257
Journal of Molecular Structure, 20 (1974) 257-267
<QElsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
MICROWAVE SPECTRUM, CONFORMATION, BARRIER TO INTERNAL
ROTATION AND DIPOLE MOMENT OF PYRUVIC ACID
K.-M. MARSTOKK
Department
AND HARALD
of Chemistry,
MØLLENDAL
The University
of Oslo, Blindern,
Oslo 3 (Norway)
(Received l June 1973)
ABSTRACT
Microwave spectra of CH3COCOOH and CH3COCOOD are reported.
The preferred conformation of the molecule is demonstrated to possess a planar
HCCOCOOH skeleton with two out-of-plane hydrogens. The two carbonyl
groups are trans to each other and a weak five-membered hydrogen bond is forrned
between the carboxyl group hydrogen atom and the carbonyl group oxygen atom.
The methyl group conformation is discussed. A computer programme based on
"the principal axis method" is described in some detail and the results of a least
squares analysis of the observed spectra are outlined. The barrier to internal rotation was determined
effect measurements
as V3 = 965:t40 cal mol-l for both isotopic species. Stark
yielded /la = 2.27:t 0.02 D, /lb = 0.35:t 0.02 D and /llol =
2.30:t 0.03 D for the dipole moment and its components along the principal axes.
INTRODUCTION
The structural properties of pyruvic acid in various states of aggregation
have been subject to numerous investigations. In the free state Schellenberger
et al. [I] using infrared spectroscopic techniques showed that the preferred conformation of the molecule possesses an intramolecular hydrogen bond forrned
between the carboxyl group hydrogen atom and the carbonyl group oxygen atom.
The enthalpy difference between this form and a non-hydrogen-bonded rota mer
was determined to be - 2.34:t 0.32 kcal mol-l whereas an unambiguous entropy
difference could not be obtained [1].
In dilute solutions of benzene [2] and carbon tetrachloride [3] the preferred
conformer has been shown to be similar to that found in the gas phase. Evidence
for the coexistence of another non-hydrogen-bonded form was also obtained
from the solution studies [2, 3]. Furthermore, Schellenberger and Oehme [2]
258
showed that at higher concentrations in benzene an equilibrium exists between
monomeric and dimeric pyruvic acid.
A very recent theoretical work by Gordon and Tallman [4] using the INDO
method was devoted to the study of the importance of intramolecular hydrogen
bonding for the conformational behaviour of pyruvic acid. They found small
energy differences between the s-cis and the s-trans forms considered in their investigation [4].
In addition to the conformational properties discussed above, a taut 0merie equilibrium between a keto form CH3COCOOH and an enol form
CH2~C(OH)COOH may exist. Recently, Becker [5] utilizing NMR spectroscopy
concluded that any enol form in neat pyruvic acid amounts to less than 2 %. No
evidence for the existence of the enol form of free molecule has be found in the
literature.
The present work was undertaken as part of a series of papers devoted to
the study of structural and conformational properties of free molecules possessing
intramolecular hydrogen bonds. In agreement with the infrared findings [1-3]
the most stable form of pyruvic acid is demonstrated to possess a plan ar
HCCOCOOH skeieton with two out-of-plane hydrogen atoms. This form is
stabilized by an intramolecular hydrogen band forme d between the carboxyl
group hydrogen atom and the carbonyl group oxygen atom.
EXPERIMENT
AL
Pyruvic acid puriss from Koch-Light Laboratories specified to be at least
99
% pure
was used without
further purification.
CH3COCOOD
was produced
by direct exchange with 99 % D20 in the cell. Small amounts of acetic acid impurities was seen in the spectrum, but pyruvic acid was quite stable in the brass
cells employed. Measurements were made with the cell cooled to about - 20°C
utilizing a conventional Stark modulated spectrometer described briefly in [6].
This apparatus has no facilities for phase-locking the source and the study of
small internal rotation splittings was made at very low pressures (a few microns).
