H H H H H H H 1 2 3 4 H 162 J. CHEM. RESEARCH (S), 1997 J. Chem. Research (S), 1997, 162–163† Dynamics of Cyclic Allenes. Conformational Energy Surface of Cyclodeca-1,2,4,5-tetraene† Issa Yavari,* Robabeh Baharfar, Davood Nori-Shargh and Ahmad Shaabani Chemistry Department, Tarbiat Modarres University, P.O. Box 14155-4838, Tehran, Iran Iterative molecular mechanics calculations using Boyd’s computer program MOLBUILD and AM1 semi-empirical SCF MO calculations for two diastereoisomeric forms of cyclodeca-1,2,4,5-tetraene are reported for four conformations and three transition states for conformational interconversions. Allenes are an important class of unsaturated hydrocarbons which contain two double bonds in an orthogonal geometry. 1,2 Ring constraints bend and twist the normally linear perpendicular allene and engender substantial strain and resultant kinetic reactivity.3 Monocyclic medium-ring diallenes with the allene groups in a ring that has more than nine members appear to be fairly stable. Simple monocyclic diallenes possess two chiral centres and should exist in two diastereoisomeric forms, one diastereoisomer being racemic and the other a meso compound.Such isomers have been isolated in the case of the 12-membered diallene cyclododeca-3,4,9,10-tetraene-1,7-dione4 and 14-membered diallene cyclotetradeca-3,4,10,11-tetraene- 1,8-dione.4 The cyclic diallenes cyclodeca-1,2,5,6-tetraene (1)5 and cyclodeca-1,2,6,7-tetraene (2)6 are available via the bis(dibromocarbene) adducts of cycloocta-1,4-diene and cycloocta-1,5-diene, respectively. However, treatment of the bis(dibromocarbene) adduct of cycloocta-1,3-diene with methyllithium at µ30 °C produces cyclodeca-1,2,4,5-tetraene as an elusive compound that affords a good yield of bicyclo[6.2.0]deca-1,7,9-triene.7 While the conformational properties of 1 and 2 have been studied both experimentally8 and theoretically,9 there are no published experimental or theoretical data on the structure or conformational features of meso- and (�)-cyclodeca- 1,2,4,5-tetraene (3 and 4).In view of the success of iterative molecular mechanics calculations and AM1 semi-empirical SCF MO calculations in investigating the conformational properties of cyclic allenes8–11 and diallenes,8,12,13 we carried out corresponding investigations of 3 and 4 and report here our results. Experimental MM calculations were carried out on an IBM 3390 computer, using Boyd’s iterative computer program MOLBUILD.14,15 The parameters used in these calculations have been previously reported.16,17 The conjugation energy terms for 3 and 4 were obtained from the torsional angle of single bonds flanked by two double bonds.A two-fold potential with a stabilization (negative strain energy) of 4.24 kcal molµ1 for the planar (0 and 180°) arrangement was chosen because this reproduces experimentally the barrier to rotation seen in buta-1,3-diene.18 Semi-empirical calculations were carried out using the AM1 method with the MOPAC 6.0 program,19 implemented on a VAX 4000-300 computer.Energy-minimum geometries were located by minimizing energy, with respect to all geometrical coordinates, and without imposing any symmetry constraints. The structures of the transition state geometries were obtained using the optimized geometries of the equilibrium conformations and the procedure of Dewar et al.20 (keyword SADDLE). We have checked that all of the conformations obtained in the present work are true local-energy minima and energy maxima, as evidenced by the fact that they all are calculated to have 3Nµ6 and 3Nµ7 real vibrational frequencies, respectively.21 Results and Discussion meso-Cyclodeca-1,2,4,5-tetraene (3).