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Far infrared studies of hydrogen bonding in carboxylic acids—I formic and acetic acids
Spectmchimics A&,
1967, Vol. ZSA, pp. 2199 to 2209.
Persamon PressLtd.
Printed
in Northe?~
Ireland
Far infrared studies of hydrogen bonding in carboxylic acids-1 Formic and acetic acids* R. J. JAKOBSEN, Y. MIEAWA,
and
J. W. BRASCH
Columbus Laboratories, Battelle Memorial Institute, Columbus, Ohio 43201 (Reeeiued 26 Jdy
1966)
Abstract-The three infrared active hydrogen bond vibrations of the oyclic dimer of formio aoid have been reassigned, with the modes of vibration verified by normal coordinate analysis of the deuterated species. For acetic acid, two of the three predicted vibrations have been observed and assigned and the third vibration established by normal coordinate analysis. Another observed frequency was shown to be a combination band in Fermi resonance with a hydrogen bond fundamental. Assignments have been made for the observed frequencies of the solid polymeria forms of formic and acetic aaids. Two separate polymorphio forms have been isolated for formio acid crystals and two polymorphic forms have been detected but not isolated for acetic acid. Liquid formic acid has been shown to consist of hydrogen bonded polymers and liquid aoetb acid, mainly of hydrogen bonded cyclic dimers.
of the recent growth in far infrared instrumentation, comparatively few studies of hydrogen bonding have been carried out in this region. However, much of what has been done was on carboxylic acids. HALFORD [l] reported a Raman band near 200 cm-r for liquid formic acid and postulated that this might be the stretching mode of a cyclic dimer. No evidence was given that the liquid is a dimer. A Raman band at 232 cm-l has been found in formic acid vapor by BONNER and SMITH [2]. A normal coordinate analysis by ~AZAWA and PITZER [3] yielded the hydrogen bond frequencies of dimeric formic and acetic acids, but incomplete spectral data did not allow confirmation of this assignment. HIROTA and NAEAI[4,5] obtained the far infrared spectra of dimeric formic and acetic acid vapor which they interpreted on the basis of a double minimum in the potential function for the hydrogen bond. KISHIDA and NAKAMOTO [6], using the spectral data of other workers, did a more complete normal coordinate analysis for the in-plane modes of dimeric formic and acetic acids and the deuterated isotopes. Three bands were observed by STANEVICH [7] in the far infrared spectra of liquid acetic acid which were interpreted on the basis IN spite
* This research has been sponsored by the Air Force Office of Scientiflo Research (SRC)-OAR U.S.A.F. grant No AF-AFOSR-91165. Presented in part at the Symposium on Far Infrared Spectroscopy, 5th National meeting of the Society for Applied Spectrosoopy, Chicago, 1966. [l] [2] [3] [4] [5] [6] [7]
J. 0. HALBORD, J. Chem. Phya. 14, 395 (1946). L. BONNER and J. S. K. SBXITH, Phye. Rev. 57, 1078 (1940). T. MIYAZAWA and K. S. PITZER,J. Am. Chem. Sot. 81, 74 (1959). K. HIROTA and Y. NAXAI, Bdl. Chem. Sot. Japan 32,769 (1969). Y. NAKAI and K. HIROTA, Nippon Kagah .tk8hi 81,881 (1960). S. KISHIDA and K. NAKAMOTO,J. Chem. Phys. 41, 1568 (1964). A. STANEVICH, Opt. &x&y 16, 243 (1964). 2199
2200
R.
J. JAKOBSEN, Y. MI~(AWA, and J. W. BRASCR
of a hydrogen bonded cyclic dimer structure. Again there was no proof that the liquid is a cyclic dimer. For solid formic acid MIVAZA~A and SA&I [S] attempted a normal coordinate analysis and observed two frequencies which did not give identical deuteration shifts. GROSS [9] and SPANQENBERO [lo] obtained Raman spectra of single crystals of formic acid and observed a series of lines in the 250 cm-’ region which were assigned to hydrogen bond vibrations. The most recent work is by CARLSON et al. [Ill. They obtained the first complete far infrared vapor spectra of dimeric formic and acetic acids, observing three bands for each compound. They also obtained and assigned the spectra of solid formic and acetic acids. For formic acid vapor, the observed frequencies agreed very well with the calculated values of MIYAZAWAand PITZER[3]. However, their assignment of the hydrogen bond bending and twisting modes agreed with those of MIYAZAWA[12] and SLUTSKYand BATTER [ 131, but was reversed from that of MIYAZAWAand PITZER[3]. For acetic acid vapor, CARLSON et al. [ll] presented two possibilities for the assignment of the three observed frequencies. For formic acid solid, both the number of bands and the frequencies observed by CARLSON et al. [ 111 disagreed with the results of MIYA~AWA[8]. In order to identify the observed bands of formic acid vapor, distinguish between the two possibilities for acetic acid vapor, and resolve the difference in results on solid formic acid, we repeated much of the past work, studied some of the deuterated isotopes and extended the normal coordinate analysis of the out-of-plane vibrations. In the course of this we were able to establish the assignment of the cyclic dimers, determine the type of hydrogen bonding in the liquids, and observe new bands in the solid polymers. EXPERIMENTAL Commercial (91 percent) formic acid was found by NMR analysis to contain 8.2 percent water; it was dried repeatedly over magnesium sulfate until the water content (as shown by NMR) was less than 1 percent. A sample of HCOOD was kindly supplied to us by Dr. FATELEYof Mellon Institute. The sample of DCOOH was purchased from MERCK, SHARP, and DOHME. Infrared analysis showed that these isotopic molecules were well over 90 percent deuterated. Commercial glacial acetic acid was dried over magnesium sulfate until no water could be detected by NMR. The far infrared spectra were obtained over the range 370-60 cm-r on a PERKINELMER 301 spectrophotometer and the middle-infrared spectra, on a PERKINELMER521 spectrophotometer. Vapors were run in a 1 m gas cell equipped with polyethylene windows. Spectra of solutions were studied in two ways. Hexane solutions were measured in ordinary liquid cells with polyethylene windows; the path [8] [9]
T.
MIYAZAWA andS. SAEKI, Proceedings
of the InternationdSymposiumm
and Spectroscopy, A-102-1,Tokyo (1962). E. GROSS, Hydrogen Bonding (Edited by D. HADZI), p. 203.
lo] H. SPANQENBERO, 2. Chem. 1, 250 (1961). 1 l] G. CARLSON, R. WITKOWSKI, and W. FATELEY, Spectrochim.
‘121T. MIYAZAWA, Busaei5, 551 (1964).
MoleoularStmture
Pergamon Press (1959). Acta 22, 1117 (1966).
