J. Phys. Chem. 1983, 87, 3839-3844
TABLE I: Dipole Polarizabilities of Naphthalene (Ci(lH8) and Its Ions, Referred to Molecular Axesa 147 145
112 106
76 41
112
160 205 139 182 223 146
111 128 85 97 115 97
34 55 3 0
102 129 76 93 114 81
3 0
97
experiment l 2 this work this work this work CNDO/S1
CNDOIS'
CNDO/S' PPPS
All values in atomic units; 1 au of dipole polarizability corresponds to 1.6488 X lo-'' F m2or 0.14819 A'. Subscripts L, M, and N denote the long, medium, and normal molecular axes.
and monoanionl also shown in the table, but with the increase for the cation nearly half that for the anion instead of only a sixth for the dication compared with the dianion. These results of both sets of calculations are consistent with the simple theory of the preceding section. Although the pairing theorem is valid only a t the semiempirical a-electron level because of the specific in-
3839
tegral approximations inherent in the Pariser-Parr-Pople formalism, many of the consequences of this theorem are still displayed by the results of more rigorous ab initio calculations. For example, the ab initio a-electron charges in neutral naphthalene all lie in the range 1.000 f 0.005, compared with the prediction from the pairing theorem of 1 exactly? and the in-plane polarizability components are close to those obtained by the Pariser-Parr-Pople m e t h ~ d .The ~ results listed in the table show that the consequences of the pairing theorem also persist in aromatic hydrocarbon ion polarizabilities. The larger polarizability of the ion compared to the molecule affects the charge-transfer-energy calculations reported earlier.8 Specifically, they lead to lower energies for small electron-hole separations in crystals of aromatic hydrocarbons. The corrections required will be too small to modify the description of the charge-carrier generation process, but they may influence the predicted position of the lowest charge-transfer band observed in electrooptical absorption spectra.6 Registry No. CloHs, 91-20-3; CI0H?+, 56481-83-5;CI0H?-, 56481-82-4.
Molecular Structure of Cyclopropylacetylene As Determined by a Combined Analysis of Electron Diffraction and Microwave Spectroscopic Data Kolchi Tamagawa and Richard L. Hilderbrandt Department of Chemistry, North Dakota State University, Fargo, North Dakota 58105 (Received: January 3, 1983)
The structure of cyclopropylacetylene has been determined by combined analysis of electron diffraction and microwave spectroscopic data. The average C-C bond length in the ring, r,(C-C)*" = 1.514 A, was resolved into two distinct distances, rg(C1-C2)= 1.526 (7) A, and rg(C2-C3)= 1.490 (14) A. The deviation from equilateral symmetry of the ring is similar to that observed for cyclopropyl cyanide and is in agreement with Hoffmann's prediction. The Cl-C4 bond length (rg = 1.445 (8) A) appears to be quite short for a single bond as a result of hybridization and electron delocalization. The C = C bond length (r, = 1.213 (2) A) was found to be in excellent agreement with the value for acetylene. Other structural parameters obtained were as follows: average r,(C-H) = 1.099 (4) A, LC2-Cl-C4 = 118.8 (4)O, LH-C-H = 112.8 (2.6)', and L C ~ - C ~ - = H 121.1 ~ (3.3)O.
Introduction Carbon-carbon bond lengths in the cyclopropane ring have been predicted to change significantly when the hydrogen atoms are replaced by substituent groups. Hoffmannl has suggested that substitution with a good T electron acceptor, e.g., a cyano group, will lead to a strengthening of the C-C bond opposite, and a weakening of the C-C bond adjacent to the substituent. On the other hand, substitution with a good a-electron donor is predicted to weaken all of the cyclopropane-ring bonds. Penn and Boggs2 calculated planar moments from available data on about 20 substituted cyclopropanes. They found a consistent shortening of the C-C bonds opposite unsaturated substituents by an average of 0.015 A relative to C-C bonds opposite saturated substitutents. More recently Laurie and co-workers3 have studied the (1) R. Hoffmann, Tetrahedron Lett., 33, 2907 (1970). (2) R. E. Penn and J. E. Boggs, J. Chem. SOC.,Chem. Commun., 11 666 (1972).
structure of cyclopropyl cyanide by microwave spectroscopy. They have found that the C-C bond adjacent to the substituent (1.528 A) is longer than the opposite bond (1.500 A) in agreement with Hoffmann's prediction. They have also studied the microwave spectrum of 1,l-difluorocyclopropane.4 For this molecule they found a decrease in the C-C bond length (1.464 A) adjacent to the fluorines, and an increase in the bond opposite the fluorines (1.553 A) relative to the C-C bond length in the parent molecule, cyclopropane (1.513 A).5 Since the acetylenic group is thought to be a good aelectron acceptor, it is expected that the cyclopropane ring in cyclopropylacetylene would deviate from equilateral symmetry. Moreover, the conjugation between the acetylenic group and the ring might well be expected to lead (3) R. Pearson, Jr., A. Choplin, and V. W. Laurie, J. Chem. Phys., 62, 4859 (1975). (4) A. T. Perretta and V. W. Laurie, J . Chem. Phys., 62 2469 (1975).
