J . Phys. Chem. 1986, 90, 2974-2987
2974
barrier in the asymmetric system is a reasonable approach to the problem. In summary, the Marcus equation reproduces quantum mechanical data for H-bonded systems quite well, supplementing ~ rates.lg If A represents an alkylated its success with S Nreaction derivative of B, it is possible to predict the dissociation energy of a complex of the type (A-H--B)+ to either product pair (AH' + B) or (A BH') with knowledge of only the H-bond energy of the unalkylated complex (B-H-B)+ and the difference in proton affinity between B and A. For a given fixed H-bond length R, the proton-transfer barrier in either direction may be expressed in terms of the barrier in the unalkylated (B-H-B)+ system at the same R and the difference in energy of the (AH- -B)+ and (A- -HB)+ wells in the potential.
(b) the proton-transfer barriers for fixed H-bond lengths within the complexes. Although the shape of the bimolecular potential may change from single- to double-well character as the degree of alkylation is varied, this problem may be overcome by extrapolation of the series to a projected single-well depth. Increasing the proton affinity of the A subunit of (A-H--B)+ by alkylation raises the barrier to unimolecular (fixed R ) proton transfer from A to B while lowering the barrier in the reverse direction by a smaller amount. These changes in the barriers are predicted extremely well by Marcus theory for the full range of H-bond lengths investigated. Evaluation of the Br~rnsteda as the derivative of the Marcus barrier height with respect to the difference in energy of the two wells seems to furnish a reasonable estimate of the progress of the reaction in the transition state. These values are about 20-30% larger than the parameter measuring the position of the transition state along the protontransfer coordinate. The agreement between quantum mechanical and Marcus barrier heights is also quite good in the mixed system involving a proton transfer between oxygen and nitrogen. This observation indicates that use of the arithmetical average of the barrier heights of the two corresponding symmetric systems as the "intrinsic"
+
Acknowledgment. Computer time was provided by Southern Illinois University Computing Affairs. This research was supported financially by the National Institutes of Health (GM29391 and AM01059) and by the Research Corporation. (19) Wolfe, S.;Mitchell, D. J.; Schlegel, H. B J . Am. Chem. SOC.1981, 103, 7692, 7694.
Theoretical Studles on the Reaction of Atomic Oxygen (O('P)) with Acetylene. 2 Lawrence B. Harding* and Albert F. Wagner Theoretical Chemistry Group, Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 {Received: November 4, 1985)
Ab initio electronic structure calculations have been used to characterize the equilibrium and saddle points for the addition of OOP) to HCCH on the two lowest triplet surfaces. Structures, frequencies, and energetics are presented and, when possible, directly compared to those from experiment. The saddle point for abstraction of H from HCCH by O(3P) has also been characterized for the two lowest triplet surfaces by analogy with recent ab initio calculations on similar abstraction reactions. Systematic errors in the calculated energetics are corrected by semiempirical arguments. Comparisons of the energetics are also made to semiempirical BAC-MP4 calculations. The final characterizations of the stationary points on the addition and abstraction surfaces are then used in RRKM calculations of the rate constants and product branching ratios. These calculations are compared to experiment. The comparisons show (1) abstraction is not an important process, (2) theory and experiment are in good agreement for the overall rate of reaction at temperatures below 1000 K but predict substantially lower rates than observed in high-temperature shock tube experiments, (3) the calculated branching ratio, production of H + HCCO over the total rate of reaction, is not small (certainly over 25% and most likely over 50%) with a relatively weak temperature dependence and no pressure dependence, and (4) the ground-state triplet surface (3A') dominates both the overall rate constant and the branching ratio with the excited triplet surface (3A') introducing only minor perturbations.
I. Introduction Acetylene is an important intermediate in many fuel rich hydrocarbon flames.'** A major pathway for its destruction is through the reaction with atomic oxygen, O(3P). There are three possible routes this reaction may take: o ( 3 ~+ ) HCCH
5 OHCCH* 7H + OCCH
o(3~) + HCCH
IC
OH
+ CCH
Reaction 1 procesds through the metastable complex OHCCH* which may decay by 0 atom dissociation (-l*), H atom dissociation (la), or H atom migration followed by C-C bond fission (1b). Measurements of O(3P) HCCH are commonly inter-
+
(1) Warnatz, 3.; Bockhorn, H.; Moser, A.; Wenz, H. W. Symp. (Int.) Combust., [Proc.],19rh, 1982 1983, 197. (2) Hucknall, D. J. Chemistry of Hydrocarbon Combustion;Chapman and Hall: New York, 1985; p 199 ff.
0022-3654/86/2090-2974$01.50/0
preted3 in terms of this reaction. Reaction IC, which is a direct abstraction reaction, has been suggested?5 but there has not been any direct experimental confirmation. This reaction must be present, but its rate will become important only a t high temperature because of the substantial endothermicity of the reaction. There have been a considerable number of measurement^^^^-^^ of the overall rate of reaction 1. Most have been at temperatures below 1300 K,3*6*8-10 but two recent shock tube are a t temperatures of 1500-2550 K. While the measured rate constants in either temperature regime are in reasonable accord (3) Herron, J. T.; Huie, R. E. J. Phys. Chem. Ref. Data 1973, 2, 467. (4) Bradley, J. N.; Kistiakowski, G. B. J. Chem. Phys. 1961, 35, 264. (5) Glass, G. P.; Kistiakowski, G. B.; Michael, J. V.; Niki, H. Symp. (Int.) Combust., [Proc.],loth, 1964 1965, 513. (6) (a) Jones, I. T.N.; Bayes, K. D. Proc. R. SOC.London, A 1973,335, 547. (b) Jones, I. T. N.; Bayes, K. D. J . Am. Chem. SOC.1972, 94, 6869. (7) Vandooren, J.; Van Tiggelen, P. J. Symp. (Inr.) Cornbust., [Proc.], 16th, 1976 1977, 1133. (8) Westenberg, A. A,; deHaas, N. J. Chem. Phys. 1969.63, 193; 1977, 66, 4900. (9) (a) Homann, K. H.; Wellmann, Ch. Ber. Bunsenges. Phys. Chem. 1981, 85, 569. (b) Homann, K. H.; Wellmann, Ch. Ber. Bunsenges. Phys. Chem. 1983.87, 609.
