J. Phys. Chem. 1984,88, 1797-1804
1797
Vibrational Analysis of Pyruvate Ion Molecules and Estimation of Equilibrium Constants for Their Hydrogen Isotopic Exchange Reactions Masato Kakihana and Makoto Okamoto* Research Laboratory f o r Nuclear Reactors, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152, Japan (Received: June 20, 1983; In Final Form: September 14, 1983)
The infrared spectra (4000-200 cm-l) of CH,COCOONa and its four isotopic substitutions including 13C-and l80-1abeled modifications suspended in KBr disks were measured. Complete vibrational assignments were established on the basis of the isotope shifts of the fundamentals and a normal-coordinate analysis. From the normal-coordinate analysis a general valence force field involving 40 force constants, 7 of them being transferred from pyruvic acid, has been determined, which reproduced 90 experimental frequencies with a root-mean-squares deviation of 2.1 cm-I. The valence force field was used to estimate fundamental frequencies which were not obtained from direct observation, and the reduced partition function ratios of the pyruvate ion molecules were evaluated by using the spectroscopic data including the predicted values of the fundamentals. The calculated equilibrium constants of some hydrogen isotopic exchange reactions between the pyruvate ion molecules were reported.
Introduction The utilization of tritium (T) and deuterium (D) as tracer isotopes of hydrogen has been widespread in many fields of chemical and biochemical research of reaction pathways and mechanisms. In connection with a significant advancement in the technology of D-T fusion reactors, it has become increasingly important to know the property and behavior of T- (or D-) labeled compqunds in a variety of materials from the point of view of both the enrichment or removal of trace amounts of T (or D) and the effect of T (or D) on organisms. The mass differences from normal hydrogen may often cause remarkable effects on the chemical behavior, that is, so-called isotope effects. The measurement of the vibrational spectra of the isotopic species in question is pn excellent tool in evaluating such isotope effects Qn cHemical reactions. Information about the normal frequencies for the isotopic molecules enables one to calculate the isotopic reduced partition function ratios, which may serve as a basis in understanding the isotope effects in terms of the zero-point energy differences between the isotopic species, and consequently the calculation of the partition function ratios for various kinds of molecules permits subsequent determination of equililjrium constants for isotopic exchange reactions between the molecules. The isotopic fractionation factors derived from the equilibrium constants may serve as a useful probe not only in estimating isotope effects for each chemical reaction but also in finding the most effective system for isotope separation. The problem here is that little is known of the normal frequencies for pure tritium-labeled species (in a certain case, even for the corresponding deuterium-labeled modifications) on account of the experimental difficulties in their observation. This situation requires one to predict the normal frequencies of the rarer isotopic molecules. In many cases, such fundamental frequencies can be approximately estimated by use of the well-known G and F matrix method,[ in which the G matrix is calculated from the geometry and masses of the constituent atoms of the molecule, and the F matrix is expressed in terms of force constants which can be related tq the potential energy of the system. However, the calculated fundamental frequencies of molecules involving hydrogen isotopes are expected to be very sensitive to the potential function used. It should therefore be emphasized that a reliable potentia1 functiqn must be determined from experimental data prior to the estimation of the equilibrium constants for isotopic exchange reactions. In a previous article,2 we reported the equilibrium constants of some hydrogen isotopic exchange reactions between the acetate ion molecules by use of their spectroscopic data, and the inclusion (1) Wilson, Jr., E. B.; Decius, J. C.; Cross, P. C. 'Molecular Vibrations"; McGraw-Hill: New York, 1955. (2) Kakihana, M.; Kotaka, M.; Okamoto, M, J . Phys. Chem. 1983, 87, 2526.
of the data from the 13C modifications was found to be very effective for determining a reliable molecular force field (F matrix). The force field was used to predict the fundamental frequencies for rare isotopic species containing deuterium and tritium. In the present study, the vibrational analysis of pyruvate ion molecules was carried out; no quantitative spectroscopic investigation has been reported on this system in spite of its biochemical importance. Katon and Covington3 first reported infrared and Raman spectra of this substance with tentative assignments based on comparisons with the vibrational assignments on related molecules, and therefore they could provide only ambiguous assignments for the fundamentals. One of the most effective ways to obtain an exact assignment is to observe the frequency shifts caused by appropriate isotopic substitutions, as has been pointed out in a previous paper.4 In the present work, the infrared spectra of '2CH312CO'2COONa (parent species), '2CH3'2C0'3COONa (l-l3C), lZCH3'3C012COONa(2-13C), 13CH313CO'2COONa (2,3-13C),and 12CH312C'8012COONa (2-180) were measured, and a detailed vibrational analysis based on the data for the parent molecule and the four isotopic species was carried out in order to establish an exact assignment of the fundamentals. The assignment of the fundamentals based on the heavy-atom isotope (l3C and l8O)shifts in combination with the qualitative empirical rules for group vibrations available5 is presented in section A. In section B, an approximate molecular force field of the pyruvate ion is determined on the basis of a normal-coordinate analysis. Finally, the calculated reduced partition function ratios of isotopic pairs of the pyruvate ion molecules and the equilibrium constants for their hydrogen isotopic exchange reactions are reported in section C. Experimental Section Potassium bromide and 12CH312C012COONa were obtained commercially (E. Merck Co. Ltd., Darmstadt). The 13C-enriched modifications of sodium pyruvate were purchased from Merck Sharp and Dohqe Canada Ltd. with 90% I3C isotopic purity. The sample containing mainly CH3C'80C160'60ion was prepared by direct exchange with H2180(Prochem. Co. Ltd. in London with 99.5% I 8 0 purity); the parent molecule was dissolved in H2180 and kept at room teIpperature for several days, and finally the sodium salt was obtained from evaporating the water. The handling of the sample and the preparation of KBr disks were the same as those described in a previous paper.4 A liquid-nitrogen ~
(3) Katon, J. E.; Covington, T. Spectrosc. Lett. 1979, 12, 761. (4) Kakihana, M.; Kotaka, y,;Okamoto, M.J . Phys. Chem. 1982, 86,
4385. (5) Bellamy, L.J. "The Infrared Spectra of Complex Molecules-Advances in Infrared Group Frequencies", 2nd ed.; Chapman and Hall: New York, 1980:Vol. 2.
