352
J . Phys. Chem. 1984, 88, 352-356
as HMX and RDX. Just as HMX decomposes while in the ring conformation other than that present in the room-temperaturestable 0-HMX phase,23 the thermal decomposition of RDX probably takes place most often in a molecule of essentially C3, symmetry rather than essentially C, symmetry as is present in the (23) 310-2.
Karpowicz, R. J.; Gelfand, L. S.;Brill, T. B. AIAA J . 1983, 21,
room-temperature-stable a-RDX phase. Acknowledgment. We gratefully acknowledge the support of this work by the Air Force Office of Scientific Research, AFOSR-80-0258. The help of Dr. Fred Van Catledge was most appreciated in obtaining the structures shown in Figure 1. Registry No. RDX, 121-82-4.
Lattice Vibrational Spectra and Intermolecular Forces in Solid Cyclopropane D. F. Eggers* and D. D. Keeportst Department of Chemistry, University of Washington, Seattle, Washington 981 95 (Received: May 12, 1983)
Far-IR spectra are reported for solid cyclopropane-d6. Far-IR spectra of cyclopropane,and also external mode Raman spectra for both species, are in good agreement with previous work. Computed external fundamentals are compared with those observed, and the values are quite close. The calculation is based on a recent crystal structure, which is Cmc2,. This structure resolves the ambiguities of earlier crystallographic and spectroscopicwork. Another structure, PnmZ1, not the actual space group, provides a computed energy lower than that calculated with the correct space group. Suggestions for further work are provided.
Introduction Work on the vibrational spectrum and crystal structure of solid cyclopropane dates back to 1961, when Brecher, Krikorian, Blanc, and Halford published results of their investigation on single crystals of cyclopropane with polarized radiation in the mid-infrared.l They showed rather conclusively that the crystal was orthorhombic with more than one molecule per unit cell, and had either C, or DZhas the factor group. From packing considerations they proposed further a 4, (PnmZ1) space group, with two molecules per unit cell. Further studies were reported by Bates, Sands, and Smith in 1969;2they included C3D6as well as C3H6,and measured Raman, mid-infrared, and far-infrared spectra at temperatures near 85 K. These workers studied powder samples, of presumably randomly oriented microcrystals; all subsequent investigators also worked with powder samples. However, Bates, Sands, and Smith included a study by powder X-ray diffraction; they found that the powder pattern could be indexed as orthorhombic. The resulting unit cell edge lengths, and approximate crystal density, required four molecules per unit cell. Combining this result with their spectra, these workers found a preference for a D2h factor group, rather than C20. Unfortunately, the Raman spectra did not reveal any lattice modes; these would have been very helpful. In 1973 Bates reported Raman spectra at 80 K that included lattice modes for both C3H6 and C3D6.3 Ratios of these frequencies seemed to favor the D2hfactor group, but comparison of splittings in infrared and Raman spectra of the internal modes seemed to favor the C, factor group. Shurvell, Daunt, and James reported a Raman study of solid C3H6at higher resolution in 1974.4 They concluded, from the lattice and especially the internal fundamental regions, that the crystal had C2, factor group. In 1977 Bertie and Jacobs reported a careful study of the lattice regions in both Raman and infrared spectra of C3H6.’ Unlike all earlier workers, they employed a range of temperatures, down to 4 K. They found three coincidences between strong, sharp lines in infrared and Raman spectra, plus another involving a strong infrared and a weak Raman line. They concluded that C2, was the favored factor group. It appeared, then, that spectroscopic and crystallographic evidence were at odds over the cyclopropane crystal structure. Since there had been no report on the far-infrared spectra of solid C3D6, ‘Present address: Department of Physical Sciences, Mills College, Oakland, CA 94613. 0022-3654/84/20,88-07~2$0150/0
we undertook to study it, and also to reinvestigate C3H6,in all spectral regions. Furthermore, as this work was progressing a new diffraction study of solid cyclopropane was carried out, this time with neutrons and on a single-crystal sample; it yielded the actual crystal structure. We therefore extended our work to include calculations of the crystal frequencies, at zero wave vector, based on the type of atom-atom potential that had been successful in a number of hydrocarbon crystals, including ethylene6 and ethane.’ As is shown below, these results bring most of the previously discordant findings into agreement.
