J . Phys. Chem. 1987, 91, 2366-2371
2366
Unimolecular Decomposition of Oxalic Add Terumitsu Kakumoto, KO Saito,* and Akira Imamura Department of Chemistry, Faculty of Science, Hiroshima University, Naka- ku, Hiroshima 730, Japan (Received: September 18, 1986; In Final Form: December 12, 1986)
Ab initio MO calculations have been carried out for the unimolecular decomposition of oxalic acid. We used the Hartree-Fock (HF) method with LCAO approximation mainly using the 3-21G basis set with standard parameters to optimize the geometries for the three conformers of oxalic acid and eight probable transition states. The energy gradient technique was employed. Normal modes and vibrational frequencies were calculated by using the 3-21G basis set. It was found that the lowest energy path was (COOH)2 C 0 2 CO + H,O (2), having a five-center transition state. From the results of ab initio calculations, the first-order rate constant for channel 2 was evaluated as kz = 1014.9exp(-29.8 kcal mol-'/RT) s-l, over the temperature range 300-1300 K, in terms of transition-state theory. The thermal decomposition of oxalic acid vapor diluted in Ar has been also briefly investigated behind reflected shock waves over the temperature range 850-1 300 K. The decomposition was monitored by IR emission and vacuum-UV absorption from products. The decomposition product analysis was also done by gas chromatography. Although the rate constant could not be evaluated because of the very low reactant concentration and the too fast decomposition, major products observed were C02, CO, and HzO, being consistent with the results of the ab initio calculations and the previous infrared multiphoton study by Yamamoto and Back.
-
+
Introduction
W03a0/
Few studies of the gas-phase reaction of oxalic acid have been reported probably because of its low vapor pressure. Lapidus et al.' studied the thermal decomposition of oxalic acid vapor over the temperature range 400-430 K. The products are equimolar quantities of carbon dioxide and formic acid, and the kinetics of the decomposition are first order with respect to oxalic acid. The observed Arrhenius parameters are E, = 30.0 f 1.3 kcal/mol, and log ( A / s - l ) = 11.9 f 0.7. Recently, the photolysis of oxalic acid vapor has been studied by Yamamoto and Back., They studied the photolysis at wavelenJths from 257 to 3 13 nm, corresponding to excitation of the A ('AU,?r* n+) first excited singlet state. The products were C 0 2 , CO, HzO, and HCOOH, all formed linearly with time and with product ratios independent of wavelength and added gases. It was concluded that two primary processes occur, yielding C02 HCOOH and CO, + CO HzO, with the yield of the former about 2.6 times that of the latter. photosensitized decomposition and the infrared The mercury (3P,) multiphoton decomposition of oxalic acid vapor were also examined and the same two processes were observed. It was suggested that the ultraviolet photolysis proceeded through the dihydroxycarbene radical, formed directly from the excited state, while the infrared multiphoton decomposition probably involved a simple decomposition of the vibrationally excited ground state. Recently ab initio molecular orbital methods have developed rapidly and have provided molecular geometries and the vibrational frequencies not only for stable molecules but for transition states. Potential barriers can be calculated with practical accuracy. This valuable information can shed light on reaction mechanisms. In particular, for complex bond-breaking reactions, information about the transition states is required to test the experimental results. In this work, we have tried to evaluate the geometry, the potential energy, and the vibrational frequencies of the probable transition states for the unimolecular decomposition of oxalic acid by ab initio MO calculations. We have al2o studied the pyrolysis of oxalic acid vapor diluted in Ar behind shock waves. The reaction mechanism for the unimolecular decomposition of oxalic acid are discussed in terms of the results of the a b initio calculations and of the shock tube experiments. +-
+
+
Reaction Mechanisms
The unimolecular decomposition of oxalic acid is considered to occur through reactions 1-5, where the heat of formation for the species were cited from ref 3. Channels 1, 2, and 3 are the (1) Lapidus, G.: Barton, D.; Yankwich, P. E. J . Phys. Chem. 1964, 68, 1863. (2) Yamamoto, S.; Back, R.A . J . Phys. Chem. 1985, 89, 622
kcal mol-' (COOH),
HCOOH + C02 C02 + CO + H20 -+ 2C02 + H2 2COOH --c :C(OH)Z + C02 HCOOH + C02 CO + H20 + CO1 C02 + H2 + C02 -+ COOH + H + CO1 --c
-*
-
+
+
-9.6 -3.3 -13.1 75 -9.6 -3.3 -13.1 83
(1) (2) (3) (4)
(5a) (5b) (5~) (5d)