0022-3654/84/2088- 1797$0 1.5010 0 1984 American Chemical Society
1798 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984
Kakihana and Okamoto I
0
I
I
1 l
LO00
I
I
l 32x
l
I
l 2253
l
/ 1800
l
l 1650
l
l
l
IY3C
l 1200
I
/ -000
/
l 80C
1
l 500
1
l 10:
/ iT0
wo\ e"L-lOel/Cr,-:
Figure 1. Infrared spectrum of '2CH312C0'2COONain KBr pellet at room temperature; 1 mg of sample suspended in 100 mg of KBr.
Model DN 70 cryostat (Oxford Instrument Co. Ltd.) with KRS-5 windows was used for a low-temperature experiment. Infrared spectra were measured in the region 4000-200 cm-' with a Jasco Model DS 701G infrared spectrometer with slit program 5 (spectral resolutions 1.C-2.4 cm-I). All frequencies were calibrated against the standard absorption bands of H 2 0 , NH3, COz, and HC1.6
Results and Discussion ( A ) Vibrational Assignment Based on Qualitative Empirical Rules. A typical infrared spectrum of the parent molecule obtained at room temperature is shown in Figure 1, covering the range from 4000 to 200 cm-'. Similar spectra with small isotopic shifts of the fundamentals were obtained for the other I3C-and '*O-labeled modifications. An initial assignment of the fundamentals was carried out on the basis of the qualitative empirical rules available: comparisons with the vibrational assignments on related molecules such as pyruvic acid' and sodium a ~ e t a t e ,and ~,~ the heavy-atom isotope (13C and l*O) shifts of the fundamentals. However, many of the normal modes are strongly intermixed or coupled with several group modes, so that the application of the empirical method to establish the band assignments is restricted to the specific regions in which the vibrations are practically free from any couplings. The straightforward assignment was therefore limited to the following selected spectral regions. ( 1 ) CH3-StretchingRegion. In the region of 3000 cm-l, three fundamentals due to methyl stretching modes are expected to be observed; one of them is classified into a symmetric vibration and the others into asymmetric vibrations. The latter normal modes may degenerate in molecules with C3, symmetry. An expanded section of the spectra for the parent and 2,3-I3C-labeled species is shown in Figure 2 in the range from 3200 to 2800 cm-'. The three fundamentals due to the CH,-stretching modes were clearly observed in each spectrum. This type of splitting suggests that the structural parameters of the pyruvate ion imply a small deviation from a tetrahedral configuration around the methyl group and/or the force field associated with the methyl-stretching internal coordinates deviates slightly from the local C,, symmetry. The I3C substitution at the methyl carbon caused lower frequency shifts of the three fundamentals. The absorption band centered at the lowest frequency (uz) in each spectrum was assigned to the symmetric CH3-stretching mode and the others (vl and u I 5 ) to the asymmetric CH,-stretching modes. ( 2 ) C=OStretching and Asymmetric COOStretching Regions. The C=O-stretching and asymmetric COO-stretching fundamentals exhibited very strong absorption in the spectral region from 1800 to 1500 cm-'; measurement of the spectrum at a lower concentration was necessary to locate the fundamentals with higher confidence. The detailed features of the spectra at a lower sample concentration (ca. 50 wg of sodium pyruvate suspended in 100 mg of KBr powder) are shown in Figure 3. The C=O-stretching fundamentals ( u 3 ) were observed at 1709.0 and 1708.4 cm-' for the parent (a) and l-I3C-labeled species (b), respectively, and at (6) International Union of Pure and Applied Chemistry (IUPAC),"Tables of Wavenumbers for the Calibration of Infrared Spectrometers";Pergamon Press: New York, 1977. (7) Hollenstein, H.; Akermann, F.; Giinthard, Hs. H. Spectrochim. Acra, Part A 1978, 34.4, 1041.
Y
v2
3200
I
I
I
I
3100
3000
2900
2800
wavenumber/cm-l
Figure 2. Characteristicabsorption bands due to CH3-stretchingmodes of '2CH312C01ZCOONa (a) and 13CH3'3C012COONa (b); 1.0 mg of sample suspended in 100 mg of KBr.
:I
:E30
170C
I.". , 1500
1503
.EC0
1:00
1503
:SO0
!E10
I7CC
AiO:
150s
*O"e""me-/CR-~
Figure 3. C=O stretching and asymmetric COO-stretchingregion of the spectra of 12CH31ZC012COONa (a), 1ZCH312C013COONa (b), and LZCH313C012COONa (c); ca. 50 wg of sample suspended in 100 mg of KBr.
