12254
J . Phys. Chem. 1993,97, 1225&12259
Reaction between OH (OD) Radicals and CO at Temperatures down to 80 K: Experiment and Theory Michael J. Frost, Paul Sharkey, and Ian W. M. Smith' School of Chemistry, The University of Birmingham, Edgbaston, Birmingham B15 ZTT, United Kingdom Received: June 15, 1993"
Using the pulsed laser-photolysis (PLP) laser-induced fluorescence (LIF) method, rate constants have been measured at low total pressure for the reactions between OH and C O (297 2 T/K 1 80) and OD CO (295 1 T/K 1 178). Calculations have been carried out based on transition-state and RRKM theories and allowing approximately for quantum mechanical tunneling through the transition state (TS2) which separates HOCO (DOCO) from H(D) C02. They indicate (a) that tunneling is important in both these systems, (b) that the barrier at TS2 is higher than previously thought and closer to the ab initio value, and (c) that the observed kinetic isotope effect can be reproduced quite well. The possible role of hydrogen-bonded complexes in facilitating these reactions is discussed briefly.
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Introduction The molecular mechanism of the reaction between OH (OD) radicals and CO, as well as its rate constant and reaction products, has been the focus of considerable attention in recent years. At low total pressure, there is no doubt that the reaction produces H(D) atoms and C02: O H (OD)
+ CO
-
H (D)
+ CO,; Moo = -102.3 kJ mol-' (1)
The kinetics of this reaction have been very extensively studied, partly in response to its importance in combustion' and atmospheric chemistry,2where it acts as the last step in the oxidation of fuel-based carbon. The recommended value of the rate constant, kl, at 298 K is (1.5 f 0.2) X lO-I3 cm3 molecule-I s-I, which corresponds to a probability of reaction per collision of ca. In view of this, it is rather surprising that the rate constant is virtually independent of temperature between ca. 250 and 500 K, although its value increases quite steeply at higher temperatures. In the 1970s, Smith and Zellner3and Smith,4following Dryer et U I . , ~analyzed the unusual temperature dependence of kl in terms of transition state theory. Going further than Dryer et al., they noted that HOCO and DOCO had been observed spectroscopically in low-temperaturematrices.6 They therefore proposed that the reaction of OH (OD) with CO proceeds by way of energized HOCO (DOCO) complexes which can suffer three possible fates: decomposition, at comparable rates, to OH(0D) + CO or H(D) + C02, and stabilization by collision. Since that proposal was made, it has been demonstrated in several experimental studies7-14that the rate of reaction between OH (OD) and CO does indeed depend on total pressure, and it is now generally accepted that the following mechanism describes the overall reaction of OH with CO:
The o b s e r v a t i ~ n of ~ ~a significant, ~ ~ ~ ~ ' ~ and unusual, isotope effect further confirms that the reaction does not proceed in a simple direct manner. ~~
Abstract published in Aduance ACS Abstracts, October 15, 1993.
0022-3654/93/2091- 12254%04.00/0
In fact, the proposal that the HOCO (DOCO) radical could be an important intermediate in gas-phase chemical kinetics had an earlier origin which has usually been ignored. In papers published in the early 1960s by M. H. Back and SehonI6and by Mearns and R. A. Back,17J8the HOCO radical was proposed as an intermediate in both the thermolysis of phenylacetic acidi6 and the photolysis of trifluoroacetic acid.17 In 1964, Ung and R. A. Back proposed HOCO as an addition product of the reaction of OH and CO.'* Although there have not been any direct, spectroscopic observations of HOCO formed as an addition product of reaction between OH and CO, three papers have recently reported the high-resolution microwavei9and infraredZospectra of the HOCO and DOCO radicals. The radicals were created either asa product of the reaction between C1 atoms and HCOOH (DCOOD or HCOOD),19 by photolysis of CH3COOH (CH3COOD, CD3COOD),20aor by photolysis of C2H3COOD.20b Sears et recorded infrared spectra in the region of the CO stretch at ca. 1850 cm-I using a tunable diode laser spectrometer, while Petty and MooreZobrecorded the OD stretch of DOCO using difference frequency mixing to generate the required infrared frequencies. An earlier, but still recent, photoionization mass spectrometric study2' obtained what appears to be the first direct experimental evidence for the existence of the HOCO (DOCO) radical in the gas-phase. In these experiments, HOCO (DOCO) radicals were formed by abstraction by F atoms of the H (D) atom bonded to the C atom in HCOOH, DCOOH, and HCOOD. From the adiabatic ionization potential which they measured for HOCO (DOCO), Ruscic et al.21were able to determine A&O(COOH) = -220 f 2.5 kJ mol-', which corresponds to an HO-CO bond energy in trans-HOC0 of DO = 148.5 f 2.5 kJ mol-I. Theoretical evidence for the stability of the HOCO radical and its role as a transitory intermediate in, or at higher pressures as a product of, the reaction between OH and CO comes from three ab initio cal~ulations.