·The results of MM calculations for important geometries of 3 are shown in Table 1.The unsymmetrical twist (3-T) conformation is calculated to have the lowest strain energy. By constraining the torsional angle f89101 from 74 to 12°, a smooth conformational change occurred, leading to a transition state (3Th3TC)#.Further changing of the same torsional angle yielded another energy minimum, namely the twist-chair (3-TC) conformation, which lacks symmetry. Since 3-TC is calculated to be 0.8 kcal molµ1 above 3-T, it is expected to be significantly populated at room temperature. The calculated strain-energy barrier for interconversion of 3-T and 3-TC is 4.6 kcal molµ1.The plane-symmetrical chair (3-C) geometry is a transition state between the chiral 3-TC and its mirror-image conformation 3-TCp. The calculated strain energy for 3-C is ca. 4.9 kcal molµ1. This pathway has the lowest calculated energy of the several pathways investigated. The relevant structural parameters and heats of formation (DHf°) for various geometries of 3, as calculated by the AM1 method, are given in Table 1 and Fig. 1. The twist (3-T) conformation has the lowest calculated heat of formation.The calculated heat of formation for 3-TC is ca. 1.8 kcal molµ1 above that of 3-T. The structure of the transition-state geometries (3Th3TC)# and 3-C were obtained from MOPAC 6.0 using the optimized geometries of 3-T, 3-TC and 3-TCp conformations and the procedure of Dewar et al. (Keyword SADDLE).20 The agreement between the AM1 and MM results is fairly good (Table 1). Representative structural parameters for the important geometries of the meso-isomer (3) are given in Table 1.The internal angles are close to the unstrained values in 3-T and 3-TC, but fairly expanded in transition-state geometries. The *To receive any correspondence. †This is a Short Paper as defined in the Instructions for Authors, Section 5.0 [see J. Chem. Research (S), 1997, Issue 1]; there is therefore no corresponding material in J. Chem. Research (M). Table 1 Calculated structural parameters [bond angles (y) and dihedral angles (f) in °] and energies (kcal molµ1) in various forms of meso-cyclodeca-1,2,4,5-tetraene (3) 3-T, C1 3-TC, C1 (3-Th3-TC)#, C1 3-C, CS MM AM1 MM AM1 MM AM1 MM AM1 Es a 6.08 6.92 10.68 10.96 DEs b 0.00 0.84 4.60 4.88 DHf c 75.27 77.09 79.85 82.08 DDHf b 0.00 1.82 4.58 6.81 y123 y234 y345 y456 y567 y678 y789 y8910 y9101 y1012 f10134 f2345 f3467 f5678 f6789 f78910 f89101 f91012 170 121 120 167 123 111 113 114 112 123 µ76 0 77 µ91 82 µ120 74 48 169 120 120 171 123 110 113 113 112 123 µ76 0 73 µ87 85 µ132 73 48 166 120 120 165 122 110 116 116 114 121 µ70 µ8 66 µ111 119 µ58 µ43 125 168 119 119 168 122 109 115 117 113 121 µ71 µ10 66 µ106 121 µ68 µ35 121 167 119 119 165 122 112 114 118 116 123 µ84 µ9 74 µ106 110 µ95 12 98 168 118 119 170 122 110 114 119 116 122 µ77 µ10 71 µ98 115 µ95 µ1 102 165 118 118 165 122 113 120 120 113 122 µ72 0 72 µ129 82 0 µ81 129 166 118 118 167 122 112 120 120 112 122 µ71 0 70 µ128 84 0 µ83 128 aStrain energy.bRelative to the best conformation of the same compound.cHeat of formation.J. CHEM. RESEARCH (S), 1997 163 C�C�C moieties are bent in various geometries of 3 and they are 10–15° compressed from the normal value of 180°. The C(sp3)-C(sp2)-C(sp2)-C(sp2) arrangements (f3467 and f10134) in the allenic moieties of all forms are fairly twisted from their energy minima at 90°, as a result of ring strain. Contributions to the overall strain energy in the four geometries of the meso-diallene 3, as calculated by the MM procedure, are shown in Table 2.The bond and out-of-plane bending terms are small in all forms. The transition-state geometries have higher bond-angle and torsional terms than the minimum-energy conformations. The other strain-energy contributions are substantial and vary over a relatively wide range of values. (�)-Cyclodeca-1,2,4,5-tetraene (4).