1670.7 cm-I for the 2-I3C-labeled modification (c). The I3C substitution at the keto carbon caused a large lower frequency shift (ca. 40 cm-') of the fundamental, which can be convenient for assignment of this mode to a group vibration. Similar isotope shifts were observed in the corresponding spectra of the 2,3-I3Cand 2-I80-labeled species. On the other hand, the asymmetric COO-stretching modes (v4) for the parent (a) and 2-13C labeled species (c) were assigned to the frequencies at 1633.0 and 1633.2 cm-'. The corresponding fundamental for the l-I3C labeled modification (b) was found at 1588.4 cm-I with a large isotope shift of about 45 cm-l, which arises from the I3C substitution at the carboxylate carbon. Katon et aL3 assigned the COO-stretching fundamental to the band observed at 1657 cm-I, but it is too large to explain the present I3C shift of the fundamental. (3)Symmetric COO-Stretching and CH3-DeformationRegion. Typical infrared absorption bands for the parent species at 290 K in the region from 1550 to 1300 cm-' are shown in Figure 4a, together with the corresponding spectrum at 80 K for comparison. In this spectral range, four fundamentals due to one COO-
Vibrational Analysis of Pyruvate Ion Molecules
L
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1799
pr
C
5'\
Figure 4. CH3-deformationand symmetric COO-stretching region of the spectra of 12CH,12COlZCOONa(a) at 290 and 80 K, lZCH,12C0'3COONa(b), and 13CH313C01ZCOONa (c); 0.5 mg of sample suspended in 100 mg of KBr
stretching and three CH3-defarmation modes should occur. However, as shown in Figure 4a, one strong absorption band ( v 6 ) with a shoulder (4 and a well-defined absorption band (v7) were observed in the room-temperature spectrum. In the spectrum measured at 80 K, the should (v5) exhibited a distinct absorption band and a new shoulder (q6) was observed at a slightly lower frequency than the v6 fundamental. The assignment of these fundamentals was assessed straightforwardly by taking into account the 13Cshifts of the vibrational modes. The corresponding absorption spectra for the l-13C and 2,3-13C labeled species are shown in parts b and c of Figure 4,respectively. The I3C substitution at the carboxylate carbon caused lower frequency shift (ca. 24 cm-I) of the symmetric COO-stretching vibration (&), so that the fundamental due to the CH3-deformation mode which was hardly discernible in the spectrum for the parent species, was clearly observed at 1404.1 cm-' as shown in Figure 4b. The absorption band centered at 1405.9 cm-' (v6) for the parent species can be reasonably assigned to the symmetric COO-stretching mode. On the other hand, the I3C substitution at the methyl carbon caused lower frequency shifts (ca. 11 cm-l) of the remaining two fundamentals (v5 and v7). On the basis of this observation of the 13C shifts, the absorption band observed at 1353.9 cm-I (Y,) for the parent species was assigned to the symmetric CH3-deformation mode to which empirical rules for group vibrations can be applied and the band at 1425.8 cm-' (v5) to the asymmetric CH,-deformation mode. ( B ) Normal-Coordinate Analysis and Determination of an Empirical Molecular Force Field. (1) Internal Coordinates. In the present vibrational analysis, all the molecules concerned are assumed to belong to the symmetry point group C, in which the vibrational representation has the form 14 A' 7 A". The definition of the stretching, bending, in-plane wagging, and inplane rocking coordinates used in this study is illustrated in Figure 5, where the in-plane wagging coordinate (-yl) is defined as the angle between the C=O bond and the line bisecting the angle w , the in-plane rocking coordinate (y2) the angle between the C,-C2 bond and the line bisecting the angle 0. In addition, one , out-of-plane rocking out-of-plane wagging coordinate ( r l )one , two torsional coordinates ( T ~and T ~ were ) coordinate ( r 2 )and introduced. The coordinate r 1is defined as the angle between the C=O bond and the C-C-C plane; r2the angle between the C1-C2 bond and the 0-C-0 plane. The torsional coordinates are chosen as the linear combinations of all-possible four mass-torsional coordinates as follows:
+
= 72
=
j/4(74123
+ 74126 + 7 5 1 2 3 + 75126)
M V ~ Z+ 7 7 3 2 6 + 78321 + 7a326 + 79321 + 79326)
where the subscripts refer to the numbering of the atoms as shown in Figure 5. Structural parameters of the pyruvate ion molecule used in the present calculation are listed in Table I, where the symbols shown are according to the notations given in Figure 5. The definition of the symmetry coordinates which are constructed
Figure 5. Definition of stretching, bending, in-plane wagging, and inplane rocking coordinates for the pyruvate ion molecule. TABLE I: Structural Parameters of the Pyruvate Iona
-
-________-_
bond lengthb/
bond angleb/ deg
nm rl (C-H) =
r,(C-H) = r,(C-H) I(C-C)
rnK-C) n(C=O) S(C-0) d(C-0)
0.109c 0.1518 0.1579 0.1 I83 0.1278 0.1242
(HCH) = a,(HCH) = a,, (HCH) p,(CCH)= 0,(CCH) = P? KCH) w(CCC) CY,
e(oco) YI
Y2
109 47d 109 47d 113.7 126.3 2.65 0.95
a Geometry at equilibrium according to ret' 17. Symbols are in accord with the notations given in t,'igure 5 . Three bond lcngths are assumed to be identical. Tetrahedral configuration around the methyl group is assumed.
as appropriate linear combinations of the internal coordinates is shown in Table 11. (2) Constraints to the Valence Force Field. Since the pyruvate ion molecule with a configuration of C, symmetry has 14 A' and 7 A'' normal modes, its general harmonic force field involves 133 parameters. However, a large number of insignificant off-diagonal force constants were found to be nonestimable from our experimental data. The set of force constants was therefore reduced by a number of constraints which are exptected to be reasonable from a physical point of view. In the present calculation, the constraints which were introduced by Hollenstein and GiinthardB were applied to the valence force field of the pyruvate ion molecule. This type of approximation was successfully used on pyruvic acid,' methyl nitrite,g glycolic acid,I0 and methyl glycolate.10 The restrictive assumptions used in this study are given as follows: (i) Interaction force constants of the methyl stretching, methyl torsional, and COO torsional coordinates with other internal coordinates were omitted, while the interaction force constants between the adjacent C-H stretchings were taken into consideration. (ii) Off-diagonal force constants associated with the methyl group were subject to a C3tilocal-symmetry constraint. (iii) Force constants associated with the carboxylate and carbonyl groups were subject to a C2, local-symmetry constraint. (iv) Interaction force constants between coordinates having less than two common atoms were excluded, while off-diagonal con(8) Hollenstein, H.; Giinthard, Hs. H. J . Mol. Spectrosc. 1980, 84, 457. (9) Ghosh, P. N.; Giinthard, Hs. H. Spectrochim. Acta, Part A 1981,37A, 1055.
(10) Hollenstein, H.; Schar, R. W.; Schwizgebel, N.; Grassi, G.; Giinthard, H s . H . Spectrochim. Acta, Part A 1983, 39A, 193.