Experimental Section The C3H6and C3D6were commercial samples, and were used with only some freeze, pump, and thaw cycles for purification. The C3D6,obtained from Merck Sharp and Dohme, had a stated isotopic purity of 98%. Infrared spectra were all run at 77 K in the sample cell described by Chao and Eggers;8 for far-infrared work the inner cold window was elemental silicon, and the outer windows were high-density polyethylene. The far-infrared instrument was an RIIC FS-720 Fourier transform spectrometer with a 50-gauge Mylar beamsplitter and a Golay detector. Extra fixtures were installed, so that the entire optical path outside the sample cell, from source to detector, could be evacuated through a cold trap at liquid nitrogen temperature with a large mechanical vacuum pump. In this way all interference from pure rotational lines of atmospheric water was eliminated. Four sample spectra were averaged, and likewise four blank runs; the interferograms were transformed on a VAX 11/780 computer. Sample thickness, based on the quantity of cyclopropane introduced and a visual estimate of the diameter of the deposit, was about 0.1 mm. Resolution was 3 crn-’, with uncertainty of 1 cm-’ in the peak values. Raman spectra were run on the Spex instrument used by Chao and E g g e q 8 but with a different sample cell. It was essentially (1) C. Brecher, E. Krikorian, J. Blanc, and R. S. Halford, J . Chem. Phys., 35, 1097 (1961). (2) J. B. Bates, D. E. Sands, and W. H. Smith, J . Chem. Phys., 51, 105 (1969). (3) J. B. Bates, J . Chem. Phys., 58, 4236 (1973). (4) H. F. Shurvell, S . J. Daunt, and D. W. James, J . Mol. Spectrosc., 53, 77 (1974). (5) J. E. Bertie and S. M . Jacobs, J . Chem. Phys., 67, 4981 (1977). (6) R. G. Whitfield and G. E. Leroi, J . Chem. Phys., 68, 2151 (1978). (7) M. G. Wisnosky, D. F. Eggers, L. R. Fredrickson, and J. C. Decius, J . Chem. Phys., 79, 3505 (1983). (8) T. H. Chao and D. F. Eggers, J . Chem. Phys., 66, 970 (1977).
0 1984 American Chemical Societv
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 353
Intermolecular Forces in Solid Cyclopropane loo
6.536 5 + y I
t
-A
a l-
40
I-
w
2oL 0
60
I
I
I
x
+ 0-4
0 N I
I
I
I20 WAVE NUMBER
90
?
I
I50
\r: -B/,/ ,/T \ \ \ \\ \
/
\
/
\ \
TABLE I: Observed External Modes, in cm-', for Crystalline Cyclopropane and Cyclopropaned, (Temperaturenear 77 K) prethis ferred Bb
SDJC
IR
108 99 93 60 52 Raman
132 118 109 100 92
Raman
Reference 2.
132
132 109
100.5 93.5
99 93
132.5 119.9
131 119 109
101.0 94.1
101
94 112 101 92 78
110 99 91 76 Reference 3.
work
110
C3D6
IR
a
132 118 109 100 93
BJd
/ /
value
132 110 100 93 132 119 109 101 94 112 101 92 78
110 98 99 90 91 76 76 Reference 5.
110
Reference 4.
-ph
+A
/
Figure 1. Far-infrared spectrum of cyclopropane-d,. The feature near 70 cm-I is an artifact due to polyethylene.
BSS'
*
a Pyrex glass evacuable dewar with a flat external bottom surface; the coolant reservoir had a piece of silicon sealed as its lower end. The sample was admitted to the annular space, and a drop was frozen at the edge of the silicon plate by suitable tilting of the cell, along with warming and cooling. The spectra were all run with liquid nitrogen as the coolant. For observation of Raman spectra the laser beam entered through the flat lower surface of the cell, and scattered light was collected through the curved side. The 514.5-nm line of Ar+ was used for excitation of Raman spectra.