0 1986 American Chemical Society
Reaction of Atomic Oxygen with Acetylene with one another (factor of 2 or better), the rate constantsat higher temperatures do not appear to interpolate smoothly to the lower temperature ~ a l u e s .Of ~ much greater concern are measurements of the branching ratio between reactions l a and lb. There have been many measurements1M2of the relative importance of these routes, and there is no consistency in the measured values or in the temperature dependence. Two recent examples are Just et al.,I2 who argue for reaction l a being 60-70% of the reaction products from 300 to 2500 K, and Aleksandrov et a1.,I0 who argue for reaction l a being 5% at room temperature to 20% at 600 K. Primarily because of this controversy, we carried out ab initio electronic structure calculation^,^^ hereafter denoted as part 1, on the saddle and equilibrium point regions of the potential energy surface governing the dissociation of OHCCH* to products. The conclusion of this first theoretical study was that reaction l a would strongly dominate. The calculations reported here are an improvement over those of part 1 in three respects. First, the wave functions used in the present calculations account for a much larger fraction of the correlation energy and are therefore expected to be more accurate than the POL-C1 wave functions used in part 1. Second, the possibility of nonplanar geometries for both the H dissociation and migration pathways was not examined in part 1. Finally, the calculations in part 1 did not examine three important regions of the surface: the saddle point region for formation of OHCCH*, the excited triplet surface 3Af (only preliminary results for 3Af are reported in part l ) , and the saddle point region governing abstraction, i.e., reaction IC. In this paper we improve and extend the a b initio electronic structure calculations and use the resulting surface properties in R R K M and TST rate constant calculations to obtain direct comparison to measured rates and branching ratios. The rest of the paper is outlined as follows. In section 11, the improved electron structure calculations are described and saddle point and equilibrium point properties concerning addition (reactions 1a and 1b) are tabulated and discussed. In section 111, electronic structure calculations on analogous systems and experimental thermochemical measurements are used to characterize the abstraction saddle point properties (reaction IC). In section IV, the overall rate constant for oxygen atom loss is calculated with conventional TST under the simplifying assumption that all OHCCH* formed decays preferentially to products. Comparison to experiment is made, and the role of abstraction and excited-state addition (on the 3Af surface) at high temperatures is assessed. In section V, the branching ratio is examined, first on the ground electronic state 3Affsurface and then with the complications of the excited 3Af surface and abstraction considered. The comparison to experiments is discussed. Finally, in section VI the results are summarized. 11. Potential Surface Calculations: Addition
A . Method. The calculations reported here employ the (IO) Aleksandrov, E. N.; Arutyunov, U. S.; Kozlov, S. N . Kinet. Catal. (Engl. Transl.) 1981, 22, 391. (11) Lohr, R.; Roth, P. Eer. Bunsenges. Phys. Chem. 1981,85, 153. (12) Bhaskaaran. K. A.; Frank, P.: Just, Th.Presented at the International Conference on Chemical Kinetics, Gaithersburgh, MD, 1985; paper E-20; private communication. (13) Williamson, D. G.; Bayes, K. D. J . Phys. Chem. 1969, 73, 1232. (14) Williamson, D. G. J . Phys. Chem. 1971, 75, 4053. (15) Jones, I. T. N.; Bayes, K. D. Symp. (Int.) Combust., [Proc.],14th, 1972 1973, 277. (16) Kanofsky, J. R.; Lucas, D.; Pruss, F.; Gutman, D. J . Phys. Chem. 1974. 78. -. - ,311. --( 1 7 ) Blumenberg, B.: Hoyermann, K.; Sievert, R. Symp. (Inr.) Combust., [Proc.],26th, 1976 1977, 841. (18) Homann, K. H.; Schweinfurth, H. Eer. Eunrenges. Phys. Chem. 1981, >
(19) Clemo, A. R.; Ducan, G. L.; Grim, R. J. Chem. Soc.,Faraday Trans. 2 1982, 78, 1231; 1983, 79, 637. (20) Buss, R. J.; Baseman, R. J.; He, G.; Lee. Y. T.Report BNL51714. 1983; Brookhaven National Laboratory, Brookhaven, NY; p 176. (21) Homann, K. H.; Wellmann, Ch. Ber. Bunsenges. Phys. Chem. 1983, 87, 609. (22) Vinckier, C.;Schaekers, M.; Peeters, J. J . Phys. Chem. 1985,89,508. (23) Harding, L. B. J . Phys. Chem. 1981, 85, 10.
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2915
y;
TABLE I: uihbrium Geometries ( a o), Principal Moments of Inertia ( a m ),' Harmonic Frequencies (cm-I), and Zero-Point Energies (kcal/mol) for C,H2 2.003 2.253 14.06
SDCI 2.009 2.290 14.42
SDCI + QC 2.015 2.306 14.60
14.25
w5
3678 2210 3592 719 844
3548 2097 3459 628 772
3467 2038 3379 58 1 738
3496b 1992b 3419b 625b 764b
ZPE
18.02
17.02
16.47
16.70
property RCH
Rcc
I *I WZ
w3 *4
RHF
exptl 2.005' 2.273'
'Lafferty, W. J.; Thebault, R. J. J. Mol. Spectrosc. 1964, 14, 79. bSuzuki, I.; Overend, J. Spectrochim. Acta, Part A 1969, 25, 977.
Dunning,24 valence, double-{ contractions of the H ~ z i n a g a ~ ~ (9s,5p) sets of carbon- and oxygen-centered primitive Gaussians. For the hydrogens the (4s/2s) contraction was used with a scale factor of 1.2. In addition, sets of d polarization functions were centered on the carbons and the oxygen (aC= 0.75, a0 = 0.85) and one set of polarization functions on each of the hydrogens (a = 1.0). With this basis set restricted HartreeFock (RHF) calculations were carried out followed by configuration interaction (Cl) calculations consisting of all single and doubly excited configurations satsifying the interacting space restriction. For planar 3Af states this leads to a C1 expansion of order 90 737 while for 3Affstates the expansions are of order 93 048. For nonplanar geometries the calculations include 174 185 configurations. The effect of higher order excitations was estimated by using the Davidson26formula. These calculations are designated here as SDCl + QC. The calculations were carried out with the Argonne QUEST2' programs, SOINTS, SORT164, GVB164, CITRAN, and UCL, on the FPS-164 attached processor. An average calculation on a nonplanar point took approximately 4 h on the FPS-164 while planar points required about 1 h. Stationary points, both minima and saddle points, were first roughly located with reduced dimensionality grid searches. Next, calculations were carried out at a grid of points surrounding each stationary point. Spacings of 0.05-0.10 au in bond lengths, S0-1Oo in bond angles, and 1Oo-2O0 in dihedral angles were used. For nonplanar stationary points complete characterization of the harmonic force field requires a minimum of 45 points. For planar stationary points, grid of only 3 1 points are required. Typically, about twice the minimum number of points was used to characterize each of the stationary points. The resulting grid of energies were then least-squares fit to a Simons-Parr-Finlan-type expansion using the program SURVIB.~~Equilibrium geometries, moments of inertia, and harmonic vibrational frequencies were then derived by using techniques described previously. The calculated properties of each of the stationary points involved in addition will now be presented. Comparison between theory and experiment for structures and frequencies will be discussed, but detailed comparisons for the energetics will be postponed to the last part of this section. B. Calculated Properties of the Reactants, Intermediates, and Products. The calculated properties of the reactant acetylene molecule are given in Table I. In these calculations an oxygen atom was included at a distance of 20 au from the acetylene in order to minimize any size consistency error. The calculated bond lengths are in good agreement with experimentally derived values, (24) Dunning, T.H., Jr.; Hay, P. J. In Methods of Electronic Structure Theory; Schaefer 111, H. F., Ed.; Plenum: New Yotk, 1971; Chapter 1 . (25) Huzinaga, S. "Approximate Atomic Wavefunctions. I"; chemistry report; University of Alberta: Edmonton, Alberta, Canada, 197 1 . (26) Langhoff, S.R.; Davidson, E. R. Int. J . Quantum Chem. 1974,8, 61. Davidson, E. R.; Silver, D. W. Chem. Phys. Lett. 1978, 52, 403. (27) Shepard, R.; Bair, R. A.; Eades, R. A,; Wagner, A. F.; Davis, M. J.; Harding, L. B.; Dunning, T.H., Jr. Int. J . Quantum Chem., Quantum Chem. Symp. 1983, No. 17, 613. (28) Harding, L. B.; Ermler, W. C. J . Comput. Chem. 1985, 6, 13.