1800 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984
Kakihana and Okamoto
TABLE 11: Symmetry Coordinates for the Pyruvate Ion
-
--___
representation
c, A
sym coord (l/J6)(2Ar, - A r 2 - Ar,) i I / J 3 ) ( ~ r , + Ar, + Ar,) An ( I / J a ) ( A s + Ad) (l/J2)(As - Ad) Al
Am (1/J6)(2Aa1 - A a , - Aa,) (l/J6)(A0, + A@, t A@, - AO, - AO, - A&) ( l / J 6 ) ( 2 A p I - A @ , - Ap,) Aw AY I A0 AY 2
+ A a , + AO, + 4, + A&)
(l/J6)(AaI + A a ,
notation
description
Vas(CH3) vs(CH, 1 v(C=O) vs(C0,) VasiCO,) v(C-CH,) II(C-CO,) &as(CH,) 6 s(CH, 1 Yin(CH,) s (CCC) yin(C=O) 6 (OCO) ~in(CO2)
d5ym CH, atr syni CH, qtr C=O str sym CO, str asym CO, str C-CH, str C-CO, str d\ym CH, deform sym CH, detorm in-plane CH, rock CCC bend in-plane C=O wag OCO bend in-plane CO, roLk rcdundant CH, str CH, deform out-of-plane CH, rock out-of-plane C-0 wag out-of-plane CO, rock CO, torsion CH, torsion
ViCH,) 6(CH,) dCH, 1 n(C=O) n(C02) TKO,)
dCH,)
stants containing adjacent stretchings, bendings with a common vertex, and stretching-bending having a common apex were taken into account. (v) Since one redundancy was involved within the six methyl-bending internal coordinates, only linear combinations of force constants associated with these coordinates could be determined. These combinations were chosen according to the convention presented by Hollenstein and Gunthard.’ (vi) Some of off-diagonal force constants associated with the C H 3 C 0 portion (h,,,, h,,,, hBIYI, h,,,,, and&’) were assumed to be transferable from pyruvic acid molecule. Such transferability of force constants between molecules with a very similar structural element has been discussed by Hollenstein and Giinthards and Hollenstein et al.1° (vii) Two diagonal force constants (Hrland HT2)associated with the methyl and COO torsional modes were transferred from the pyruvic acid molecule. These vibrational modes are expected to be observed in a low-frequency region (less than 20Q cm-’). The potential function which was restricted by the abovementioned assumptions i-v is introduced in order to define the force constants:
’
-
TABLE 111: Harmonic Force Constants for the Pyruvate Iona notationb 1 0 7 K r I / Nnm-’ 107Kr2/Nnm-I 107K1/N nm‘l
109HaI’/N nm IO9Ha2’/Nnm 109Hp,’/N nni 109Hp2’/Nnm 109H,/N nm lOpHYl/N nni
Values
notationb
values
Stretch 4.938 I0.010 107Km/N nn1-l 4.809 t 0.003 I07K,/N nm‘l 4.255 i 0.230 107Ks/N nm-’
4.038 t 0.366 12.13 * 0.23 9.848 I0.309
Bend 0.523 I0.014 1O9He/Nnni 0.5 10 t 0 007 109Hyz/Nniii 0.628 t 0.049 109H,, /N n m 0.496 2 0 049 1OYH,,/N nm 2.331 t 0 259 IO9HTI/N nni 2.241 t 0.156 109HT,/N nni
1.818 t 0.147 2. I23 II 0.206 0.549 2 0.027 0.458 t 0.022 0. I 12c 0.033c
Stretch-Stretch Interaction I07k,/N nm“ 0.057 t 0 001 I07kms/N nm-l IO7klm/N nm-I -0.473 I0.1 16 10‘ksd/N nm“ 107kl,/N nni-’ 0.692 t 0.207
0.207 t 0.1 1 1 1.940 t 0.309
Interaction 1O8/,e/N 108f~y,/N 1O8JL,,/N
0.915 t 0.160 0.7 17 t 0.084 0.525 2 0.078
108fme/N
St re t ch-Bcnd -0.228‘ 0.178 I0.115 -1.156 t 0.186 -0.354 F 0.137
10ghp‘/N nit1 I O Y h a ~ ’ / nm N IO’hg, w / N ntii lOYhp2,/N nm IO’hp, y,/N niii
Bend-Bend -0.602 f 0.024 -0.018 t 0.016 O.23Oc -0.03F -0.095c
Interaction 1 0 y h p , y l / N nm 0.076c l O y h w r 2 / N nni 0.284 F 0.072 10yhy,,2/Nn m -0.282 t 0.125 1 0 y h ~ 2 n I /ntn N -0.063 t 0.01 1 10’h,ln2/N n m 0.061 II 0.012
1 OBjia’/N 1O8fiW/N 1O8)’nw/N
a Thc errors shown are standard deviations. Primed quantities follow thc convention given in rcf I I , Taken from ref 7 .
(1 1) Hollenstein, H.; Giinthard, Hs. H. Chem. Phys. 1974, 4, 368.
where the primed quantities follow convention v. The potential function contains 40 parameters in total; 7 (H,,, H,,, h,,,, he,,, hSiYI,h,92YI, andf;,‘) of them were transferred from pyruvic acid7 and were kept constant for all isotopic species. The remaining 33 force constants were adjusted simultaneously to fit 90 observed fundamental frequencies by the least-squares iteration procedure; a distinct stable minimum was obtained. The final values of the harmonic force constants associated with the internal coordinates are shown in Table 111. By this valence force field the experimental frequencies can be reproduced with a root-mean-squares (rms) deviation of 2.1 cm-l. (3) Discussion. (a) Assignment. All the observed fundamentals for the parent molecule and the four isotopic species, along with
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1801
Vibrational Analysis of Pyruvate Ion Molecules
TABLE IV: Observed and Calculated Fundamental Frequencies for "CH, '2C012COONa freq/cin-l _________
representation CS
A'
VI u2
3
v4 1) 5 '6
u7 1'
n
VY lJl11
VII 1'1 2
1/13 '14
A"
obsd
calcd
po tcntial energy distribution' __________
3024.2 2932.0 1709.0 1633.0 1425.8b 1405.9 1353.9 1188.4 981.8 834.1 631.2 545.5 396.0 298.9 2988.5 1406c 1017.5 749.6 432.3 not obsd not obsd
3024.2 2932.4 1710.0 1633.9 1421.9 1405.9 1353.5 1187.2 981.8 835.1 630.9 545.9 394.7 295.3 2989.5 1404.1 1018.2 749.5 434.1 134.1 91.9
95 l>as(CH,) 96 v,(CH,) 97 u(C=O). 11 S(CCC) 94 Vas(C0,) 74 6,,(CH3). 17 u,(CO,) 64 vJCO,), 22 Sa,(CH,), 21 v(C-CO,). 10 S(OC0) 97 fi s(CH3 1 32 v(C-CH,), 24 7in(C=O), 18 7in(CH,), 17 u,(CO,), 13 V(C-CO,) 46 yin(CN3). 19 u(C-CH,) 54 fi(OCO), 23 ~ ( C - c o , ) , 17 v(C-CH,) 44 7iniC=O), 23 u(C-CH,), 14 o(C-CO,), 13 yin(CH,) 39 S(CCC), 26 yin(C02), 17 S(OCO), 10 7in(CH3), 10 u(C-CO,) 25 rin(C=O), 22 S(CCC), 21 fiiOCO), 15 u(C-CO,) 56 yin(C02). 29 S(CCC), 14 rin(C=O) 99 J ~ C H , ) 98 6 (CH,) 54 n(CH,), 20 niC=O) 55 n(CO,), 32 n(CH,), 12 n(C=O) 71 n(C=O), 37 n ( C 0 2 ) ,13 n(CH,) 98 T(CH,) 99 d C H , 1
assignt
1119
VI6
Y17
I/," 1/19
1/20
1'21
-
Contributions smaller than 10% are omitted. force field. a
Measured at 8 0 K .
