Analysis of OpP) plus Olefin Reactions
2509
Reactive Branching Ratios. Prior Expectation Values and Analysis for O(3P) plus Olefin Reactions Denis J. Bogan Code 6 180, Chemistry Division, Naval Research Laboratory, Washington, D.C. 20375 (Received April 26, 1977) Publication costs assisted by the Naval Research Laboratory
Prior expectation values have been calculated for the relative rates of formation of the products, alkyl (or substituted alkyl) radical + formyl (or substituted formyl) radical, and carbene + carbonyl, from the reactions of O(3P)atoms with olefins. These two channels are known to account for 80% or more of the reaction in all cases. The predicted branching ratios were obtained from an energy limited phase space calculated for the well-separated products. Comparison with the experiments of Gutman and co-workers shows that in general, these reactions are statistical, however, in some cases, effects not accounted for in the calculation cause disagreement between predicted and observed results. It is suggested that one such effect is preferential attack at one end of the double bond. The calculation has the advantage of simplicity,in that only the available energy, heats of formation, vibrational frequencies, and rotational moments of inertia of the separated products are required as input data. The method is applicable to product channels reached from long-lived complexes where only one bond is broken in the exit channel without a significant exit barrier, and the products are both polyatomics with approximately equal rotational moments of inertia.
Introduction In complex chemical kinetic systems, reactions often occur in which one set of reactants leads to more than one set of chemically distinct products. When this occurs, knowledge of the relative rates of formation of each set of products, Le., the reactive branching ratios, is as important as knowledge of the overall rate constant. The reactions of ground state O(3P)atoms with olefins fall in this category. These reactions are important in combustion and photochemical smog, subjects which are receiving much attention from kinetic modelers. This paper represents an initial approach toward a theoretical rationalization of the complex problem of reactive branching. The energetically accessible product channels for the reaction 0 plus ethylene are as follows: A H = -7.8 kcal/mol 0 + C,H, -, CH, + H,CO (1)
+ HCO C,H,O + H
A H = -30.8
(2)
A H = -38.0
(3)
CH,CH,O
A H = -84.7
(4)
A H = -86.7
(5)
A H = -111.8
(6)
A H = -116.4
(7)
CH,
H,CCO
+ H,
CH,CHO
CH,
+
CO
-
This reaction, 0 + C2H4 “products”, has been studied intensively since 1955.1-3 Based upon very careful product analyses, under various conditions of reactant concentration and total pressure, CvetanoviE inferred that a long-lived complex is formed which can be collisionally stabilized to give acetaldehyde or ethylene oxide and that the principal product channel at pressures less than 1atm is (2). Gutman and co-workers have established that, under low pressure conditions, the product channels and branching ratios are channel 2,95%, and channel 5 , 5%.3 Their experiments were done at P x Torr using high intensity, crossed, uncollimated beams of 0 and CzH4. Photoionization mass spectrometry was used to detect the parent ions of the primary products CH3, HCO, and HZCCO. Gutman et al. have also studied the reactions of 0 plus fluoroethylenes in order to elucidate the effects of changing
structure and therm~chemistry.~ The reaction of CzF4 goes exclusively via the carbene channel (CFZ + FZCO), whlch is more exoergic than the alkyl channel (CF3 + FCO) by 30 kcal; and the reaction of CzH4goes via the alkyl and ketene channels. For the remaining fluoroethylenes the carbenefalkyl branching ratios follow the changing exoergicity; where the carbene channel is more exoergic, it is favored and where the alkyl channel is more exoergic, it is f a ~ o r e d .The ~ number of product quantum states in a channel is proportional to exoergicity. Hence, Gutman’s experiments suggest the applicability of statistical phase space theory in which the probability of following each channel is proportional to the number of product states in each channelq5 In this paper we are interested in the relative rates of decomposition of the collision complex into the various product channels. The rate of formation of the complex from reactants and its absolute rate of decomposition to products are not of interest herein. The latter problems can be treated rigorou~ly,~-~ but require knowledge or reasonable estimates of the properties of the complex and the entrance and exit transition states. Kinematic information on the reactions of 0 plus olefins, which could help to provide such knowledge, is presently not available. For this reason and for simplicity, we desired an approach requiring no prior informations about the entrance and exit transition states. Thus, we use an energy limited phase space calculation. The required input data are the vibrational frequencies and rotational moments of inertia of the products, and the exoergicity. These are properties of the well-separated products which can be obtained from standard referencesg or estimated with (generally) good We develop the argument that product phase space volumes, calculated on this basis, are reasonable approximations to the true phase space volumes only if stringent requirements are met. These are (i) there must be no significant exit barrier in the product channel; (ii) the two products must both be polyatomics with approximately equal rotational moments of inertia; (iii) the bond breaking process which occurs in the exit channel must involve only a single b9nd scission; (iv) the reactant orbital angular momentum, L, must be small. The carbene The Journal of Physical Chemistry, Vol. 8 1, No. 25, 1977
Denis J. Bogan
2510 REACTANTS
COMPLEX
~
PRODUCTS
~
Flgure 1. Reaction coordinate diagram for the principal product channels of the 0 C2H4reaction. The drawing is to approximate scale only. See text for discussion of the large exit barrier in the ketene channel.