four-, the five, and the six-center reaction, respectively, therefore, these have tight transition states. Channel 4, on the other hand, is simple bond fission having a loose transition state. Channels Sa-5d produce dihydroxycarbene and COz via a five-center transition state and then the dihydroxycarbene isomerizes to formic acid (5a) or decomposes (5b-d). For the simple fission reactions, that is, channels 4 and 5d, the threshold energies can be assumed to be nearly equal to the heat of reaction. On the other hand, the threshold energies for the complex bond-breaking reactions, channels 1-3 and 5a-c, cannot be presumed empirically, because these channels have high barriers between the reactant and the products. Lapidus et al.' proposed that the decomposition proceeds by hydrogen transfer through a five-membered cyclic transition state and dihydroxycarbene is followed by a rapid isomerization to formic acid, channel 5a, because of the low preexponential factor, 10'' s-'. On the other hand, Yamamoto and Back, suggested that in infrared multiphoton decomposition the energy probably required to form dihydroxycarbene makes this path unlikely, and a four-center transition state is more probable, channel 1. Formation of C 0 2 + C O + H 2 0occurs via a five-center transition state from cis-oxalic acid, channel 2. Although it is unambiguous that the decomposition occurs on So in these two experiments, these two studies suggested different mechanisms for oxalic acid decomposition. Yamamoto and BackZalso reported that ultraviolet photolysis may proceed through the initial fast formation of :C(OH), + COz from the excited state, and the dihydroxycarbene radical could then either isomerize to formic acid or decompose to carbon monoxide and water, channels 5a and 5b. Several channels are considerable for the unimolecular decomposition of oxalic acid, thus the calculations of the probable transition states are essential to the discussion of the reaction mechanism. Method of Calculation
To describe the reaction mechanisms occurring in the unimolecular decomposition of oxalic acid, we have identified 15 sta(3) Benson,
1976.
S.W. Thermochemical Kinetics, 2nd ed; Wiley: New York,
0022-3654/87/2091-2366$01.50/00 1987 American Chemical Society
Unimolecular Decomposition of Oxalic Acid
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 2367 TABLE II: Total Energies (in hartrees) and Relative Energies (in Parentheses in kcal/mol Relative to Conformer I) for the Three Conformers of Oxalic acid
method HF/3-21G
I
I1
111
Figure 1. Three conformers of oxalic acid: I, “hydrogen bonded” conformer (Czr);11, “free” trans conformer (C2& 111, cis conformer (C2&
MP2/3-2 1 Go HF/4-3 1G MP2/4-31Gb
TABLE I: Experimental and Optimized Geometries for the Three Conformers of Oxalic Acid” “hydrogen bonded” “free” trans cis (1) (11) (111) exptb 3-21G 4-31G 3-21G 4-31G 3-21G 4-31G r(C-C) 1.548 1.525 1.519 1.510 1.508 1.510 1.508 r(C=O) 1.208 1.199 1.200 1.194 1.198 1.196 1.198 r(C-0) 1.339 1.326 1.320 1.340 1.331 1.337 1.330 r(O-H) 1.056 0.971 0.957 0.968 0.955 0.969 0.956 LC-C=O 123.1 120.8 120.4 125.2 124.2 122.4 121.7 LC-C-0 111.9 113.5 114.9 109.7 111.2 112.7 113.8 LC-0-H 104.4 113.0 115.9 112.7 114.5 112.5 114.2
Geometrical Structures and Energetics of Oxalic Acid. Of the six possible monomeric conformations of oxalic acid, the symmetrical structures are of present interest. Three conformers of oxalic acid are shown in Figure 1. Conformer I, with two intramolecular hydrogen bonds, is believed to be most stable by electron diffraction6 and spectroscopic investigations (IR and Ramar~).~?’ Conformer I1 is the ”free” trans form and conformer I11 is the cis form. The optimized geometries for the “hydrogen-bonded” conformer (I) are shown in Table I along with the available experimental values? It is known that the calculated bond length at the Hartree-Fock method with the D Z (double 0 basis set is shorter than experimental value by sometimes about 0.02 A.8 The calculated bond distances are shorter than the experimental values by 0.008-0.099 A, being consistent with this tendency. The optimized geometries for the ”free” trans (11) and (4) Binkley, J. S.; Whiteside, R. A.; Krishnam, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topil, S.; Kahn, L. R.; Pople, J. A. QCPE 1980, 102, 939. Program Library of Institute for Molecular Science (IMS), No. 482. ( 5 ) Dupuis, M.; Sprangler, D.; Wedolski, J. J. QGOI GAMESS, Program Library of IMS, No. 481. (6) Nihlovska, Z.; Nihlovskv, B.; Strand, T. G . Acta Chem. Scand. 1970, 24, 2617. (7) Redington, R. L.; Redington, T. E. J . Mol. Struct. 1978, 48, 165. (8) Iwata, S. In Quantum Chemistry Literature Data Base Ohno, K., Morokuma, K., Eds.; Elsevier: Amsterdam, 1982.