131 L. SLUTSKY and S. H. BAUER, J. Am. Chem. Sot. 76, 270 (1954).
2201
Far infraxed studies of hydrogen bonding in carboxylic acid&I
length varied from 0.1 mm to 6.0 mm. The second method used a technique [14, 151 in which the sample is absorbed into a polyethylene film. Depending on the amount of sample used, either a liquid or a solution spectrum could be obtained. Spectra of solids were obtained either by cooling a liquid film between polyethylene plates in a Dewar-type cell, or by cooling the polyethylene matrix containing the sample in a Dewar cell. Spectra of single crystals of formic acid were obtained in the 1800-400 cm-l range using a high-pressure cell with diamond windows and techniques described previously [16, 171. These spectra were used to establish definitely the presence of polymorphic forms of formic acid. NORMAL COORDINATE
CALCULATIONS
Formic and acetic acid vapors have been shown by electron diffraction [18] to have planar dimer ring structures of C,, symmetry. This structure is shown in Fig. 1.
Fig. 1. Molecular model of dimeric formic acid. The bond&stances usedare [6]: r(C=O) = 1.25& r(C-0) = 1.368, r(O-H) = 0) = 2.738, r(C-H) = 1.0858, andr(C-CH,) = 1.54A. All angles l.olA,r(O~~*~ were taken as 120’ except the -0-H * . * * 0- angle which was taken as 180”. The potential function for the out-of-plane vibrations of formic and acetic acids is expressed by eight internal coordinates as ;
+ H&%a + &) +
KVT2,
+
Td2
+
(722
+
%.a)21/4.
(1)
Here &Ii, Til, and /Iirk are out-of-plane internal coordinates defined as shown in Fig. 2. Ho and H, are intramolecular out-of-plane wagging and torsional force constants, respectively. H, and H,’ are force constants related to hydrogen bonding; the former * * -0 bending and the latter is a torsional force constant is an out-of-plane O-H around the C=O bond. The internal coordinates R and the Cartesian coordinates X are related by a matrix B:
R=BX The
elements
of B were numerically
computed
(2) with
a program
originated
by
E4] J. BRASCH md R. JAKOB~EN, Spectrochim. Acta 20, 1844 (1964). [15] R. JAKOBSEN and J. BRASCH, Spectrochint. Acta 21, 1753 (1965). [10] J. BRASCH and R. JAKOBSEN, American Society of Mechanical Engineers Preprint So. 64-WA/PT-26. [17] J. BRASCH, Spectrochina. Acta 21, 1183 (1965). [la] J. KARLE and L. BROCKWAY, ‘J. Am. Chem. Sot. 88, 574 (1944).
2202
R. J. JAKOBSEN, Y.
MIEAWA, and J. W.
BRASCH
A k
Fig. 2. Internal coordinates of dimeric carboxylic acids.
and revised by NAKAGAWA [20]. The secular equation was set up by the Cartesian coordinate method [20]. This equation SCHACHTSCHNEIDER
[19]
F Xslll -EEl=O
(3)
was solved utilizing a Data Control 3400 computer, yielding either frequencies or force constants. RESULTS
Formic acid The far infrared spectra of formic acid in different physical states are shown in Fig. 3. The cyclic dimer of formic acid has 24 vibrational degrees of freedom of which six are intermolecular vibrations involving motions of the hydrogen bonds. The
300
200
100
0
cm-’
Fig. 3. Low frequency spectra of formic acid.
calculated and observed values for these six hydrogen bond frequencies are shown in Table 1. Descriptions of the modes of vibration are approximate. The frequencies observed in solutions are included to demonstrate that the cyclic dimer exists in solution as well as in the vapor. Other tables with cyclic dimer frequencies will also include the data for solutions. Table 1 also gives the calculated and observed values for the hydrogen bond frequencies of the cyclic dimers of the deuterated formic acid. The isotope effect on some of the frequencies of formic acid solid polymer is shown in Table 2. The data in Table 2 are only for one polymorphic form of formic acid crystal. In another paper [21] we have demonstrated that two polymorphic forms of 1191 J. SCHACHTSCHNEIDER, Shell Development Company Technical Report NO. 231-64. [20] I. NAKAOAWA, Jikken Kugaku Koza 10, Ma-en, Tokyo (1966). [21] Y. MIKAWA, R. JAKOBSEN, and J. BRASCH, J. Chem. Phys. 45, 4750 (1906).
2203
Far infrared studies of hydrogen bonding in carboxylic aoids-I Table 1. Hydrogen bond frequenciesof deuterated formic acid-cyclic dimer, (cm-l)
Mode *
c 2h
y(OH . . . 0) v(OH . . ~0) v(OH . . ~0) y(OH . . . 0) B(OH - - - 0)
B, B, A, A,
Y(t*t)
4
260 249t 2247 167
A,
91t
68
Vapor $
Obs.
Obs.
Obs. Calc.
(DCOOH),
(HCOOD),
(HCOOH),
Calc.
soln.
248
248
164
173
248 243t 222t 168
Calc.
soln.
232 242t 221t 146
240 167
240 148
got
=t
68
sohl.
68
68
68s
* v(OH . . . 0) = hydrogen bond stretching vibration, B(OH * * * 0) = m-plane hydrogen bond bending mode, y(OH . * -0) = out-of-plane hydrogen bond bending mode, and y(twist) = a twisting of one monomer unit against the other along the hydrogen bond. 7 h-plane calculated frequenciestaken from Ref. [6]. $ Vapor data from Ref. [ll]. Table 2. Deuteration effects on solid formic acidpolymer, N - 150°C, (cm-l) -
Frequencies (Obs.)
Compound (HCOOH), (HCOOD), (DCOOH),
271 261 239
232 228 229
formic acid crystal can be detected and single crystals isolated in a diamond windowhigh pressure cell. With this cell, mid-infrared spectra of the two crystals were obtained. The assignment of the forms has been given [21] and will not be discussed here. Various techniques of low-temperature solidification were then utilized to reproduce crystalline forms which gave the same mid-infrared spectra, The necessary techniques were then repeated to obtain far infrared spectra of the two crystalline forms. These frequencies and a summary of the data on formic acid are given in Table 3. Table 3. Hydrogen bond frequenciesof formic acid, (cm-l) Mode r(OH ***O) Y(OH . * -0) v(OH . . -0) y(OH . . -0) B(OH - * * 0) y(twist)
Cyclic dimer freqs. (C,)
Polymer frequencies (_
Calc.
Obs.
Glass
260 2491 224+ 167 91* 68
248 173 -
249 -
‘W
* Calculated m-plane frequenciestaken from Ref. [6]. t Vapor frequency taken from Ref. [Ill.
193 111
-
160°C)
Crystal-a&?,) Crystal-/?(Cs) 280 239 200 92
271 232 88
R. J. JAJXOBSEN, Y. MIKAWA, and J. W. BRASCH
2204
Acetic acid The far infrared spectra of acetic acid are shown in Fig. 4 and the frequencies are summarized in Table 4. In the diamond window-high pressure cell at least two polymorphic forms of acetic acid have been detected and mid-infrared spectra of these
a
1 200
loo cm-’
0
Fig. 4. Low frequency spectra of acetic acid.
have been obtained. The differences between the polymorphic forms appear to be similar to those in formic acid. However, it has not been possible to isolate the two polymorphs by freezing techniques so we are not certain which polymorph corresponds to our far infrared data. Table 4. Hydrogen bond frequenciesof acetic acid, (cm-l)
Mode
C,,
Cyclic dimer (Calc.)
v(OH .**O)
A,
210*
v(OH . * -0)
B,
187*
y(OH . . -0) ,!?(OH . . . 0) y(OH . . . 0) Y(tww
B, A, A, AU
130 81* 79 54
Polymer (Obs.)