+
H,CO + :CHX
\ /
H2+ HXCCO
Hi0
1
t
*CH2X
-1
*CH3 XCO
Figure 2. Mechanism for the principal product channels of the 0 4C2H3X reactions. The mechanism is taken from CvetanoviE’ and Gutman3z4: X = H, CH3, halogen.
and alkyl channels satisfy these requirements. Prior expectation values for branching between the carbene and alkyl channels are calculated for reactions of 0 with ethylene, tetrafluoroethylene, vinyl fluoride, vinyl chloride, and propene. The calculations are in good agreement with the experimental measurements of Gutman et aL3l4except for vinyl fluoride, In this case it is suggested that the disagreement between calculation and experiment indicates a strongly preferential addition of 0 to the CH2 carbon.
Computational Method A. Necessary Conditions. A schematic of the reaction coordinate diagram for channels 1, 2, and 5 is shown as Figure 1. Figure 2 shows the mechanism, derived from CvetanoviEl and G ~ t m a n ?of~ complex decomposition into product channels 1, 2, and 5. All of the bracketed configurations, shown in Figure 2, occur in the region of the reaction coordinate labeled “complex” in Figure 1. The configurations which are bracketed and labeled by ‘‘3” in Figure 2 are transition states for decomposition into the product channels. These transition states occur in the cross hatched area of Figure 1. Configurations I and I1 of Figure 2 are the initial adducts resulting from attack of O(3P) upon ethylene. The activated complex (transition state) has been defined as the position, on the reaction coordinate, of minimum phase space density.24 This will be near, but not necessarily at, the highest point on the potential energy surface due to the fact that both energy and angular momentum must be conserved. The mechanism of Figure 2 shows several long-lived complexes which can be interconverted by H (or X) migration or via formation of the epoxide. In order for a statistical theory to be valid, the The Journal of Physical Chemistry, Vol. 8 1,
No. 25, 1977
phase space densities must be significantly lower at the exit channel barriers than at the barriers to interconversion among these complexes. Hence the exit barriers must be significantly higher than the barriers to interconversion. If this is true as suggested (in general) by the results presented below, then the partition among the various complexes of Figure 2 will be statistical. A necessary condition for the validity of a calculation of the type we propose is that the region of phase space through which the complex must pass in order to enter the product channel must not be significantly constricted relative to the phase space of the well-separated products. For channel 5 , a large exit barrier undoubtedly occurs (Figure 1) and this will produce such a constriction. Gutman et al. have established that the elimination of H2 is a three-centered, aa p r o c e ~ s . Kim ~ and Setser have established that the barrier to aa elimination of HX is ca. 65 kcal/mol.1° The barrier to aa elimination of H2 is expected to have at least the same magnitude. The volume of phase space in the region of the product channel transition state can also be reduced by the occurrence of a tight complex. Tight complexes are the rule in three-centered (and other multicentered) processes such as channel 5.6 For the above reasons, we confine the application of our method to product channels which can be reached by the scission of one bond in the exit channel, without a significant exit barrier. Channels 1 and 2, which account for 80% or more of the totalobserved products in low pressure 0 plus C2H3Xreactions, are believed to meet these criteria. Information concerning the lack of a barrier for channel 2 comes from the observation that the unimolecular decomposition of ethylene oxide, giving HCO plus CHBvia a vibrationally excited acetaldehyde complex, has an Arrhenius activation energy of 57 kcal/mol.11J2 Based on the heats of formation of ethylene oxide and the products? the exit barrier for this channel is ca. 3 kcal/mol, which is insignificant. This plus the fact that the fluoroethylenes exhibit changes in the branching ratios of the carbene and alkyl channels which follow the thermochemistry4 (see Introduction) is good evidence for the absence of a significant exit barrier in channel 1. B. Product Energy States. For the reaction A + B C + D, the number of energy allowed product states, considered as a volume in phase space is
-
V“(C, DIE) = JE;f:-”TRd.E;cPc
(Ec)J&,%iETR~
(ED) x
D P D
ED)
PTR ( E - E c
(8)
where Vo(C, DIE) is the phase space volume in product channel C, D at fixed available energy E. Ec, ED,and E m are the vibration-rotation energies of products C and D and the center of mass translational energy, respectively, and pc, pD, and pTR are the corresponding densities of states. Since we are counting product states, available energy is referenced to products in their ground uibrational, rotational, and translational states. The mean available energy, based upon Tolman’s interpretation of activation energy,13is given by ( E )=-AH,’
f
E,
f
(E,)
f
(E,) 4- (ETR)
(9)
where AH: = exoegicity is the enthalpy of reaction at 0 K, E , is the Arrhenius activation energy which was taken to be 1.0 kcal/mol for all olefins, (E,) is the mean vibrational energy of the olefin (C0.5 kcal at 300 K), and (ER) (ETR)= 3RT is the mean rotational energy of olefin plus mean translational energy of reactive collisions.