cis
(11) -374.2498 (0.6) -374.9076 (0.9) -375.7927 (-0.4) -376.4669 (-0.8)
(111) -374.2487 (1.3) -374.9068 (1.3) -375.7921 (-0.1) -316.4669 (-0.7)
“At HF/3-21G optimized geometries. bAt HF/4-31G optimized
TABLE 111: Observed and the 3-21G SCF Calculated Vibrational Frequencies (in cm-’) for the “Hydrogen-Bonded”Conformer of Oxalic Acid ~~
SYm species a,
“Bond distances are in A and angles in degrees. bElectron diffrac-
Results and Discussion
“free” trans
(1) -374.2507 (0.0) -374.9090 (0.0) -375.7920 (0.0) -376.4657 (0.0)
geometries.
tion; ref 6.
tionary points on a relevant energy surface: three oxalic acid conformers, five transition states (two types of T S l , TS2, TS3, and TSS), three dihydroxycarbene conformers, carbon dioxide, and three transition states (TSSa, TSSb, and TSSc). The loose transition states, TS4 and TSSd, seem not to be essential, because these channels are appreciably endothermic, 75 and 83 kcal/mol, respectively. We used the Hartree-Fock (HF) method with LCAO approximation mainly using the 3-21G basis set with the standard parameters to calculate the geometrical and the vibrational structures for oxalic acid and probable transition states. The energy gradient technique was employed for the geometry optimizations. All structures were assumed to be planar. Correlation effects are known to lower significantly the barrier heights for many unimolecular reactions. Therefore, we applied Mdler-Plesset second-order perturbation (MP2) at the HF/3-21G optimized geometries. The program used for geometry optimiThe vibrational analyses were done zations was GAUSSIAN with the GAMESS program5 to perform the numerical differentiation of the energy gradient.
“hydrogen bonded”
a,
1 2 3 4 5 6 7
approx type of mode OH stretch C=O stretch COH ip bend C-O stretch CC stretch OCO rock OCO scis
1800 1423 1195 815 (538)b 405
COH op bend OCO wag
666 460
W,lcd/
uOwa
w,,~
?
3827 2006 1474 1310 846 607 443
8 9 10
torsion
b,
11 12
OCO wag COH op bend
(590)b (512)b
b,
13 14 15 16 17 18
OH stretch
3484 1826 1330 1278 660 264
C=O stretch COHipbend C-O stretch OCO scis OCO rock
c
667 524 160
uOM
1.11 1.04 1.10 .04
.09
.oo .14
904 660 3828 2016 1359 1294 722 278
.10 .10 1.02 1.01 1.08 1.05
“Observedvalues are cited from ref 7 and 10. bTentativefrequency. cNot observed. the cis conformer (111) are also listed in Table I. The calculated geometries for the three conformers were found to be nearly independent of the choice of the basis set. In Table I1 total energies (in hartrees) and relative energies (in parentheses in kcal/mol relative to the conformer I) are listed for the three conformers of oxalic acid. Conformer I, with hyOn drogen bonds, is believed to be most stable e~perimentally.~,~ the other hand, Aj6 et aL9 reported that the “free” trans conformer I1 is most stable by the 6-31G S C F calculations. According to their results, the internal rotational barrier was found to be 1.2 kcal/mol and the energy difference between cis and trans form was 0.5 kcal/mol. The “hydrogen-bonded” conformer is more unstable than “free” trans conformer by 2.1 kcal/mol. Since they did not perform the geometry optimizations, such a m a l l energy difference cannot be discussed at the SCF level calculations. In these calculations, the relative stability of the three conformers is still ambiguous. However, an energy difference of a few kcal/mol is not necessary to consider for the discussion of the decomposition mechanism. Vibrational Analysis of the Three Conformers of Oxalic Acid. Unfortunately a complete assignment of vibrational frequencies for oxalic acid has not been available experimentally and there remains several tentative frequencies. Table I11 shows the 3-21G S C F calculated normal frequencies (w’s) for the “hydrogenbonded” conformer I together with the fundamental frequencies (Y’s) observed in the gaseous ~ t a t e . ~ . In ’ ~this table the values (9) Aj6, D.; Condorelli, G . ;Fragali, I.; Granozzi, G. J . Mol. Struct. 1977, 37, 160. (10) Stace, B. C.; Oralratmanee, C. J . Mol. Struct. 1973, 18, 339.
Kakumoto et al.
