Sept. 20, 1952
MOLECULAR ORBITAL CALCULATIONS OF
SMALL-RING HYDROCARBONS 4570
for the binary melting point diagram was very kindly supplied by Professor W. G. Dauben,26 m.p. 109.9'. N-(trans-2-Methylcyclohexyl)-benzamide (Ib).-2Methylcyclohexylamine was prepared by the sodium-alcohol reduction of 2-methylcyclohexanone oxime. 27 After conversion to the benzamide in the usual manner with benzoyl chloride, Ib was obtained by three crystallizations from ethanol, m.p. 151.0". Mixed Melting Point Behavior of Ia and 1b.-The binary melting point diagram of N-(trans-2-methylcyclohexyl)benzamide was determined using various mixtures in a modified Hershberg melting point apparatus according to the method described in detail by Cason and Winans.28 The temperature a t which the last crystalline material was no longer visible was easily reproducible to 0.1". The results are shown in Fig. 1. 2-Methylcyclohexylamine by the Leuckart Reaction.In a 100-ml. round-bottomed flask fitted with a take-off condenser, were placed 10 g. of 2-methylcyclohexanone, . b 40.4 g. of formamide and 1 g. of magnesium chloride. The 90 I I 1 1 1 1 1 1 1 mixture was heated a t 175-180' for three hours, the wpter being formed removed periodically, and the ketone codistilling returned to the reaction mixture. The reaction mixture was poured into 100 ml. of water, and extracted continuously with ether. The ethereal solution was concentrated, and to the crude N-2-methylcyclohexylformamide was added 25 ml. of concentrated hydrochloric acid. This mixture was heated under reflux for three hours, cooled, and neutral compounds removed by extraction with ether. Ana2. Calcd. for Ci4HI90N: C, 77.42; H , 8.76; N, The aqueous solution was basified, saturated with sodium 6.45. Found: C, 77.54; H, 8.77; Tu', 6.59. chloride, and continuously extracted with ether. After A small sample was sublimed (97% recovery), and the drvinz over sodium hvdroxide. distillation afforded 5.52 P. of mixed cis-* and tr~ns-2-methylcyclohexylamin~,melting point redetermined in the manner used in constructing the binary melting point diagram, m.p. 114.1' (correb.p. 74-75' (52 mm.). Skita2Qreports 153' (760 mm.). N-~2-Methvlcvclohexvl)-benzamide.-To a mixture of sponding to 60% cis isomer in this mixture). From Sodium-Alcohol Reduction of the Oxime.-A 6.04 g. of 2-me~hylcycfohexylamineand 50 ml. of 20% sodium hydroxide was added with shaking 14.0 g. of benzoyl sample of the amine prepared by sodium-alcohol reduction chloride. The precipitate of crude benzamide was ground of 2-methylcyclohexanone oxime2? was converted to the and thoroughly washed with sodium carbonate and water. benzamide as above. It melted a t 141.0' (corresponding to The yield of colorless benzapide was 10.2 g. (88.5%), final 80% trans isomer in this mixture). From Hydrogenation of Aceto-o-to1uidide.-Aceto-omelting temperature, 113.1 . toluidide was hydrogenated with platinum oxide in acetic (26) See W.G. Dauben and E. Hoerger, THIS JOURNAL, 73, 1504 acid solution. The 2-methylcyclohexylamine resulting (1931). from hydrolysis of the X-(2-methylcyclohexyl)-acetamide (27) "Organic Syntheses," Coll. Vol. 11, John Wiley and Sons, Inc., was converted to the benzamide as above. It melted a t Xew York, N. Y., 1943, p. 318. 98.5' (corresponding to 79% cis in this mixture).
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(28) J. Cason and W. Robert Winans, J . Org. Chem., 15, 148 (1950). (29) A. Skita, Be?., 56, 1014 (1923).
[COSTRIBUTIOU FROM
THE
BERKELEY 4, CALIFORNIA
DEPARTMENT OF CHEMISTRY AND LABORATORY FOR NUCLEAR SCIENCE AND ENGINEERING, MASSACHUSETTS
INSTITUTE O F TECHNOLOGY]
Small-Ring Compounds. X. Molecular Orbital Calculations of Properties of Some Small-Ring Hydrocarbons and Free Radicals1 BY JOHN D. ROBERTS, ANDREWSTREITWIESER, J R . , ~AND CLAREM. REGAN RECEIVED MARCH17, 1952 The molecular orbital (LCAO) method has been used t o calculate the electron delocalization energies, bond orders and freevalence indexes of some cyclic small-ring hydrocarbons and free radicals including a number of cyclobutadiene derivatives. 2 ) rr-electron rule of aromatic stability can only be justified by the simple molecular orbital I t is concluded that the (4n treatment for monocyclic conjugated polyolefins.
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One of the substantial successes of the simple molecular orbital theory as developed by Hiickel* is the prediction that, of the completely-conjugated planar monocyclic polyolefins as cyclobutadiene, benzene, etc., those which possess (4% 2) r-elec-
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(1) Supported in part by the program of research of the United States Atomic Energy Commission under Contract AT(30-1)-905. (2) U. S. Atomic Energy Commission Post-Doctoral Fellow, 19511932. (3) E. Huckel, 2. Physik, 7 0 , 204 (1931); "Grundziige der Theorie ungesattiger and aromatischer Verbindungen," Verlag Chemie, Berlin, 1938, pp. 77-85.