Cyclic dimer (Obs.) Vapor 188 168 50t
Liq.
soln.
(-
Glass Crystal -15O”)C (- -150°C)
-
-
-
-
184
176
186
198
-
-
-
126 82
-
* Calculatedin-plane frequenciestaken from Ref. [B]. t Vapor frequency taken from Ref. [ 1I]. DISCUSSION
Formic a&!-cyclic
dimer
Table 1 shows that there is reasonable agreement between the calculated and observed values of formic acid vapor. Obviously this agreement is expected, since the observed frequencies are used to calculate the best-fit force constants, which are used in turn to recaiculate the frequencies. The real test for the normal coordinate analysis lies in whether these force constants can then be used to calculate the frequencies of the deuterated isotopes of formic acid. Another test is whether the force constants can be transferred and used to calculate the frequencies of the cyclic dimer of acetic acid. These calculations will then also serve as proof of the assignment.
2206
Far infrared studies of hydrogen bonding in carboxylic aoida-I
Even without the normal coordinate analysis there can be little doubt of the assignment for the cyclic dimer of formic acid. Three bands are predicted and three et al. [ 1l] assigned are observed in the proper frequency regions. However, CARL~ON the 164 cm-l band to the twisting mode and the 68 cm-l band to the out-of-plane and PITZER [3]. bending mode. This disagreed with the predictions of MIYAZAWA To help settle this, we obtained the spectra and calculated the frequencies of the deuterated formic acids. These frequencies are shown in Table 1. In addition, the .
______L
~1 y(OH---0) 167 cm“
\L __t.______.
Fig. 5. Cartesian displacements of out-of-plane hydrogen bond frequencies of formic acid. Arrows are used instead of the conventional + or - signs for out-ofplane vibrations in order to show the length of the displacements.) displacements were calculated for the three out-of-plane vibrations of the dimer of formic acid. These are shown in Fig. 5. If the normal coordinate treatment is successful in predicting the frequencies of the deuterated species (and these can be experimentally verified), then the validity of the normal coordinate analysis is established and the Cartesian displacements will readily show which frequency is due to the bending mode. The frequencies in Table 1 show little predicted or observed shifts upon deuteration of the -OH proton. However, a large shift is predicted for both the 260 cm-l frequency and the 167 cm-l frequency of (HCOOH), upon deuteration of the -CH proton. This shift could only be experimentally verified for the infrared active 167 cm-l frequency, where in (DCOOH), this band shifted to 148 cm-l just as predicted.
Cartesian
Thus the normal
coordinate
deuterated molecules.* Then from Fig. 5, the frequency
of (HCOOH),
treatment Cartesian
must
be the
was successful displacements twisting
in predicting clearly
mode
and
show the
the shifts of the that
16’7 cm-l
the
68 cm-1
frequency
* Since this paper was submitted for publication, Dr. CARLSONhas obtained vapor spectra 140 cm-l, and 68 cm-l. This agrees with the of DCOOH and observed bands at 242 cm-l; calculated values for this molecule and further establishes the validity of the normal coordinate analysis.
2206
R. J. JAKOBSEN,Y. MIKAWA,
and J. W. BUSCH
(as well as the 260 om-l band) shows considerable bending motion of the hydrogen bond. These figures also show large displacement of the -CH proton for the 167 cm-r and the 260 cm-l vibrations which explains why these modes are sensitive to deuteration of the -CH proton. (This point will be referred to later both in discussion of formic acid polymer and acetic acid cyclic dimer.) Thus the motion is more nearly a HCOH . . . 0 bending mode or a pseudo-torsion mode about the line bisecting the hydrogen bonds. For convenience we shall continue to refer to this mode as an out-of-plane hydrogen bond bending mode. .Formic
acid-polymer
The spectrum of liquid formic acid is shown in Fig. 3. The one band observed (peak maximum at N 216 cm-l) is exceptionally broad compared to that in spectra of the cyclic dimer in solution or of the solid polymer of formic acid. This broad band shape is characteristic [22] of liquids which form hydrogen bonded polymeric chains. On this basis alone it would be safe to assume that liquid formic acid consists of polymeric chains. However, the spectrum of glassy formic acid confirms this (Table 3) since it resembles spectra of crystalline polymers more than the cyclic dimer spectrum. CONSTANT and LEBRTJN [23] have deduced by dielectric relaxation methods that liquid formic acid is composed of long polymeric chains. CARLSON et al. [l l] observed three frequencies for solid formic acid which they attributed to crystal splitting of the hydrogen bond stretching mode. The deuteration effects on solid formic acid (shown in Table 2) confirm that crystal splitting cannot account for the several bands since these do not show the same deuteration shifts. From Table 2 it can be seen that the stretching frequency of (HCOOH), at 232 cm-l shifts little with deuteration. The 271 cm-l frequency shows little shift with deuteration of the -OH proton but gives a large shift on deuteration of the -CH proton. This is analogous to the predicted and observed shift (Table 1) for the out-of-plane bending mode of the cyclic dimer of formic acid at 167 cm-l. Since the Raman active out-of-plane bending mode of the cyclic dimer (Table 1) at 260 cm-l is predicted to have a similar shift, it is apparent that the 271 cm-l band of the solid polymer must also arise from a similar motion. It will be shown later that the Raman active mode in the cyclic dimer becomes infrared active in the solid polymer. The deuteration shifts indicate that these are indeed different vibrational modes and cannot be due to crystal splitting. The differences both in frequencies and number of observed bands reported by CARLSON et al. [ 1l] and MIYAZAWA and SA&CI[8] can be explained by polymorphism. As mentioned previously, two polymorphic forms of formic acid crystal have been isolated and assigned [21]. These two forms have been shown [21] to possess a factor group isomorphous to C, for the far infrared frequencies, rather than C, as reported by MILLIKAN and PITZER [24] for the mid-infrared frequenoies. One polymorph has [22] R. JAKOBSEN and J. BRSACH, Far infrared studies of hydrogen bonding. Paper presented at the 8th European Congresson Molecular Spectromopy, Copenhagen (1966). [23] E. CONSTANTmd A. LEBRUN, J. C&a. Phy8. 61,163 (1964). [24] R. MILLIKAN and K. PITZER,J. Am. Chem. Sot. 80, 3515 (1958).