2368 The Journal of Physical Chemistry, Vol. 91, No. 9, 1987
i.212
112.1
TS 2
TS3
Figure 2. HF/3-21G optimized geometries for TSl, TS2, and TS3. The values in parentheses are the HF/4-31G results. Bond distances are in 8, and angles in degrees. All structures are planar.
of wcald/v,,~ are also shown. The harmonic frequencies calculated are systematically overestimated by 0-1 4% relative to the experimental anharmonic frequencies, being consistent with the tendency of the calculations at this level. That is, the harmonic frequencies calculated by the H F method with the DZ basis set are known to overestimate by about 10% relative to the experimental anharmonic frequencies, due to a combination of electron correlation and vibrational anharmonicity effects8 Table IV shows the 3-21G S C F calculated normal frequencies for the “free” trans and cis conformer. Compared with the calculated results for the three conformers, the OH stretching mode for the “hydrogenbonded” conformer is smaller than that for the “free” conformers by 15-25 cm-l, being consistent with the fact that hydrogen bonds have usually smaller shifts in the OH stretching frequency. Because the energy differences between the three conformers are small, it may be difficult to assign the vibrational frequencies of oxalic acid vapor experimentally. So the ab initio calculation is a powerful tool for the assignment of the vibrational frequencies. Geometrical Structures and Energetics of the Transition States. Figure 2 shows the HF/3-21G optimized geometries of transition state (TS) for channels 1-3. Two types of the four-center transition state are probable for channel 1, that is, TSI(A) and TS1 (B), producing trans- and cis-formic acid, respectively. In TS2 corresponding to channel 2 the 4-31G optimized parameters are also shown in parentheses. The largest difference between the 3-21G and the 4-31G optimized geometry is the C-C distance. Although this difference of 0.169 8, is very large in the sense of quantitative predictions, the qualitative similarity is, nevertheless, evident. In the process of oxalic acid decomposing to CO, + CO H,O, the 0-H bond length becomes longer than that of the reactant by about 50%, and somewhat smaller bond distance changes of ca. 10% and ca. 20% are found for the C-C and the C-0 distances, respectively. The H - - 0 bond which is newly formed is longer than that of the water produced by ca. 8%. TS3 corresponding to channel 3 has C,, symmetry. As the reaction proceeds, the C-C bond and the two 0-H bonds break and the H-H bond is formed. Figure 3 shows the 3-21G SCF optimized geometries for channels 5a-c. These channels produce dihydroxycarbene and carbon dioxide via a five-center transition state, TS5, and then the dihydroxycarbene isomerizes to HCOOH via a three-center transition state, TSSa, or decomposes to CO + H 2 0 via a four-center transition state, TSSb, and or to C 0 2 + H, via a five-center transition state, TS5c. The ground state of the dihydroxycarbene is a singlet as reported by Feller et al.”
+
(1 1) Feller, D.; Borden, W. T.; Davidson, E. R. J . Chem. Phys. 1979. 71, 4987.
TS5b TS5c TS 5a Figure 3. HF/3-21G optimized geometries for channel 5 . The values in parentheses are the HF/4-31G results. Bond distances are in 8, and angles in degrees. All structures are planar.
-
Figure 4. Reaction coordinate of TS2 (w = 6831’cm-I) for channel 2, (COOH)* C02 CO HzO. Note that this mode clearly connects the reactant with the three product molecules.
+
+
80
-2
.
60
?
1 I
@ 40 ?
-5
20
m
0
-20
Figure 5. Relative energy diagram for the unimolecular decomposition of oxalic acid by the MP2/3-21G calculations. Relative energies (in kcal/mol) indicated are corrected for zero-point energies. Values in parentheses are the results of the MP2/4-31G calculations.
Of the three probable conformers, the most stable ‘A dihydroxycarbene has the conformation 0, = O’, 0, = 180’ (for a definition of OCOH dihedral angles) as shown in Figure 5 , being consistent with the results by Feller et al.” Table V shows the total energies (in hartrees) and relative energies compared to the “hydrogen-bonded” conformer of oxalic acid (in kcal/mol) for channels 1-3 and 5a-c. Correlation effects are known to lower significantly the barrier heights for many unimolecular reactions. Therefore, we applied Mdler-Plesset second-order perturbation (MP2) at the HF/3-21G and the HF/4-3 1G optimized geometries. As expected, the potential barriers decreased by 8-44%. The differences between the values of the MP2/3-21G and of the MP2/4-3lG calculations are within 7 kcal/mol. The potential barriers by the M P calculations can be 5-10 kcal/mol in error on the basis of the systematic
Unimolecular Decomposition of Oxalic Acid
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 2369
TABLE I V 3-216 SCF Calculated Vibrational Frequencies (in cm-I) for the “Free” Trans and the Cis Conformer of Oxalic Acid
1 2 3 4 5 6 7
“free” trans (11) approx type of mode O H stretch C=O stretch C O H ip bend C-0 stretch CC stretch OCO rock OCO scis
a”
8 9 10
COH op bend OCO wag torsion
683 468 87
b*
11 12
OCO wag COH op bend
927 612
b”
13 14 15 16 I7 18
O H stretch C = O stretch COH ip bend C-0 stretch OCO scis OCO rock
3852 1986 1462 1193 68 1 284
SY?
species aB
1 2 3 4 5 6 7
cis (111) approx type of mode O H stretch C=O stretch COH ip bend C - 0 stretch CC stretch OCO scis OCO rock
a2
8 9 10
OCO wag COH op bend torsion
933 613 77
bl
11 12 13 14 15 16
O H stretch C=O stretch COH ip bend C-O stretch OCO scis OCO rock
3841 1968 1441 1223 690 542
b2
17 18
COH op bend OCO wag
697 469
SY?
