered ring, (b) the 4-membered ring. 682 (a) 9 -I-r-- .... 0 / ',.,__ ' . t ;.._ . I-.... ,' '----" 8 7 0 0 8 0 8 8 0 4 8 3 0 ' ' ' 0 H . YAMAGUCHI ET AL. .~ (b) : 9'- 9>-8 L- ,........ ,........ 8 >-r'' .. , ,' ........ . D . ' ' . ', ' ) 7 '-''-----/ '·~---/ 71-6 '- 6 I-0 51- 0 ·5,... 0 0 41- 4-g 3- 31-' ' I 4 0 1 2 0 Number (c) 0 r-- .... , ' --·<' \ . ' . ' •• .J, ) '-···' 0 0 0 0 I 0 8 ~ I 2 3 Number g ' 4 Figure 9. The SCF screened potentials in cyclobuta[l,2 :3,4]-dicyclooctene plotted against the number (for the meaning of the number, see the text) ; (a) the 8-membered ring, (b) the 4-membered ring, (c) the 8-membered ring. 9 8 7 0 ,,...._ 0 > 3.6 ~ -c 25 0 a. 0 4 0 0 0 0 3 0 2 3 4 Number Figure 10. The SCF screened potentials in 1,3,5, 7-cyclooctatetraene plotted against the number (for the meaning of the number, see the tex t) . SCF SCREENED POTENTIAL 683 (a) (b) 9(~ ) 9(~ ) B /~ 8 ~. ...... ~ '::::7 .!l! 0 7 0 ..... c (!) 06 6 0. 5 5 0 0 0 0 0 0 4 4 I I I 0 1. 2 3 0 1 2 3 Number Number Figure 11. The SCF screened potentials in 1,3-butadiene plotted against the number (for the meaning of the number, see the text); (a) trans-1 ,3-butadiene, (b) cis-1,3-butadiene. B (a) 8( (b) ( l I a,..-· .. > 7 (--o 7 ', ...... ' ........ -'"" 6 6 ...... ~ ~5 § 5 8 ..... c (!) 0 ~ 0.4 8 4 8 3 3 0 2 3 0 1 2 Number Number Figure 12. The SCF screened potentials in azulene plotted against the number (for the meaning of the number, see the text); (a) the 7-membered ring, (b) the 5-membered ring. those of 1,3,5,7-cyclooctatetraene (see Figure 10). It is well known that the 1,3,5,7-cyclooctatetraene molecule exhibits a strong bond alternation, as revealed by its tub form.a1 Figures 5(a) and 6(c) show that the position dependence of the screened potential in the five-membered rings of 3 and 4 has a tendency similar to that of 1,3-butadiene (see Figure 11). Figure 11 shows that there are no significant 684 H. YAMAGUCHI ET AL. differences between the tendency of the potentials of trans-1,3-butadiene and that of cis-1,3-butadiene. In the seven-membered rings of 4 and 6, at each of the numbers the characteristics of the screened potentials are almost the same as those of polyenes such as 1,3-butadiene and 1,3,5-hexatriene. In the four-membered rings of all molecules (1-7), a tendency similar to that in the polyenes appears. The SCF screened potential is very sensitive to a bond alternation. There are two kinds of screening (screening and anti-screening) at the odd numbers in molecules such as polyenes and cyclooctatetraene, in which there exists a strong double-bond fixation.21 The screened potential in the six-membered ring of 5 shows a tendency similar to that of aromatic molecules such as azulene, in which there exist no double-bond fixations (see Figure 12).21 In azulene, there is only one kind of screening at the odd numbers and the various screened potentials have almost the same value at each of the numbers. From the characteristics of the SCF screened potentials, it can be concluded that the six-membered ring in 5 is aromatic and the remaining rings in 5 and molecules 1, 2, 3, 4, 6, and 7 are polyolefinic. Molecule 5 may have both aromatic and polyolefinic characters. Acknowledgment. - One of the authors (H. Y.) is grateful to the Yoshida Foundation for Science and Technology for financial support. The authors wish to thank Dr. T. Morita of Tohoku University for his fruitful discussions. The numerical calculations were carried out on the HITAC M-180 at the Computer Center of the Institute for Molecular Science. REFERENCES 1. 