(5) 0. Bastiansen, F. N. Fritsch, and K. Hedberg, Acta Crystallogr., 17, 538 (1964).
0022-3654/83/2087-3839$0 1.50/0 0 1983 American Chemical Society
3840
The Journal of Physical Chemistry, Vo/. 87, No. 20, 7983
Tamagawa and Hilderbrandt
TABLE I: Estimated Force Field for Cyclopropylacetylene'
~
_
_
C-C ring C-C acetylenic C=C C-H ring C-H acetylenic L C-C-C acetylenic L H-C-H L H-c-c i H-C=C
-c-c=c C-C C-C, C-C, C-H,
tors C-C ring C-C acet C-H ring
force constantb
force constantb
4.152 5.301 15.87 5.1 25 5.974 1.00 0.423 0.650 0.230 0.361 0.226 -0,060 0.183 0.068
0.024 -0.015 0.270 - 0.085 0.049 0.143 0.141 -0.005 0.045 -0.044 0.033 -0,019 0.129 0.220
L H-c!-H, i H-C-c L H-C,-Cp, L H-C,-C iH-C,-Co, i H'-C,--G cis LH-C,-Cp, IH-CI(I-C, trans L H-C,-Cp, L H-Cp-C, H-C,-Cp, L H -C,-C, cis L H-C,-Cp, L H-C,-Cp cis LH-C,-C+, LH-C,~, iC-C&, LH-C-C C-C tors, C-C tors
~
' Most of the force constants are taken from cyclopropane13 and methylacetylene." Stretching force constants and stretch-stretch interaction force constants have units of mdyn/A, Bending force constants and bend-bend interaction force constants have units of mdyn A . Stretch-bend interaction force constants have units of mdyn. to a shortening of the C-C bond between the substituent and the ring. The structure of cyclopropylacetylene has been studied by microwave spectroscopy. Collins, Britt, and Boggs6 have observed the microwave spectra of the normal and singly deuterated species, C3H5CrCD. With a number of assumptions (including equilateral symmetry for the ring), they determined a value of 1.466 (18) A for the length of the C-C bond between the ring and the acetylenic group. This value is somewhat longer than the r,(C-C) of 1.4586 (3) A in methyla~etylene~ and is not in accordance with prediction. More recently Harmonf has determined a complete heavy-atom-substitution structure for the molecule. Harmony's results of the heavy-atom structure of the molecule are as follows: 1.527 (6) A for the length of the C-C bond adjacent to the substituent, 1.503 (7) A for the length of the C-C bond opposite the substituent, 1.422 (6) A for the C-C bond length between the ring and the acetylenic group, and 1.211 14) A for the CGC bond length. We initiated an electron diffraction study of cyclopropylacetylene in order to explore the effects of acetylenic substitution on ring geometry. We expected at the outset of our analysis that it would be difficult, if not impossible, to determine all of the structural parameters for the molecule using diffraction data alone. However, since microwave rotational constants were available for six isotopic species in the ground vibrational state, we felt that a combined electron diffraction-microwave spectroscopic analysis would help in determining a precise molecular geometry for the molecule, and in resolving the splitting in the three-membered-ring distances. Soon after we started our analysis, another electron diffraction study on cyclopropylacetylene was published by Klein and S ~ h r u m p t .This ~ study employed electron diffraction data only, and the authors made no attempt to resolve the three-membered-ring distances. It is thus also of interest t o c o m p a r e the results of t h e present study with those of Klein and Schrumpf. Experimental Section The sample of cyclopropylacetylene was prepared by Professor Stuart Staley of The University of Nebraska and (6) M. J. Collins, C. 0. Britt, and J. E. Boggs, J. Chem. Phys., 56, 4262 (1972). (7) A. Dubrulle, D. Boucher, J. Burie, and J. Demaison, J . Mol. Spectrosc., 72, 158 (1978). ( 8 ) M. D. Harmony, presented at the 9th Austin Symposium on Molecular Structure, Austin, TX, March 3, 1982, Paper WM6. (9) A. W. Klein and G. Schrumpf, Acta Chem. Scand., Ser. A , 35, 431 (1981).