FIX infrared studies of hydrogen bonding in carboxylic acids-1
2207
been shown to be the same as that reported by X-ray analysis [25] and its structure is shown in Fig. 6. It was concluded from the mid-infrared spectra that the second structure had the carbon atoms in a tram position with respect to the -0-H *.*Obond as shown in Fig. 7. In both crystalline forms the two monomer units are not quite coplanar, giving rise to C, symmetry. For this symmetry the eight vibrations are all infrared active (two rotational degrees of freedom of the cyclic dimer become vibrational degrees of freedom in the polymer). The observed frequencies and assignments are listed in Table 3. The 230 and 271 cm-l frequencies are assigned as the out-of-plane bending
Fig. 6. Chain unit cell of p-form of acid crystal.
formio
Fig. 7. Chain unit cell of a-form of formio mid crystal.
modes because they show the same deuteration shift predicted and observed for the out-of-plane bending modes of the cyclic dimer. Furthermore, these frequencies are close to that of the Raman active out-of-plane bending mode of the cyclic dimer at 260 cm-i. Since the Raman active frequencies of the cyclic dimer become infrared active in the polymer, this is a reasonable assignment. The 239 and 232 cm-l frequencies from both intensity and frequency considerations must belong to the hydrogen bond stretching mode of the polymer. The 200 cm-l band appears as a very weak shoulder on the strong 239 cm-l band. This 200 cm-l frequency could be due either to the second hydrogen bond stretching mode or to the second out-of-plane bending mode. Since it is not observed in (DCOOH), we favor the assignment to the polymeric counterpart of the out-of-plane bending mode of the cyclic dimer at 167 cm-l. The 88 and 92 cm-l bands were not observed by CARLSON et al. [ll], but as will be discussed later, this probably arises from the method of crystallization. These two bands are assigned to the twisting modes because we would expect a higher frequency for this mode in the solid polymer at low temperatures than in the vapor cyclic dimer at room temperature. Several predicted frequencies were not observed. This, however, is not surprising as these bands are probably extremely weak. The two new modes of the polymer [26] F. HOLTZBERG, B. POSTmd I. FANKVCEEN,Acta Cryet. 6, 127 (1963).
2208
R.
J. JAIZOBSEN, Y. MIKAWA, and J. W.
BRASCH
(eight intermolecular modes for the polymer compared to six for the cyclic dimer) should be at low frequencies, beyond the 50 cm-l limit of our instrument.
CARLSONet aE. [l l] observed three bands in the far infrared vapor spectra of acetic acid. The highest frequency (188 cm-l) and the lowest frequency (50 cm-l) agreed with calculated values for the acetic acid dimer. However, the third frequency (168 cm-r) is much higher than the calculated 79 cm-r for the hydrogen bond bending mode. They offered two possible explanations for this. The first was that the normal coordinate analysis was wrong and the three observed frequencies were those of the hydrogen bond stretching (188 cm-l), bending (168 cm-l), and twisting modes (50 cm-l). The second explanation was that the normal coordinate analysis was correct and for some reason the bending mode was not observed, but should be near 80 cm-l. The 188 cm-l and the 168 cm-l frequencies would then arisefrom the stretch-
ing mode in Fermi resonance with a combination band. While unable to decide definitively, they favored the theory that the normal coordinate analysis was wrong, based mainly on their belief that the CH, substituent would not greatly influence this vibration. Our evidence shows that the 168 cm-r frequency cannot belong to the
bending mode and that the normal coordinate treatment is correct. Therefore, Fermi resonance interaction between the stretching mode and a combination band (130 + 50 = 180 cm-l) must be the explanation. First the bending mode in question is the same mode as that responsible for the 173 cm-l band of formic acid. This band was shifted from 173 to 148 cm-l on going from (HCOOH),, to (DCOOH),. Thus the substituent certainly influences this frequency (as shown by the Cartesian displacements in Fig. 5). Then, going from (HCOOH), to (DCOOH), to (CH,COOH), must cause a shift from 173 to 148 to << 148 cm- l. The 79 cm-r predicted for this frequency is certainly reasonable and the 168 cm-l value is much too high. A second argument is that the spectra of the cyclic dimer of acetic acid in dilute solution (Fig. 2) show only one band (at 176 cm-l) in this frequency range. Since the vapor and the solution spectra of formic acid both show the cyclic dimer, it is reasonable to expect the same behavior for acetic acid. However, it is possible that the solution spectra would not show Fermi resonance whereas the vapor spectra do. Thus the Fermi resonance explanation must be strongly favored.* Although several attempts have been made, we have not observed a band at 80 cm-l in liquid acetic acid. STANEVICH [7] however, does report seeing such a band. Considering the extreme broadness
and low intensity
of hydrogen
bond vibrations
(especially
in the liquid
state) it is entirely possible that we have just failed to observe it. All these observed frequencies are listed in Table 4. From four considerations, it appears that liquid acetic acid is composed mainly of cyclic dimers. The band width of the 184 cm-l hydrogen bond stretch in the liquid is approximately the same as in the solutions. No broad band such as in liquid formic acid is observed. Secondly, the spectrum
of acetic acid glass at low temperatures
gives only one band,
show that the Fermiresonance that the frequencies involved in the combination band do not shift enough on deuteration to remove the resonance effect.
* The vapor spectra of CDsCOOH [II] and CD,COOD
[4,5]
occursin these compounds.Thecalculations [thispaperand 61show
Far infrared studies of hydrogen bonding in carboxylio acids-1
2209
resembling the narrow bands of the liquid and the solution but not many bands as seen in the polymer crystal. Third, the dielectric relaxation work of CONSTANTand LEBRUN [23] also shows the liquid to be mainly cyclic dimers. Lastly, liquid acetic acid shows a lack of Raman and infrared coincidences [26]. This strongly indicates a center of symmetry as found in the dimer. Acetic acid-polymer The observed spectrum of solid acetic acid is shown in Fig. 4 and the frequencies are listed in Table 4. Neither the 126 cm-l or the 82 cm-l bands were observed by CARLSONet al. [11] and the 126 cm-1 band was not observed by STANEVICH [7]. However, STANEVICHdid see the 82 cm-l band in solid acetic acid. This is of interest because both STANEVICH and our group crystallize directly from the liquid, while CARLSONet al. [l l] crystallize by condensing the vapor directly onto a cold window. Thus the cooling rates and crystallization rates are vastly different and could easily produce different results. Of the frequencies listed in Table 4, that at 198 cm-l band is unquestionably assigned to the hydrogen bond stretching mode. Assuming that the structure of the observed crystal is approximately the same as one of the two forms of formic acid, the 126 cm-l band must arise from an out-of-plane hydrogen bond bending mode. The assignment of the third frequency (82 cm-l) is more closely dependent upon the symmetry of this crystal. We favor an assignment to the twisting mode because the shift between dimer and polymer is about the same as in the twisting mode of formic acid. CONCLUSIONS All the observed frequencies have been reasonably assigned for several physical states of both formic and acetic acid. It is clear, however, that the data from all physical states, comparison of deuteration shifts, and normal coordinate analyses were all needed in order to obtain these interpretations. are grateful to Drs. CARLSON, FATELEY,and WITKOWSIUfor providing us with & preprint of their paper ELnd for providing us with EJsample of HCOOD.
Acknowledgments-We
[26] M. HAURIEand A. NOVAE,J. China. Phys. 62, 146 (1965).