In the case of CH3COCOOD splittings of less than 0.60 MHz were not resolved
because of the higher pressures that had to be used.
RESULTS
Microwave spectrum and assignment
Pyruvic acid is closely related to glyoxylic acid previously studied in this
laboratory [7], and its preferred conformation was thus expected to be similar
to that of the latter compound. Preliminary rotational constants of the rotamer
depicted in Fig. 1 was obtained from the selected structural parameters listed in
259
b
H
o
a
H,H'
Fig. 1. Stable form of pyruvic acid projected in the a-b principa1 axes plane.
TABLE 1
PLAUSIBLE STRUCTURAL
MAN'S COORDINATES
PARAMETERS',
WITH RESPECT TO THE a-PRINCIPAL
Structural
OBSERVED AND PREDICTED
OF THE HYDROXYL HYDROGEN,
ROTATIONAL
AXES OF CH3COCOOH
AND CH3COCOOD
parameters
C~O
C-O
1.208 Å
1.339 Å
H 3C-C
C-C
O-H
1.500 Å
1.548 Å
0.950 Å
Rotational constants (MHz)
Observed
CH3COCOOH
Ao
Bo
Co
CH3COCOOD
Ao
Bo
Co
L Cc~o
LOCO
LCCC
LCOH
LCCH
Calculated
5535.578
3583.355
2204.834
5531.857
3545.821
2190.857
5377.569
3560.530
2170.759
5372.009
3525.762
2157.842
Kraitchman' s coordinates of the hydroxyl hydrogen
Observed
Calculated
!aH[
0.9301 Å
0.8785 Å
[bHI
1.6588 Å
1.6660 Å
Angles between methyl group symmetry
Observed
CH3COCOOH
49°49'
CH3COCOOD
45°57'
. Not a derived structure; see text.
CONSTANTS, KRAITCH-
AND ANG LES OF METHYL GROUP
axis and a-axis
Calculated
53°16'
51°38'
123.1°
125.0°
115.0°
105.0°
109.5°
SYMMETRY AXIS
260
Table 1. The dipole moment and its components along the a and b principal axes
were predicted by vectorial addition of bond moments take n from [8]. A dipole
moment of about 2 D with the main component along the a axis was calculated.
Search was therefore initially made for the intense low J a-type ,M = + l, ~K_1
= Otransitions which were found within a few hundred MHz from their predicted
positions in the spectrum. Besides their high intensities, these lines had very characteristic Stark patterns and internal rotation splittings confirming their assignments. The measured transitions are shown in Table 2. Each of these lines were
split into doublets as aresult ofinternal rotation of the methyl group. As indicated
in Table 2, these doublets belong to the A and E species, respectively, of the ground
torsionallevel. The A species transitions depend only on the even order terms of
the angular momentum operator and may thus be fitted to a rigid rotor spectrum.
The result of a three parameter least squares fit of the A species lines is shown in
Table 3. Attempts to fit the same transitions to Watson's eight parameter [9]
first order centrifugal distortion formula yielded unacceptable values for the five
TABLE
2
MICROWAVE SPECTRUMOF THE GROUND VIBRATIONALSTATEOF CH3COCOOH
Transition
Observed
VAa
21.2-->-31.3
20,2 -->-30, 3
21.1-->-31,2
22,0 -->-32,1
31.3 -->-41,,,
30,3 -->-40."
32,2 -->-42. 3
33,1 -->-43,2
41,,, -->-51,5
40,,, -->-50,5
31,2-->-41,3
33,0-->-43,1
32. 1 -->-42,2
42.3 -->-52."