~~-2~ The studies of McLean and Ellinger22and of Aoyagi and KatoZ3concentrated on the properties of the potential energy surface in the region of the minima corresponding to trans- and cis-HOCO. The calculations of Schatz et on the other hand, explored the variation of energy along the minimum energy path for reaction 1 . They have fitted a full surface to their ab initio points and used the fitted surface in quasiclassical trajectory and quantum scattering calculat i o n ~ on ~ ~the- ~OH ~ + CO reaction and its reverse. There have been several attempts4J4Js,26s27 to model the mechanistic scheme given above in order to match all the kinetic data for the overall reaction between OH radicals and CO. Here, 0 1993 American Chemical Society
OH (OD) Radicals and C O Reaction
The Journal of Physical Chemistry, Vol. 97,No. 47, 1993 12255
a summary is given of the calculations performed by Brunning et al.Is Inter alia, they measured the rates of removal of OH(u=l) and OD(u=l) by CO a t 298 K. They argued that these rate constants correspond to those for formation of HOCO (DOCO) complexes from OH(v=l) (OD(v-1)) C O since, even if the complexes dissociate back to OH (OD) + CO, vibrational relaxation of the radicals would occur. The correctness of this argument was supported by conclusions from quasiclassical trajectory calculationsZSand has recently been confirmed by measurements of rate constants for the reaction between OH and CO at total pressures up to 200 bar.2s Using standard transition state theory and structural parameters and frequencies from the ab initio calculations of Schatz et Brunning et al.Is inferred that the height of thevibrationally adiabatic barrier for formation of HOCO from OH(u=O) + CO corresponds to ca. 280 cm-l. They then employed the theoretical methods of TroeZ9to estimate the rate constant for association of OH and CO in the limit of low pressure and hence deduced a value for k,. The ratio of kp/k, could be deduced from a comparison of the observed values of kl and the value estimated for k,, since the model predicts kl = k,(k,/k, kp)J. Finally, microcanonical transition-state calculations were performed with the difference in energy of the zero-point levels in TSl and TS2 taken as an adjustable parameter. Agreement with the previously deduced value of kp/k, was reached with AE,,/hc = ((EZp,~s2 - Ezp,TSl)/hc} = -30 cm-I. Subsequent calculations based on this model were able to reproduce quite well the dependence of the rate constant for the overall reaction between OH and CO on temperature, total pressure, and isotopic substitution. The calculations just described were extended to low temperatures by Smith30to see whether reaction 1 might be an important source of C02 a t the ultralow temperatures of interstellar clouds. These calculations predicted that, as the temperature falls below ca. 200 K and the adiabatic barrier becomes larger than kBT, the value of kl should fall steeply. In the present paper, we report rate constants for the reactions of OH and OD with C O at low temperatures: in the case of OH CO down to ca. 80 K, and for OD CO down to 178 K. Some of the experimental results for OH CO have been given in an earlier paper32which also reported measurements of the vibrational-state distribution of C02 formed in reaction 1. In addition to extending the low-temperature experimental results, we have extended the calculations of Brunning et a1.Is and Smith30in two ways. First, the effect of quantum mechanical tunneling through the potential barrier between the energy minimum associated with HOCO (DOCO) and that corresponding to separated H (D) C02 has been estimated using an approximate method described by Miller.31 Although these calculations do indicate that quantum mechanical tunneling through TS2 is important and that the barrier a t TS2 is probably higher than inferred by Brunning et and closer to that expected on ab i n i t i o g r ~ u n d s , ~ ~ tunneling cannot explain our experimental observation that the rate constant only decreases by about 40% as the temperature is lowered from 298 to 80 K. In a second set of calculations, we have explored the possible role, especially at low temperatures, of the formation of transient hydrogen-bonded complexes.
