Low frequency vibrations of acrolein

JOURNAL

OF

MOLECULAR

SPECTKOSCOPY

48,232-245 (1973)

Low Frequency Vibrations A.IR.:H.

COLE

AND A. A.

of Acrolein ’ GREENS

ScIzool of Chemistry, University of Western Australia, Nedlands, 6009, Australia

The absorption bands in the far infrared due to the torsional and in-plane bending vibrations have been examined under moderately high resolution. Torsional energy level spacings up to o = 4 have been measured. A Coriolis interaction between the in-plane bending and the torsional modes and a Fermi resonance between 1)= 1 of the in-plane bend and v = 2 of the torsion have been studied in detail. INTRODUCTION

Acrolein magnetic

vapor

has been extensively investigated in many regions of the electroand all these measurements have shown that the trans species (I) common rotamer, comprising at least 9.5% of the acrolein at room

spectrum,

is the most temperature.

H

I

Microwave measurements by Cherniak and Costain (1) have established an accurate ra structure for tram acrolein and have provided some of the rotational constants for molecules in the first few levels of the torsional vibration. The ground state rotational constants are A = 1.5795 cm-‘, B = 0.1554 cm-‘, C = 0.1415 cm+. The electron diffraction results of Kuchitsu et al. (2) have been shown (3) to agree well with Cherniak and Costain’s structure leaving no doubt as to the geometry of the ground state. Harris (4) has made a complete vibrational assignment based on infrared measurements and gives ~18 = 157 cm-’ and ~13 = 327 cm-l as the frequencies of the torsional and in-plane bending vibrations, respectively. YE+has been further studied by Campagnaro and Wood (5) who resolved some of the PQ~ peaks in this band. 1 Thii work is based on part of the Ph.D. thesis of A. A. G., submitted February, 1972. 2 Present address: Mineral Physics Section, C.S.I.R.O., North Ryde, N.S.W., Australia, 2113. 232 Copyright 0 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.

LOW FREQUENCY

VIBRATIONS

OF ACROLEIN

5

IO

233

Acrolein

t : IIIII

Kd’

10 1111III 10

I I I I I I 5 I I I 1.

rlllllllIl

5

5

10

FIG. 1. Absorption due to the torsion “18of acrolein. Path length 3.6 m, pressure (a) 15 Torr, (b) 50 Torr. The K.” assignments for the fundamental (upper) and the first hot band (lower) are indicated. The Y” leading lines identify the Q (1 + 0) peaks of the fundamental and hot bands.

A large number of authors have studied the ultra-violet absorption of acrolein (6-11). The work of Alves, Christoffersen, and Hollas (10) and of Bair, Goetz, and Ramsay (11) has shown the existence of a second rotamer (probably the cis species but possibly guuclze) existing to the extent of about 4%, at room temperature. The electronic measurements have confirmed the vibrational spacings in the ground electronic state and have provided some ground state rotational constants. De Groot and Lamb (12) studied the cis-trans isomerism in the liquid state and concluded that the cis form lies 720 cm-’ above the ground state and separated from it by a barrier of 2460 cm+. The most recent estimate of the cis-trans energy difference (10,II) is 660 f 40 cm-‘. The C, symmetry of trans-acrolein allows all the vibrations, to appear in the infared spectrum, but severe overlapping between neighboring bands hinders rotational analysis of the higher frequency bands (13). However, the lowest two fundamentals are free from overlap except for their associated hot bands. These vibrations, the torsion and the skeletal in-plane bend, have been studied in detail in this work and are described below. EXPERIMENTAL

Reagent grade acrolein was purified by distillation. The spectra were recorded on a vacuum grating far infrared spectrometer (14) which has been modified by the addition of a White cell of path length 1.2 m per pass. The torsional band ~18 was recorded with a path length of 3.6 m and pressures of 15-50 Tor?, and the in-plane bending band ~13with path lengths of 1.2 and 3.6 m with pressures between 5 and 40 Torr. The spectrometer was calibrated by using rotation lines of water vapor (15, 16). The spectral slit width in the range 12@400 cm-’ was about 0.3 cm-‘. THE TORSION

~18

The absorption band, shown in Fig. 1, is of type C with a number of strong central Q branches between 150 and 160 cm-‘. On the high frequency side the subband ‘Qz

a 1 Torr = 133.3 Pa.