51,5 -->-61,6
50,5 -->-60,6
41.3 -->-51,,,
4".1 -->-5",2
4", 0-->- 5",1
43.1-->-53,2
42,2 -->-52. 3
51,,, -->-61,5
53,3-->-63,,,
15018.25
15651.49
19024.26
19079.59
19644.92
19943.00
22739.73
23905.45
24147.50
24255.92
24461.23
24604.56
25923.48
27812.87
28590.16
28624.50
29117.04
30072.22
30274.55
31 696.96
32297.14
33319.88
35380.40
(MHz)
Calculated
VA-VEa
0.42
0.67
1.73
4.62
0.48
0.44
1.14
-17.35
0.46
0.54
2.15
22.33
3.24
1.47
0.50
0.45
2.13
-39.53
46.42
6.19
3.57
1.79
2.28
(MHz)
VA-VE
0.57
0.70
2.15
4.50
0.63
0.64
1.37
-16.87
0.64
0.63
2.27
21. 73
3.43
1.81
0.64
0.63
2.07
-40.37
46.36
6.52
3.82
1.92
2.44
and VEare considered to be accurate to within ::1::0.09MHz for splittings
and to within ::1::0.06 MHz for the other transitions.
a VA
small er than 0.8 MHz
261
TABLE 3
GROUND
VIBRATIONAL
STATE MOLECULAR
CONSTANTS FOR
CH3COCOOH
AND
CH3COCOOD
Conversion facto r 505376 uA' MHz. The uncertainties represent one standard deviation.
CH3COCOOH
Ao (MHz)
Bo (MHz)
Co (MHz)
AOA(MHz)
BOA(MHz)
COA(MHz)
hO+lBo-lco
(uA')
V3(cal mol-')
Åa
la" (uA')
CH3COCOOD
5535.578
::1::0.091
5377.569::1::0.240
3583.355
::1::0.011
3560.530::1::0.037
2204.834::1::0.011
2170.759::1::0.052
5536.064
::1::0.056
5377.932::1::0.150
3583.675
::1::0.007
3560.774::1::0.025
2204.829
::1::0.006
2170.805
3.1175
::1::0.0019
964.0::1::6.5
0.6457
3.20
::1::0.017
::1::0.035
3.1062::1::0.0072
967.2::1:: 12.3
0.6953
::1::0.035
3.20
aAssumed.
determinable centrifugal distortion coefficients. This was probably a result of the
small centrifugal perturbations the assigned lines possess.
Pyruvic acid is a highly asymmetric top (K~ -0.17) and the observed a type
A species transitions thus yield high accuracy effective rotational constants as
shown in Table 3. These constants were used to predict the strongest low J b type
A species transitions. A search was made for several of these lines, but none could
be identified with certainty owing to their small absolute intensities. This is in
keeping with the small b-axis dipole moment component of about 0.35 D producing insufficient intensities.
Microwave spectrum of CH3COCOOD and the conformation of pyruvic acid
The microwave spectrum ofCH3COCOOD was studied to obtain additional
information about the structural and conforrnational properties of the acid. A
search was made initially for the low J a-type R-branch transitions which were
found within a few MHz of the predicted frquencies. The measured lines are shown
in Table 5 and the derived spectroscopic constants are listed in Table 3.
The rotational constants of the main and the deuterated species furnish
insufficient information to make a detailed determination of bond lengths and
angles feasible. Yet, important conc1usions may be drawn about the structure
of the acid. The molecule has undoubtedly a symmetry plane and two out-of-plane
hydrogen atoms because la + lb - le is almost identical for the main and the deuterated species and very c10se to their counterparts in related molecules [10]. The
exact conformation of the methyl group must thus either be the one shown in Fig. 1
or a form where the methyl group is rotated through 60° from the depicted conformation in order to satisfy the symmetry plane condition. The rotamer shown
in Fig. 1 is believed to be the most stable because the non-bonded H2C-H' . . O
262
distance is probably shorter in this case than for the other possibility. With the
structural parameters of Table l, this distance was calculated to be about 0.16 Å
shorter for the Fig. l conformation than for the other form. A definite distinction
between the two cannot be made until substitution of the methyl group hydrogen
atoms has been made.
The good agreement between the substitution coordinates of the hydroxyl
hydrogen and those calculated from the model of Table l shows conclusively that
pyruvic acid possesses an intramolecular hydrogen bond forrned between the
carboxyl group hydrogen and the carbonyl group oxygen.