Results The far-infared spectrum of C3D6is shown in Figure 1. Our Raman spectra of both C3H6and C3D6were in good agreement with those obtained by other workers, and they are not shown here. Our far-infrared spectra of C,H6 were also in agreement with those given by Bertie and J a c ~ b showever, ;~ in the earlier work of Bates, Sands, and Smith2 some lines were reported in addition to those found by Bertie and Jacobs and by us. We believe these extra lines were artifacts. The various observations in infrared and Raman spectra for the lattice modes of C3H6 and C3D6 are summarized in Table 1. Values quoted for the far-infrared spectra of C3D6are from this work; for the far infrared of C3H6,and for
Figure 2. Crystal structure of solid cyclopropane. Space group Cmc2, (Ci:); Z length is 5.755 A. Molecular C, plane oriented 50.481" from crystal x y plane. Molecules marked + have their centers in the x,y plane; molecules marked - are centered above and below the x,y plane, by one-half the z length. Dashed lines indicate a primitive unit cell, corresponding to the C,, factor group; see text. For clarity only carbon atoms are shown; hydrogens are omitted.
the Raman spectra of both molecules, all published values are given along with those from the present work, plus the preferred wavenumbers. Because we were limited to 77 K in the work on C3D6,all peak locations are for samples at or near that temperature. Since all spectra were measured on powder deposits, assignments had to be based on the positions and relative intensities of the various lines. However, lines that appeared in the Raman, but were absent from the infrared spectrum, could be assigned to a2 symmetry with confidence. Thus the mode at 119 cm-' for C3H6 is so assigned. Each of the other observed lines is found in both infrared and Raman spectra, with allowance for the combined uncertainties. After the crystal structure had been determined, we carried out some lattice dynamical calculations, as an aid in making further assignments. All calculations were limited to vibrational modes of zero wave vector, as in the work on ethane.' Essential information for the calculation is found in the crystal structure and space group; the latter was determined to be Cmc2, (C&, with four molecules in the orthorhombic unit cell on sites of C, symm e t r ~ .A~ diagram of the structure is given in Figure 2, in which only the carbon atoms are shown. The edges of the unit cell, shown on the figure, differ significantlyfrom those reported in the powder X-ray work of Bates, Sands, and Smith. The discrepancy is not due to difference in temperatures (85 K for X-ray, and 20 K for neutron), as we obtained a few preliminary alignment X-ray photographs on some single crystals in a cold nitrogen gas stream, finding approximately 7.9, 6.4, and 6.0 8, as the unit cell edges. These agree much better with the neutron values than do the Bates, Sands, and Smith distances of 10.0, 6.8, and 6.1 A. It is possible that some of the powder lines in their work were composites of several h,k,l sets. It is important to recognize that the neutron diffraction work on a single crystal of cyclopropane has uniquely determined the crystal structure. From the space group we can conclude that the factor group, as used in vibrational spectroscopy, must be CZD; (9) R. Thomas, private communication, and to be published
354 The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 TABLE 11: Nonbonded Interaction Potential Parameters A/kJ A 6 mol-' potentials C...C C...H H...H c..c I and 111 I1 a n d I V
2140 467 102 2414 136 573 a QH is given in multiples of the electronic charge.
ala
h/A
CIA
300000 367250
EjkJ mol-'
e/deg
K~
1.811 7.770 6.093 6.586 46.039 -23.773 1.797 7.949 6.324 6.718 46.264 -24.179 2.004 111 7.954 5.928 6.873 45.043 -22.046 IV 8.080 6.281 6.912 45.895 -23.566 1.919 exptb 7.920 6.536 5.755 50.481 -29.568 Tabulated values of compressibility are in multiples of 10.'' cm3 erg-'. From ref 9 and 12; see text. I I1
thus the controversy dating back some 14 years has been settled. Note, though, that the unit cell commonly treated in crystallography is the one sketched in Figure 2; all of its angles are 90". It contains four molecules, as first suggested by Bates, Sands, and Smith;2 however, a center of symmetry is clearly absent, so it can not represent factor group DZh.Another unit cell is indicated in Figure 2 by dashed lines; it has edges 5.134, 5.134, and 5.755 A, and angles go", go", and 100.9". This smaller unit cell contains two molecules and is primitive; it corresponds to the C2, factor group. Its group of symmetry operations can be considered to be a mirror plane parallel to the yz plane and passing through x = 7.920/2; a twofold screw axis parallel to the z axis and passing through x = 7.920/2, y = 6.536/4; a glide