Harding and Wagner
2976 The Journal of Physical Chemistry, Vol, 90, No. 13, 1986
TABLE 11. Equilibrium Geometries,@Principal Moments of Inertia (amu A2), Harmonic Frequencies (cm-I), Zero-Point Energies (kcal/mol), and Relative Enerdes (kcal/mol) [with respect to Ot3P) C,HJ for the 3A‘ and 3AffStates of OHCCH ’A’ state ’A“ state
+
property
RHF
SDCI
SDCI + QC
RHF
SDCI
SDCI + OC
2.469 2.548 2.032 2.024 127.9 122.3 138.1
2.491 2.561 2.052 2.032 129.2 121.5 139.8
2.483 2.574 2.062 2.038 129.7 121.5 140.4
2.768 2.262 2.064 2.032 122.9 115.6 128.2
2.748 2.312 2.072 2.041 122.1 116.3 129.6
2.739 2.336 2.078 2.049 121.6 116.9 129.8
6.41 42.18 48.59
6.27 43.40 49.67
6.23 43.69 49.92
7.11 40.13 47.24
7.34 40.28 47.62
7.48 40.30 47.78
3430 3361 1760 1262 1106 940 484
3367 3239 1656 1204 1038 879 465
3314 3168 1 I96 1113 954 835 459
3410 3240 1917 1513 1180 1040 518 1067 536
3359 3173 1776 1474 1158 985 479 1030 582
3320 3133 1704 1460 1147 965 464 1024 614
20.62
20.04
19.77
-6.1
-18.2
-20.1
-30.4
-46.9
-49.2
the largest errors occurring in the CC bond length where the R H F result is 0.02 au too short while the SDCl QC result is 0.03 au too long. The calculated SDCl QC harmonic frequencies are in good agreement with the experimentally derived results. The largest error in the SDCl QC frequencies is 46 cm-’ for the C C stretching mode. The zerc-pint energies calculated from the RHF, SDCl, and SDCl QC frequencies are in error, relative to the experimentally derived value, by 1.5,0.3, and -0.2 kcal/mol, respectively. There are two triplet states of the OHCCH complex accessible in this reaction, !A’ and 3A”. The calculated properties of these two states are given in Table 11. Note that for the upper state, ’A’, it was not possible to do the nonplanar grid points necessary to obtain the out-of-plane bending force constants because the calculations collapsed to the lower electronic state. For this reason only the vibrational frequencies corresponding to planar modes are listed for this state. Also shown in Table I1 are the calculated differences in energy between the reactants and the complexes. For each of the two states, two conformations exist, one in which the hydrogens are trans and one in which they are cis. In each case only results for trans conformers are given. For the 3A” state the cis conformer is predicted to lie approximately 1.5 kcal/mol higher in energy. The calculations predict the 3Af’state to be the lower of the two electronic states, lying 49 kcal/mol below the reactants and 29 kcal/mol below the 3A’ state. The electronic structure of the 3A’ state is found to be that of a 1,3-biradical having a carbon-oxygen single bond and a carbon-carbon double bond. The 3A’’ state however is a carbene-type structure having a carbon-oxygen double bond and a carbon-carbon single bond. The calculated geometry and vibrational frequencies of the ketyl radical are listed in Table I11 along with recent experimental results of Inoue et al. The ketyl radical is predicted to have a bent, trans geometry with a ground electronic state of 2Af’symmetry. The *A’’ ground state correlates with a degenerate 211 state in linear geometries. The barrier to linearity is predicted to be very small, 2.2 kcal/mol. The calculated frequencies are in poor agreement with the two values reported by Inoue, implying errors of 1070 cm-’ in the calculated C H stretching frequency and 380 cm-’ in the C O stretch. For comparison, SDCl + QC calculations on the related molecule H C O predict frequencies of 2570, 1880, and 1115 cm-l compared with experimental values of 2488, 1861, and 1090 cm-I. The maximum error in the calculated frequencies of HCO then is 82 cm-’, for the CH stretch. The cause of the much larger
+
+
+
+
TABLE III: Equilibrium Ceometries,b Principal Moments of Inertia (amu A*), Harmonic Frequencies (cm-I), Zero-Point Energies (kcal/mol), and Relative Energies (kcal/mol) [with respect to O(”) + C2H31for HCCO(’A”) property RHF SDCI SDCI QC exptl‘ 2.218 2.238 2.170 Rco 2.485 2.453 2.472 Rcc 2.024 2.033 RCH 2.013 169.5 168.3 eocc 171.6 134.0 132.8 OHCC 136.1
+
I,
0.44 45.63 46.07
0.50 46.75 47.24
0.53 47.26 47.80
w6
3517 2290 1327 742 628 532
3456 2201 1275 699 589 555
3404 2144 1246 692 587 545
ZPE
12.92
12.54
12.32
A&,
19.3
-0.7
-4.4
Ib IC
“1 *2
“3 *4 “5
“Inoue, G.; Suzuki, M., private communication. * R in
2334 1764
a,, B in
deg.