Internal rotation
A computer programme was written to treat the A-E internal rotation
splittings observed in the microwave spectrum of pyruvic acid. The programme is
based on the "principal axis method" (PAM) developed by Wilson [11], Herschbach [12], et al. [13, 14]. According to this method, the spectra can be treated by
fitting to the Hamiltonian [12]
00
H va
-
J[,R +F"~
n=l
w(n)
va
pn
(1)
where HR is the rigid rotor Hamiltonian, and P is defined by
p = rxPa+/3Pb+yPe
(2)
rx = Åal) la' /3 = Åblallb' Y = Åelj le
(3)
where
and la is the moment of inertia of the methyl group about its symmetry axis. Åa'
Åb,and Åeare the direction cosines of the methyl group symmetry axis with respect
to the principal 'inertial axes. la' lb' and le are the principal moments of inertia.
F and r are defined through
F = h2j2rla,r = 1-
Ig Å~lallg
(4)
The perturbation coefficients W;;) depend only on the ratio V3jF for an assumed
potential function of the form
v = !V3 (l-cos 3rx)
(5)
In the computer programme the W~~)'swere generated as described by
Herschbach [12] using his "bootstrap" method through "approximation C".
This procedure is based upon appropriate linear combinations of eigenvalues,
b, of Mathieu's equation (6)
d2yjdx2+(b-s
COS2X)Y= O
(6)
263
where
2x = Nrx+n p = -io;ox
VN = iN2Fs
(7)
EYIT= tN2Fb
and p is the angular momentum operator of the methyl group torsion. In the PAM
representation the boundary condition requires that the Mathieu eigenfunction
y is invariant under the transformation rx--*rx+ 2n. y may then be expandedin the
form
y = exp(imx)
Lk Ak exp(iNkrx)
(8)
where (J is a symmetry number ((J = 0,:1::I) and Ak a coefficient.Substitution
of y in eqn. (6) yields an infinite tri diagonal matrix which must be diagonalized to
obtain the eigenvalues b. This diagonalization may be done in various ways. A
continued fraction procedure has for example been devised by Herschbach [15].
However, we found an alternative way very convenient. In our computer programme the b's possessing the necessary symmetri es (Jand periodicities N of VN
[12] were obtained by diagonalization of matrices of dimension 40. The matrix
elements were those given by Wollrab [16] which were corrected for a few misprints. Givens' diagonalization procedure [17] was utilized and only the ground
state eigenvalues were computed. This requires a minimum of computer time.
By comparing the b's obtained in this way to those found in existing tables [15]
complete agreement was found in all test cases.
With the b's and w~~2's calculated as described above, Herschbach's matrix
formulation [12] of eqn. (I) was set up in a pro late rotor representation. Matrix
elements through third order were included. The matrix was then diagonalized
employing the Jacobi method [18].
In order to optimize the parameters a least squares fit was carried out. The
individual A and E lines were fitted to eqn. (1). The five parameters Ao, Bo, Co,
Åa'and V3 were fitted simultanously. The sixth parameter, IlT.'on which the spectrum depends, was preset to a constant value. The partial derivatives of the individual A and E lines with respect to the five parameters were generated numerically. Thiswas carried out foreach least squares cycle and is the most time consuming part of the procedure. For small internal rotation splittings, the A and E lines
partly overlap and the data are thus correlated. This should require an off-diagonal
weight matrix, however, a diagonal weight matrix was used. For the lines appearing in Table 2, those split by less than 0.8 MHz were estimated to be accurate to
within about 0.09 MHz whereas the other A and E transitions individually were
assumed to be correct to within approximately 0.06 MHz. One standard deviation
should thus be 0.03 MHz and 0.02 MHz, respectively, in the two cases. The diagonal weight matrix was therefore chosen with the inverse squares of the standard
deviations taken as weights. For the transitions appearing in Table 5, unit weights
were used because there is no difference in the spectral accuracy.
