2885
Studies of Conjugated Ring Hydrocarbons. Structure of Spiro[2.41hepta-4,6-diene
II.la,b
Joseph F. Chianglc and C. F. Wilcox, Jr.*ld Contribution from the Departments of Chemistry, State University of New York, College at Oneonta, Oneonta, New York 13820, and Cornell University, Ithaca, New York 14850. Received April 24, 1972
Abstract: The structure of spiro[2.4]hepta-4,6-dienehas been determined by electron diffraction in the gas phase. The internuclear distances and bond angles were obtained by applying a least-squares analysis to the experimental molecular inte?sities. The conjugated carbon-carbon double bond in the five-memberedoring was found to be 1.341 i 0.003 A. The spysp2single bond between the two double bonds is 1.460 0.005 Aowhilethe spLsps single bond is 1.509 & 0.002 A. The C-C bonds in the three-membered ring are 1.510 =k 0.002 A. The angle C2C3C4 = 1-9.5 & 0.2'. The three-membered ring is perpendicular to the five-membered ring and bisects the angle C2C1C4. From these data it follows that the three-membered ring shows little interaction with the five-membered ring, a conclusion opposite to that drawn from nmr data.
*
T
he hydrocarbon spiro[2.4]hepta-4,6-diene (1) has been investigated by ultraviolet2 and nmr3 spectroscopy for evidence of electron delocalization of the strained three-membered ring bonds into the cyclopentadiene ring. In both studies there were implicit assumptions regarding the structure of 1. The present
1
2
3
paper describes the results of an electron diffraction structure determination of 1 and compares it with those of dimethylfulvene (2) and cyclopentadiene (3). The degree of cyclopropyl conjugation is examined in light of these structural parameters.
Experimental Section A sample of spiro[2.4]heptadiene was prepared as described earlier and purified by distillation. Glpc analysis indicated greater than 99% peak purity. Sectored electron diffraction patterns were taken with the Cornell instrument4 on Kodak Electron Image plates. Two sets of data were obtained for this compound under the following conditions: 65 kV at 262.4 mm samFle-to-plate distance covered the angular range from q = !O-54 A-1, and 65 kV, 129.4 mm, covered the rangeq = 43-115A-l[q = (40/X)sin8/2]. Three plates were taken at each distance with exposures ranging from 15 to 90 sec at a beam current of 0.3 PA. The sample was kept at -20" during scattering. MgO diffraction patterns were also recorded concurrently to establish the scale factor. The Patterns were microphotometered with a double beam Jarrell-Ash microdensitometer interfaced with a digital recorder6 (each plate was measured twice and the readings averaged). The procedure for data reduction and structure analysis has been described in several previous publications.6 The elastic and inelastic form factors of (1) (a) Presented, in part, at the 162nd National Meeting of the American Chemical Society, Washington, D. C., Sept 12-17, 1971 ; (b) part I : J. F. Chiang and S. H. Bauer, J. Amer. Chem. Soc., 92, 261 (1970); (c) State University of New York; (d) Cornell University. (2) C. F. Wilcox, Jr., and R. R. Craig, J. Amer. Chem. SOC.,83, 4258 (1961). (3) R. A. Clark and R. A. Fiato, ibid., 92,4736 (1970). (4) S. H. Bauer and K. Kimura, J. Phys. SOC.Jap., 17,300 (1962). (5) J. F. Chiang and S. H. Bauer, Trans. Faraday Soc., 64, 2247 (1968). (6) K. Kimura and S. H. Bauer, J . Chem. Phys., 39, 3171 (1963); I. L. Hencher and S. H. Bauer, J . Amer. Chem. Soc., 89,5527 (1967).
Tavard, et al.,' were used in conjunction with the Ibers and Hoernie phase-shift approximation in the intensity calculations.
Analysis and Results The total experimental intensity curves for the two sets of data along with the refined background are plotted in Figure 1. The data are given in Table 1. The reduced experimental molecular intensity curve and that calculated for the best model are compared in Figure 2; the lower oscillating curve is the difference curve between the experimental and theoretical curves. The refined radial distribution curve and the difference between that and the best theoretical radial distribution curves are shown in Figure 3. Cz and C2,symmetries have been assumed for calculating the geometry of spiro[2.4]heptadiene. For symmetry, the following geometrical parameters were used (the numbering is given in Figure 4): Cl-Cn, C1-C3, Cs-Cd, C4=Cs, C r C s , C2-Hi4, CrHs, LCsCeC7 (CUI, LCjCdI9 (a), LH12C3H13(p), and 8, the angle between CrHB and the x-axis. For Czsymmetry, in addition to the abovementioned geometrical parameters, another parameter is also used, the angle between the planes of the fivemembered and three-membered rings. None of the Cz symmetry models tried fit the experimental intensity better than the Czvsymmetry model, and when the parameters were allowed to vary, the structure always converged on the Czvstructure shown in Figure 4. The Cartesian coordinates are given in Table 11. The values of all geometrical parameters and some of the mean amplitudes of vibration, h,, lI2(Iz3), lsg, 1 6 7 , were refined by applying a least-squares analysis on the reduced molecular intensity. All the geometrical parameters and the above-mentioned mean amplitudes of vibration were allowed to vary, except the C-H distances which were determined from the radial distribution function. All other mean amplitudes of vibrations were chosen at values which had previously been determined for typical hydrocarbons. The final values of the parameters are listed in Table 111. The error matrix is reproduced in Table IV. The error limits cited in Table I11 are three times the standard devia(7) C. Tavard, D. Nicholas, and M. Rouault, J . Chim. Phys. Physicochim. Biol., 64,540 (1967). ( 8 ) J. A. Ibers and J. A. Hoerni, Acta Crystallogr., 7,405 (1954).