17
1967, Vol. ZSA, pp. 2199 to 2209.
Persamon PressLtd.
Printed
in Northe?~
Ireland
Far infrared studies of hydrogen bonding in carboxylic acids-1 Formic and acetic acids* R. J. JAKOBSEN, Y. MIEAWA,
and
J. W. BRASCH
Columbus Laboratories, Battelle Memorial Institute, Columbus, Ohio 43201 (Reeeiued 26 Jdy
1966)
Abstract-The three infrared active hydrogen bond vibrations of the oyclic dimer of formio aoid have been reassigned, with the modes of vibration verified by normal coordinate analysis of the deuterated species. For acetic acid, two of the three predicted vibrations have been observed and assigned and the third vibration established by normal coordinate analysis. Another observed frequency was shown to be a combination band in Fermi resonance with a hydrogen bond fundamental. Assignments have been made for the observed frequencies of the solid polymeria forms of formic and acetic aaids. Two separate polymorphio forms have been isolated for formio acid crystals and two polymorphic forms have been detected but not isolated for acetic acid. Liquid formic acid has been shown to consist of hydrogen bonded polymers and liquid aoetb acid, mainly of hydrogen bonded cyclic dimers.
of the recent growth in far infrared instrumentation, comparatively few studies of hydrogen bonding have been carried out in this region. However, much of what has been done was on carboxylic acids. HALFORD [l] reported a Raman band near 200 cm-r for liquid formic acid and postulated that this might be the stretching mode of a cyclic dimer. No evidence was given that the liquid is a dimer. A Raman band at 232 cm-l has been found in formic acid vapor by BONNER and SMITH [2]. A normal coordinate analysis by ~AZAWA and PITZER [3] yielded the hydrogen bond frequencies of dimeric formic and acetic acids, but incomplete spectral data did not allow confirmation of this assignment. HIROTA and NAEAI[4,5] obtained the far infrared spectra of dimeric formic and acetic acid vapor which they interpreted on the basis of a double minimum in the potential function for the hydrogen bond. KISHIDA and NAKAMOTO [6], using the spectral data of other workers, did a more complete normal coordinate analysis for the in-plane modes of dimeric formic and acetic acids and the deuterated isotopes. Three bands were observed by STANEVICH [7] in the far infrared spectra of liquid acetic acid which were interpreted on the basis IN spite
* This research has been sponsored by the Air Force Office of Scientiflo Research (SRC)-OAR U.S.A.F. grant No AF-AFOSR-91165. Presented in part at the Symposium on Far Infrared Spectroscopy, 5th National meeting of the Society for Applied Spectrosoopy, Chicago, 1966. [l] [2] [3] [4] [5] [6] [7]
J. 0. HALBORD, J. Chem. Phya. 14, 395 (1946). L. BONNER and J. S. K. SBXITH, Phye. Rev. 57, 1078 (1940). T. MIYAZAWA and K. S. PITZER,J. Am. Chem. Sot. 81, 74 (1959). K. HIROTA and Y. NAXAI, Bdl. Chem. Sot. Japan 32,769 (1969). Y. NAKAI and K. HIROTA, Nippon Kagah .tk8hi 81,881 (1960). S. KISHIDA and K. NAKAMOTO,J. Chem. Phys. 41, 1568 (1964). A. STANEVICH, Opt. &x&y 16, 243 (1964). 2199
2200
R.
J. JAKOBSEN, Y. MI~(AWA, and J. W. BRASCR
of a hydrogen bonded cyclic dimer structure. Again there was no proof that the liquid is a cyclic dimer. For solid formic acid MIVAZA~A and SA&I [S] attempted a normal coordinate analysis and observed two frequencies which did not give identical deuteration shifts. GROSS [9] and SPANQENBERO [lo] obtained Raman spectra of single crystals of formic acid and observed a series of lines in the 250 cm-’ region which were assigned to hydrogen bond vibrations. The most recent work is by CARLSON et al. [Ill. They obtained the first complete far infrared vapor spectra of dimeric formic and acetic acids, observing three bands for each compound. They also obtained and assigned the spectra of solid formic and acetic acids. For formic acid vapor, the observed frequencies agreed very well with the calculated values of MIYAZAWAand PITZER[3]. However, their assignment of the hydrogen bond bending and twisting modes agreed with those of MIYAZAWA[12] and SLUTSKYand BATTER [ 131, but was reversed from that of MIYAZAWAand PITZER[3]. For acetic acid vapor, CARLSON et al. [ll] presented two possibilities for the assignment of the three observed frequencies. For formic acid solid, both the number of bands and the frequencies observed by CARLSON et al. [ 111 disagreed with the results of MIYA~AWA[8]. In order to identify the observed bands of formic acid vapor, distinguish between the two possibilities for acetic acid vapor, and resolve the difference in results on solid formic acid, we repeated much of the past work, studied some of the deuterated isotopes and extended the normal coordinate analysis of the out-of-plane vibrations. In the course of this we were able to establish the assignment of the cyclic dimers, determine the type of hydrogen bonding in the liquids, and observe new bands in the solid polymers. EXPERIMENTAL Commercial (91 percent) formic acid was found by NMR analysis to contain 8.2 percent water; it was dried repeatedly over magnesium sulfate until the water content (as shown by NMR) was less than 1 percent. A sample of HCOOD was kindly supplied to us by Dr. FATELEYof Mellon Institute. The sample of DCOOH was purchased from MERCK, SHARP, and DOHME. Infrared analysis showed that these isotopic molecules were well over 90 percent deuterated. Commercial glacial acetic acid was dried over magnesium sulfate until no water could be detected by NMR. The far infrared spectra were obtained over the range 370-60 cm-r on a PERKINELMER 301 spectrophotometer and the middle-infrared spectra, on a PERKINELMER521 spectrophotometer. Vapors were run in a 1 m gas cell equipped with polyethylene windows. Spectra of solutions were studied in two ways. Hexane solutions were measured in ordinary liquid cells with polyethylene windows; the path [8] [9]
T.
MIYAZAWA andS. SAEKI, Proceedings
of the InternationdSymposiumm
and Spectroscopy, A-102-1,Tokyo (1962). E. GROSS, Hydrogen Bonding (Edited by D. HADZI), p. 203.
lo] H. SPANQENBERO, 2. Chem. 1, 250 (1961). 1 l] G. CARLSON, R. WITKOWSKI, and W. FATELEY, Spectrochim.
‘121T. MIYAZAWA, Busaei5, 551 (1964).
MoleoularStmture
Pergamon Press (1959). Acta 22, 1117 (1966).