discrepancy in the frequencies of HCCO is not clear. The 3A’fstate of ketene is accessible in this reaction via 1,2hydrogen migration from the 3A’f state of the OHCCH complex. The calculated geometry and vibrational frequencies of this state are shown in Table IV along with previous theoretical results. The agreement between the two set of theoretical results is excellent. No experimental results are available for comparison. The calculations predict that this state lies 66 kcal/mol below the reactants or 17 kcal/mol below the 3Af’state of OHCCH. The caiculated properties of the products CH2(3Bl) CO are shown in Table V along with the corresponding experimental values. The agreement between the calculated and experimental geometries and vibrational frequencies is excellent. C. Calculated Properties of the Transition States. Since atomic oxygen has a threefold spatial degeneracy, there are three triplet potential surfaces which must be considered in this reaction, two of 3A” symmetry and one of 3Af. The higher of the two ’A’’ surfaces is expected to be repulsive and can therefore be neglected. The remaining two surfaces however both correlate with bound addition complexes. The calculated properties of the transition
+
Reaction of Atomic Oxygen with Acetylene
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2977
TABLE IV: Equilibrium Geometries,b Principal Moments of Inertia (amu A2),Harmonic Frequencies (em-'), Zero-Point Energies (kcal/mol), and Relative Energies (kcal/moi) [with respect to O(3P) C,HJ for H2CCO(3Af')
+
property
TABLE VI: Calculated Geometries; Principal Moments of Inertia ( a m A'), Harmonic Frequencies (em-'), Zero-Point Energies (kcalhnol), and Relative Energies (kcal/mol) [with respect to O(3P) + C2H2] for the 3A' and )A'' Transition States for Addition of Atomic Oxygen to Acetylene
RHP
RHF
SDCI
SDCI + QC
2.757 2.268 2.033 2.033 131.7 121.1 121.1
2.168 2.214 2.034 2.026 129.4 119.7 119.9
2.168 2.258 2.045 2.036 127.7 120.1 119.8
2.771 2.278 2.052 2.043 127.0 120.3 119.8
4.35 45.93 50.27
4.59 46.07 50.66
4.70 46.22 50.93
3469 3331 2063 1560 1151 1042 503 724 367
3420 3269 1956 1514 1101 1017 47 3 741 357
3372 3220 1889 1494 1082 1003 463 746 353
Ib
20.31
19.80
19.47
W8
-41.4
-63.1
-66.1
w9
~~
3A' state
RHF
SDCI SDCI + QC A. CO
exptl
Rco I
2.112 8.56 2428
2.153 8.90 2261
2.132"
W
2.168 9.03 2195
SDCI
SDCI + OC
SDCI
SDCI + OC
Rcc Rc,o Rc~H,
Om,cb
2.331 3.482 2.020 2.011 115.9
eH&aCb 'HbCbC.
169.3
2.343 3.569 2.028 2.019 114.1 151.4 167.6
2.331 3.458 2.020 2.022 102.3 155.0 168.6
2.352 3.551 2.023 2.019 102.7 155.0 167.8
8.54 53.87 62.41
9.04 54.95 63.99
11.10 45.19 56.89
11.25 41.94 59.19
3680 3553 1795 88 1 622 334 1153i
3687 3549 2168 870 575 328 9621'
3492 3401 1962 886 606 246 1059i 1107 873
3504 3389 1816 877 502 244 919i 1014 883
11.97
17.57
19.1
13.7
16.4
10.6
RCbHb
4 4 W1
W2
w3 w4
w5 w6 Wran
ZPE m e 1 a
TABLE V Equilibrium GeOmetries,E Principal Moments of Inertia ( a m A2),Harmonic Frequencies (em-'), Zero-Point Energies (kcalhol), and Relative Energies (kcal/mol) [with respect to O('P) + C2H2Jfor CH#B,) and CO
property
Prouerty .~ ~
aDykstra, C. E.; Schaefer 111, H. F. J. Am. Chem. Soc. 1976, 98, 2689. b R in ao, 0 in deg.
'A" state
R in ao,0 in deg.
OPP)
+ HCCH
.+
OHCCH
A'
2 170a
B. CH2 RCH
6ncn la
Ib IC
W1
w2 WI
2.030 129.4 0.36 1.90 2.26 3298 1306 3507
2.037 131.4 0.34 1.94 2.28 3263 1208 3481
2.043 132.1 0.33 1.97 2.30 3221 1169 3438
2.03Ib 133.9b
a,,,
C. CHI + CO 2PE AE,,
15.07 -34.3
14.61 -44.2
962 i cm''
919 i crn-'
Figure 1. The calculated SDCI
+ QC saddle point structure, normal-
mode eigenvector along the minimum-energy path, and imaginary frequency for 0 addition to HCCH on the 'A' and )A" surfaces.
14.33 -45.3
Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand: Princeton, NJ, 1950; Vol. I. bJensen, P.; Bunker, P. R.; Hoy, A. R. J. Chem. Phys. 1982, 77, 5370. c R in ao, 0 in deg.
Vibrational Levels
a
states for formation of these complexes are summarized in Table VI. The geometries and reactive normal-mode eigenvectors for these two transition states are plotted in Figure 1. A plot showing the correlation of normal-mode vibrational frequencies from reactants, through the transition state, to products for the lower 3A" surface is given in Figure 2. The transition states are similar in structure, both occurring early, as expected for an exothermic reaction. The reaction coordinate for both transition states consists almost entirely of C O stretch. Note that, as found in the H HCCH reaction, the acetylene molecule takes on a trans geometry as the oxygen atom approaches, with one hydrogen bending away from the oxygen and one bending toward it. The 3A'r and 3A7 transition states lie 10.6 and 13.7 kcal/mol, respectively, above reactants. The calculated properties of the transition state for CH bond cleavage from the 3Ar' state of O H C C H are given in Table VI1 and plotted in Figure 3. The vibrational level correlation diagram for this reaction is given in Figure 4. The net reaction is predicted
for t h e Reaction 0 (3P) t HCCH+ OHCCH (3A")
40007 CH stretchs
3000
+
CC stretch 7
exptl
colcd
HCCH
0-HCCH OHCCH Figure 2. The calculated SDCl + QC frequency Correlation diagram for 0 addition to HCCH on the )A'' surface.
to be 44.8 kcal/mol endothermic. Consequently, the transition state is both late and 'loose". The calculated barrier for the reverse
2978 The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 TABLE VII: Calculated Geometries," Principal Moments of Inertia (emu A*), Harmonic Frequencies (cm-'), Zero-Point Energies (kcal/mol), and Relative Energies (kcal/mol) [with respect to O(3P) C2H2]for the Transition State for OHCCH(3A") HCCO(2A") + H(%
-
+
property
OHCCH
Harding and Wagner TABLE VIII: Calculated Geometries," Principal Moments of Inertia (amu A2), Harmonic Frequencies (cm-'), Zero-Point Energies (kcal/mol), and Relative Energies (kcal/mol) [with respect to O('P) C2H2]for the Transition States for 1,2-Hydrogen Migration from OHCCH(3A") transition state 1 transition state 2
+
SDCI
SDCI + QC
2.539 2.219 3.320 2.033 158.0 97.6 127.7
2.548 2.239 3.448 2.040 157.8 97.7 127.5
4.40 46.71 51.1 1
4.74 47.14 51.87
3417 2123 1203 718 58 1 559 1464i 538 478
3367 2070 1186 736 576 561 126% 529 467
13.75
13.57
w7
8.7
2.7
ws
+
H
+
HCCO
SDCI
SDCI + QC
SDCI
SDCI + QC
2.623 2.295 2.428 2.060 139.3 64.6 135.7 126.0 5.8
2.636 2.314 2.489 2.066 138.4 65.6 135.9 122.7 12.0
2.649 2.295 2.41 3 2.037 129.7 64.3 131.8 119.5 181.3
2.641 2.324 2.414 2.044 127.7 64.8 1131.8 116.8 183.1
4.38 45.53 48.67
4.59 45.92 49.09
4.03 45.14 47.60
4.26 44.88 47.42
wrx,
3148 2172 1778 1308 956 863 652 434 1789i
3090 1995 1702 1274 94 1 790 544 285 1655i
3390 2139 1841 1277 1007 872 623 301 2017i
3349 2099 1715 1272 1005 884 610 35 1 1910i
ZPE
16.17
15.18
16.37
16.13
4
9.03
3.30
18.2
12.5
property
w4
w5 w6
1
R in ao, 0 in deg.