+
251 1
Analysis of O(3P) plus Olefin Reactions
TABLE I: Frequency Assignments (cm-’ ) Molecule Ref HCO CH, CH,b H,CO C,H,C C,H, CH,CHO CH,COC FCO CF3 CF, F,CO CH,F CH,C1 ClCO
22 23, 22 9a 9a 22 9d 9d Est 9a 9a 9a 9a 23, 22 23, 22 9a
3414 3002 2960 2766 2951 3056 2928 2928 1018 1090 1222 965 3056 3176 1880
5)
4) 2)
3)
2)
Frequency( degeneracy)a 1889 580 1114 ( 2 ) 1746 1434 ( 5 ) 1411 ( 4 ) 1471 ( 6 ) 1471 ( 5 ) 626 701 665 1928 1435 3086 570
1101 3184 ( 2 ) 3200 1501 1190 935 ( 4 ) 1113 850 ( 2 ) 1855 1259 ( 2 ) 1110 626 1305 1390 281
1383 (2) 1167 995 850 3 ) 509
2843 822 ( 2 )
1251 289
509 150
150
584 600 826
774
500 2) 1249 1171 1000
397
a Frequencies were grouped t o lessen the computing time required direct count states. This procedure causes minimal The frequencies of This frequency assignment is also discussed in the text. error and has been discussed in detaiL6 these free radicals, R, were estimated by deleting one C-H stretch ( - 3000) and two C-C-H bends (- 1000) from the assignment of the parent RH molecule; compare CH,CHO and CH3C0.
The translational density of states is calculated from the classical expression14
where p = product reduced mass, and the vibration-rotation density of states isI5
where is the gamma function, EVR is the total vibration-rotation energy, Ev the vibrational energy, P(Ev) the number of vibrational states at energy E”, and QR the rotational partition function (at 300 K). The value of QR can be calculated from the rotational moments of inertia of the molecule, or alternatively from the rotational constants;6 both quantities are tabulated in standax‘d reference ~ o r k s Molecular . ~ ~ ~ ~vibrational frequencies can likewise be obtained from standard references,ga’cpd or estimated.ge The P(EV)values used in our calculations were obtained by direct state counting at low energies6(Ev < 0.2 of the zero point energy) and by the Haarhoff approximation at higher energies.16 The frequency assignments used for this work are given in Table I. C. Product Angular Momentum States. Product states can be reached only if the complex which forms them has sufficient energy and angular m ~ r n e n t u m . ~The J ~ available angular momentum, J, in an atom-molecule collision is given by IL - JI < J < IL + JI (12) where L is the orbital angular momentum of the complex forming collision and J the rotational angular momentum of the reactant molecule. The accessible product angular momentum states are given by the conservation equation
s’= E’+ 5,’ + +I2’ where-z’ is the_ product channel orbital angular momentum, J1’and J2’are the rotational angular momenta of products 1and 2. The primes denote the product channel as distinguished from the (unprimed) reactant channel. The orbital angular momenta for reactant and product channels are related by
where 1.1 and p’ are reduced masses, ( u ) and (u’) are mean
velocities, and b is the impact parameter. The maximum values of L and L’will occur for the largest possible impact parameter, b, which in turn can be estimated from the bulk rate constant, assuming a hard sphere cross section.” The 0 plus olefin reactions all have rate constants k I cm3/molecule s at 300 K3n4and this leads to L Il h . The product channels 1and 2, to which these calculations are applied, have near zero exit barriers, hence ( u ) ( u ’ ) and L ’ x L p’/g. The mean rotational angular momentum of ethylene at 300 K is 16h, thus the distribution of J will be closely approximated by the distribution of rotational states of the reactant ethylene. Since p and p’ are not greatly different for the alkyl and carbene channels, centrifugal barrier effects will be and, hence there will be no significant constriction in the exit channel phase space. On the average, L’, 5,: and JZ’can take up all orientations in space. If products 1and 2 are polyatomic species with approximately equal mom_ents of_inertia, then there will be partial cancellation of J1’by Jz’such that many, if not most, of the Jl’and Jz’values which exceed J will still satisfy eq 13. I t should also be noted that the magnitude and direction of the errors arising from neglect of angular momentum conservation will be approximately the same for the alkyl and carbene channels due to the dynamical similarities noted in sections A and C, above.