COLE AND GREEN

234

TABLE

1

ACKOLEINTORSIONFUNDAMENTAL

K”

AK

Obsd

Calcd

O-C

13 12 11 IO 9 8 7 6 5 4 4 5 6 7 8 9 IO 11 12 13

$_I

186.97 185.13 183.67 181.71 180.09 178.14 176.25 173.83 171.82 169.64 147.48 144.58 140.96 137.55 134.00 130.50 126.84 123.01 119.13 115.22

186.90 185.30 183.63 181.88 180.06 178.16 176.16 174.08 171.89 169.61 147.57 144.33 141.00 137.57 134.05 130.43 126.73 122.94 119.07 115.14

0.07 -0.17 0.04 -0.17 0.03 -0.02 0.09 -0.25 -0.07 0.03 -0.09 0.25 -0.04 -0.02 -0.05 0.07 0.11 0.07 0.06 0.08

+I -1

-1

= 158.06 f 0.21. = 1.4311. DX” = 0.15 x IO-‘. (A’-8’) = 1.377 i 0.006. Dg’ not significant. Ground state (A”4”) constrained. Standard deviation of fit = 0.12. va @“-I?‘)

peaks are strong and easily located with a 10 cm absorption cell and 1.5 Torr pressure, but the PQK peaks on the low frequency side are very weak and could only be found by using the long path cell with a higher pressure. The pQx peaks diverge towards low frequency and this allows clear resolution of hot band structure. The series of central peaks with maxima at 158.6, 156.2, 155.0 and 153.5 cm-l is interpreted as the Q (1 +- 0) branches of the fundamental and various hot bands similar to those previously described for glyoxal (17) and butadiene (18). However, in this case the band center is not adjacent to the most intense peak. On close examination, it becomes obvious that the first hot band (V18 = 2 +- ~18 = 1) has been displaced from its expected position (-157.5 cm-r) to low wave number by approximately 1.2 cm+ so that its central Q branch is superimposed upon that of the 018 = 3 + 018 = 2 hot band, while the higher hot bands appear at approximately equal spacings. This displacement is due to a Fermi resonance between the v18= 2 level and the 1~13= 1 level (see below). The K assignment of the fundamental band (central Q branch at 158.6 cm-l) is shown in Table 1 and on Fig. 1. The Q-peak values were taken as subband origins and

LOW FREQUENCY

I

VIBRATIONS

I

t

182 100 la8

I

1%

OF ACROLEIN

I

I

154

152

235

I IY

cm-’

FIG. 2. (a) Observed and (b) calculated band contours near the center of the acrolein torsion band. The dotted section is an estimate of the contribution of the ~(5 + 4) transition which was not included in the computation.

the data treated by constraining A” - B” at Cherniak and Costain’s value and determinmg DK” from combination differences. The band origin, ~00, and the upper state constants A’ - B’ and DKrwere found by fitting the data to the equation vQ+

(A”

_

B"),'

_

tmt

&"h4

=

voof (A’ - B’)(k +

tmt

FIG. 3. Vibrational levels of acrolein (cm-‘).

1)’ - DK’@ + I)‘,

(1)

COLE AND GREEN

236

TABLE

2

SOMEROTATIONALCONSTANTS OF ACROLEIN(cm-l)

A

v18

VI8

Ba

C*

DK

0 0 0 0

0 1 2 3

1.57958 1.527 1.479b 1.429b

0.1554 0.1556 0.1558 0.1560

0.1415 0.1421 0.1425 0.1430

0.15 x 10-d -

1 2 1

0 0 1

1.621 1.664 1.560

0.1554 0.1554 0.1554

0.1415 0.1415 0.1415

0.19 x 10-d 0.23 x lo-4 0.08 x 10-d

From the data of Cherniak and Co&in (1). b Obtained from a contour analysis of the torsion (j~O.01). For levels where the B and C values could not be obtained from the microwave work the value of A was calculated from A-8 by using the ground state 8. l

c& = 0.052 alpd = -0.042

where k = K” for AK = -I- 1 subbands and k = - K” for AK = - 1. This procedure led to 158.06 f 0.21 cm-’ for the band center of the torsion. A somewhat more precise value for this band center (158.1 f 0.1 cm-l) is obtained below from a study of the central band contour. The subband Q branches of the hot bands were not resolved sufficiently well from those of the fundamental, especially on the AK = -I- 1 side, to allow the hot band centers to be determined in this manner. Therefore, the central region of the band contour was synthesized by calculating all the rotation line frequencies and relative intensities using the asymmetric rotor program of Birss and Ramsay (19). The B and C rotational

Acrolein

I

400

I

I

360

I

I

320

I

I

280

cm-’ FIG. 4. Absorption due to the in-plane bend ~11of acrolein. Path length 3.6 m, pressure (a) 5 Torr (b) 20 Torr. The K.” assignments for the fundamental (upper set) and hot bands are indicated. The lower set of;leading lines applies to-the vIp = 1 hot band, the central set to the via = 1 hot band.