%Id
3852 2007 1522 1263 829 568 458
species a1
%Id
3843 1995 1564 1246 831 466 293
TABLE V Total Energies (in hartrees) and Relative Energies (in Parentheses in kcal/mol Relative to Conformer I) for Channels 1-3 and 5a-c method TSl(AI TSl(B) TS2 TS3 TS5 :C(OHL+CO, TS5a+CO, TS5b+CO, TS5c+CO, -374.2025 -374.1390 HF/3-21G -374.0947 -374.0766 -374.1845 -373.9999 -374.1941 -374.1010 -374.0851 (30.3) (97.9) (109.2) (41.6) (157.4) (35.5) (94.0) (70.1) (103.9) -374.8588 MP2/3-21G4 -374.7813 -374.7686 -374.8639 -374.7483 -374.8572 -374.1948 -374.8 177 -374.8166 (31.5) (58.0) (80.1) (88.1) (28.3) (100.9) (32.5) (57.3) (71.7) -375.7383 HF/4-31G -375.7169 -375.6388 -375.6117 -375.6675 (33.7) (113.2) (78.1) (47.1) (96.1) -376.41 15 MP2/4-31Gb -376.4135 -376.3491 -376.3618 -376.3655 (34.0) (65.2) (62.9) (73.2) (32.8) ‘At HF/3-21G optimized geometries. b A t HF/4-31G optimized geometries.
Mailer-Plesset s t u d i e ~ . ’ ~ *This ’ ~ level of calculations may be insufficient in the sense of quantitative predictions. However, so far regarding the relative tendency of the potential barriers, the calculation level used in this work seems to be enough. Figure 5 shows a schematic potential diagram for the relative energies by the MP2/3-21G calculations with zero-point energy corrections. In this figure the MP2/4-31G results are also shown in parentheses. For the results of the MP2/3-21G calculations, the lowest energy path for the unimolecular decomposition of oxalic acid is channel 2, having a potential energy of 23.7 kcal/mol. The potential barriers of channels 1 and 3 are higher than that of channel 2 by more than -50 kcal/mol. The threshold energies of channels 4 and 5d, which are simple bond fissions, can be assumed to be nearly equal to the heat of reaction, that is, 75 and 83 kcal/mol, respectively. These values are significantly high compared to the potential barrier of channel 2. On the other hand, TS5 has a low potential barrier of 31.2 kcal/mol. The energy difference between TS2 and T S 5 4 . 2 kcal/mol, is relatively small, and so it is impossible to decide which is the major process, channel 2 or 5 , only on the basis of energetics. The entropy of activation terms must be taken into consideration as discussed later. The second potential barriers of channels 5a, 5b, and 5c are 39.6,25.0, and 24.0 kcal/mol, respectively. The last two values are lower than the value of the first potential barrier; therefore, the dihydroxycarbene produced via TS5 will decomposes rapidly to CO HzOor COz H2.It can be concluded that for thermal systems the unimolecular decomposition of oxalic acid seems to occur via channels 2, 5b, and or 5c. Vibrational Analysis of the Transition State. The vibrational frequencies from the HF/3-21G calculations for the eight transition states are presented in Table VI and VII. In Table VI1 the vibrational frequencies for dihydroxycarbene are also listed.
+
+
(12) Harding, L. B.; Schlegel, H. B.; Krishnan, R.; Pople, J. J. Phys. Chem. 1980,84, 3394. (13) Sosa, C.; Schlegel, H. B. In?. J . Quantum Chem. 1986, 29, 1001.