______
Not used in the refincme nt procedure for the determination of the
TABLE V: Observed and Calculated Fundamental Frequencies for ' T H , 'ZC0'3COONa
_-
representation
freqlcni"
assignt obsd calcd cs _______________ A' I not obsd 3024.2 1.' , 2933.1 2932.4 3 1708.4 1708.9 2'4 1588.4 1589.0 1's 1420.6 1419.5 u(' 1381.9 1381.9 1J 1352.5 1352.8 1'" 1187.3 1187.0 1) 98 1 .O 981.2 VI,, 824.3 824.2 1') I 630.4 630.6 1/12 544.0 544.6 1/13 393.4 394. I 294.9 I3 29 1.6 A' 1'15 2989.0 2989.6 1404.1 1404.1 1/16 1014.9 1014.7 1/17 734.7 1'1 h 733.6 43 I .7 430.3 ~ ' 1 0 not obsd 134.1 "20 not obsd 91.9 1'2 I 7
potential cnergy distribution' ______-- ___ 95 I/as(CH,31 96 i>,iCH,3) 99 v(C-O), IO S(CCC) 96 va,iCO,) 93 6as(CH,) 77 u , ~ C O , ) ,24 ~ ( C - c o , ) , 1 1 S(OC0) 93 fi ,iCH,)
___
L)
JJ
a
39 6(CCC), 25 yin(CO,). 17 S(OCO), 10 rin(CH3) 24 yin(C=O), 23 S(CCC), 21 6(OCO). 16 u(C-CO,) 57 ~ i n ( C 0 , ) .29 S(CCC), 14 n n ( C = O ) 99 IJ(CH,) 9 8 6(CH,) 56 niCH,). 20 niC=O) 54 n(C0,). 31 n(CH,), 15 n(C=O) 70 n(C=O). 40 n(CO,), 12 n(CH,) 98 7-(CH,) 99 T K O , )
Contributions smnller than IO%> iirc omitted.
the corresponding normal frequencies calculated from the harmonic force field, are listed in Tables IV-VIII. The present vibrational assignment is strongly supported by the excellent agreement between the observed and calculated fundamental frequencies. Therefore, the present constraints to the general valence force field are to be reasonable. In Tables IV-VIII, the approximate description of the normal modes is given in terms of main contributions of the symmetry coordinates (group vibrations) to the potential energy distribution. Many of normal modes, especially those located below 1200 cm-', turned out to be complex combinations of several group vibrations, while the fundamentals discussed in section A were found to be highly characterized by the corresponding group modes; e.g., the vl(A'), v3(A'), v7(A'),and V16(A") normal modes can be expressed as the group vibrations of vas(CH3),v(C=O), 6,(CH3), and 6(CH,), respectively. It should be noted that the u4(A') normal mode can be well described by the asymmetric COO-stretching mode, va,(C02), whilst the corresponding symmetric COOstretching mode, v s ( C 0 2 )is, dispersed into several normal modes,
v,(A'), v6(A'), and v,(A'). The v6(A') normal mode can be regarded as the symmetric COO-stretching vibration, but many other vibrations contribute significantly to this normal mode. Similar potential energy characterization of these COO-stretching fundamentals was found for the acetate ion2 and glycine.12 (b) Vulence Force Field. As shown in Table 111, the difference between the two CH3-stretching force constants, K,, and K,,, appear to be significant; however, in view of the fact that the calculated asymmetric CH3-stretching frequency (v,) for the 2,3-13C species differs from the observed value by -9 cm-', additional experimental data are needed to examine to what degree the C-H-stretching force field of the methyl group deviates from the local C,, symmetry. Meanwhile, the methyl bending force constants, H f P ,and H'p2,were found to differ considerably from each other, and the difference between Hto1and H',, turned out to be insignificant. A similar trend in the methyl-bending force (12) Destrade, C.; Garrigou-Lagrange, C.; Forel, M. T.J . Mol. Sfrucf. 1971, 10, 203.