LOW FREQUENCY

VIBRATIONS

OF ACROLEIN

237

Table 3 Acrolein in-plane bend Fundamental

K"

AK

Obs.

21

+1

Calc.

o-c

403.85

403.91

-0.02

20

399.50

399.50

0.00

19

395.16

395.15

0.01

18

390.91

No.85

0.06

17

386.jl

386.61

0.10

16

382.47

382.43

0.04

15

378.29

378.30

-0.01

14

374.25

374.25

0.00

13

370.19

370.26

-0.07

12

366.24

366.33

-0.05

11

362.45

362.45

0.00

10

358.67

358.70

-0.03

5

354.90

355.00

-0.10

8

351.24

351.37

-0.13

7

347.78

347.82

-0.04

6

344.30

344.34

-0.04

5

340.58

340.95

0.03

4

337.58

337.63

-0.05

3

+1

334.46

334.34

0.06

5

-1

311.65

311.51

0.14

6

309.15

305.03

0.12

7

306.58

306.62

-0.04

8

304.38

304.32

0.06

5

302.02

302.08

-0.06

10

299.82

255.54

-0.02

257.54

257.85

11

-1

constantsin the excited

0.05

torsional levels are available from the data of Chemiak and Costain (1). It was assumed that the auA value determined from the analysis of the torsional fundamental would be constant and could be used to predict the values of A in the higher torsional levels. The calculation included all lines corresponding to J = 0 -50, K = 0 - 5 for the levels ~118= 0 - 4, and confirmed that the “central” Q branch

COLE AND GREEN

238

Table

3

(Continued)

K”

AK

Obs .

Calc.

12

-1

295.94

295.91

13

294.00

293.95

0.05

14

292.08

292. I8

-0.10

15

290.43

290.45

-0.02

16

288.77

288.75

0.02

17

287.32

287.21

0.11

18

285.89

286.07

-0.18

o-c

0.03

19

284.25

284.23

0.02

20

283.00

283.08

-0.08

21

281.53

281.62

-0.09

280.29

280.40

-0.11

22

-1

V

=

323.70 f 0.09

(;"_$I)

=

1.4311

D” K

=

0.15 x 10-4

(Al-i’)

=

1.4731 f o.ooog

ok

=

0.19 x 10-4 f 0.02

Ground State Standard

(A”-i”)

Deviation

x 10-4

Constrained of Fit

=

0.081

of the fundamental and each hot band is due to the unresolved lines of the K(l +- 0) subband Q branch which runs to low frequency from the subband origin for 0.9 cm-‘, where it forms a band head, turns around and diverges towards high frequency. Since A-B = 1.4 cm-l, this means that each band origin lies 0.5 cm-” from the Q(l +- 0) contour peak on its low frequency side. The resulting lines, numbering about 7000, were convoluted with a Lorentzian slit function of half width 0.3 cm--’ with intensities multiplied by appropriate Boltzmann and matrix element factors, and the fundamental and hot band origins were adjusted for best fit of the Q branch maxima with those in the observed contour (Fig. 2). The resulting band origins are summed to give the torsional energy levels (Fig. 3). This procedure gives the spaces between neighboring energy levels to f0.1 cm-’ and the series of energy levels 158.1 f 0.1, 313.8 f 0.2,469.5 f 0.3, 624.0 f 0.4, and 777.0 f 0.5 cm-1

LOW FREQUENCY

VIBRATIONS Table

Acrolein

In-plane

bend,

239

OF ACROLEIN

4 Hot

band

from

K

AK

Obs.

Calc.