TABLE VI: 3-21G SCF Calculated Vibrational Frequencies (in cm-’) for the Transition States TSl-TS3 and TS5 TSl(A) TSl(B) Ts2 TS3 TS5 a’ 3753 a’ 3927 a’ 3927 a , 2140 a’ 3745 2521 2437 2685 1898 3146 2234 1945 2126 1341 2037 1856 1829 2118 850 1898 1372 1308 1412 555 1631 1208 1229 1231 290 1543 1070 1131 1029 39341’ 1256 897 719 799 a2 1054 969 678 640 711 721 796 383 419 552 124 675 254 233 477 bl 2028 519 164 52 23 1 1436 427 1706i 22521’ 6833 1275 21523 a” 1039 a” 1023 a” 1070 1216 a” 1190 727 554 79 1 665 833 575 502 419 403 765 345 347 182 b2 576 42 1 46i 17 72 505 159 TABLE VII: 3-21G SCF Vibrational Frequencies (in cm-I) for Dihvdroxvcarbene and TSSa-TS5c :C(OH)2 TS5a TS5b TS5c a’ 3960 a’ 3672 a’ 3901 a, 1963 3725 2693 2348 1458 1521 1590 1665 1037 1388 1395 1156 23321’ 1202 1228 957 a2 1352 1155 619 680 bl 1819 632 24491’ 18931 1624 a’’ 842 a” 782 a” 1241 898 709 404 238 b2 868
A true transition state will have a single imaginary vibratiQna1 frequency at the saddle point. The transition states except for TSl(A) have only a single imaginary vibrational frequency as
2370 The Journal of Physical Chemistry, Vol. 91, No. 9, 1987
Kakumoto et al.
TABLE VIII: Thermochemical Parameters Evaluated for Channel 2 at 400 K
thermochemical parameters (P = 1 atm, T = 400 K) internal energy/au enthalpy/au
reactant ("hydrogen bonded") LIO = -374.8486
IT= -374.8098
Ho = -374.8413
H' = -374.8085
total energy/au' translational energy/kcal mol-' rotational energy/kcal mol-' vibrational energy/kcal mol-'b
-374.9090 Etrans = 1.2 E,,, = 1.2 Evib = 35.5
-314.8639 Ettrans= 1.2 E*,,, = 1.2 E*"ib= 3 1.6
Standard entropy/cal mol-' K-' translational entropy/cal mol-' K-' rotational entropy/cal mol-' K-' vibrational entropy/cal mol-' K-'
So = 11.9 SotranS = 40.9 So,,, = 25.7 Sovlb = 11.3
S' = 83.9 Sttrans = 40.9 S',,, = 27.4 S*"ib = 15.7
TS2
"Total energies are the results of MP2/3-21G calculations. Vibrational frequencies used are the results of HF/3-21G calculations. Molecular structures used are the results of HFI3-2lG calculations. shown in these tables. The imaginary vibration for TS2 is sketched in Figure 4 as an example. This mode clearly indicates the connection between oxalic acid and the three molecular products C 0 2 C O H20. It was confirmed that the imaginary vibrations for the other transition states indicate the courses of the reaction. On the other hand, exceptionally there are two imaginary frequencies for TSl(A) (1706i and 46i cm-I). The larger imaginary vibration indicates the course of the decomposition to trans-HCOOH and C 0 2 , while the smaller one is an out-of plane vibration. That is, it appears that TSl(A) occurs for a nonplanar geometry displaced from the geometry in Figure 2 in the direction of the 46i cm-I normal mode. Due to the extreme flatness of the potential hypersurface in the direction of the 46i cm-I displacement, it seems likely that the true (nonplanar) saddle point energy will only be slightly less (perhaps 1 kcal/mol) than that of the planar stationary point. Application of Transition-State Theory. A theoretical prediction of the rate constant for the unimolecular reaction may be given by the transition-state theory:I4
+
+
-
k = (kT/h)e-AG*/RT = (kT/h)&*/Re-Af"/RT
s-1
where AG* is the free energy of activation, AS*,the entropy of activation, and AH*, the heat of activation. These thermochemical parameters can be evaluated in terms of the structures, the total energies, and the vibrational frequencies for the reactant and the transition state. With the information from the a b initio M O calculations, it is possible to predict the values of A S * and AH* for the reaction via a tight transition state. Table VI11 shows the thermochemical parameters for channel 2 evaluated on the basis of the results of the present a b initio calculations. In this evaluations, we used the results of the HF/3-21G calculation for the structures and the vibrational frequencies, and the results of the MP2/3-21G calculation for the total energies. As a result, AH* is 24.3 kcal/mol and AS*is 6.1 cal/(mol K) at 400 K for channel 2, and then the preexponential factor and the activation energy can be estimated as log (Ais-') = 14.7, E, = 25.1 kcal/mol. In a similar manner, the rate constants for the other channels can be estimated and the results are summarized in Table IX along with the rate constants at 400 and 1000 K. The values in this table include the tunneling effect in terms of the Wigner model,I4 1 - (hv,/kn2/24, where v, is the frequency along with the reaction coordinate. The tunneling effect is about 25% at 400 K and 4% a t 1000 K for channel 2. Thus, the tunneling effect is not important at the temperatures considered here. The preexponential factors for the simple fission, channels 4 and 5d, can be evaluated by the empirical methodI5 with relative accuracy. The heat of activation, AH*,is assumed to be equal to the heat of formation. The evaluated rate constants for channels 4 and 5d are also listed in Table IX. Of the two Arrhenius parameters, the absolute values of the activation energy, E,, have some uncertainty; however, the preexponential factors can be evaluated with relatively high ac(14) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rare Processes; McGraw-Hill: New York, 1941. (15) Reference 3 , Chapter 111.
