Norman 8. Colthup
American Cyanomid Company Stamford, Connecticut
Vibrating Molecular Models Frequency shifts in strainedring double bonds
carhonyl groups and double bonds in strained rings have been extensively studied in the literature. Their vibrational frequencies in the infrared and Raman spectra are observed to he displaced from the comparable poskions in unstrained or noncyclic compounds (1, 2 ) . Calculations on ketones by Halford (3) and Bratoz and Besnainou (4) indicate that the bond angle changes in rings will shift the C=O frequency due to mechanical effects, Bratoz specifying that most of the shift is due to changes in double bond-single bond mechanical int,eraction. The frequency shifts have alternately been ascribed to changes in the double bond force constant as a result of strain. It was decided to study the general effect of double bond-single bond int,eract,ionusing vibrating molecular models. Vibrating mechanical molecular models were first used by Kettering, Shults, and Andrews (5) to demonstrate and study modes of vibration in various molecules. Basically, the nuclei are represented by weights and t,he interatomic bonds by helical springs. When this model is freely support,ed and connected through a loose coupling to an eccentric on a variable speed motor, the model will perform all t,he normal modes of vibration. When the "disturbing" frequency of the eccentric oscillation matches one of the natural vibrational frequencies of the model, resonance occurs and the model vibrates. At other frequencies, the model remains quiet.
Figure I. The photograph shows the apparatus for a mechanical onology o f rnolecvlor vibrations. The dc motor is connected to o vorioc through o selenium rectifier. An eccentric in the form of a nail on the ride o f the motor $haft is connected to the ~ m p e n d e dmolecular model (the skeleton of n-butane in this care1 through o coupling wire.
If the models are correctly made and supported, and their limitations realized, they can be studied profitably. 394
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There are many ways to construct models, one of which is as follows. Spring ire 16 mils in diameter was wound into a helical coil about '/8 in. in diameter. 4 single bond included 9 coils a t the end of which the wire was shaped to hold a '/,,-in. diameter steel ball within suitable wire turns, on the spring axis, after which the wire cont,inued for 9 more coils to form the next bond. "Double bonds" consisted of two "single bond" springs. "Atoms" were about Z1/2 in. apart. These were low frequency models, about 7 cycles per second for the C=C stret,ching vibration. An alternate set of high frequency models (about 50 cycles per second) using heavier weights (1 in. diameter) and stiffer springs (0.4-in. wire diameter, 7/ls-in. coil diameter) was also made. The ends of the springs were brought to the axis and extended into holes in the "atoms." "Double bonds" consisted of single springs twice as stiff as the springs used for "single bonds." The stretching and bending force constants of the springs were measured by suspending a weight from one end of a spring held vertically and horizontally by the other end and noting the strain. The ratio of stretching to bending force constants was made about 8 to 1 to approximate the average molecule. This is most easily adjusted by stretching the springs out somewhat, increasing all the coil spacings. This does not dist,urb the relative molecular geometry but lowers the bending force constant relative to the stretching until the desired ratio is ohtained. Since only planar vibrations of planar molecules were studied, the models were suspended with the molecular plane horizontal. Every "at.om" was supported by a long thread to a support high enough for pendulum frequencies to be relatively low. Thus, every "atom" is free to move within the plane. A dc motor with redurtiou gears was connected t,hrough a selenium rectifier to a variac. A nail was taped to the motor shaft to provide an eccentric. One of the double bonded carbon atoms of the model and the eccentric were connect,ed by a large turn of very fine wire (10 mils). As the motor speed varied and resonance was ohtained, the normal modes were performed and the frequencies measured with a stroboscope. For the high frequency models, a motor without reduction gears was used. In this study, the effect of only one variable was investigated, namely the change in double bond-single bond interaction as a function of angle. The weights were all the same, the double bond springs were twice as stiff as single bond springs, and the ratio of stretching to bending force constants was about 8 to 1. Thus, frequency shifts, if any, would be due to mechanical effects rather than to changes in force constant, as
Toble 1
Model
Double bondsingle botld an&
Description of vibration
Model freq. cm.?
Molecule freq. ern.?
Analogous molecule
Rci. -
...
'/a
C=C, '11 sym. C-C,
out ai phase
Hypothetical
'/e
C=C,
out of phase
Cyclohexcne
2
Cyclopentcne
i?
Cyclobutme
-*
Cyclopropene
1s
Acetylene
Q
'/a
sym. C-C,
Yo nlodel made C=C (no C-C $16
C=C,
'I?C=C,
stretch)
' I 6 gym. C-C,
in phase
C 4 , in phase
I12
C=C (no C-C
...
Hppothctical
stretch)
C = C , ' / o sym. C 4 , out of p h a ~ e KOn d e l made C=C,
'1, sym. C 4 , out of phase
sym. C-C,
C=C,
'12
O=O=O
.-.
C=C,
'/2
out of phase
sym. C - 4 , out of phase
'I?C=C, '1s sym. C-C,
out of phase
force constants were unchanged. Frequencies were measured in cycles per minute and were multiplied by a single proportionality constant (different for the high and low frequency models) to give wavenumbers. The constant mas chosen which gave the best wavenumber fit between the models and the molecules. Sample calculation: 410 c.p.m. X 4.05 = 1660 em-'; 385 c.p.m. X 4.05 = 1559 em-'. The results are listed in Table 1. Similar results for both internal and external double bonds were obtained with the two quite different types of high and low frequency models. The models for the unsubstituted internal double bond C-CH=CH-C were made with and without "hydrogen atoms." The hydrogen atoms had little effect on the trends noticed. I n the external double bond system the hydrogens with their nonchanging small interaction were left out so the system also resembled the ketone carbonyl system in its trend. As was suspected, in most of the models (allene excepted) the carbon atoms attached only to single bonds did not move much during the double bond
1740
1781
1815
...