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Experimental Section The apparatus and experimental method used in the present experiments were similar to those employed in our laboratory in several series of low-temperature experiments on reactions of the OH and C N radicals over the past few year^.^^-^^ Therefore only a brief description of these features of the present work will be given here. Our experiments on the reactions of OH and OD with CO used two reaction cells. Both were constructed from three concentric tubes of Pyrex, so that the central tube in which the reaction occurred was provided with a double jacket. The inner
jacket is ca. 30 cm long, and coolant was passed through it. The outer jacket completely surrounded the inner jacket and was evacuated. In the first experiments on the OH CO reaction, the photomultiplier and optical filters were mounted in a housing which was clamped to the centre of the cooled section of the reaction cell. Fluorescence from OH, induced by the probe laser, was collected by a lens and observed through the two jackets. In later experiments, in an attempt to improve the signal levels, a new cell was built. It incorporated a short sidearm fitted with two quartz windows: one window was mounted on the central reaction tube and was joined by a short tube to the evacuated jacket; the other window was mounted on the outer wall of the evacuated jacket. The housing containing the photomultiplier tube, filter, and lens was mounted on the reaction cell assembly in a similar manner to before. The photolysis and probe laser beams propagated in opposite directions along the axis of the cylindrical reaction cell. The photolysis laser beam from a frequency-quadrupled Nd:YAG laser (Spectron Lasers, Model SL803) was ca. 5 mm in diameter in the center of the reaction cell and it provided 20-30 mJ/pulse at 266 nm. With the concentrations of H N 0 3 (or DNO,) present in typical experiments, we estimate that the initial concentrations of OH (or OD) were ca. 2 X 10l2 molecules ~ m - ~The . probe laser was a frequency-doubled dye laser (JK Lasers, System 2000) pumped by a second Nd:YAG laser (Spectron Lasers, Model SL404). It was tuned to a line at ca. 282.5 nm in the (1,O) band of the A2Z+-X211 system of OH. Fluorescence in the (1,l) and (0,O)bands was observed through a broad-band filter (Corning UG11) and an interference filter with a bandpass (fwhm) of 10 nm centered at 310 nm. To reach temperatures down to ca. 138 K, isopentane was passed through a U-tube immersed either in a solid CO2-acetone mixture or in liquid N2 and then through the inner jacket of the reaction cell assembly. To reach the lowest temperatures, liquid N2 was used as the refrigerant.32 As b e f ~ r e ,the ~ ~temperatures -~~ achieved in the center of the reaction cell for a particular flow of gas and given cooling conditions were measured, using a thermocouple, in separate experiments. Some variation in the actual temperatures obtained by liquid Nz cooling was achieved by varying the speed of the gas flow through the reactor and the total pressure. It is estimated that the temperatures which are cited should be accurate to f 2 K. Nitric acid and deuterated nitric acid were prepared by our usual m e t h ~ d . ) ~Argon J~ (zero grade, oxygen-reduced, purity 99.998%) and carbon monoxide (Cambrian Gases, purity 99.9%, or Air Products, purity 99.5%) were used without further purification.
+
Results Rate constants for the reaction between O H and CO have been successfully measured from room temperature down to ca. 80 K. Measurements proved more difficult to make for OD CO and results are reported only for 295, 216, and 178 K. Attempts to measure reliable rate constants for OD C O a t temperatures below 178 K failed. O D radicals were more difficult to observe satisfactorily partly because of reduced sensitivity but also because the OD CO reaction is appreciably slower than that between OH and CO. Consequently, larger CO concentrations had to be used to obtain satisfactory first-order decay rates with a resultant increase in the extent of fluorescence quenching. A typical plot of the first-order constants determined with different concentrations of CO but the temperature and total pressure maintained constant is shown in Figure 1. The results of all our measurements and the experimental conditions under which they were obtained are summarized in Tables I and 11. As mentioned earlier, the initial concentration of OH (OD) radicals created by photolysis of HNO3 (DN03) is ca. 2 X 10l2
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Frost et al.
12256 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
14003
-
1mn ..
1
-"
-1
TABLE Ik Summary of the Experiments and the Rate Constants Derived for the Repctio~of OD with CO
''
1 m ..
-
iean-4003
.-
2005.