plane parallel to the xz plane and passing through y = 6.536/4, with glide translation of one-half the z cell length; and the identity. Application of the correlation diagram to the external modes shows that nine lattice vibrations of zero wave vector are expected, with three of symmetry a2, and two in each of the al, bl, and b2 irreducible representations. The external modes are here treated separately from the internal modes. This approximation is reasonable from the large spacing between them (about 500 cm-' for the lowest internal mode, and roughly 150 cm-' for the highest external mode). Vibrations of a], bl, and b2 irreducible representation are allowed in the infrared; for the Raman all four species, al, a2, bl, and b2 are allowed. The calculations were carried out with the computer programs used in the earlier work on ethane? Molecular geometry was not allowed to vary, but was taken as that used by Blom and Alton'O in their force field calculations. The intermolecular atom-atom potential was assumed of the form:
V ( r )=
Cia-'
BjkJ mol-'
TABLE 111: Calculated and Experimental Crystal Parameters potential
Eggers and Keeports
+ Be-" + Q1Q/
in which r is the atom-atom distance, and the other quantities are parameters. Computations were limited to four of the best atom-atom potentials found for ethane; values of the parameters
C.-H
H...H
C...C
C...H
H...H
35600 65485
9 080 11 677
3.60 3.60
3.67 3.67
3.74 3.74
Q H ~
0.000
0.102
employed are given in Table 11. Sets I and I1 were directly from the work of Williams and Starr," and based on crystal structures of aliphatic and aromatic hydrocarbons. The parameter set I1 contains Coulombic terms; these are omitted from set I. Sets I11 and IV are identical with I and 11, respectively; they differ only in that the interaction centers for the hydrogens are located at the nuclei. For sets I and I1 we followed the scheme of Williams and Starr," in which the interaction centers for hydrogens are located 0.07 A from the hydrogen nucleus toward the carbon to which it is bonded. In ethane we had found that interaction centers at the hydrogen nuclei gave results somewhat better than with the shifted interaction centers. For each of these four potential sets the lattice energy was minimized by allowing the a, 6 , and c orthorhombic unit cell edge lengths, plus the tilt angle of the C, planes, to be simultaneously varied, subject to the symmetry restrictions of the space group. The starting point for all minimizations was the experimental crystal structure. The energy was minimized for a central molecule interacting with all of its neighbors in a block consisting of 125 units cells, arranged with five cells along each of the x,y , and z directions. Interaction of all atoms in the central molecule with all atoms in the neighboring 499 molecules led to the minimized crystal parameters and energies listed in Table 111. The experimental lattice energy was obtained from the work of Ruehrwein and Powell,12with a correction for the enthalpy of cyclopropane gas. This enthalpy was calculated by standard statistical-mechanical principles. Thus the experimental lattice energy reported in Table I11 represents the enthalpy of sublimation of the crystal, at 0 K. When the crudeness of the model is considered, the general agreement of all computed results with experiment is found encouragingly good. Potential 11, with shifted interaction centers and Coulombic terms, is seen to be slightly superior in giving a lattice energy lower than any of the others, and in somewhat better agreement with the observed a and b lattice distances. In several instances the agreement between computed and observed parameters is quite poor, for all of the potentials used. First, the angle of tilt for the C, ring is off by some 4 or 5 " . Second, the discrepancy in the c axis length is almost 1 A, and much larger than the differences for a and b. Third, the magnitude of the computed lattice energy is at best 16% smaller than that observed. The lattice energy computed for the ethane crystal was much closer to the experimental value, even through this was based on only 280 neighboring molecules. These three discrepancies probably mean that the atom-atom potentials employed were not quite optimal for cyclopropane. For each of these minimum energy structures and their corresponding potential parameter sets, the lattice vibration frequencies were calculated for both C3H6and C3D6;the results are
TABLE IV: Observed (at 77 K ) and Calculated External Frequencies for Crystalline Cyclopropane, in cm-' ________ obsda ________
IR -_____
Raman
132m
132(55)
93 s
94 (100) 119 (45) 94 (100) 109 (25) 101 (20) 109 (25)
symmetry ___a,
a?
110 s 100 s 110 s a
h, b,
78.6 131.8 56.7 87.1 120.6 85.4 115.5 95.9 113.3
Values in parentheses are relative intensities.