Vibrational Levels
P
for the Reaction OHCCH (3A")* CH,
+ CO
4000; 3
3ooojy7 s+retchs CH
3 h
3
zoooi .--
1000
w,,,
j
h C H bend
1268 i
Figure 3. The calculated SDCl + QC saddle point structure, normalmode eigenvector along the minimum-energy path, and imaginary frequency for H dissociation from OHCCH.
OHCCH
OCCH,
CH,+CO
+
Figure 5. The calculated SDCl QC frequency correlation diagram for H migration in OHCCH followed by CC bond fission.
Vibrational Levels for t h e Reaction OHCCH (3A")+ H
+ HCCO
this is not the lowest energy path for the reaction of atomic hydrogen with ketyl radical, and thus studies of the H HCCO reaction do not yield information on this barrier height. The calculations predict that there are two nonplanar transition states for hydrogen migration from the 3A" state of OHCCH, one from each of the two conformers of this species. The calculated properties of these transition states are summarized in Table VIII, and the vibrational level correlation diagram is given in Figure 5. Since interconversion of the two conformers of OHCCH is expected to be rapid and since the two transition states for migration are predicted to be well separated in energy (by 9 kcal/mol), the reaction should be dominated by passage over the lower transition state, labeled transition state 1 in Table VIII. Perhaps the most unusual feature of these transition states is the high degree of nonplanarity. In both transition states the migrating hydrogen is approximately 60° out of the OCC plane. It appears as though the hydrogen is migrating to a position trans to its starting point (cis to the oxygen atom). Confirmation of this would require following a reaction path from the transition state to the products.
+
4000-
CH strelch h
i
E
CO stretch
CO stretch
2000
3
C C slretch
OJ
OI-ICCH
Figure 4. The calculated SDCl
H dissociation from OHCCH.
H-OCCH
HCCO
+ QC frequency correlationdiagram for
reaction, addition of atomic hydrogen to HCCO on a triplet surface, is predicted to be 7.1 kcal/mol. It should be noted that
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2979
Reaction of Atomic Oxygen with Acetylene
OHCCH + OCCH,
TABLE I X Calculated Geometries,’ Principal Moments of Inertia (amu A*)),Harmonic Frequencies (an-’), Zero-Point Energies (kcal/mol), and Relative Energies (kcal/mol) (with respect to OOP) C2Hl] for the Transition State for H2CCO(3A’’) CH2(3B1)
-
+ co
property
a
SDCI
SDCI
+
+ QC
3.902 2.171 2.039 2.033 117.0 119.3 112.0
4.033 2.185 2.049 2.044 116.3 117.1 113.8
6.67 63.03 69.70
6.89 65.95 72.84
3513 3225 2513 1233 457 227 4433 510 162
3451 3161 2093 1204 486 228 4413 506 148
16.41
16.11
-35.5
-38.9
2235 i cm-’
w,,,
+
Figure 6. The calculated SDCl QC planar saddle point structure, normal-mode eigenvector along the minimum-energy path, and imaginary frequency for planar H migration in OHCCH.
(3A-) + CO
H,CCO
Previous calculations in part 1 on this reaction assumed a planar transition state for migration. Constraining the reaction to a planar pathway leads to a barrier 4 kcal/mol above the lower of the two nonplanar transition states. A normal-mode analysis of this stationary point indicates two imaginary frequencies, one corresponding to migration and the other to an out-of-plane bend. This point then represents a barrier in a path perpendicular to the migration reaction path, connecting two equivalent migration transition states. A plot of the geometry and migration normal-mode eigenvector for this planar barrier is given in Figure
\
w,,,
6.
Figure 7. The calculated SDCl QC saddle point structure, normalmode eigenvector along the minimum-energy path, and imaginary frequency for CC bond fission in H2CC0.
estimates for the true energetics will be made and compared in Table X with the SDCl Q C energetics of Tables I-IX. Both AEe, and AH(0 K), relative to O(3P) C2H2,are listed, the connection between the two always being based on the SDCl Q C zero-point energies (ZPE) in Tables I-IX. The two equilibrium points where there is the most direct experimental measurement of the energetics are CH2 C O and H HCCO. The JANAFB value for CO and a more recent value
+
+
+
+
+
+
+ QC, Best Estimated, and BAC-MP4 Addition Energetics AEd and Enthalpies AH(0 K) for the Listed Structures Relative to SDCI
structure 0.* sHCCH(~A’) O-.*HCCH(3A”) OHCCH(3A’) OHCCH(’A’’) H*..OCCH
H
441 i cm-’
+
The calculated properties of the transition state for C C bond cleavage from the 3A” state of H2CC0 are listed in Table IX and plotted in Figure 7. In the reverse direction, the calculated bamer height for addition of methylene to carbon monoxide is 6.4 kcal/mol. D. Estimated Corrections to Calculated Energetics. The SDCl QC energetics of all the stationary points involved in addition are displayed in Figure 8. There is experimental and theoretical evidence that the calculated energetics in the figure, although qualitatively correct, contain systematic errors. That evidence will now be discussed, first for the equilibrium points where the evidence is more direct, and then for the saddle points. Best
+
%H,
t
R in q,, 8 in deg.
TABLE X SDCI O(~PP) HCCH~
+
+ OCCH co
@.I
+ QC AH(0 K)
13.7 10.6 -20.1 -49.2
15.9 11.7 -18.5 -45.9
2.7 -4.4 3.3
-0.2 -8.6 2.0
-66.1 -38.9 -45.3
-63.1 -39.3 -47.4
best estimate M ( 0 K) 4.1 f 1.3 6.3 f 1.3
AE.,
2.2 -33.7 -62.8 -62.0 -13.2 -14.9 -14.3
f 5.0 f 5.0 f 4.0 f 2.5 f 2.5 5.0
*
3.3 -32.1 -59.5 -58.7 -16.1 -19.1 -15.6
f 5.0 f 5.0 f 4.0 f 2.5 f 2.5 f 5.0
AE-1
BAC-MP4 AH(0 K)
7.3
8.4
-53.4
-50.1
-8.5 -14.5 -4.3
-1 1.4 -18.7 -5.6
-72.2 -44.8 -48.2
-69.2 -45.2 -50.6
H***l CH
H2CC0(3A”) H2C. *CO CH2 CO
-
+
-78.9 f 4.0 -41.6 f 2.0 -44.8 f 0.1
-15.9 f 4.0 -42.0 f 2.0 -46.9 0.1
*
“For each pair of columns, the differences between AEeland AH(0 K) are determined by the SDCI kcal/mol.
+ QC ZPE from Tables I-IX.