22

+1

v,~ =

1

o-c

405.71

405.65

0.06

21

401.41

401.48

-0.07

20

397.36

-0.01

19

397.35 --

18

389.25

389.27

-0.02

17

385.28

385.30

-0.02

16

381.54

381.56

-0.02

15

377.53

377.39

0.14

14

373.53

373.54

-0.01

--

13

370.19

370.40

-0.21

12

366.24

366.07

0.17

11

362.49

362.58

-0.09

10

359.27

359.50

-0.23

9

355.33

355.69

-0.36

8

351.93

351.59

0.34

7

348.99

348.93

0.06

6

345.73

345.65

0.08

5

342.57

342.43

0.14

4

+l

339.33

339.29

0.04

4

-1

316.75

316.67

0.08

5

314.23

314.30

0.07

6

311.65

311.72

-0.07

7

309.15

309.36

-0.21

8

307.03

307.07

-0.04

9

304.80

304.84

-0.04

IO

302.79

302.70

0.09

I1

300.78

300.62

0.16

12

298.91

298.60

0.31

compares more than favorably with earlier measurements based on electronic spectra (8,9), which were accurate to about f2-3 cm-l. With the accurate band centers it was then possible to obtain experimental values of A-B for each torsional level by calculating the contour for the higher K ?QK and PQK

COLE AND GREEN

240

Table

K

4

(Continued)

Obs.

Calc.

o-c

13

296.72

296.66

0.06

14

394.80

294.78

0.02

AK

15

293.04

292.96

0.08

16

291.27

291.21

0.06

17

289.56

289.52

0.04

287.87

287.89

-0.02

18

-1

V

325.98

=

f

0.15

(;+)

=

I .378

D;;

=

0.0

(A'-6')

=

1.413

not

D;c Ground

significant

State

Standard

f 0.001

Constants

Deviation

Constrained

of Fit

=

0.14

branches. The best fit to the observed contour was obtained by initially including only to the value found in the analysis of the the first hot band, constraining (A-&,,,,I value. This was then constrained while the fundamental and adjusting the (A-@,,,,2 second hot band was added by adjusting (A - &8=3. The final constants are shown in Table 2. THE IN-PLANE

BEND ~13

This vibration produces an A/B hybrid band which is principally of type B (Fig. 4). The QK peaks show a marked convergence to low wave number, indicating a large negative CYIB*,and in general the hot band QK peaks are resolved from those of the fundamental band. By using the microwave value for (A”@), it was possible to find an assignment which gave a fairly good fit to Eq. (1) at low K, values. The value of DK” can then be obtained from a combination difference analysis by using the formula AzKF”(J,K)

= ~QK_-I- PQR+~ = 4(A” - B”)K

- 8Dd’K(K2

+ 1).

(2)

LOW FREQUENCY

VIBRATIONS TABLE

OF ACROLEIN

241

5

ACROLEININ-PLANE BEND, HOT BAND FROM~3 = 1

K” 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 7 8 9 10 11 12 13 14 1.5 16 17

AK

Obsd

Calcd

o-c

+1

403.31 398.96 394.56 390.22 386.09 381.54 377.53 373.50 369.57 365.40 361.47 357.67 353.97 350.22 346.67 343.33 339.97 308.17 305.55 302.79 300.78 298.91 296.72 294.80 293.04 291.27 289.56 287.87

403.42 398.95 394.53 390.17 385.87 381.63 377.47 373.37 369.33 365.37 361.48 357.67 353.94 350 28 34b.7P 343.21 339.80 307.89 305.52 303.22 301.01 298.91 296.87 294.92 293.06 291.28 289.59 287.98

0.11 0.01 0.03 0.05 0.22 -0.09 0.06 0.13 0.24 0.03 -0.01 0.00 0.03 -0.06 -0.03 0.12 0.17 0.28 0.03 -0.43 -0.23 0.00 -0.15 -0.12 -0.02 -0.01 -0.03 -0.11

+1 -1

-1

YO = 325.46 f 0.24. Lower state constants constrained. (A’-B”) = 1.4731. DR1’ = 0.19 x 10-4. (A/-B’) = 1.516 f 0.001. DR’ = 0.23 X lO-4 f 0.06 X 10-4.

When the ground state

(A” - B”) is known, this can be rearranged

AzKF”(J,K)

- 4(A” _B”)=

to give

- ~DK”(K’ + 1).