______ 0.0 100.0 21.2 12.7 42.5 68.8
calculated _______________-_ __
80.4
__-_
73.5 0.0 128.1 100.0 131.7 100.0 59.7 19.4 42.4 28.1 85.9 13.6 91.7 8.5 122.4 39.9 116.0 46.2 72.0 65.1 84.8 86.8 11.4 115.9 10.2 11.1 115.4 0.2 91.7 0.0 0.1 95.2 0.1 120.2 0.0 0.1 110.2 Values following frequencies are relative clilculated intensities. 0.0
-
___ 76.1 129.5 51.1 89.2 121.2 86.4
117.2 91.5 111.1
0.0
100.0 23.6 11.9 41.3 69.3 8.9 0.1
0.1
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 355
Intermolecular Forces in Solid Cyclopropane
TABI,E V: Observed (at 77 K) and Calculated External Frequencies for Crystalline Cyclopropane-d,, in cm-’
_ _ _ _ l _ l _ _ _ _
obsda
IR
Raman
112 m
110 (45)
calculatedb -
symmetry
a,
73.6 109.8
0.0
100.0
75.3 106.6
68.8 109.7
0.0
100.0
26.7 39.0 52.0 28.2 54.7 79.9 74.8 12.7 75.8 12.5 35.5 98.1 38.2 104.0 99 (40) 102.4 70.3 70.9 74.6 12.6 76 (100) b, 71.5 78 s 7.3 100.5 8.1 100.2 100.1 101 s 99 (40) 0.2 0.3 81.3 0.0 91 (40) b* 82.8 81.0 92 s 101 s 99 (40) 101.9 0.0 100.6 0.0 105.4 0.0 Values in parentheses are relative intensities, Values followinr frequencies are relative calculated intensities. a2
a
0.0
100.0 34.4 9.1 42.4 77.9 8.4
displayed in Tables IV and V. The computer programs made no use of symmetry, but operated in terms of crystal-fixed Cartesian coordinates. Symmetry of the vibrations was determined by examination of the eigenvectors that comprised a part of the output. Choice of b, and b2 is arbitrary, and we have taken the b, as the modes that have pure rotational displacements (with no translation); the b2 vibrations then have a considerable admixture of z axis translation, plus rotation. Relative Raman intensities were also computed, on the oriented-gas model. This omits any molecule-molecule interactions, and simply assumes the polarizability tensor has two equal components in the C3 plane, but a different one perpendicular to this plane. As in the treatment of ethane, the structure with minimized energy was employed in these calculations, even though it differs somewhat from the structure found experimentally. This provides internal consistency and avoids the possibility of producing imaginary “frequencies”, when the structure employed is near a saddle point in the potential energy hypersurface. However, we must remember that we are treating a “model” system, somewhat different from the real crystal. A suggested assignment of the observed spectra is also included in Tables IV and V . Assignment of the 119-cm-I Raman line in C,H6, without an infrared counterpart, is certainly sound, as are probably also the strong Raman lines at 132 and 94 cm-’ in C3H6 and the strong ones in C3D6at 110 and 76 cm-I. These latter four all correspond to large computed Raman intensity, and the agreement between calculated and observed wavenumber values is quite good. The remaining four observed lines, two in each isotope, are not so readily assigned. We have chosen to place one for each molecule in b,, and one for each molecule in b,. However, the calculated values suggest that there may well be some overlapping of b, and b2 modes that have frequencies close together. The other two a2 modes have calculated frequencies probably too low for them to be assigned as overlapped by observed Raman lines. A better choice of the experimental temperature would be 4 K, but there are no far-IR values for C3D3at that temperature. This would generally raise the observed frequencies, giving poorer agreement with values calculated here. The lower calculated a, frequencies in both molecules are interesting; their eigenvectors shows that they are almost pure molecular translation parallel to t h e y axis; this is the basis for their zero calculated Raman intensity. The reason for the low Raman intensity computed for both b2 modes is also found in their eigenvectors. They have large contributions from torsions; however, both molecules move such that their (extended) C, planes maintain a constant relative dihedral angle, at all stages of their vibrational displacements. The computed vibration frequencies are so close to each other in most all instances that we cannot single out one as superior. This results in part from our limiting the calculations to a few of the best potentials from the ethane work. Furthermore, there (10) C. E. Blom and C. Altona, Mol. Phys., 31, 1377 (1976). (11) D. E. Williams and T. L. Starr, Compuf. Chem., 1, 173 (1977). (12) R. A. Ruehrwein and T. M . Powell, J. Am. Chern. SOC.,68, 1063 (1946).