Units are
2980
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 Schematic Ot3P)
.-a,>
%
-
2
-751
OHCCH
I
+ HCCH Surface
=A’’ H I C C O
-1002
Figure 8. The calculated SDCl + QC energy correlation diagram for addition of 0 to HCCH on the ’A‘ and 3A” surfaces.
for CHZ3Ogive a M ( 0 K), relative to 0 + HCCH, of -46.9 f 0.5 kcal/mol, in excellent agreement with the SDCl Q C value of -47.4 kcal/mol. This good agreement implies that electronic correlation errors in reactants and products are similar. This should not be surprising since the reactants and products are isoelectronic. For the H HCCO asymptote, the AHf(298 K) has recently been measured3’ which can be corrected to AHf(O K) by the calculated structure and frequencies of Table 111. The result is a AH(0 K) of -19.1 f 2.5 kcal/mol, compared to the SDCl + QC value of -8.6 kcal/mol. The calculated value is too high by 10.5 kcal/mol. This error is symptomatic of a trend in the calculated energetics which can be understood as follows. Electron correlation is dominantly a pairwise effect. In a molecule with 22 electrons, such as ketene, there are 231 pairs of interacting electrons. For the H + H C C O asymptote 21 of these pairwise interactions disappear. For the reactant asymptote, 119 of these interactions disappear. Thus, the H HCCO products have 98 more nonzero electron-electron pair interactions than do the reactants, O(3P) HCCH. Since the SDCl QC wave function does not account for 100%of the correlation associated with each of these pairs, it is not surprising that the exothermicity of this reaction is underestimated. This will be a consistent feature of the calculated energetics. Although indirect, the empirical evidence for the energetics of H 2 C C 0 is substantial. The H2CCO(3A”)involved in this reaction is the lowest triplet state of ketene. The heat of formation of ground-state singlet ketene is w e l l - k n o ~ n . ~The ~ electron impact energy loss spectrum of the ground state has been measured,33 and it shows a feature about 20 kcal/mol wide with a peak at about 85.3 f 3.5 kcal/mol. This peak is interpreted as vertical transitions to both the first excited singlet state and the lowest triplet state of ketene. The two electronic states are too close together to be separately resolved in the experiment. The SDCl Q C vertical transition to the lowest triplet state is 84.3 kcal/mol, in excellent agreement with the experimental result. This gives confidence that the subsequently calculated SDCl + Q C adiabatic transition of 48.1 kcal/mol is also correct. That number plus the AEel for ground-state ketene (obtained from the measured enthalpy corg ~ ~ the Me, for rected for ZPE as determined from H e r ~ b e r gives triplet H,CCO. Given the calculated ZPE, the resulting semiempirical estimate of AH(0 K) is -75.9 kcal/mol with an uncertainty of 3 or 4 kcal/mol. The direct SDCl + QC value based on Tables I and IV is -63.1 kcal/mol. The nominal difference
+
+
+
+
+
+
(29) Chase, Jr., M. W.; Curnutt, J. L.; Downey, Jr., J. R.; McDonald, R. A.; Syverus, A. N.; Valenzuela, E. A. J. Phys. Chem. ReJ Data 1982.11, 695: JANAF Thermochemical Tables, 1982 Supplement, and references therein. (30) McCulloh, K. E.; Dibeler, V. H. J . Chem. Phys. 1976, 64, 4445. (31) Oakes, J. M.; Jones, M. E.; Bierbaum, V. M.; Ellison, G. B. J . Phys. Chem. 1983,87, 4810. (32) Nuttall, R. L.; Laufer, A. H.; Kildaiy, M. V. J . Chem. Thermodyn. 1971, 3, 167. (33) Frueholz, R.P.; Flicker, W. M.; Kuppermann, A. Chem. Phys. Letf. 1976, 38, 51. (34) Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand: New York, 1966; Vol. 111.
Harding and Wagner of 12.8 kcal/mol is higher than the 10.5 kcal/mol overestimation in HCCO, consistent with the hypothesis of greater error in the calculated energy with increasing numbers of interacting electron pairs in the molecule. The energetics of the OHCCH(3A’) equilibrium point can also be indirectly connected to empirical measurements. This adduct is the biradical that would be formed from vinyl alcohol upon dissociation of the CH2CHO-H and the H-CHCHOH bonds. The heat of formation of vinyl alcohol at 300 K has been recently measured.35 The enthalpy changes at 300 K upon dissociation of the 0-H bond in methanol and the C-H bond in ethylene are also available.36 Under the assumption that the change in enthalpy at 300 K for the dissociation of vinyl alcohol to OHCCH(3A’) 2H is equal to the sum of the methanol and ethylene dissociation enthalpies, the heat of formation at 300 K of OHCCH(3A’) can be determined. Then the desired AH(300 K) can be obtained and corrected to 0 K with the calculated properties in Tables I and 11. The final AH(0 K) is -32.1 kcal/mol. Since each of the three experimental measurements used in this estimate is uncertain by about 2 kcal/mol, the uncertainty in this estimate is on the order of 5 kcal/mol. The SDCl + QC AH(0 K) from Tables I and I1 is -1 8.5 kcal/mol, a nominal overestimation of 13.6 kcal/mol. This is noticeably higher than the overestimate of HCCO but similar to the overestimate in H2CC0, again consistent with the idea that there is a larger error in the energy of species with more interacting pairs of electrons. There is no direct or indirect experimental evidence for OHCCH(3A”), a carbene radical. However, as discussed above, the calculations in Tables I-IX do give correct energy differences if the number of interacting electron pairs is conserved. Thus, the SDCl + QC 3A’-3A’’ splitting in Table I11 or the SDCl QC difference between OHCCH(3A”) and H 2 C C 0 in Tables I1 and IV plus the estimated energies for the 3A’state or triplet ketene allow an estimate of AH(0 K). Those values are -59.5 kcal/mol (3A’-3A’’ splitting) and -58.7 kcal/mol (triplet ketene), relative to reactants. The uncertainty in these values is probably about 5 kcal/mol. The SDCl + QC value from Tables I and I1 is -45.9 kcal/mol. Of the five saddle points whose calculated barrier heights remain to be examined, only two (O-.HCCH(3A”) and Ha-OCCH) have any dynamics measurements to provide experimental activation energies. Of those two, the most direct evidence is for the barrier to 0 addition. Later sections of this paper will argue that the activation energy for the overall addition rate constant at low temperatures is sensitive only to this barrier height. The value of AH(0 K) listed in Table X, 3.3 kcal/mol, is the result of comparing transition-state theory calculations for the overall rate (as described in section IV) to the experimental measurements. This estimated barrier height is 8.4 kcal/mol below the SDCl Q C value from Tables I and VI, somewhat less than the approximately 1 3 kcal/mol lowering of the SDCl QC energy for the adduct OHCCH. For the He-OCCH barrier, there is evidence from the two molecular beam r n e a s u r e m e n t ~of ’ ~the ~ ~0 ~ + HCCH reaction that this barrier must be several kcal/mol above the H OCCH asymptote. This evidence comes from the measured translational energy spectrum of the H + OCCH fragments from the addition reaction. The activation energy for addition of H to several small a systems is well-known: e.g., 2.6 kcal/mol for H HCCH,37 2.2 kcal/mol for H + H2CCH2,38and 2.0 kcal/mol for H C0.39 Calculated barrier heights, AH(0 K), for these three reactions, with wave functions of similar quality to those reparted here, overestimate the activation energy by about 5.5,375.5,40 and 2.6
+
+
+
+
+
+
+
(35) Holmes, J. L.; Lossing, F. P. J . Am. Chem. Soc. 1982, 104, 2648. (36) McMillen, D. F.; Golden, D. M . Annu. Reu. Phys. Chem. 1982, 33, 493. (37) Harding, L. B.; Wagner, A. F.; Bowman, J. M; Schatz, G. C.; Christoffel, K. J . Phys. Chem. 1982, 86, 4312. (38) Sugaware, K.; Okazaki, K.; Sato, S. Bull. Chem. SOC.Jpn. 1981, 54, 2872.