Chiang, Wilcox / Spiro[2.4]hepta-4,6-diene
2886 Table I. Set 1 4
Intensity
9
Intensity
4
Intensity
4
Intensity
9
Intensity
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
1.4317 1.4511 1.3804 1.2382 1.1640 1.2764 1.5426 1.8179 1.9203 1.7567 1.4384 1.1457 0.9648 0.8659 0.7923 0.7670 0.7914 0.8465 0.8860 0.8804 0.8173 0.7295 0.6447 0.5805 0.5326
34 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
0.4932 0.4617 0.4504 0.4558 0.4593 0.4491 0.4355 0.4330 0.4421 0.4550 0.4555 0.4396 0.4130 0.3897 0.3728 0.3664 0.3702 0.3816 0.4105 0.4396
43 44 45 46
0.5693 0.5675 0.5460 0.5053 0.4539 0.4058 0.3722 0.3504 0.3358 0.3293 0.3278 0.3276 0.3266 0.3180 0.3010 0.2836 0.2755 0.2723 0.2688 0.2607 0.2477 0.2378 0.2321 0.2304 0 2297
68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
0.2297 0.2304 0.2327 0.2335 0.2326 0.2296 0.2253 0.2250 0.2277 0.2328 0.2388 0.2438 0.2463 0.2494 0.2538 0.2566 0.2593 0.2620 0.2650 0.2700 0.2760 0.2815 0.2895 0.2971 0.3060
93 94 95 96 97
0.3152 0.3238 0.3308 0.3372 0.3432 0.3470 0.3500 0.3550 0.3595 0.3662 0.3123 0.3802 0.3876 0.3980 0.4071 0.4150 0.4222 0.4285 0.4340
48 47 49 50 51 52 53 54 55 56 57 59 58
60 61 62 63
64 65 66 67
I
90 91 92
99 98 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115
0.4400 0.4440 0.4478 0.4540
Table III. Structural Parameters and Vibrational Amplitudes of Spiro[2.4]heptadiene rid.
A
1.5101 ZIZ 0.0054 1.5094 f 0.0033 1.5098 f 0.0114 1.3407 f 0.0021 1.4604 f 0.0054 1.120 1.100 109.5 f 0.2' 131.3 f 0.6" 10.1 f 0.3" 114.0 ZIZ 0.3"
10
10
10
40
70
M
x)
M
m ( o 0
IW
PWJ
Figure 1. Relative intensities as a function of diffraction angle [q = (40/X) sin 0/2] for long and short sample-platedistances and the
refined background. Table 11. Coordinates of Spiro[2.4]heptadiene X
Y
2
0.00 0.00
2,2077 3,5154 3.5154 1,2637 0.00 0.00 1.2637 1.4568 -0.8266 -0.8266 1.4568 3.8203 3.8203 3.8203 3.8203
0.00 0.7550 -0.7550 0.00
0.00
- 1.1779 -0.7301 0.7301 1.1779 2.2608 1.4558 - 1.4558 -2.2608 0.9395 -0.9395 0.9395 -0.9395
Journal of the American Chemical Society
0.00 0.00 0.00
0.00 0.00 0.00 0.00 1.2830 1.2830 - 1.2830 - 1.2830
1 95:9 /
May 2, 1973
lii.
A
0.0633 f 0.0057 0.061Oo f 0.0093 0.0633 =!= 0.0057 0.0503 f 0.0024 0.0592 ZIZ 0.0024
tions which are the diagonal elements of the error matrix. The Rf value was 0.0406. The sensitivity of the least-squares structure fit to small variations of the twist angle of the three-membered and five-membered rings about the C2 axis was explored. In a structure refinement in which the rings were constrained to a 5" twist about the C2 axis the bonded distances showed no appreciable changes but the Rr value increased t o 0.051. Application of the F test9 (92 degrees of freedom, 15 parameters) to the increase in Rf value indicated that the 5" twisted structure could be rejected at better than the l e 8 significance level; Le., if the twisted structure were correct, there is only one chance in lOS, assuming random errors, that the observed ratio of variances would be found. In Figure 3, the first peak is due to C T H ~= 1.100 A, CS-HI, = 1.120 A, Hl2-HlS = 1.879 A, and all bonded carbon-carbon distances: CrC5 = 1.341 A, s 5 - C ~= 1.460& C1-C4 = 1.509A,and S1-C2 = 1.510A. The peaks between 1.90 and 3.0 A are contributed by C . . . C nonbonded distances, C4-Ce = 2.289 A, (9) (a) W. C. Hamilton, "Statistics in Physical Science," Ronald Press, New York, N. Y.,1964, pp 157-162; (b) "Handbook of Mathematical Functions," M. Abramowitz and I. A. Stegun, Ed., Report NO. NBS-AMS 55, U. S. Government Printing Office, Washington, D. C., 1964, eq 26.6.15 and Tables 26.1 and 26.2.
2887
n
E"..
DtFPERtPKE
-
I
I
I
1
I
I
I
I
I
I
I
Figure 2. The experimental and theoretical qM(q) curves; the lower oscillating curve is the difference between the theoretical and experimental curves. Table IV. Error Matrix of Spiro[ZA]heptadiene c1-c4
CIS5
C&6
cl