71.3 107.8 46.9 17.7 102.8 72.2 101.7
0.0 100.0
79.0 100.0
0.1
30.0 12.1 37.4 74.3 6.5 0.0
TABLE VI: Computed Crystal Parameters for Cyclopropane, Based on Pnm2, Crystal Structure Suggested by BKBH,‘ Energy and Structure from Energy Minimization That Started with Parameters Suggested by BKBH potential
7.708 I1 7.911 I11 7.788 1V 7.985 Reference 1. I
a
alA
h/A
CIA
eideg
E/kJ mol-’
4.815 4.939 4 851 4.978
4.121 4.237 4.221 4 334
12.726 11.539 13.592 12.837
-24.538 -25.775 -23.100 -24.540
are no experimental symmetries as a basis for the assignments. Such information, readily obtained from infrared and Raman measurements on oriented single crystals with polarized radiation, would be invaluable. The most striking differences among the various calculated frequencies are found in the lowest of the three a2 modes, ranging from 42 to 60 cm-’ in C3H6and from 39 to 55 cm-l in C3D3. These modes have appreciable predicted Raman intensity, some 20-30% of that of the strongest Raman vibration; their definite detection, and verification by polarization studies, would be most useful. However, it may well be that other studies, as by neutron scattering, will be necessary for location of these modes. A computation of the relative infrared intensity, and an improved calculation of the Raman intensity, with allowance for molecular polarizabilityin the crystal depending on intermolecular interactions, would also be he1pf~l.l~ The program employed to determine the energy minima also produced second derivatives of energy with respect to the crystal parameters. We have therefore also computed the compressibility for solid cyclopropane, and it is reported in Table 111. This quantity does not appear to have been measured, as yet, for cyclopropane. We have also determined the contributions of the different types of atom-atom interaction to stabilizing the crystal. It turns out that the C-C and Cs-H interactions contribute nearly equally to the non-Coulombic parts of the summed potential. For parameter sets with Coulombic terms, the H-H interactions contribute some 5 or 6% to the crystal stability. However, in sets I and 111, without Coulombic terms, the summed H-H interactions actually give a slight positive energy, contributing to destabilizing the crystal. In sets I1 and IV the total effect of all Coulombic terms provides additional stabilization, by several percent of the total computed energy. As in ethane, the smallness of the Coulombic contribution is probably due to the symmetrical arrangement of the charges. Since the crystal structure proposed by Brecher, Krikorian, Blanc, and Halford had been quite reasonable, a computation of its lattice energy, with minimization, seemed interesting. The surprising results of this calculation are shown in Table VI; comparison with Table I11 shows that the incorrect crystal structure is computed to be more stable than the true structure for each of the four potentials, by amounts ranging from 0.7 to (13) V. Schettino and S. Califano, J . Chim.Phys., 76, 197 (1979).
356
J . Phys. Chem. 1984, 88, 356-363
1.O kJ mol-'! Furthermore, these very low energies were computed with only 299 neighboring molecules, rather than with 499 neighbors as used for the entries in Table 111. This is yet another indication that the potentials employed are not optimal for cyclopropane. We suggest that the cyclopropane crystal structure may provide a crucial test for evaluating additional potentials, and modifications of the present ones. It would be especially useful to have intermolecular potentials that could be reliably used in the prediction of crystal structures, such as by computation of the minimized energy for a variety of assumed space groups; the true structure should be that corresponding to the lowest energy, assuming that its space group was included among those in the calculations. A similar situation prevailed for some years with respect to the crystal structure of chlorine. Energy computations favored a cubic structure, but experimentally it has long been known to be orthorhombic. However, in 1979 Nyburg and Wong-Ng reported some extensive calculations that showed an atom-atom potential with interaction energy suitably varying with the angle between the atom-atom vector and the bond direction, as well as with the atom-atom distance, could yield a computed lattice energy lower for the orthorhombic structure than for the cubic onesi4 Perhaps such directional dependence would correctly reorder the energies computed for various crystal structures of cyclopropane. Alter(14) s. C. Nyburg and W. Wong-Ng, Proc. R. Soc. London, 367, 29 (1979).
natively, addition of electric multipole terms could be helpful.