Results A. Calculated Results. The calculated prior branching ratios and the experimental branching ratios of Gutman and c o - w o r k e r ~are ~ ~shown ~ in Table 11. Also shown are the product rotational partition functions and ( P ’ ) ~ / ~All . of the calculations are for products in their ground electronic states. In a few cases, there is uncertainty in the input quantities. Recent theoretical and experimental work suggests that the ground triplet state of CH2is bent.lg We did not find a three frequency vibrational assignment for methylene and instead used the JANAF,S”four frequency assignment which assumes a linear molecule. These frequencies (presumably) were chosen to be consistent with the other reported thermochemical properties. Deletion of the lowest frequency in the JANAF assignment gives a prior branching ratio for channel 1 of 0 plus ethylene which is lower by a factor of 2 than the Table I1 value. The rotational moments of ground state CH2 are likewise uncertain. We used Herzberg’s value of ABC = 1562 cm-3 for the (a ‘Al) state to calculate the rotational partition The Journal of Physical Chemistry, Vol. 81, No. 25, 1977
Denis J. Bogan
2512
TABLE 11: Observed and Predicted Branching Ratios Products
Q,
CH, t H,CO CH, t HCO H, t H,CCO
12.2 34.4 91.1
FCO t CF, CF, t F,CO
68.6 100
CH,CHO + CH, CH,CO t CH, HCO t C,H, H,CO t C,H, CH,CHCO t H,
Q, 0 t C,H, Reaction 67.3 715 42.3 775 1.8 2569
Ef
17.7 30.6 36.3 85.1 92.6
CH, t FCO CH,F t HCO
41.7 27.1
CH, + ClCO CH,Cl t HCO
41.4 32.6 1
5326 3966
(fi03'*
Predicted
29.6 31.1 2.64
0 t C,F, Reaction 11730 15280
0.0013 0.9987 NAa
148 152
0 t Propene Reaction 12030 67.3 12030 42.3 775 815 715 663 28520 1.8
34.6 37.1 55.2 55.1 2.68
0.03 0.97 0.019 0.235 0.763 (0.9996)b NAa
0 t Vinyl Fluoride Reactiond 42.3 5326 38.6 2772 775 60.6
Observed None 0.95 0.05 None 1 None Major Major Minor ?C
0.77 0.23
0.92
0.55 0.45
0.24 0.76
0 t Vinyl Chloride Reactione 42.3 5259
12820 775
42.3 78.2
a NA means calculation not applicable, see text. The number in parentheses is the prediction for a zero exit barrier. The experimental evidence suggests a sizeable exit barrier, see text. Gutman e t al., ref 3b, c, were uncertain about the presence of methyl ketene product. a Gutman et al., ref 4b, reported the branching fractions for alkyl, fluoroalkyl, and ketene (H,CCO) channels as 0.82, and 0.11, respectively. The correct application of information theory requires that the prior and observed branching fractions be normalized to the same sum. Gutman et al., ref 4b, reported the branching fractions for alkyl, chloroalkyl, and ketene (H,CCO) channels as 0.22, 0.70, and 0.08, respectively. See also footnote d , above. The available energy, E , is related t o the reaction enthalpy by eq 9 of the text. In general AHrxnz= 4 - E kcalimol.
TABLE 111: Information Theoretic Analysis for the Reactions 0 t Vinyl Fluoride and Vinyl Chloride ASm, ASCH,X,
,
I' GH ,,cH X I'CH,,CH,X