K A linear fit of the left side of Eq. (3) against (K2 + 1) then gives DK”. The values of DK” and (A”-&‘) can then be used in Eq. (1) to determine (A’-B’) and DK’. The analysis of the band (Table 3) shows that the origin (323.7 cm-l) is not at the central minimum of the type B contour (327 cm-r). A similar result was found for the skeletal in-plane bend of glyoxal (17) and is due to the displacement of the central minimum by the cumulative effects of the hot bands which appear with relatively high intensities at higher frequency.

COLE AND GREEN

242

The analysis of the hot bands in this spectrum is interesting as two of them appear with approximately equal intensities. These are the band from the 018 = 1 level and that from the vra = 1 level. Although the Boltzmann factor of the latter is approximatel! half that of the former, the increase in the magnitude of the (v’/P] 21”) matrix element almost exactly compensates for the decrease in population. The two main hot bands were located by taking the series of “Qx peaks which had not been assigned to the fundamental transition and using combination difference relations to predict the positions of the rQx peaks. This method proceeded by trial and error until the correct assignment was obtained. It was found that there is an almost exact overlap of the “Qx peaks of these two hot bands while the rQ~ peaks form two distinct series. Fig. 4 and Tables 4 and 5 show the assignments and the resulting rotational constants and band centers. The AK, = + 1 side of the band still shows a number of unassigned Q peak series which must belong to the hot bands originating from the higher levels of the torsion and the in-plane bend. However, with obvious peaks on one side only, there is little point in attempting to assign K values. DISCUSSION (i)

Vibrational Ejects

The values for ~r~(158.1 cm-‘) and vra(323.7 cm-l) have been established more accurately than previously published results (157,327 cm-’ (4)) which were determined from measurements at lower resolution. The shift in the first hot band of the torsion of about 1.2 cm-’ towards lower wave number can only be accounted for in terms of a Fermi resonance between the levels with ~18 = 2 (02) and ~113= 1 {lo}. This resonance was first suggested by Brand (5) and later invoked by Cherniak and Costain to explain anomalies in the rotational constants of torsionally excited molecules. The interaction must arise through the anharmonic term &,~,rsq~~qr~, where Q~Sand q13are the dimensionless normal coordinates and ku,ls,ls has units of cm-l. The general form of the matrix element which connects the two unperturbed levels (20) is w = ((WLs)O I ~ls.ls.13q182q18

This term will cause successive interactions

I ha

-

1, 2118+

2J0)

of the form

{lOI.+-+WI> (111 t+ 1031, { 12) - (04), etc. The interacting energy levels “repel” one another perturbed vibrational spacings, are related by

and 6 and 60, the perturbed

6 = (602+ 4W2)i.

and un-

(4)

LOW FREQUENCY

VIBRATIONS

OF ACROLEIN

243

The microwave spectrum (1) shows the usual series of satellite lines associated with rotational transitions of molecules in the excited torsional levels. However, Cherniak and Costain found that all the satellite lines except the first are displaced equally implying that the Fermi resonance affects the levels above (01) approximately equally. Since the matrix elements of the interaction become larger as ~118increases, the vibrational spacings must also increase to maintain an approximately constant interaction. This is in fact what is observed here (see Fig. 3) since only the first torisonal hot band is displaced from its “expected” position. By studying the changes in the rotational constants due to the resonanceycherniak and Costain calculated that W = 4.12 cm-r by using a perturbed vibrational spacing of 15 cm-‘. Actually, the spacing is much smaller (9.9 cm-l) and since the (01) level is displaced by 1.2 cm-r as judged from the series of torsional levels, Eq. (4) leads to W = 3.2 cm-l. This value implies a somewhat weaker interaction than would be expected using previously published results for the vibrational frequencies. It is interesting to note that the value of x13,r3 determined from the difference in band centers of the fundamental and the hot band originating in the (lo} level is positive, indicating that the vibrational spacing increases as ~13 increases. This, however, may not be a true indication of the potential function for this vibration since there is a further Fermi resonance possible between {20) and { 12) which is of the same form as that discussed above. This would tend to force the { 20) level upwards producing the observed value of ~13.1~. (ii) Rotational Ejects The rotational constants of acrolein obtained in this work are summarized in Table II. In their microwave work Cherniak and Costain were able to determine accurate values for B and C in the excited vibrational levels of the torsion, but they published an erroneous value (equivalent to 1.5968 cm-l) for A in the ~~18= 1 level, based on incorrect assignments of weak b-type rotational transitions. There is no doubt that the value of (A - B) decreases markedly as the torsional quantum number increases, as shown by the convergence of the Q peaks of the torsion band towards high frequency. Campagnaro and Wood (5) found a decrease in (A - B), although their actual value is in doubt as they appear to have used an incorrect formula to calculate their rotational constants and band center. The convergence of the subband origins towards high frequency in the torsional (~18) band and towards low frequency in the m-plane bending (~1~) band indicates a Coriolis coupling between the two modes, similar to the effects already described by us for glyoxal (17) and butadiene (18). It is possible to calculate a value for {w,r3@) in the same way as was done for butadiene although the various simplifying assumptions made in Ref. (18) are no longer as valid, since the lower symmetry of acrolein permits many more interaction terms to be nonzero. However, the main contribution to a large positive ~~18~can still be expected to come from the Coriolis term. By using Eq. (14) of Ref. (18) one obtains I[~.13 (a)1 = 0.50, based on the alsA value calculated from the decrease in A between the level (00) and the level (01). The spectrum of the torsion shows a considerable intensity asymmetry, the AK, = + 1 side being much more intense than the AK, = - 1 side. Compagnaro and Wood ob-