Summary With the far-IR spectra of solid cyclopropane-d,, reported here, there are now complete data on the lattice Raman and infrared spectra of solid C3H6and C3Ds. The external modes and their Raman intensities were calculated in this work; a recent crystal structure determination was employed, along with several atomatom potentials. Agreement with experiment was fairly good, though some uncertainties remained. Compressibility of the solid was computed. Spectroscopic measurements on single crystals, with polarized radiation, would permit experimental determination of symmetries in the observed vibrations, and thus provide unique assignments. Calculation of lattice infrared intensities is needed, plus computation of Raman intensities that goes beyond the oriented gas model. The structure suggested over 20 years ago by Brecher, Krikorian, Blanc, and Halford,' with energy minimization, yielded lattice energies indicating it to be more stable than the structure computed by using the now known space group. This result, and the uncertainties in the lattice vibrations, indicate the need for further work on intermolecular potentials for solid cyclopropane. Acknowledgment. We are grateful to the Graduate School Research Fund, University of Washington, for a grant to support purchase of a plasma tube used in the laser. Registry No. C3H6,75-19-4; C3D6, 2207-64-9,
Vibrational Spectrum and Structure of Hexafluoroacetonet D. A. C. Compton,*J. D. Goddard,s S. C. Hsi,lI W. F. Murphy,* and D. M. Rayner Division of Chemistry, National Research Council of Canada, Ottawa, Canada KIA OR6 (Received: May 16, 1983)
The vibrational spectrum of hexafluoroacetone has been reexamined. The improved quality of the Raman polarization data for the vapor-phase spectrum, in particular, allows a better identification of the symmetry properties of the vibrational modes, especially in the low-frequency region. An ab initio SCF calculation of the geometry and vibrational force field has been carried out. The theoretical geometry agrees qualitatively with the literature electron diffraction determination (both studies find that the hexafluoroacetone structure has C, symmetry), but there are unexpected quantitative differences. A vibrational frequency calculation based on the theoretical force field has been used to assign the vibrational spectrum.
Introduction Developments in the field of infrared photochemistry have led to an increased interest in the vibrational spectroscopy of fluorinated compounds. Carbon-fluorine stretching frequencies lie in the wavelength range of high-power C 0 2 lasers, making fluoroorganic compounds prime candidates for infrared multiphoton dissociation (IRMPD) studies. Hexafluoroacetone (hexafluoropropanone,hereinafter referred to as HFA) has proven to be an ideal model compound in such studies. In particular, 13Cisotope enrichment experiments have helped to unravel the processes involved in IRMPD.'-3 However, it is important to the conclusions of this and future work that the vibrational spectrum of HFA and its interpretation be as well understood as possible. Recent work in this laboratory on vibrational studies of fluorinated corn pound^^^^ has led us to ieexamine the literature results for HFA,6*7in which several inconsistencies became apparent. In Issued as NRCC No. 22866. 'Present address: The Standard Oil Company (Ohio), Research and Development Department, Cleveland, OH 44128. $Present address: Department of Chemistry, University of Guelph, Guelph, Ontario, Canada N1G 2W1. 'I Present address: Institute of Applied Chemistry, Chinese Academy of Sciences, Chanchun, China.
0022-3654/84/2088-0356$01.50/0
particular the quality of the published Raman spectra is not comparable to current state of the art results, making consistent interpretation extremely difficult. This, in fact, caused problems in making the initial vibrational assignment,6 which was later revised.8 The revised assignment has been used in a normalcoordinate a n a l y ~ i s . ~ HFA is a relatively large molecule when considering the detailed assignment of its vibrational spectrum. Many of its vibrational modes are expected to include contributions from several molecular coordinates. A normal-coordinate analysis can be of aid in confirming vibrational assignment, but, in the case of HFA, the large (1) Hackett, P. A,; Gauthier, M.; Willis, C. J . Chem. Phys. 1978, 69, 2924-5, (2) Hackett, P. A,; Gauthier, M.; Willis, C.: Pilon, R. J . Chem. Phvs. 1979, 71, 546-8. (3) Hackett, P. A.; Gauthier, M.; Willis, C J . Chem. Phys. 1979, 71, 2682-92, (4) Compton, D. A. C.; Rayner, D. M. J . Phys. Chem. 1982,86, 1628-36. ( 5 ) Compton, D. A. C.; Chatgillaloglu, C.; Mantsch, H. H.; Ingold, K. U. J . Phys. Chem. 1981, 85, 3093-100. (6) Berney, C. V. Spectrochim. Acra 1965, 21, 1809-23. (7) Pace, E. L.; Plaush, A. C.; Samuelson, H. V. Spectrochim. Acta 1966, 22, 993-1 006. ( 8 ) Miller, F. A.; Kiviat, F. E. Spectrochim. Acta, Part A 1969, 25, 1577-88.
(9) Perttila, M. Acta Chem. Scand. Ser. A 1974, 28, 933-4.
Published 1984 American Chemical Society