264
TABLE 4
CORRELATION
MATRIX FOR THE ROTATIONAL
Ao
Bo
1.000
0.640
-0.744
-0.073
-0.063
1.000
-0.751
0.171
0.171
CONSTANTS,
A., AND V3
Co
Aa
V3
1.000
0.018
0.016
1.000
0.995
1.000
TABLE 5
MICROWAVE
SPECTRUM
Transition
OF THE GROUND
33. 0--+ 43. 1
32.1 --+ 42.2
42.3 --+ 52.4
51.5 --+ 61.6
50.5 --+ 60.6
41.3 --+ 51.4
43.1 --+ 53.2
42.2 --+ 52. 3
53.3 --+ 63.4
55.1 --+ 65.2
55. o --+ 65.1
54.2 --+ 64. 3
a
b
STATE OF CH3COCOOD
Observeda (MHz)
VA
21,1 --+ 31.2
31.3--+41.4
30. 3 --+ 40.4
32.2 --+ 42. 3
33.1--+43.2
41.4--+51.5
40.4 --+ 50. 5
31.2 --+ 41.3
VIBRATIONAL
18838.23
19359.66b
19619.49b
22484.21
23713.33
23783.86b
23873.09b
24141.10
24491.66
25757.67
27458.84
28153.05b
28179.77b
28647.94
31587.81
32002.62
35008.67
35836.86
35897.68
35977.56
Calculated
VA -VE
VA-VE
1.85
-
1.90
0.58
0.64
1.16
-16.52
0.60
0.62
2.06
20.57
2.98
1.61
0.61
0.61
1.99
5.67
3.35
2.09
- 24.15
30.11
-13.70
1.19
-16.61
2.24
20.65
2.93
1.50
2.20
5.59
3.43
1.95
-23.69
30.10
-13.67
:1:0.10 MHz for individual VA and VE transitions.
Average frequency. Splitting unresolved. Transitions
(MHz)
not used in least squares fit.
TAB LE 6
STARK COEFFICIENTSAND DIPOLE MOMENTOF PYRUVIC ACID
The uncertainties represent one standard deviation. The standard deviations of the dipole moment
and its components
along the principal
axes were half the values
Transition
20.2
--+ 30. 3
M=O
M = 1
M=2
!-ta = 2.27 :1:0.02 D
!-tb = 0.35:1:0.02 D
!-ttot = 2.30 :1:0.03 D
given in this table.
!:!..v/E2
IMHz (V/cm)21 x 106
Observed
Calculated
-4.90 :1:0.05
-0.415 :1:0.007
12.8 :1:0.1
-4.82
-0.418
12.9
265
The results of the least squares treatment with Jafixed at 3.20 uA 2 are shown
in Tables 2-5. It is seen that V3 is alm ost identical for CH3COCOOH
and
CH3COCOOD
as one would expect. Furthermore,
Åa and V3 are strongly correlated, while there are very small correlations between the rotational constants
on the one side and Åaand V 3 on the other as seen in Table 4.
The influence of Ja was also examined. Calculations with Ja preset at 3.15
UA2, 3.10 UA2, and 3.05 UA2 were performed for both isotopic species. The rotational constants obtained in these latter cases were almost identical with those
found in Table 3. Small changes were observed in Åa and V3. The results were:
= 0.642IO.017 and V3 = 977.5I6.5 cal mol-I, Åa= 0.638IO.017 and
V3 = 991.4I6.6 cal mol-I, and Åa= 0.634IO.017 and V3 = 1005.7I6.7 cal
mol-I, respectively, for CH3COCOOH. The findings for CH3COCOOD closely
parallei the CH3COCOOH results. The standard deviation of the fit varied insignificantly in all cases. Taking the influence of Ja and other effects into account,
arealistie value of the barrier height is 965 I 40 cal mol-l for both isotopic species.