Kakihana and Okamoto
1802 The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 TABLE VI: Observed and Calculated Fundamental Frequencies for ' T H , '3C01ZCOONa
freq/cm-l
-____-
representation assignt
c . 9
A'
VI
u2 v3 114
US
"6 v7
"n u9 Ii I I1 IJlI u12
1) I 3
'14
A"
'ili
VI6
Vi7 lilh Ji
I9
2.' 2 0 v21
a
obsd
calcd
potential energy distributiona
30 18.0 2932.0 1670.7 1633.2 1420.5 1402.4 1353.3 1161.3 977.0 833.8 627.3 542.7 390.4 298.1 2989.8 -1402b 1006.8 747.7 432.0 not obsd not obsd
3024.2 2932.4 1670.1 1632.2 1420.6 1402.7 1353.4 1163.1 977.6 833.5 621.5 542.6 394.6 295.0 2989.6 1404.0 1005.7 747.1 427. I 134.1 91.9
95 vas(CH,) 96 u&H, 1 90 u(C=O), 1 1 S(CCC) 88 vas(CO,), 11 viC=O) 8 3 6as(CH,), 1 1 vs(CO2) 74 I J ~ ( C O2~2)v(C-CO,), , 13 6as(CH,), 12 S(OC0) 96 6s(CH,) 30 aj(C-CH,), 23 yin(C=O), 22 ?in(CH,), 14 u(C-CO,), 13 v S ( C O 2 ) 4 3 yin(CH,), 21 v(C-CH,) 5 4 S(OCO), 22 u(C-CO,), 18 v(C-CH,) 45 yin(C=O), 22 v(C-CH,). 14 v(C-CO,), 13 7in(CH3) 40 S(CCC), 25 r i n ( C 0 2 ) , 17 S(OCO), 11 I/(C-CO,), 11 ?in(CH,) 24 rin(C=O), 22 6(CCC), 21 S(OCO), 16 dC-CO,) 5 6 yin(C02), 29 6(CCC), 15 rin(C=O) 99 u(CH,) 98 6 (CH, 57 n(CH3), 18 n(C=O) 57 n(CO,), 30 n(CH,), 12 n(C=O) 7 3 n(C=O), 36 n ( C 0 2 ) ,13 n(CH,) 9 8 7(CH3) 99 7 ( C 0 2 )
Contributions smaller than 10% are omitted.
Not used in the refinement procedure for the determination of the forcc field.
TABLE VII: Observed and Calculated Fundamental Frequencies for "CH, I3C0l2COONa frcq/cm-I
representation
cs
assignt
obsd
calcd
_ _ ~ ~ - - _ _ _ _ _ _ A' Ji 1 3020.0 3011.4
potential energy distributiona __ --__ ___ __--94 "as(CH,) 95 us(CH, 1 90 u(C=O), 11 6CCCC) 88 uas(CO,). 11 u(C=O) 80 6 as(CH, 1, 1 3 u s ( C 0 21 73 LJ,(CO,): 22 u(C-CO,), 16 6as(CH,), 11 S(OC0) 9 8 6 s(CH,$) 31 v(C-CH,), 24 rin(C=O), 21 yin(CH,), 15 ~(C-co,),13 us(C0,) 44 rin(CH,), 20 u(C-CH,) 54 6 (OCO), 2 1 u(C-C02), 18 u(C-CH3) 44 rin(C=O), 24 u(C-CH,), 14 v(C-C02), 13 7in(CH3) 39 6 (CCC), 26 yin(C02). 17 S(OCO), 11 v(C-CO,), 10 ?in(CH,) 25 yin(C=O), 21 6(CCC), 21 6(OCO), !5 U(C-CO,), 10 rin(CO,) 55 yin(CO,), 31 6(cCC), 14 yin(C=O) 100 d C H , ) 97 6(CH1) 56 n(CH3), 18 n(C=O) 57 n(CO,), 30 n(CH3), 12 n(C-0) 73 n(C=O), 36 n(CO,), 13 n(CH,,) 98 .r(CH,) 99 r ( C 0 , )
2028.6 2928.2 1670.1 1669.8 1632.2 1632.2 v4 I), 1414.8 1418.6 1401.3 1401.3 u6 v7 1343.2 1343.5 U8 1155.9 1155.6 UY 968.7 969.2 u10 832.0 831.5 VII 6 19.6 6 19.4 VI2 541.7 541.9 1113 393.4 391.9 '14 290.9 293.0 A' ' 5 2979.9 2977.1 156 -140Ib 1401.6 17 1000.3 1000.2 !>in 746.8 746.4 li I ' I 43 I .7 427.0 u20 riot obsd 134.1 lJ21 not obsd 91.3 a Contribution smaller than 1 0 4 are oniitted. Not uscd in the refinement procedure for the determination o f t h e forcc field. u2
li 3
Ji
field has been found for several molecules, e.g. the acetate ion,2 acetone,8 and acetic acid.8 It should be noted that most of the off-diagonal force constants are evidently different from zero as shown in Table 111. The inclusion of the characteristic frequencies from the 13C- and 180-substituted species has served to determine the important interaction force constants associated with the heavy-atom skelton with considerable reliability. Among the bend-bend interaction constants, h', turned out to be indeterminable from our experimental data; it is not significantly different from zero. It should be finally pointed out that the interaction force constant ksd has a large value of 1.940 X lo-' N nm-' in contrast to the corresponding value of 0.7762 X lo-' N nm-' for pyruvic acid.8 The large value of this off-diagonal force constant in the pyruvate ion molecule can be interpreted to be a consequence of the resonance between two possible electronic ~tructures.'~Similar large values (13) Ohwada,
K. Spectrochim. Acta, Part
A 1978, 34A, 147.
for this type of interaction force constant have been found for the formate ion14 and the acetate ion.* ( C ) Calculation of Reduced Partition Function Ratios and Equilibrium Constants of Hydrogen Isotopic Exchange Reactions. The well-known expression for the reduced partition function ratio of isotopic molecules was derived by Urey15 and Bigeleisen and Mayer16 in the harmonic oscillator, rigid-rotor approximation: 3 ~ - 6ui exp(-ui/2) 1 - exp(-u,') (2) (s/s?f = irI =l 7 ui exp(-u,'/2) 1 - exp(-u,) where the primed symbols are for the lighter isotopic species, s is the symmetry number, ui is equal to hcu,/kT, ui is the ith normal vibrational frequency in cm-', h is Planck's constant, c is the (14) (15) (16) (17) 1281.