TABLE IX: Evaluated Rate Constants for the Unimolecular Decomposition of Oxalic Acid k/s& log (Ais-') E./kcal mol-' 400 K 1000 K kl 15.4 76.8 3.3 x 10-27 4.1 x 10-2 k2 14.9 25.2 1.4 X IO' 2.5 X lo9 k3 13.9 92.2 3.7 x 10-37 6.0 x 10-7 kqa 16.0 76 3.0 X 2.5 X lo-' 30.4 kS 13.2 3.9 x 10-4 3.6 x 106 kSa kSb
ksc kSda
13.6 13.8 12.8 13.5
36.2 21.8 20.1 56
6.0 x 7.3 x 6.6 X 8.0 X
10-7 101
IO' lo-'*
4.5 x 105 1 . 1 x 109 2.5 X lo8 1.8 X 10'
'Values evaluated by the empirical method.I3 curacy even at S C F level The preexponential factor of k5 is smaller than that of k2 by a factor of 1/50. The value of k2 is significantly larger than that of k5, even if the activation energy of k5 is similar to that of k2. The values of k5b and k5, are larger than that of k5 by 2-5 orders, and so the dihydroxycarbene decomposes rapidly to C O + H 2 0 or C 0 2 + H2. The rate-determining step for channels 5b and 5c is the process to produce dihydroxycarbene and carbon dioxide. kl, k3, and k4 are negligibly small compared with k2. We have tried to simulate concentration profiles for all species involving opposite reactions. Together with these results it can be concluded that the unimolecular decomposition of oxalic acid is mostly governed by channel 2 over the temperature range 300-1300 K. The rate constant for the decomposition was evaluated as k2 = 1014.9exp(-29.8 kcal mol-l/RT) s-I using the more reliable MP2/4-31G results for the estimation of AH*. The thermal decomposition of oxalic acid, at temperatures up to 430 K, yielded only formic acid and C02.' Lapidus et al.' suggested that this reaction proceeded by hydrogen transfer through a five-membered cyclic transition state, TS5. On the other hand, in the multiphoton infrared decomposition, C O and H 2 0 are more important products than HCOOH.2 Yamamoto and Back2 pointed out that the energy required to form dihydroxycarbene makes channel 5a unlikely, and a four-center transition state, channel 1, is more probable. Although it is clear that the decomposition occurs on So in these two experiments, these two studies suggested different mechanisms. From the present ab initio calculations, channel 1 has a high potential barrier of 74 kcal/mol, suggesting that this channel is unimportant. TS5 has the relatively low potential barrier of 31 kcal/mol and the barriers of TS5b and TS5c are lower than that of TS5a. Thus, the dihydroxycarbene (16) Saito, K.; Kakumoto, T.; Murakami, I . J . Phys. Chem. 1984, 88, 1182. (17) Kakumoto, T.; Saito, K.; Imamura, A. J . Phys. Chem. 1985,89,2286. (18) Saito, K.; Ito, R.; Kakumoto, T.; Imamura, A. J . Phys. Chem. 1986, 90, 1422.
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 2371
Unimolecular Decomposition of Oxalic Acid
the reciprocal of the time constant of the detecting system. A similar profile was also obtained at 4.6 pm. Since at this wavelength the contribution from the C 0 2 band is more significant than from the C O fundamental band, the production of CO was confirmed by observing the vacuum-UV absorption at 155 nm (% A). The emission due to the C H stretching at 3.4 pm could not be detected suggesting that HCOOH was not the major product. The H-atom absorption at 122 nm and the 0-atom absorption at 131 nm could not be detected; therefore, it was confirmed that the pyrolysis of oxalic acid does not involve any radical reactions under the present conditions. In addition, the decomposition product analysis by the gas chromatography showed that the major products were C 0 2 , CO, and H 2 0 . Thus, from the shock tube experiment the main process for the pyrolysis of C 0 2+ oxalic acid vapor was found to proceed via (COOH), CO H 2 0 , being consistent with the results of the ab initio calculations and of the infrared multiphoton study by Yamamoto and Back.2
t co2
-
3 y1
*w
-
+
Figure 6. Typical emission profiles at 4.2 pm for C 0 2(upper trace) and 2.7 pm for H20(lower trace). Upper trace: T = 941 K, [Ar] = 1.08 X lW5mol/cm'; lower trace: T = 1254 K, [Ar] = 1.33 X mol/cm3. IS denotes the incident front.