1950
1980
Mrthrlenc eyclopropone
8,I1
...
Hypothetical Allene
10
stretching vibration; hence, the relatively small mass effectswhen these masses are changed to masses greater
.I
F
a
- --
----
- - - -.
Figure 2. T h e photograph rhowr the response of a ball ond spring model of COI to w r y i n g "disturbing" mechanical frequencies. In the asymmetric
stretching vibration ltopl and bending vibration lbonom) the two end "otomr" move in the some direction while the middle "atom" mover twice 0 %f a r a n d in t h e opposite direction. in the symmetric stretching vibration Imiddle) t h e center atom stays motionlers ar the end atoms move in opporite directions. The mechanical frequencies are proportional to t h e m t ~ d~ O I ~ C Y I O Ifrequencies. They occur ot obovt 1.4 cycler per second for bending, 2.7 c.p.r. for symmetric stretching, and 4.6 c.p.r. for orymmetric stretching.
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than carbon (4), and heuce the localization of the double bond vibration to t,he atoms studied. Since the attached atoms do not move much, the attached single bonds must be altered in length as the double bond stretches and contracts. When t,he double bond-single bond angle is 90°, there is no stretching interaction as the double bond stretching vibration merely bends the bond angle. As the double bond-single bond angle becomes larger than 90°, t,he single bonds must be increasingly contract,ed as t,he double bond stretches. This added resistance to motion increases the frequency which reaches a maximum for the 180' bond angle case. This is an out-of-phase interactiou of the double bond stretching vihration with the symmetrical single bond stretching vibration. -4s the double bond-single bond angle becomes less than 90' the single bonds must be increasingly &etched as the donble bond stretches (in-phase interaction). The added resistance to motion again increases the frequency relative to the 90' case. The cyclic internal double bonds studied were unsubstituted (C-CH=CH-C). In molecules, further changes occur when the hydrogens are substituted. Cyclobutene absorbs at 1566 cm-' (2) but various 1,2dimethyl cyclobutenes absorb at 1685 cm-I (6). This is extremely difficult to explain if the cyclobutene double bond is weakened by strain hut easy to explain in terms of additional double bond-single bond interaction in the substituted case. The same thing occurs in the cyclopentene case. Cyclopentenes with the two double bond hydrogens intact absorb at 1617-1614 cm-', 1-alkyl cyclopentenes absorb a t 1657-1650 cm-', and 1,2-dialkyl cyclobutenes absorb at 1686-1671 cm-I (7). From the 6 membered ring to the 4 membered ring, t,he 1,2-dialkyl cyclo-enes absorb in nearly the same place a t 169&1670 cm-'. This is markedly differentfrom the unsubstituted rings. The decrease in the cyclic single bond-double bond angle is somewhat compensated for by an increase in the non-cyclic single bond-double bond angle which keeps the effect of
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interaction nearly constant. When the cyclic angle gets below 90°, however. the effert of interaction is to increase rather than decrease the frequency, and this combined with a non-ryclie single bond-double bond angle in cyclopropene of 1.19' 35' (14) will sharply inincrease the frequency of 1.2-disubstituted cyclopropenes. These are found at 1900-1880 em-' (1.5, 16). In the same manner, dimethyl acetylene absorbs at 2313 cm-I (17, 18) rompared nith 1974 cm-' for acetylene (9). Thus, it seems t,hat t,he rhange in double bond-single bond interaction as a funrtion of bond angle issufficient in itself to explain most of the frequency shifts, and is the most i m ~ o r t a nvariahle t inrolred. Literature Cited (1) LORD,R. C., .LSD > ~ I L L E R . F. A,, AppL. Spectroscopy, 10, 115 (1956). 12) R . W..J . A m . Chem Soe.. . . LORD.R. C.. AAll \\LLKER. 76,2518 (1954). (3) HALFORD, J. O., J. ?hem. Phlisl 2 4 , 830 (1956). (4) BRATOE, S., AND BESX.~ISOL-, S., Compt. Rend., 248, 546
--
119.501 \ . ,.
(5) KE~TERING, C. F., H H ~ L T S , L. \V., AND ANDREWS, D. H., Phys. Rev., 36, 531 (1930). (6) CRIEGEL, R., AND LOT-IS. G., Chem. Ber., 90, 417 (1957).
(7) SVERDLOV, L. M., I N D ~ R ~ I S O I .E. , N., Optics and Spectroscopy, 6, 214 (1959). (8) BALU.E. J.. Disser!ation Abstr.. 18. 1628 (1958). ~ ,~
~
.
~
(10) LINNETP, J. W., A N D ATERI.17. H., J . Chem. Phys., 6,686 (1938). (11) GRAYSON, J. T., E T A L . . J . .1m. Chern. Soe., 7 5 , 3344 (1953). (12) APPLEQUIST, D. E., A H D ROBERTS,J. D., J. Am. Chem. Soe., 78,4012 (1956). (13) EGGERS, D. F., WIBERG.I