Kidd, K. G.; Mantsch, H. H. J . Mol. Spectrosc. 1981, 85, 375. Urey, H . C. J . Chem. Soc. 1947, 562. Bigeleisen, J.; Mayer, M. G. J . Chem. Phys. 1947, 15, 261. Tavale, S. S.; Pant, L. M.; Biswas, A. B. Acta Crystallogr. 1961, 14,
Vibrational Analysis of Pyruvate Ion Molecules
The Journal of Physical Chemistry, Vol. 88, No. 9, 1984 1803
TABLE VIII: Observed and Calculated Fundamental Frequencies for CH, CI’OCOONa freq cm-l
representation
cs
assipn t
A’
VI 1) 2
”3 1.’4 1’5
U6
1) 7
Vn
ut, Vlll
UI I
VI2
1) I 3 1114
A”
‘)I5
VI6
VI.,
V I ii
li I
,’
V20
v2 1
a
obsd
calcd
potential energy distribution‘
302 1.9 2932.0 1680.2 1630.8 1420.6 1406.2 1353.4 1185.8 976.1 832.0 623.4 539.3 391.7 291.1 2988.1 -1406‘ 1016.7 749.2 422.0 not obsd not obsd
3024.2 2932.4 1679.6 1630.3 1421.7 1405.9 1353.1 11 86.0 974.8 831.8 623.5 5 38.1 389.5 292.5 2989.6 1404.1 1017.3 149.2 431.2 133.9 91.0
95 v,,(CH,) 96 us(CH3 1 87 u(C=O), 1 3 S(CCC), 10 uas(CO,) 86 uas(C02), 12 v(C=O) 74 Sas(CH,), 17 v,(CO,) 64 uS(CO,), 2 2 haS(CH,), 21 v(C-CO,), 1 0 S(OC0) 97 6 ,(CH, 1 32 ”(C-CH,), 24 yin(C=O), 18 yin(CH,), 17 uS(CO,), 13 ~ ( C - c o , ) 47 yin(CH,), 17 u(C-CH3) 55 S(OCO), 21 ~ ( C - c o , ) , 17 u(C-CH,) 42 yin(C=O), 24 v(C-CH,), 15 v(C-CO,), 13 yin(CH,) 40 S(CCC), 27 yin(CO,), 15 S(OCO), 10 yiH(CH3), 10 u(C-CO,) 25 yin(C=O), 23 S(CCC), 21 6(0CO), 16 u(C-CO,) 57 +yin(C02),28 6(CCC), 17 yin(C=O) 99 u(CHJ) 9 8 6(CH3) 55 n(CH,), 20 v(C=O) 56 n ( C 0 2 ) , 32 n(CH,$),1 2 n(C=O) 72 n(C=O), 37 n ( C 0 2 ) , 13 n(CH,) 9 8 7(CH,) 99 T(C0,)
Contributions snialler than 10% are omitted.
Not used in the refinement procedure for the determination of the force field.
TABLE IX: Calculated Reduced Partition Function Ratios of Pyruvate Ion Molecules with respect to Isotope Substitution of Deuterium for Hydrogen isotopic species pairs
9.549
6 285
4.619
3652
3.039
for hydrogen, tritium for hydrogen, and tritium for deuterium are given in Tables IX-XI, respectively; the values were evaluated by using eq 2, where the fundamental frequencies which were not observed were calculated with use of the G and F matrix method.’ Finally, the calculated equilibrium constants at 300 K for the following isotopic exchange reactions were introduced as typical examples:
10.899
7.027
5.082
3.967
3.267
(i) H-D exchange reactions
11196
7.158
5.149
4004
3.289
11.325
7 213
5.175
4018
3.297
_____ _tcmp/K _ _
_ _ _ _ ~ 500
~ _ _ _ _300 _ _ _ _ 350 _ _ _ _ 400 _ _ _ _ _450
CHD,COCOO-/ CH, DCOCOOCH,DCOCOO-/ CH,COCOO‘ CD eocoo-/ CHD,COCOOCDT,COCOO-/ CHT,COCOO-
CH,COCOO-
isotopic species pairs CHT,COCOO^/ CH,TCOCOOCH,TCOCOO-/ CH,COCOOCD,TCOCOO-/ CHD,COCOOCT,COCOO CHT,COCOO-
- ~ _ _ _ _
CH,COCOO-
___
300
350
400
450
500
23.211
12.841
8.314
5.974
4.615
27673
14913
9456
6681
5 090
2CHzDCOCOO-
+ CD,COCOO- 2CH,DCOCOO- +
28 767
15 311
9631
6768
5 138
29252
15 480
9702
6803
5 156
K2
= (s/s’)~(CH~DCOCOO/CH~COCOO)/ (s/s’)f(CD3COCOO/CHDzCOCOO) = 0.973
(ii) H-T exchange reactions CH,COCOO-
+ CHT2COCOO- 22CH2TCOCOO-
K3 = (s/s’)~(CH~TCOCOO/CH~COCOO)/
(~/x’)~(CHT~COCOO/CH~TCOCOO) = 1 192 I
CH,COCOO-
K4 = (s/s’)~(CH~TCOCOO/CH,~~COCOO)/
t cnip/K I
_
_
_
_
_
_
_
~
_
300
350
400
450
500
2.539
2.122
1.861
1.684
1.558
2.430
2.042
1.800
1.635
I .5 19
2569
2 139
I871
1690
1562
2583
2 146
1875
1693
1564
-_________
+ CT,COCOO- & CH,TCOCOO- + CHTZCOCOO-
__--___-_____
I _ _ _ _ _
CH,TCOCOO-/ CH, 1)COCOOCDT2COC0O-/ CD, TCOCOO‘ CD,TCOCOO / C1~,CoCooCT,COCOO-/ CDT , C o C O o -
K
CHDZCOCOO-
TABLE XI: Calculated Reduced Partition Function Ratios of Pyruvate Ion Molecules with respect to Isotope Substitution of Tritium for Deuterium isotopic species pairs
.+
K1 = (s/s’)~(CH~DCOCOO/CH~COCOO) / (s/s’)~(CHDZCOCOO/CH~DCOCOO)= 1.141
TABLE X: Calculated Reduced Partition Function Ratios of Pyruvate Ion Molecules with respect to Isotope Substitution of Tritium for Hydrogen teiiip/K
+ CHD,COCOO-
velocity of light, k is Boltzmann’s constant, and T is the temperature. The calculated reduced partition function ratios of the pyruvate ion molecules with respect to isotopic substitutions of deuterium
_
_
_
_
(s/~’)~(CT~COCOO/CHT~COCOO) = 0.946
(iii) D-T exchange reactions CD,COCOO-
+ CDT,COCOO- 22CD,TCOCOO-
Ks = (s/s’)~(CD~TCOCOO/CD~COCOO)/
(s/s~~(CDT~COCOO/CD~TCOCOO) = 1.057 CD,COCOO-
+ CT,COCOO- &’CD,TCOCOO- + CDTZCOCOO-
K6
=
(s/s~f(CD2TC0C00/CD3C0c00)
/
(s/~’)~(CT~COCOO/CDT~COCOO) = 0.995
J . Phys. Chem. 1984,88, 1804-1807
1804
Acknowledgment. We heartily thank Dr. M. Akiyama of Rikkyo University for the use of his computer program for determining force constants. Thanks are also due to Professor E. Miki of Rikkyo University for the use of the Oxford Instrument
Model DN70 cryostat. Registry No. CH3COCOONa,113-24-6; CH,C013COONa,879767 1-4; CH3l3COCOONa,87976-70-3; 13CH,13COCOONa, 89196-78-l; CH,C180COONa,89196-79-2.