+
produced via TS5 mostly decomposes to C O H 2 0 or C 0 2 + H2. On the other hand, the production of formic acid cannot be accounted for reasonably by the results of the ab initio calculations. The predictions on the basis of this calculated results is that the formation of C 0 2 C O + H,O is more important than that of HCOOH CO, which was found in the multiphoton infrared The estimated activation energy of 29.8 kcal/mol is in good agreement with the results of Lapidus et al,' E, = 30.0 f 1.3 kcal/mol, although their mechanism is not consistent with that proposed here. Shock Tube Experiment. From the present ab initio calculations, we found that the unimolecular decomposition of oxalic acid is mostly governed by channel 2 and yields C 0 2 C O H20. Then, we have tried to check this prediction experimentally. The experiments have been performed in a shock tube made of stainless steel, which was used in previous s t u d i e ~ . ' ~The ~ ' ~pyrolysis of oxalic acid vapor diluted in Ar was performed behind reflected shock waves. The decomposition of oxalic acid was monitored by observing the time-resolved IR emission (2.68 f 0.10 pm for H20, 3.37 f 0.13 pm for HCOOH, 4.23 f 0.09 pm for C 0 2 , and 4.63 f 0.05 pm for CO) and the vacuum-UV absorption (122 nm for the H atom, 131 nm for the 0 atom, and 155 nm for CO) with a half-band path of 2.0 nm. A detailed explanation of the time-resolved system has been given in previous papers."*'* The decomposition product analysis was also done by fractionation at -196 O C and measured by gas chromatography. Mixtures used for the experiment were prepared by heating commercial anhydrous oxalic acid (ca. 80 "C) and diluting the saturated vapor of oxalic acid with high-purity argon gas a t about 60 OC. The experimental conditions behind the reflected shock waves were in the temperature range of 850-1300 K around atmospheric pressure. The concentration of oxalic acid was estimated to be less than 50 ppm. Figure 6 shows typical emission profiles a t 4.2 pm for CO, (upper trace) and 2.7 pm for H 2 0 (lower trace). Although the signal intensities are significantly low because of the low reactant concentration, the emission signals increase rapidly at reflected shock fronts and show steady levels. It was ascertained that C 0 2 and H 2 0 were produced rapidly under the present conditions. Because the S/N ratio is poor and the increase rate of the emission intensity is too fast, the rate constants for the CO, and the H 2 0 production could not be evaluated. The first-order rate constants are expected to be larger than 3 X lo4 at 850 K from the results of the a b initio calculations. This value was about the same as
+
+
+
+
Conclusions The mechanism for the unimolecular decomposition of oxalic acid was studied with the use of the ab initio M O method. The 15 stationary points on the relevant energy surface were located by the energy gradient technique. We discussed the decomposition mechanism considering nine elementary processes. It was found that the lowest energy path was (COOH), CO, + C O + H2O (2), having a five-center transition state. From the results of the ab initio calculations, the first-order rate constant for channel 2 was evaluated as k2 = 10'4,9exp(-29.8 kcal mol-'/RT) s-l, over the temperature range 300-1300 K, in terms of the transition-state theory. The evaluated rate constants for the other channels were found to be negligibly small over this temperature range. The results of the ab initio calculations were checked by experimental investigations. The thermal decomposition of oxalic acid vapor diluted in Ar was investigated behind reflected shock waves over the temperature range 850-1300 K. The decompositions was monitored by I R emission and vacuum-UV absorption from probable products. The decomposition product analysis was also done by gas chromatography. Because the emission intensity was too low and the decomposition rate was too fast, the rate constants for the decomposition could not be evaluated. However, it was clear that the major products were CO,, CO, and H 2 0 , being consistent with the results of the ab initio calculations and of the infrared multiphoton study by Yamamoto and Back.2 The results presented in this paper are based on the geometry optimization and the vibrational analysis by the Hartree-Fock method with the 3-21G basis set and the energy calculations by the M~ller-Plesset second-order perturbation at the HF/3-21G optimized geometries. In order to obtain a more quantitative understanding of the mechanism for the unimolecular decomposition of oxalic acid, more systematic calculations including the correlation effect with an improved basis set may be required. Despite the approximate method of the calculations employed here, some important features of a reaction involving many elementary processes are clarified in the present calculations. Furthermore, the experimental investigation of the gas-phase reaction of oxalic acid is difficult because of its low vapor pressure and ease of thermal decomposition. A more elaborate experiment may be necessary to determine the rate constant of the decomposition. In the case where several channels are considerable like the unimolecular decomposition of oxalic acid as presented in this paper, the ab initio calculations of the probable transition states are essential to discuss the reaction mechanism.
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Acknowledgment. We thank Mr. K. Komoguchi, Mr. T. Ushirogouchi, and Miss M. Ishikawa for their experimental assistance and Dr. K. Kanda for useful suggestions. Numerical calculations were carried out at the Computer Center of the Institute for Molecular Science and the Information Processing Center of Hiroshima University. Registry No. Oxalic acid, 144-62-7; dihydroxycarbene, 71946-83-3.