Åa
Dipole moment
Stark coefficients of the 20,2 --+30,3 transition were used to determine the
dipole moment. A d.c. voltage was applied between the Stark septum and the cell,
with the modulating square wave voltage superimposed. The d.c. voltage was measured with a digital voltmeter having an accuracy of 0.025%. The electric field was
calibrated using the OCS l --+2 transition with floes= 0.71521 D [19]. A least
squares fit using a diagonal weight matrix was performed. The weights were
chosen to be (5-2, where (5is the experimentally determined standard deviation
of the second order Stark coefficient appearing in Table 6. From the fit, fla =
2.27 I 0.01 D and flb = 0.35 IO.01 D were obtained. However, taking into account possible systematic errors, the latter standard deviations are probably toa
small, possiblyby a factor of 2. As the final result fla = 2.27 IO.02 D, flb = 0.35
IO.02 D, and fllol = 2.30IO.03 D are given. The uncertainties quoted represent
one standard deviation. Calculations performed by vectorial addition of bond
moments [20] resulted in fltol = 2.02 D. The CNDOj2 method [21] yielded fltol =
2.36 D.
DlSCUSSION
The reason why the conformation of pyruvic acid shown in Fig. 1 is more
stable than other forms by 2.34IO.32 kcal mol-l [l] is probably quite complex.
The two effects, conjugation between the two carbonyl groups and the fivemembered intramolecular hydrogen bond should both stabilize the observed
rotamer. It is not easy to estimate quantitatively how much each of these effects
266
contributes. If conjugation were of prime importance thepertinentC-C bond length
should be rather small. An accurate determination of this bond length cannot
be made from the present data, but in the closely related substances glyoxal [22]
and free oxalic acid [23] rather long C-C singlebonds of 1.525Å and 1.548Å,
respectively, have been determined indicating that conjugation is not very important for this type of compound. The other effect, the intramolecular hydrogen
bond, thus seems to be of greater importance than conjugation for the stabilisation of the identified rotamer. With the plausible structural parameters of Table l,
the non-bonded O' . ,0 and H- . ,0 distancesrelating to the hydrogen bond were
calculated to be about 2.72 Å and 2.11 Å, respectively, indicating a hydrogen bond
strength in the order of 2-5 kcal mol-l.
For molecules having methyl groups attache d to carbonyl groups intermediate barrier heights have been found in most cases. E.g., the barriers to internal
rotation are 1168::1::30cal mol-l in acetaldehyde [12], 1041::1::6cal mol-l acetyl
fluoride [24], 1296::1::30cal mol-l in acetyl chloride [25], 1305::1::30cal mol-l in
acetyl bromide [26], 1210::1::30cal mol-l in acetyl cyanide [27],480.8::1::0.5 cal
mol-l in acetic acid [28], and 757.1 ::1::2.5cal mol-l in acetone [29], respectively.
The barrier height of pyruvic acid of 965::1::
40 cal mol-l is thus slightly lower
than in the majority of the above mentioned compounds. In comparison with
acetaldehyde [12], the barrier to internal rotation is about 200 cal mol-l lower
in pyruvic acid than in the former molecule. A drop in the pertinent non-bonded
O' . 'H-CHz distance might explain this. With the Fig. 1 conformation, this
distance is calculated as 2.34 Å which is approximately 0.16 Å shorter than in
acetaldehyde [11], and it is about 0.3 Å shorter than the sum of the O and H van
der Waals' radii [30]. According to Beaudet and Wilson [31], a lowering of the
barrier height is expected to occur in molecules where non-bonde d distances are
shorter than the sum of the pertinent van der Waals radii of the individual atoms.
The low barrier in pyruvic acid as compared to acetaldehyde [12] thus supports
the view that the methyl group conformation is indeed that shown in Fig. 1.
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31 R. A. Beaudet and E. B. Wilson, Jr., J. Chem. Phys., 37 (1962) 1133.
NOTE ADDED IN PROOF (received
14 November
1973)
The microwave spectrum of the main speeies has been studied independently by C. E. Kaluza, A. Bauder and Hs. H. Gunthard (Chem. Phys. Lett.,
22 (1973) 454.) who obtained results in good agreement with ours.