(39) Wang, H. Y.; Eyre, J. A.; Dorfman, L. M. J . Chem. Phys. 1973,59, 5199.
Reaction of Atomic Oxygen with Acetylene
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2981
kcal/mol$’ respectively. All this evidence suggests that the true value for M ( 0 K) is 3 f 1 kcal/mol relative to the H OCCH asymptote or about 5.4 kcal/mol below the SDCl Q C value. Relative to the 0 HCCH asymptote, M ( 0 K) is -16.1 f 2.5 kcal/mol. (The increased uncertainty comes from the experimental uncertainty in the H + OCCH asymptote as discussed above.) The remaining three saddle points have the most uncertain energetics. Consider first the barrier for addition on the upper, 3A’, surface. One can estimate the magnitude of this barrier either by assuming that the calculated ratio of the O-.HCCH(’A’) and O-SHCCH(~A”)barrier heights is accurate or by assuming the calculated difference between the two barriers is accurate. The former assumption leads to an estimated barrier height on the upper surface, AH(0 K), of 5.0 kcal/mol while the latter yields a barrier of 7.5 kcal/mol. The average estimate is 6.3 f 1.3 kcal/mol. For the migration barrier, a reasonable assumption is that the SDCl QC difference in the migration OC-H-CH and dissociation H--OCCH barrier heights is correct. This leads to a best estimate for the migration barrier, AH(0 K), of -15.6 kcal/mol relative to reactants. The uncertainty in this estimate is at least 5 kcal/mol. Finally, the H2C-.C0 barrier can be estimated with the assumption that the relative change in the calculated barrier needed to obtain the experimental activation energy in H C O (a 50% reduction41)carries over to H2C CO. This yields a AH(0 K) barrier of 4.9 kcal/mol relative to CH2 CO or -42.0 kcal/mol relative to 0 HCCH. The uncertainty is probably f 2 kcal/mol. All the SDCl Q C and best estimate energetics are listed in Table X. Also listed in Table X are the results of recent unpublished calculations of the energetics of most of the stationary points in the reaction by C. F. Melius of Sandia National Laboratory. The method used is bond additivity corrected M ~ l l e r Plesset fourth-order perturbation theory (BAC-MP4).42 As the name implies, this semiempirical method consists of high-quality ab initio calculations with bond additive corrections derived from a comparison of theoretical and experimental energetics for a representative set of stable molecules. In an extensive test of this method, the calculated values of AHA0 K) for 70 stable molecules and radicals, not included in the representative set, were on the average 0.8 kcal/mol different from their experimental values.42 The method has not been extensively tested for the energetics of saddle points, biradicals, or carbenes. With the best estimated values of M ( 0 K) at the equilibrium points as the standard, the BAC-MP4 values are within experimental error for H + HCCO, too low for CH2 + CO by about 3.5 kcal/mol, and too high for the adducts H2CC0(’A”) and OHCCH(3A”) by about 7 and 9 kcal/mol, respectively. Except for C H 2 CO, these differences are significantly smaller than that for the fully ab initio SDCl QC results. However, the size of the differences for the two adducts is still surprisingly large. The best estimate for H2CC0(’A”) is based on the measured heat of formation for singlet ketene, which is reproduced exactly by the BAC-MP4 value,“2and the SDCl Q C calculation of the adiabatic transition to the triplet. The spin-projected MP4 value
+
+
+
+
+
+
+
+
+
+
+
+
(40) Harding, L. B. J . Am. Chem. SOC.1981, 103, 7469. The calculated barrier height to addition (Table 111) involves incomplete geometry optimization. As a result, the absolute value is not correct. However, the close similarity of H + CH2CH2and H + HCCH in the table (within 1 kcal/mol) suggests that geometry optimization would produce the same error as found for H HCCH in ref 36. (41) Unpublished results by the authors. (42) No detailed description of this method has been published. Extended abstracts of talks are available: Melius, C. F.; Binkley, J. S . ; Koszykowski, M. L. Abstracts of Papers, D.O.E. Combustion Research Contractors Meeting; Sandia National Laboratory: Livermore, CA, 1984; p 27; Melius, C. F.; Binkley, J. S. (Sandia National Laboratory, Livermore, CA) Chem. Phys. Processes Combust. 1983, paper 39. Applications of the method to ‘specific chemical problems are also available, for example: Melius, C. F.; Binkley, J. S . ACS Symp. Ser. 1984, No. 249 (Chem. Combust. Processes), 103; Melius, C. F.;Binkley, J. S. Symp. (hr.) Combust., [Proc.],ZOth, 1984 1985, 5 7 5 ; Perry, R. A.; Melius, C. F. Ibid. 1985, 639. The results of the method quoted in this article come from a compendium of calculations on several hundred chemical species kindly made available to us by C. F. Melius.