244

COLE

AND

GKEEN

served this effect and explained it in terms of the presence of the difference band { 10) +(01) which would become weakly allowed due to the Fermi resonance. Although this is possible, it is more likely that the asymmetry in the intensity arises from the Coriolis coupling with the in-plane bend, especially as a similar effect has been observed in glyoxal (17) and in acrylonitrile (21). Mills (22) has shown how this asymmetry can arise in one of two forms. In the first form, which occurs in these molecules, the AK, = - 1 side of the high frequency band, and the AR, = + 1 side of the low frequency band are intensified at the expense of their respective AK, = + 1 and AK, = - 1 sides. This is known as a positive intensity perturbation and the intensity of the fundamentals of the interacting levels can be expressed as (5) and St = a,t2M,2 + bdMb2 ZII akbkMt,Mt,

(6)

where ah and bk are positive functions of K and are the mixing coefficients of the levels which are coupled by the Coriolis interaction. Mb and Mt are the unperturbed transition moments of the in-plane bend and the torsion, while the upper and lower signs refer to the AK, = + 1 and AK, = - 1 sides of the bands, respectively. It can be seen that it is the third term in Eqs. (5) and (6) which produces the asymmetry in this intensity. In acrolein and glyoxal the intensity of the in-plane bend is high while that of the torsion is very low implying Mb >> Mt. Then the effect of the Coriolis coupling on the torsion will be to cause quite a large percentage of the total intensity of the band to come from the third term in Eq. (6) producing a very obvious intensity asymmetry. The intensity of the in-plane bending band will not show as marked an asymmetry however, because the ak2Ma2 term is dominant and the percentage contribution of the third term will not be as important as for the torsion. A considerable amount of information is available [f, IO, Ii?] about the nature of the torsional potential energy curve in acrolein and, in principle, our spectroscopic results could be combined with that data in an attempt to evaluate the general torsional potential function. However, the vibrational and rotational interactions in these lower energy levels are so complicated that it is questionable whether any useful values for wr8 and ~~1.18can be obtained at present. ACKNOWLEDGMENTS We wish-to record our thanks to Mr. G. D. Reece who constructed and maintained the spectrometer. of Western Australia An I.C.I.A.N.Z. Scholarship (to A.A.G.) and research grants from the University and the Australian Research Grants Committee are gratefully acknowledged. We also thank the Commonwealth Scientific and Industrial Research Organization for the loan of diffraction gratings. RECEIVED :

February

21, 1973 REFERENCES

1. 2. 3. 4. 5.

E. K. K. R. G.

A. CHERNIAKAND C. C. COSTAIN,J. Chew Phys. 45, 104 (1966). KUCIIITSU,T. FUKUYAMA,AND Y. MORINO,.7. Mol. Shwt. 1, 463 (1968). KUCHITSU,T. FUKUYAMA,AND Y. MORINO,J. Mol. Stmct. 4, 41 (1969). K. HARFJS, S#eclrochim. Ada 20, 1129 (1964). E. CAMPAGNARO AND J. L. WOOD, Trans. Faraday Sot. 62, 263 (1966).

LOW FREQUENCY 6. 7. 8. 9. 10. 11. 12. 13. 14. IS. 16. 17. 18. 19. 20. 21. 22.

VIBRATIONS

OF ACROLEIN

245

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