131 L. SLUTSKY and S. H. BAUER, J. Am. Chem. Sot. 76, 270 (1954).
2201
Far infraxed studies of hydrogen bonding in carboxylic acid&I
length varied from 0.1 mm to 6.0 mm. The second method used a technique [14, 151 in which the sample is absorbed into a polyethylene film. Depending on the amount of sample used, either a liquid or a solution spectrum could be obtained. Spectra of solids were obtained either by cooling a liquid film between polyethylene plates in a Dewar-type cell, or by cooling the polyethylene matrix containing the sample in a Dewar cell. Spectra of single crystals of formic acid were obtained in the 1800-400 cm-l range using a high-pressure cell with diamond windows and techniques described previously [16, 171. These spectra were used to establish definitely the presence of polymorphic forms of formic acid. NORMAL COORDINATE
CALCULATIONS
Formic and acetic acid vapors have been shown by electron diffraction [18] to have planar dimer ring structures of C,, symmetry. This structure is shown in Fig. 1.
Fig. 1. Molecular model of dimeric formic acid. The bond&stances usedare [6]: r(C=O) = 1.25& r(C-0) = 1.368, r(O-H) = 0) = 2.738, r(C-H) = 1.0858, andr(C-CH,) = 1.54A. All angles l.olA,r(O~~*~ were taken as 120’ except the -0-H * . * * 0- angle which was taken as 180”. The potential function for the out-of-plane vibrations of formic and acetic acids is expressed by eight internal coordinates as ;
+ H&%a + &) +
KVT2,
+
Td2
+
(722
+
%.a)21/4.
(1)
Here &Ii, Til, and /Iirk are out-of-plane internal coordinates defined as shown in Fig. 2. Ho and H, are intramolecular out-of-plane wagging and torsional force constants, respectively. H, and H,’ are force constants related to hydrogen bonding; the former * * -0 bending and the latter is a torsional force constant is an out-of-plane O-H around the C=O bond. The internal coordinates R and the Cartesian coordinates X are related by a matrix B:
R=BX The
elements
of B were numerically
computed
(2) with
a program
originated
by
E4] J. BRASCH md R. JAKOB~EN, Spectrochim. Acta 20, 1844 (1964). [15] R. JAKOBSEN and J. BRASCH, Spectrochint. Acta 21, 1753 (1965). [10] J. BRASCH and R. JAKOBSEN, American Society of Mechanical Engineers Preprint So. 64-WA/PT-26. [17] J. BRASCH, Spectrochina. Acta 21, 1183 (1965). [la] J. KARLE and L. BROCKWAY, ‘J. Am. Chem. Sot. 88, 574 (1944).
2202
R. J. JAKOBSEN, Y.
MIEAWA, and J. W.
BRASCH
A k
Fig. 2. Internal coordinates of dimeric carboxylic acids.
and revised by NAKAGAWA [20]. The secular equation was set up by the Cartesian coordinate method [20]. This equation SCHACHTSCHNEIDER
[19]
F Xslll -EEl=O
(3)
was solved utilizing a Data Control 3400 computer, yielding either frequencies or force constants. RESULTS
Formic acid The far infrared spectra of formic acid in different physical states are shown in Fig. 3. The cyclic dimer of formic acid has 24 vibrational degrees of freedom of which six are intermolecular vibrations involving motions of the hydrogen bonds. The
300
200
100
0
cm-’
Fig. 3. Low frequency spectra of formic acid.
calculated and observed values for these six hydrogen bond frequencies are shown in Table 1. Descriptions of the modes of vibration are approximate. The frequencies observed in solutions are included to demonstrate that the cyclic dimer exists in solution as well as in the vapor. Other tables with cyclic dimer frequencies will also include the data for solutions. Table 1 also gives the calculated and observed values for the hydrogen bond frequencies of the cyclic dimers of the deuterated formic acid. The isotope effect on some of the frequencies of formic acid solid polymer is shown in Table 2. The data in Table 2 are only for one polymorphic form of formic acid crystal. In another paper [21] we have demonstrated that two polymorphic forms of 1191 J. SCHACHTSCHNEIDER, Shell Development Company Technical Report NO. 231-64. [20] I. NAKAOAWA, Jikken Kugaku Koza 10, Ma-en, Tokyo (1966). [21] Y. MIKAWA, R. JAKOBSEN, and J. BRASCH, J. Chem. Phys. 45, 4750 (1906).
2203
Far infrared studies of hydrogen bonding in carboxylic aoids-I Table 1. Hydrogen bond frequenciesof deuterated formic acid-cyclic dimer, (cm-l)
Mode *
c 2h
y(OH . . . 0) v(OH . . ~0) v(OH . . ~0) y(OH . . . 0) B(OH - - - 0)
B, B, A, A,
Y(t*t)
4
260 249t 2247 167
A,
91t
68
Vapor $
Obs.
Obs.
Obs. Calc.
(DCOOH),
(HCOOD),
(HCOOH),
Calc.
soln.
248
248
164
173
248 243t 222t 168
Calc.
soln.
232 242t 221t 146
240 167
240 148
got
=t
68
sohl.
68
68
68s
* v(OH . . . 0) = hydrogen bond stretching vibration, B(OH * * * 0) = m-plane hydrogen bond bending mode, y(OH . * -0) = out-of-plane hydrogen bond bending mode, and y(twist) = a twisting of one monomer unit against the other along the hydrogen bond. 7 h-plane calculated frequenciestaken from Ref. [6]. $ Vapor data from Ref. [ll]. Table 2. Deuteration effects on solid formic acidpolymer, N - 150°C, (cm-l) -
Frequencies (Obs.)
Compound (HCOOH), (HCOOD), (DCOOH),
271 261 239
232 228 229
formic acid crystal can be detected and single crystals isolated in a diamond windowhigh pressure cell. With this cell, mid-infrared spectra of the two crystals were obtained. The assignment of the forms has been given [21] and will not be discussed here. Various techniques of low-temperature solidification were then utilized to reproduce crystalline forms which gave the same mid-infrared spectra, The necessary techniques were then repeated to obtain far infrared spectra of the two crystalline forms. These frequencies and a summary of the data on formic acid are given in Table 3. Table 3. Hydrogen bond frequenciesof formic acid, (cm-l) Mode r(OH ***O) Y(OH . * -0) v(OH . . -0) y(OH . . -0) B(OH - * * 0) y(twist)
Cyclic dimer freqs. (C,)
Polymer frequencies (_
Calc.
Obs.
Glass
260 2491 224+ 167 91* 68
248 173 -
249 -
‘W
* Calculated m-plane frequenciestaken from Ref. [6]. t Vapor frequency taken from Ref. [Ill.
193 111
-
160°C)
Crystal-a&?,) Crystal-/?(Cs) 280 239 200 92
271 232 88
R. J. JAJXOBSEN, Y. MIKAWA, and J. W. BRASCH
2204
Acetic acid The far infrared spectra of acetic acid are shown in Fig. 4 and the frequencies are summarized in Table 4. In the diamond window-high pressure cell at least two polymorphic forms of acetic acid have been detected and mid-infrared spectra of these
a
1 200
loo cm-’
0
Fig. 4. Low frequency spectra of acetic acid.
have been obtained. The differences between the polymorphic forms appear to be similar to those in formic acid. However, it has not been possible to isolate the two polymorphs by freezing techniques so we are not certain which polymorph corresponds to our far infrared data. Table 4. Hydrogen bond frequenciesof acetic acid, (cm-l)
Mode
C,,
Cyclic dimer (Calc.)
v(OH .**O)
A,
210*
v(OH . * -0)
B,
187*
y(OH . . -0) ,!?(OH . . . 0) y(OH . . . 0) Y(tww
B, A, A, AU
130 81* 79 54
Polymer (Obs.)