+
+
for that transition is 2.6 kcal/mol larger than the SDCl Q C value. Both calculations get about a 0.15-A increase in the C C bond length as the major bond length change in going from the singlet to the triplet. The BAC correction, which depends only on bond lengths, adds another 4 kcal/mol to the MP4 adiabatic transition, resulting in the quoted difference of about 7 kcal/mol. There are two overlapping best estimates for OHCCH(’A”). The first is based on the SDCl + Q C difference between this adduct and the triplet ketene. That difference is only 1.3 and 2.2 kcal/mol smaller than the spin-projected MP4 and the BAC-MP4 value, respectively. Thus, the BAC-MP4 discrepancy in triplet ketene largely carries over to OHCCH. The second best estimate comes from the experimental heat of formation of vinyl alcohol plus two assumptions: (1) that the ethylene and methanol energies for H atom dissociation apply to analogous dissociations in vinyl alcohol; (2) that the SDCl + Q C A’-A” splitting for OHCCH is accurate. If the same two assumptions are applied to the BAC-MP4 value42 for vinyl alcohol, the result would be value for OHCCH(3A”) only about 3.3 kcal/mol larger than the best estimate. Thus, in order for the BAC-MP4 energetics of the two adducts to be correct, the SDCl Q C vertical transition in ketene must be underestimated by about 5 kcal/mol and a similar error must be present in either the SDCl + Q C A’-A” splitting of O H C C H or the semiempirical estimates of the dissociation energies of vinyl alcohol. This seems doubtful but cannot be ruled out. Relative to the energetically closest asymptote, the BAC-MP4 AH(0 K) values for the saddle points are 44.5 (HC-H-CO), 8.4 (0.-HCCH), 7.3 (H-OCCH), and 5.4 kcal/mol (H2C.-CO). These values are all 1-3.5 kcal/mol smaller than the ab initio QC values but still 0.5-5 kcal/mol higher than the SDCl nominal best estimates. However, the differences with the best estimates for the first and last saddle point are within the uncertainty of the estimates. There are three main conclusions to be drawn from the energetics in Table X. First, the best estimates of the energetics confirm the result of both the ab initio SDCl + Q C calculations and the semiempirical BAC-MP4 calculations that both the H dissociation and H migration barriers to fragmentation of the adduct OHCCH are much lower than the 0 dissociation barrier back to reactants. This will have important consequences for the branching ratio to be discussed in section IV. Second, there is a systematic error in the SDCl QC energetics. For the minima, the magnitude of the errors, relative to 0 HCCH, is in the order of C H 2 CO < H + HCCO < OHCCH = H 2 C C 0 , corresponding to increasing numbers of interacting electron pairs. For saddle points, relative to the energetically closest asymptote, the overestimation is in the order of H2C-C0 < He-OCCH < 0. -HCCH, with the migration saddle point HC.-H-CO too uncertain to rank. Third, the semiempirical BAC-MP4 results are always an improvement over the ab initio results, but large errors, 25 kcal/mol, still remain in energetics of the adducts OHCCH and H 2 C C 0 and in the saddle points He-OCCH and O-eHCCH. In the case of the adducts, the BAC-MP4 values seem unlikely but cannot be ruled out.
+
+
+
+
+
111. Potential Energy Calculations: Abstraction While no ab initio potential energy calculations were directly performed for the abstraction reaction (IC),calculations on related reactions and recent measurements regarding the energetics of the reaction permit an accurate enough description of the transition state to determine whether abstraction is important. The measurement is that of AHA0 K) for CCH reported recently by Lee43 as 134.0 & 2.0 kcal/mol. With the JANAF valuesz9for the other species involved in abstraction, the total enthalpy change from reactants to products, M ( 0 K), is 27.2 2.0 kcal/mol. Removal of ZPE correction^^^ gives a AEe, of 32.3 f 2.0 kcal/mol. Re-
*
(43) Lee, Y. T.; Wodtke, A. M. Presented at the 190th National Meeting of the American Chemical Society, Chicago, 1985; Division of Physical Chemistry, paper 101. (44) The ZPE for HCCH is the experimental value listed in Table I, the ZPE for CCH is the calculated value in ref 46, and the ZPE for OH is from ref 2 5 .
2982 The Journal of Physical Chemistry, Vol. 90, No. 13, 1986
Harding and Wagner
TABLE XI: Estimated Geometries (eo), Principal Moments of Inertia (amu A*),Harmonic Frequencies (cm-I), Zero-Point Energies (kcal/mol), and Relative Energies (kcal/mol) [with respect to O(3P) + C2H2]for the Transition State for Hydrogen Abstraction from Acetvlene bv Atomic Oxvgen property estd value property estd value Rcc 2.32 T modes ~
RH,O
2.04 2.87 1.99
I
115.8
RCaHb
RC,Ha
u modes w2
3361 209 1
a 3
815
wrx,
1517i
ai
a5
614,' 674'
w6
538,O 538b 169; 148'
w7
ZPE
12.9
%
35.4 f 2.9
a' value. ha" value.
cently, the barriers to abstraction of an H from H2 by both C N and C C H have been determined to be 3.945and 2.346kcal/mol, respectively. These reactions both involve H atom abstraction by a triple-bonded carbon radical center, and both reactions have an exothermicity within 4.5 kcal/mol of that given above for the reverse abstraction of OH + CCH. Under the assumption that O H + C C H has a similar barrier to abstraction, i.e., 3.1 f 0.9 kcal/mol, then AEe, for the change in energy from 0 HCCH to the transition state O...H-CCH is 35.4 f 2.9 kcal/mol. The frequencies and structure of the transition state can be roughly estimated by scaling the values for H-Ha-CCH calculated46 in a manner similar to what is used here for the addition transition states. Of the nine real frequencies at the transition state, two are barely changed from the two stretch frequencies in C C H and four are in two doubly degenerate pairs of bends that are about 50 cm-' lower than similar pairs in HCCH. There remains one doubly degenerate pair of bend frequencies representing the rocking of H2 relative to C C H and one stretch frequency involving motion of the partially bonded central H atom. These last three frequencies along with the imaginary frequency along the reaction path have to be scaled to reflect the end 0 atom instead of an H atom. The scaling factor is derived from the ratio of similar calculated frequencies for O--H-.CH~7 and H.-H-. CH3.48 The resulting frequencies are listed in Table XI. Note that, unlike the H-.H-.CCH transition state, there are two sets of bends involving either A' or A" electronic symmetry. The dynamic consequences of two potential energy surfaces that are degenerate along the collinear reaction path but are split by bending motion will be discussed in the next section. The structure at the transition state is derived from similarly scaled values of H-H-CCH. Only the 0.-H and H-C distances are changed; the CC and C H distances are assumed to be the same in the two transition states. The resulting structure and moment of inertia are listed in Table XI. While approximate in its derivation, the characterization in Table XI of the abstraction process will be shown in the next section to rule out its contribution over temperatures at which measurements have been done.
+
IV. Overall Rate Constant Measurements of the overall rate constant k , Le., the total rate of loss of 0 or C2HZ,are represented in Figure 9. These results are the measurements judged most reliable by Herron and Huie in their 1973 re vie^,^ four later direct measurements,6.s-'0 and two recent high-temperature shock tube measurements.11*12 Other less direct measurement^^^^ are not included. As mentioned in the Introduction, the two shock tube measurements appear to be (45) Wagner, A. F.; Bair, R. A. In?. J . Chem. Kinet., in press. (46) Harding, L. B.; Schatz, G. C ; Chiles, R. A . J . Chem. Phys. 1982, 76. 5172. (47) Schatz, G.C.; Wagner, A. F.; Dunning, Jr., T. H. J . PIiys. Chem. 1984, 88, 221. (48) Walch, S. P.; Dunning, T. H., Jr. J . Chem. Phys. 1980, 72. 3221. The 1
.S
Figure 9. Comparison of theory and experiment for the overall rate of loss of 0 by reaction with H C C H as a function of inverse temperature. The calculated curves are labeled. For the experiments: 0 , ref 12; 0 , ref 1 I ; $, ref 9; 0,ref 8; 0,ref IO; @, ref 6 ; A and symbols at room temperature, see ref 3.
mutually consistent but larger in magnitude and activation energy than lower measurements. All the lower temperature measurements were performed at relatively low buffer gas pressure (generally about 1 Torr). However, in one measurement,8bbuffer gas pressure of N2 was varied from 11 to 81 Torr with no noticeable pressure dependence and with no significant difference (