TABLE 11: Calculated Vibrational Amplitudes and Shrinkage Corrections for Cyclopropylacetylene" distanceb Cl-C2 C1-C4
c- c
C-H6 C-H11 c1. ' . c 5 c2. . . c 4 c2.. . c 5 C. . .Hgem
1041ii 51 2 461 360 769 740 501 698 91 3 1050
104(ra r,(T)) 37 36 91 179 443 31 34 17 107
r,( 0) r,(T) 0.0009 0.0003 0.0035 0.001 5 0.0113
a Atomic numbering employed is illustrated in Figure 1. 1" parameters are the parallel mean amplitudes in angstroms, r , - r,(T) values are the shrinkage corrections in angstroms, and ra( 0) - r (2') values are the temperature corrections in angstroms. Only calculated values for the prominent distances in the radial distribution curve are shown.
was used without further purification. Electron diffraction data were collected on the North Dakota State University (NDSU) electron diffraction instrument at nozzle-to-plate distances of 250 and 100 mm. The accelerating voltage used was 40 keV, and the background pressure was maintained at 1.0 X torr during exposure. Exposure times for the 0.44-PA beam current were 60-70 s for the long camera distance plates and 160-190 s for the short camera length plates. Kodak 4 x 5 in. electron image photographic plates were used. Approximate voltage/ distance calibrations were made with a digital voltmeter and cathetometer, but all final scale calibrations were based on benzenelo (rg(C-C) = 1.397 (4) A) plates obtained under identical operating conditions as those used for the experimental data. The photographic plates were microphotometered on the NDSU microcomputer-controlled densitometer with data being collected at intervals of 0.150 mm. The data were corrected in the usual manner for emulsion saturation, plate flatness, and sector inperfections after which they were interpolated at integral values of q = (40/X) sin (8/2) for analysis. The data were analyzed by using a leastsquares procedure similar to the one employed by Gundersen and Hedbergl' with elastic scattering factors and phase shifts calculated by Schafer, Yates, and Bonham.'* (10)
(1976).
K. Tamagawa, T. Iijima, and M. Kimura, J . Mol. Struct., 30, 243
(11) G. Gundersen and K. Hedberg, J . Chem. Phys., 51,2500 (1969). (12) L. Schafer, A. C. Yates, and R. A. Bonham, J . Chem. Phys., 5 5 , 3055 (1971).
Molecular Structure of Cyclopropylacetylene
The Journal of Physical Chemistry, Vol. 87, No. 20, 1983
3841
H9
Flgure 1. Atomic numbering system used in defining structural parameters for cyclopropylacetylene.
OIFF. I
Analysis Vibrational Analysis. In order to determine a structure by the combined analysis of electron diffraction and microwave spectroscopic data, it is necessary to have a complete quadratic force field for the molecule. Unfortunately neither a force field nor a vibrational assignment exists for cyclopropylacetylene a t the present time. We therefore had to resort to estimating the force field for cyclopropylacetylene by transferring force constants from cyclopropane13and methyla~etylene.'~The force field used in the calculation is shown in Table I. The vibrational amplitudes, shrinkage corrections, and the corrections required to extrapolate the average structure to 0 K are shown in Table 11. The corrections required to convert the Bo rotational constants into B, rotational constants (also calculated from the harmonic force field) are shown in Table IV. Electron Diffraction Analysis. In the initial stages of refinement, only the electron diffraction data were employed. In order to reduce the number of geometrical parameters required to define the molecular model, the following assumptions were introduced: (1) The molecule was assumed to have C, symmetry. (2) All C-H bond lengths of the ring were assumed to be equal. (3) The LC-C-C planes were assumed to be the perpendicular bisectors of the LH-C-H planes of the ring. (4) The acetylenic group was assumed to be linear. (5) The C-H bond length of the acetylenic group was assumed to be equal that in acetylene, r,(C-H) = 1.078 8,.15 (6) The Cl-C2 and C2-C3 bond lengths wre constrained to be equal. The atomic numbering of cyclopropylacetylene is shown in Figure 1. Assumptions 1-5 were maintained throughout the analysis, but constraint 6 was relaxed in the later stages of combined analysis using both electron diffraction and microwave spectroscopic data. The structural parameters which were used to define the molecular model were chosen as follows: (1) an average C - C bond length for the ring, (2) the C1