Cyclic dimer (Obs.) Vapor 188 168 50t
Liq.
soln.
(-
Glass Crystal -15O”)C (- -150°C)
-
-
-
-
184
176
186
198
-
-
-
126 82
-
* Calculatedin-plane frequenciestaken from Ref. [B]. t Vapor frequency taken from Ref. [ 1I]. DISCUSSION
Formic a&!-cyclic
dimer
Table 1 shows that there is reasonable agreement between the calculated and observed values of formic acid vapor. Obviously this agreement is expected, since the observed frequencies are used to calculate the best-fit force constants, which are used in turn to recaiculate the frequencies. The real test for the normal coordinate analysis lies in whether these force constants can then be used to calculate the frequencies of the deuterated isotopes of formic acid. Another test is whether the force constants can be transferred and used to calculate the frequencies of the cyclic dimer of acetic acid. These calculations will then also serve as proof of the assignment.
2206
Far infrared studies of hydrogen bonding in carboxylic aoida-I
Even without the normal coordinate analysis there can be little doubt of the assignment for the cyclic dimer of formic acid. Three bands are predicted and three et al. [ 1l] assigned are observed in the proper frequency regions. However, CARL~ON the 164 cm-l band to the twisting mode and the 68 cm-l band to the out-of-plane and PITZER [3]. bending mode. This disagreed with the predictions of MIYAZAWA To help settle this, we obtained the spectra and calculated the frequencies of the deuterated formic acids. These frequencies are shown in Table 1. In addition, the .
______L
~1 y(OH---0) 167 cm“
\L __t.______.
Fig. 5. Cartesian displacements of out-of-plane hydrogen bond frequencies of formic acid. Arrows are used instead of the conventional + or - signs for out-ofplane vibrations in order to show the length of the displacements.) displacements were calculated for the three out-of-plane vibrations of the dimer of formic acid. These are shown in Fig. 5. If the normal coordinate treatment is successful in predicting the frequencies of the deuterated species (and these can be experimentally verified), then the validity of the normal coordinate analysis is established and the Cartesian displacements will readily show which frequency is due to the bending mode. The frequencies in Table 1 show little predicted or observed shifts upon deuteration of the -OH proton. However, a large shift is predicted for both the 260 cm-l frequency and the 167 cm-l frequency of (HCOOH), upon deuteration of the -CH proton. This shift could only be experimentally verified for the infrared active 167 cm-l frequency, where in (DCOOH), this band shifted to 148 cm-l just as predicted.
Cartesian
Thus the normal
coordinate
deuterated molecules.* Then from Fig. 5, the frequency
of (HCOOH),
treatment Cartesian
must
be the
was successful displacements twisting
in predicting clearly
mode
and
show the
the shifts of the that
16’7 cm-l
the
68 cm-1
frequency
* Since this paper was submitted for publication, Dr. CARLSONhas obtained vapor spectra 140 cm-l, and 68 cm-l. This agrees with the of DCOOH and observed bands at 242 cm-l; calculated values for this molecule and further establishes the validity of the normal coordinate analysis.
2206
R. J. JAKOBSEN,Y. MIKAWA,
and J. W. BUSCH
(as well as the 260 om-l band) shows considerable bending motion of the hydrogen bond. These figures also show large displacement of the -CH proton for the 167 cm-r and the 260 cm-l vibrations which explains why these modes are sensitive to deuteration of the -CH proton. (This point will be referred to later both in discussion of formic acid polymer and acetic acid cyclic dimer.) Thus the motion is more nearly a HCOH . . . 0 bending mode or a pseudo-torsion mode about the line bisecting the hydrogen bonds. For convenience we shall continue to refer to this mode as an out-of-plane hydrogen bond bending mode. .Formic
acid-polymer
The spectrum of liquid formic acid is shown in Fig. 3. The one band observed (peak maximum at N 216 cm-l) is exceptionally broad compared to that in spectra of the cyclic dimer in solution or of the solid polymer of formic acid. This broad band shape is characteristic [22] of liquids which form hydrogen bonded polymeric chains. On this basis alone it would be safe to assume that liquid formic acid consists of polymeric chains. However, the spectrum of glassy formic acid confirms this (Table 3) since it resembles spectra of crystalline polymers more than the cyclic dimer spectrum. CONSTANT and LEBRTJN [23] have deduced by dielectric relaxation methods that liquid formic acid is composed of long polymeric chains. CARLSON et al. [l l] observed three frequencies for solid formic acid which they attributed to crystal splitting of the hydrogen bond stretching mode. The deuteration effects on solid formic acid (shown in Table 2) confirm that crystal splitting cannot account for the several bands since these do not show the same deuteration shifts. From Table 2 it can be seen that the stretching frequency of (HCOOH), at 232 cm-l shifts little with deuteration. The 271 cm-l frequency shows little shift with deuteration of the -OH proton but gives a large shift on deuteration of the -CH proton. This is analogous to the predicted and observed shift (Table 1) for the out-of-plane bending mode of the cyclic dimer of formic acid at 167 cm-l. Since the Raman active out-of-plane bending mode of the cyclic dimer (Table 1) at 260 cm-l is predicted to have a similar shift, it is apparent that the 271 cm-l band of the solid polymer must also arise from a similar motion. It will be shown later that the Raman active mode in the cyclic dimer becomes infrared active in the solid polymer. The deuteration shifts indicate that these are indeed different vibrational modes and cannot be due to crystal splitting. The differences both in frequencies and number of observed bands reported by CARLSON et al. [ 1l] and MIYAZAWA and SA&CI[8] can be explained by polymorphism. As mentioned previously, two polymorphic forms of formic acid crystal have been isolated and assigned [21]. These two forms have been shown [21] to possess a factor group isomorphous to C, for the far infrared frequencies, rather than C, as reported by MILLIKAN and PITZER [24] for the mid-infrared frequenoies. One polymorph has [22] R. JAKOBSEN and J. BRSACH, Far infrared studies of hydrogen bonding. Paper presented at the 8th European Congresson Molecular Spectromopy, Copenhagen (1966). [23] E. CONSTANTmd A. LEBRUN, J. C&a. Phy8. 61,163 (1964). [24] R. MILLIKAN and K. PITZER,J. Am. Chem. Sot. 80, 3515 (1958).