0 . L. Ch a pm an, C. L. McIntosh, and J. Pac ans k y, J. Amer. Chem. Soc. 95 (1973) 614. 2. 0 . L. Chapman, D. De La Cruz, R. Roth, and J . Pacansky, J. Amer. Chem. Soc. 95 (1973) 1337. 3. A. Krantz, C. Y. Lin, and M. D. Newton, J . Amer. Chem. Soc. 95 (1973) 2744. 4. G. Maier, Angew. Chem. Int. Ed. Engl. 13 (1947) 425. 5. S. Masamune, T. Machiguchi, and M. Aratani, J . Amer. Chem. Soc. 99 (1977) 3524. 6. C. Y. Lin and A. Krantz, J. Chem. Soc., Chem. Commun. (1972) 1111. 7. A. Ke k u 1 e, Justus Liebigs Ann. Chem. 162 (1872) 77. 8. S. Mas am u n e, F. A. Souto - Bach i 11 er, T. Machi g u chi, and J. E. B e rt i e, J. Amer. 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Fu j i mu r a, and T. Na k a j i ma, Bull. Chem. Soc. Japan 46 (1973) 1301. 22. T. Koyanagi, Y. Shin, and H. Yamaguchi, Bull. Chem. Soc. Japan 50 (1977) 345. 23. M. Higa sh i and H. Yamaguchi, J. Chem. Phys. 70 (1979) 2198. 24. R. Pariser and R. G. Parr, J. Chem. Phys. 21 (1953) 446, 767. 25. J . A. Pop 1 e, Trans Faraday Soc. 49 (1953) 1375. 26. T. Na k a j i ma and S. Kat a g i r i, Mol. Phys. 7 (1964) 149. 27. N. Mat a g a and K. Nishimoto, Z. Phys. Chem. 13 (1957) 140. 28. M. J. S. D e war, Tetrahedron Suppl., Part I, 8 (1966) 75. 29. T. Nakajima, A. Toyota, and S. Fujii, Bull. Chem. Soc. Japan 45 (1972) 1022. 30. A. Toyota, Bull. Chem. Soc. Japan 48 (1975) 1152. 31. T. Na k a j i ma and S. Koh d a, Bull. Chem. Soc. Japan 39 (1966) 804. SAZETAK Ovisnost SCF zasjenjenog potencijala o polofaju u nekoliko nebenzenoidnih ugljikovodika s cetveroclanim prstenom H. Yamaguchi, K. Ninomiya i M. Ogata Interes za elektronsku strukturu nebenzenoidnih ugljikovodika s cetveroclanim prastenom pobuden je posto su Lin i Kranz dali fizikalne dokaze o strukturi ciklo-butadiena. Uporabom MO CI metode sa SCF zasjenjenim potencijalom istrazena je ovisnost SCF zasjenjenog potencijala kod nekoliko nebenzenoidnih aromatskih ugljikovodika s cetveroClanim prstenom. Sve pocetne distorzije veza koje pripadaju Ag, B1g i B3u reprezentacijama kon-vergiraju u jedinstven samouskladeni skup duljina veza kc je pripadaju molekulskoj grupi simetrije D2h dok distorzije koje pripadaju B2u reprezentaciji konvergiraju u drugi skup koji pripada grupi C2v· Za D211-strukture postoji samo jedna vrsta zasjenjenog potencijala dok za C2v-strukture postoje dvije vrste potencijala, zasjenjeni i anti-zasjenjeni, tendencija sliena onoj koju nalazimo u poliena. ODJEL ZA KEMIJU SVEUCILISTA U KUMAMOTU KUMAMOTO 860, JAPAN Prispjelo 3. rujna 1979. 

The Position Dependence of the SCF Screened Potential in Several Nonbenzenoid Hydrocarbons Containing a Four-Membered Ring

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