·Three geometries (two energy minima and a transition state) were found to be necessary in a description of the conformational properties of the (�)-diallene (4).The most stable conformation of 4, as calculated by the MM method, is the axial symmetrical twistboat- chair (4-TBC) The calculated torsional and internal angles of 4-TBC are given in Table 3. The calculated strain energy for the second energy-minimum conformation, viz. twist-chair-chair (4-TCC) (C2) is 0.4 kcal molµ1. Conformations 4-TBC and 4-TCC are important because they are expected to be significantly populated at room temperature. The calculated strain-energy barrier (8.17 kcal molµ1) for interconversion of the two forms is substantial.This feature makes a dynamic NMR spectroscopic study of the (�)-isomer 4 attractive. The relevant structural parameters and heats of formation (DHf°) for various geometries of 4 are given in Table 3. The twist-boat-chair (4-TBC) conformation has the lowest calculated heat of formation. The calculated heat of formation of 4-TCC is 1.68 kcal molµ1 above that of 4-TBC.The structure of the transition state (4-T) was obtained from MOPAC 6.0 using the optimized geometries of 4-TBC and 4-TCC conformations and the procedure of Dewar et al.20 (see Fig. 2). Received, 10th December 1996; Accepted, 24th January 1987 Paper E/6/08314E References 1 A. Greenberg and J. F. Liebman, Strained Organic Molecules, Academic Press, New York, 1978. 2 M. Traetteberg, P. Bakken and A. Almenningen, J. Mol. Struct., 1981, 70, 287. 3 R. P. Johnson, Chem.Rev., 1989, 89, 1111. 4 P. G. Garrat, K. C. Nicolaou and F. Sondheimer, J. Am. Chem. Soc., 1973, 95, 4582. 5 M. S. Baird and C. B. Reese, Tetrahedron, 1976, 32, 2153. 6 E. V. Dehmlow and T. Stiehm, Tetrahedron Lett., 1990, 31, 1841. 7 S. Masamune, C. G. Chin, K. Hojo and R. T. Seidner, J. Am. Chem. Soc., 1967, 89, 4804. 8 F. A. L. Anet and I. Yavari, J. Am. Chem. Soc., 1977, 99, 7640. 9 I. Yavari, S. Asghari and A. Shaabani, J. Mol. Struct. (THEOCHEM), 1994, 309, 53. 10 I. Yavari, J.Mol. Struct., 1980, 65, 169. 11 I. Yavari, R. Baharfar and S. Asghari, J. Mol. Struct. (THEOCHEM), 1993, 283, 277. 12 I. Yavari, F. Aghajani and A. Shaabani, J. Chem. Res. (S), 1994, 110. 13 I. Yavari, R. Baharfar and D. Nori-Shargh, J. Mol. Struct. (THEOCHEM), 1996, in press. 14 R. H. Boyd, J. Chem. Phys., 1968, 49, 2574. 15 F. A. L. Anet and R. Anet, Tetrahedron Lett., 1985, 26, 5355. 16 F. A. L. Anet and I. Yavari, Tetrahedron, 1978, 34, 2879. 17 F. A. L. Anet and I.Yavari, J. Am. Chem. Soc., 1977, 99, 7640. 18 L. A. Carreira, J. Chem. Phys., 1975, 62, 3851. 19 J. J. P. Stewart, QCPE 581, Department of Chemistry, Indiana University, Bloomington, IN, USA; J. J. P. Stewart, J. Comput.- Aided Mol. Des., 1990, 4, 1. 20 M. J. S. Dewar, E. F. Healy and J. J. P. Stewart, J. Chem. Soc., Faraday Trans., 1984, 80, 227. 21 O. Ermer, Tetrahedron, 1975, 31, 1849; J. W. McIver, Jr., Acc. Chem. Res., 1974, 7, 72. Fig. 1 Calculated AM1 profile for conformational enantiomerization of 3-T and 3-Tp via the plane-symmetrical chair (3-C) geometry Fig. 2 Calculated AM1 profile for conformational interconversion of 4-TBC and 4-TC via the axial-symmetrical 4-T geometry Table 2 Calculated strain energies in different conformations of meso-cyclodeca-1,2,4,5-tetraene (3) and (�)-cyclodeca-1,2,4,5-tetraene (4 Strain-energy contributions (kcal molµ1) 3-T, C1 3-TC, C1 (3-Th3-TC)#, C1 3-C, Cs 4-TBC, Cs 4-TCC, C2 4-T, C2 Bond stretching Bond-angle bending Torsional strain Out-of-plane bending Non-bonded interactions Total strain energy 0.25 2.74 2.02 0.21 0.86 6.08 0.27 4.91 0.25 0.58 0.91 6.92 0.39 5.57 2.68 0.16 1.88 10.68 0.42 8.02 0.47 0.36 1.69 10.96 0.24 1.90 2.92 0.46 0.76 6.28 0.26 4.78 1.03 0.37 0.24 6.68 0.41 11.14 0.82 0.54 1.54 14.45 Table 3 Calculated structural parameters [bond angles (y) and dihedral angles ( f) in °] and energies (kcal molµ1) in various forms of (�)-cyclodeca-1,2,4,5-tetraene (4) 4-TBC, C2 4-TCC, C2 4-T, C2 MM AM1 MM AM1 MM AM1 Es a 6.28 6.68 14.45 DEs b 0.00 0.40 8.17 DHf c 75.45 77.13 87.75 DDHf b 0.00 1.68 12.30 y345 y456 y567 y678 y789 f2345 f3467 f5678 f6789 f78910 120 172 124 113 112 µ62 72 µ31 µ65 161 119 172 124 112 113 µ54 77 µ45 µ58 155 118 167 123 112 116 µ33 73 µ123 95 µ69 117 168 123 112 116 µ34 76 µ119 97 µ77 119 163 119 116 121 µ25 68 µ130 39 µ26 116 164 120 116 123 µ27 75 µ129 34 µ26 aStrain energy.bRelative to the best conformation of the same compound. cHeat of form