FIX infrared studies of hydrogen bonding in carboxylic acids-1
2207
been shown to be the same as that reported by X-ray analysis [25] and its structure is shown in Fig. 6. It was concluded from the mid-infrared spectra that the second structure had the carbon atoms in a tram position with respect to the -0-H *.*Obond as shown in Fig. 7. In both crystalline forms the two monomer units are not quite coplanar, giving rise to C, symmetry. For this symmetry the eight vibrations are all infrared active (two rotational degrees of freedom of the cyclic dimer become vibrational degrees of freedom in the polymer). The observed frequencies and assignments are listed in Table 3. The 230 and 271 cm-l frequencies are assigned as the out-of-plane bending
Fig. 6. Chain unit cell of p-form of acid crystal.
formio
Fig. 7. Chain unit cell of a-form of formio mid crystal.
modes because they show the same deuteration shift predicted and observed for the out-of-plane bending modes of the cyclic dimer. Furthermore, these frequencies are close to that of the Raman active out-of-plane bending mode of the cyclic dimer at 260 cm-i. Since the Raman active frequencies of the cyclic dimer become infrared active in the polymer, this is a reasonable assignment. The 239 and 232 cm-l frequencies from both intensity and frequency considerations must belong to the hydrogen bond stretching mode of the polymer. The 200 cm-l band appears as a very weak shoulder on the strong 239 cm-l band. This 200 cm-l frequency could be due either to the second hydrogen bond stretching mode or to the second out-of-plane bending mode. Since it is not observed in (DCOOH), we favor the assignment to the polymeric counterpart of the out-of-plane bending mode of the cyclic dimer at 167 cm-l. The 88 and 92 cm-l bands were not observed by CARLSON et al. [ll], but as will be discussed later, this probably arises from the method of crystallization. These two bands are assigned to the twisting modes because we would expect a higher frequency for this mode in the solid polymer at low temperatures than in the vapor cyclic dimer at room temperature. Several predicted frequencies were not observed. This, however, is not surprising as these bands are probably extremely weak. The two new modes of the polymer [26] F. HOLTZBERG, B. POSTmd I. FANKVCEEN,Acta Cryet. 6, 127 (1963).
2208
R.
J. JAIZOBSEN, Y. MIKAWA, and J. W.
BRASCH
(eight intermolecular modes for the polymer compared to six for the cyclic dimer) should be at low frequencies, beyond the 50 cm-l limit of our instrument.
CARLSONet aE. [l l] observed three bands in the far infrared vapor spectra of acetic acid. The highest frequency (188 cm-l) and the lowest frequency (50 cm-l) agreed with calculated values for the acetic acid dimer. However, the third frequency (168 cm-r) is much higher than the calculated 79 cm-r for the hydrogen bond bending mode. They offered two possible explanations for this. The first was that the normal coordinate analysis was wrong and the three observed frequencies were those of the hydrogen bond stretching (188 cm-l), bending (168 cm-l), and twisting modes (50 cm-l). The second explanation was that the normal coordinate analysis was correct and for some reason the bending mode was not observed, but should be near 80 cm-l. The 188 cm-l and the 168 cm-l frequencies would then arisefrom the stretch-
ing mode in Fermi resonance with a combination band. While unable to decide definitively, they favored the theory that the normal coordinate analysis was wrong, based mainly on their belief that the CH, substituent would not greatly influence this vibration. Our evidence shows that the 168 cm-r frequency cannot belong to the
bending mode and that the normal coordinate treatment is correct. Therefore, Fermi resonance interaction between the stretching mode and a combination band (130 + 50 = 180 cm-l) must be the explanation. First the bending mode in question is the same mode as that responsible for the 173 cm-l band of formic acid. This band was shifted from 173 to 148 cm-l on going from (HCOOH),, to (DCOOH),. Thus the substituent certainly influences this frequency (as shown by the Cartesian displacements in Fig. 5). Then, going from (HCOOH), to (DCOOH), to (CH,COOH), must cause a shift from 173 to 148 to << 148 cm- l. The 79 cm-r predicted for this frequency is certainly reasonable and the 168 cm-l value is much too high. A second argument is that the spectra of the cyclic dimer of acetic acid in dilute solution (Fig. 2) show only one band (at 176 cm-l) in this frequency range. Since the vapor and the solution spectra of formic acid both show the cyclic dimer, it is reasonable to expect the same behavior for acetic acid. However, it is possible that the solution spectra would not show Fermi resonance whereas the vapor spectra do. Thus the Fermi resonance explanation must be strongly favored.* Although several attempts have been made, we have not observed a band at 80 cm-l in liquid acetic acid. STANEVICH [7] however, does report seeing such a band. Considering the extreme broadness
and low intensity
of hydrogen
bond vibrations
(especially
in the liquid
state) it is entirely possible that we have just failed to observe it. All these observed frequencies are listed in Table 4. From four considerations, it appears that liquid acetic acid is composed mainly of cyclic dimers. The band width of the 184 cm-l hydrogen bond stretch in the liquid is approximately the same as in the solutions. No broad band such as in liquid formic acid is observed. Secondly, the spectrum
of acetic acid glass at low temperatures
gives only one band,
show that the Fermiresonance that the frequencies involved in the combination band do not shift enough on deuteration to remove the resonance effect.
* The vapor spectra of CDsCOOH [II] and CD,COOD
[4,5]
occursin these compounds.Thecalculations [thispaperand 61show
Far infrared studies of hydrogen bonding in carboxylio acids-1
2209
resembling the narrow bands of the liquid and the solution but not many bands as seen in the polymer crystal. Third, the dielectric relaxation work of CONSTANTand LEBRUN [23] also shows the liquid to be mainly cyclic dimers. Lastly, liquid acetic acid shows a lack of Raman and infrared coincidences [26]. This strongly indicates a center of symmetry as found in the dimer. Acetic acid-polymer The observed spectrum of solid acetic acid is shown in Fig. 4 and the frequencies are listed in Table 4. Neither the 126 cm-l or the 82 cm-l bands were observed by CARLSONet al. [11] and the 126 cm-1 band was not observed by STANEVICH [7]. However, STANEVICHdid see the 82 cm-l band in solid acetic acid. This is of interest because both STANEVICH and our group crystallize directly from the liquid, while CARLSONet al. [l l] crystallize by condensing the vapor directly onto a cold window. Thus the cooling rates and crystallization rates are vastly different and could easily produce different results. Of the frequencies listed in Table 4, that at 198 cm-l band is unquestionably assigned to the hydrogen bond stretching mode. Assuming that the structure of the observed crystal is approximately the same as one of the two forms of formic acid, the 126 cm-l band must arise from an out-of-plane hydrogen bond bending mode. The assignment of the third frequency (82 cm-l) is more closely dependent upon the symmetry of this crystal. We favor an assignment to the twisting mode because the shift between dimer and polymer is about the same as in the twisting mode of formic acid. CONCLUSIONS All the observed frequencies have been reasonably assigned for several physical states of both formic and acetic acid. It is clear, however, that the data from all physical states, comparison of deuteration shifts, and normal coordinate analyses were all needed in order to obtain these interpretations. are grateful to Drs. CARLSON, FATELEY,and WITKOWSIUfor providing us with & preprint of their paper ELnd for providing us with EJsample of HCOOD.
Acknowledgments-We
[26] M. HAURIEand A. NOVAE,J. China. Phys. 62, 146 (1965).
17