Electron Paramagnetic Resonance Study of Ph,P(O)CH,CI- Trapped in X-ray Irradiated (Chloromethy1)diphenylphosphine Oxide Crystals at 3 K and Ph,P(O)CH, at 77 Kt Per-Olof Samskog,i Su-hwa Lee, Carmen M. Arroyo, Lowell D. Kispert,* Department of Chemistry, The University of Alabama, Tuscaloosa, Alabama 35486
and Michel Geoffrey* Department of Chemical Physics, University of Geneva, 121 1, Geneva, 4, Switzerland (Received: July 6, 1983)
The radical Ph2P(0)CH2CI-is observed in 3 K X-ray irradiated crystals of (chloromethy1)diphenylphosphine oxide. The X-ray irradiation was carried out in the dark. The hyperfine coupling tensors were found to be A(35Cl)= (40.4, 17.9, 16.1 G), A,(") = (24.0, 17.2, 13.1 G), A2('H) = (25.0, 16.4, 9.0 G), and A(31P)= (42.1, 33.6, 23.8 G). The g-tensor components are equal to 2.0021, 2.0040, and 2.0046. The maximium 35Clcoupling and the minimum g value are !ocated within 5O of the parent C-C1 bond direction. Upon thermal annealing to 170 K, the anion decays and the Ph2P(0)CH, radical appears. UV photolysis of the anion at 3 K results in the disappearance of the anion and the formation of PhzP(0)CHz. Ph2P(0)CH2 decays above 230 K, giving rise to a room-temperature-stable species.
-
Experimental Section Crystalline plates of (chloromethy1)diphenylphosphineoxide were grown from an acetone solution by evaporation at room temperature. A recent crystal structure determinationZshows that they are monoclinic and are elongated along the b axis with c* located perpendicular to the plate. The crystal was mounted on a rotatable gear attached to the side of a T E l l l X-band cavity. The X-ray irradiation and EPR measurement were performed in the dark with a Janis Supervaritemp Dewar. Rotation of the magnet about the tail of the Dewar, plus rotation of the gear, permitted complete rotation over all Eulerian angles. The EPR spectra were recorded on a Varian E-12 spectrometer using 270-Hz field modulation with the applied magnetic field in each of the crystallographic planes ab, bc*, and c*a. The magnetic field was measured with a N M R gaussmeter and the microwave frequency was measured with a Hewlett-Packard frequency counter Model 5246 L. Bleaching experiments were carried out with a Kratos variable-wavelength (200-700 nm), 1-kW (Hg/Xe lamp) illumination system.
Introduction Organic molecules containing heteroatoms are very sensitive to ionizing radiation. It is however difficult, in general, to propose a reaction mechanism when more than one site for electron capture is possible because not enough is yet known about the identification and structure of the primary radicals and the associated thermal and photolytic stability. Some mechanistic studies of electroncapture processes and subsequent radiation aspects have been reported for some phosphorus compounds.' Unfortunately, the corresponding experiments were carried out at 77 K with frozen glasses and powders, so comparison of principal directions to crystallographically derived directions was not possible. In the present work we study the radiolytic behavior of a molecule in which three sites can give rise-a priori-to competitive addition: (I) the benzene ring, (2) the phosphine oxide moiety, and (3) the C-Cl bond. To carry out this study, we have irradiated (chloromethy1)diphenylphosphine oxide crystals at 3 K in the dark. Electron capture in the p--O group to form a phosphoranyl radical is not detected. In addition, no clear evidence exists for electron capture in the phenyl ring to form a r* anion although an unassigned EPR (line width equals 11 G) line is detected at g = 2. Rather, the primary radical formed by the radiation is shown to be the radical anion Ph2P(0)CH2Cl-. As the present study was performed with single crystals, direct information about the structure of this anion was obtained: (i) the directions of the hyperfine coupling tensors were compared with the bond directions of the parent molecule; (ii) the magnitude of these couplings was compared with calculated INDO spin densities. It is found that the unpaired electron is confined to an orbital aligned along the parent C-C1 bond. The INDO results indicate a lengthening of this bond during the anion formation. EPR spectra modifications induced by annealing or photolytic treatments allow us to identify two intermediates following the decay of the PhzP(0)CHzC1radical.
Results Radical A . The EPR spectrum of (chloromethy1)diphenylphosphine oxide (Ph2P(0)CH2C1) after irradiation in the dark at 3 K with H/1(0,0,1)is given in Figure 1. The same spectrum is also observed when the irradiation and the measurement are performed at 77 K, but with less resolution of the high- and low-field lines. The stick spectrum in Figure l a identifies one of the radicals (A) as consisting of three nonequivalent I = nuclei in the (0,0,1) direction with couplings of 35.4, 29.0, and 18.6 G, respectively, and one I = 3 / 2 nucleus with a coupling of 35.4 G. The largest coupling for one of the I = nuclei accidentally equals that for I = 3/2 and thus the spectrum simplifies in this direction. The assignment of the three I = couplings is made possible by examining the EPR spectrum of an X-ray
'This is U S . Department of Energy Document 010-4062-75. *Permanent address: The Studsvik Science Research Laboratory, S-61182 Nykoping, Sweden
(1) S.P. Mishra and M. C. R. Symons, Faraday Discuss. Chem. Sot., 63, 175 (1977). (2) G. Bernardinelli and R. Gerdil, Cryst. Struct. Commun. 8,921 (1979).
0022-3654/84/2088-1804$01.50/0
0 1984 American Chemical Society