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trons (n = 0 , 1 , 2 , 3 . . ) will be peculiarly stable by virtue of having fully-filled molecular orbitals with substantial electron delocalization (resonance) energies as compared to the classical valence bond structures. The same rule may be applied3s4without known exceptions, to the cyclopropenyl, cyclopentadienyl, cycloheptatrienyl, etc., cations, anions and free radicals although but few quantitative cal(4) (a) H J Dauben, Jr., and H. J. Ringold, THIS JOURNAL. 73, 876 (19.511; (11) W. v. E. Doering and F, L. Detert, ibid., 73, 876 (1931).
culations3S5on such species have been published previously. It has been sometimes assumed6 without proof that the (471 2) n-electron rule holds for polycyclic as well as monocyclic conjugated polyolefins despite the fact that a number of seemingly anomalous stable substances are known ; e.g., dibenzcyclobutadiene (diphenylene), acenaphthylene, pyrene, fluoranthene, etc. In the present work, the general applicability of the rule has been considered as part of it search for new cyclic conjugated systems, particularly derivatives oi cyclobutadiene which might be predicted on theoretical grounds to be reasonably stable. Cyclobutadiene itself has been well studied from the standpoint of the molecular orbital and has been predicted to have an unstable triplet ground state. Cyclobutadiene is of course highly symmetrical and it has been of interest to determine whether the simple molecular orbital theory predicts that lesssymmetrical substituted cyclobutadienes would be more stable and have triplet ground states. A11 of the calculations in the present paper have been made by the simple molecular orbital method3,.9,9with neglect of resonance integrals between non-adjacent atoms and of non-orthogonality of atomic orbitals on different nuclei. Wherever possible the secular determinants were factored by group theory proceduresP The results must be regarded as being uncertain and essentially qualitative by virtue of the known limitations of the method, including not only the general difficulties discussed by Coulson and Dewar”’ but also the uncertainties introduced by non-self-consistent fields in other than “alternant” hydrocarbons.’* For each compound, we have calculated the &loin units oi p calization (resonance) energy (DE) (about 17 kcal.!, the bond orders8.12and the “freevalence’’ indexes.!:’ The results are given in Fig. 1. n’here the simple molecular orbital theory predicts a triplet ground state, the coinpotmds in
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\V. TVheland, J . C ~ P ; J Pnys., I. 2 , 174 (1
(7) (a) W. G. Penney, Pvoc. Roy. Soc. (London), A146, 223 (1934); G. W. Wheland, ihid.. A164, 397 (1938); (c) C. 9.Coulson, ; b i d . , 8169, 113 (1939); ( d j 6. \T, Wheland, THIS JOUXNAI., 63, 2023 (1941); (e) C. 4.Coulson arid W E. Moffitt, Phil. J l a f , [71 40, 1 \ l 9 4 9 ) ; (f)D. P. Craix, Fvnr. Roy. Sor. f L o n d o v ) ,A202, 498 (10.50); (1,)
D P. Crxix, J C‘krm ,Sor , .‘ili5 ~ 1 $ 1 5 1 l , (8) C. .4.. Coulson a11d t l C.. 1.onrriet-Hiyaini. Proc !Lotidoti),Al91, 39 (1947) ‘gl
R o y . .%,.
(9) H. Eyring, J Walter and G. E. Kimball, “Quantum Chemistry,” rohn Wiley and Sons, Xew Uork, N. I-., 1944, Chap. XIII. I 10) C . A Coulson a n d M T S . n e w a r , Dirt i ~ s s i n v so i i h I;
a, 5 4 (1947, 1 1 ) (a) C. A . Coulson ani1 G . S Rushbrooke, Pro,. Cnnzb. Phzl. \ , i t . , 36, 193 (1940); (b) D. P. Craig and A. Maccoll, .T. Chew S u c . ,
Fig. 1 are tnarked with R T following; the figures for DE. Compounds I-XI11 are cyclobutadiene derivatives of various types. Cyclobutadiene itself (I) is predicted to have zero DE, a triplet ground statelbae (cf. however, C~-aig’~>g), but not unusual iree-valence indexes ( F ). I 4 The apparent instability of the substance might be ascribed to the triplet ground state7” on the basis of the molecular orbital treatment since the known cyclopropene should have comparable or greater angular strain. It is interesting that various types of substituted cyclobutadienes without fused rings (11-VI) are predicted to have moderate DE-values but also triplet ground states arising from accidental degeneracies. The vinyl derivatives (11-IV) show quite high F-values a t the terminal positions of the double bonds. VII-XI are benzcyclobutadienes, the calculations for which indicate clearly the lack of theoretical justification for the (4n 2) n-electron rule when applied to other than monocyclic systems. VII, VIII15 and XI violate the rule, but are predicted to have singlet ground states, substantial DE-values (particularly for VI11 which has actually been shown to be quite stableI6) and Ffigures a t all positions lower than those of ethylene. On the other hand, IX which is an isomer of naphthalene with ten n-electrons is predicted to have a triplet ground state although its position isomer X should have a singlet ground state. IX is particularly interesting as an example of a possible “arohydrocarbon with a pre~ n a t i c “ ~“alternarit”ll ” dicted triplet ground sta.te. Cotnparisons of XI1 and XI11 with cyclobutadiene [I) are very interesting. Classical valence theory can only predict that fusion of double bonds onto I would result in considerably less stable substances. However, the simple molecular orbital treatment suggests that XI1 and XI11 would be very different from I in having singlet ground states with substantial DE- and low F-values. If XI1 could be prepared,I7 studies of its bond distances would be of considerable importance since they would provide an excellent competitive test of the predictions of the simple valence bond and molecular orbital treatments. The valence bond method predicts the order of the central bond to be $.33 corresponding to a C-C distance of about 1.42 X.as in graphite while the molecular orbital approach, with a calculated bond order of 1.OO, predicts a bond ciistance of about 1.54 A. as in normal single bonds. XIV-XVII are cross-conjugated polymethylenesubstituted systems which irrespective of symmetry and number of a-electrons are predicted to
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