1
o i
T/K
plTorr (M)
k1.H
no.of
max [CO] measts ( 10l6molecules cm-3) 7.2 6.2 7.7 7.9 7.8 7.9
296 297 297 296 296 297
5.0 (N2) 5.1 (Ar) 10.0 (Ar) 10.0 (Ar) 10.0 (Ar) 10.0 (N2)
12 11 12 9 9 13
216 216
4.0(Ar) 7.0(Ar)
12 10
8.0 10.1
178 178
2.0 (Ar) 2.0 (Ar)
10 14
5.9 5.2
138 138 138 138 138 138
2.0 (Ar) 2.0 (Ar) 2.0 (Ar) 2.0 (Ar) 2.0 (N2) 2.0 (N2)
12 9 11 12 9 12
7.0 6.1 6.9 7.0 4.3 6.3
107 106 105.5
4.0 (Ar) 4.0 (Ar) 4.0 (Ar)
7 11 7
7.6 9.0 7.1
85.5 83 79.5 85 83 82.5 82
2.0 (Ar) 2.05 (Ar) 2.3 (Ar) 5.0 (Ar) 5.0 (Ar) 5.0 (Ar) 5.0 (Ar)
6 8 11 5 6 9 10
3.7 9.3 12.0 6.7 7.3 5.7 6.4
( 1V13cm3
molecule-I s-l) 1.84 f 0.03' 1.31 f 0.07 1.76 f 0.01 1.85 f 0.03 1.73 f 0.04 1.80 f 0.05 av = 1.71 f 0.2 1.74 f 0.06 1.81 f 0.05 av = 1.78 f 0.05 1.82 f 0.05 1.79 f 0.05 av = 1.80 f 0.05 1.3 1 f 0.07 2.23 f 0.10 2.40 f 0.14 1.71 f 0.06 2.02 f 0.06 2.1 1 f 0.04 av = 2.0 f 0.35 1.02 f 0.15 0.89 f 0.04 1.24 f 0.07 av = 1.05 f 0.15 1.05 f 0.24 0.98 f 0.1 1 1.04 f 0.10 1.07 f 0.20 0.89 f 0.21 1.12 f 0.07 0.81 f 0.07 av = 1.0 f 0.1
0 The errors quoted correspond to a single standard deviation in the gradients of kist versus [CO].
molecules ~ m - ~In.these experiments, in contrast toothers which we have carried out recently,33it was unnecessary to make any correctionsfor secondary reactions, since the association reactions O H H and OD D will be third-order and slow under our experimental conditions. In the absence of added CO, the processes mainly contributing to decay of the O H LIF signal would be diffusion of the radicals from the zone illuminated by the probe laser and, to a lesser extent, reaction with HN03 (DNOs). Experiments were conducted using both N2 and Ar as diluent gas. No significant difference between the results was observed. In all the experiments on O H + CO, the total pressure was kept sufficiently low for the kinetics to be in the low-pressure limit, in which no stabilization of the HOC07 occurs and the only products are H COz. Experiments by ~ t h e r s l - ~ ~have J * shown that pressure effects are more noticeable in the OD + CO reaction than in OH + CO, and they may be in part responsible for the increase in the rate constant for this reaction observed in our
+
+
+
T/K
plTorr (M)
295 295 295 216 216 216 216 216 216 216 178 178
10.0 (Ar) 15.1 (Ar) 25.1 (N2) 4.0(Ar) 8.0 (Ar) lO.O(Ar) 15.O(Ar) 25.0 (Ar) 50.0 (Ar) 80.0(Ar) 2.0 (Ar) 5.0 (Ar)
kl,D
measts
max [CO] ( 10l6 molecule cm-')
(10-14om3 molecule-l s-I)
7 7 9 8 7 7 7 8 7 10 9 7
12.8 12.8 28.7 9.8 10.8 16.7 10.8 9.7 9.4 10.3 5.1 6.2
5.2 f 0.1" 4.9 f 0.4 7.5 f 0.25 5.1 i 0.2 5.4 f 0.1 6.0 f 0.2 5.9 f 0.2 7.0 f 0.2 8.5 0.4 9.1 f 0.5 4.8 f 0.5 5.0 f 0.6
no.of
a The errors quoted correspond to a single standard deviation in the gradients of kilt versus [CO]. experiments at the highest total pressure (and in N2) and at room temperature. A systematic study of the pressure effect in this reaction was made at 216 K. A clear increase in the rate constant was observed as the pressure was raised, similar to that observed for this reaction at room t e m p e r a t ~ r e . ~ - l ~ . ~ *
Discussion and Calculations The results reported in Tables I and I1 demonstrate clearly that,contrary toexpectation,3°the rateconstan tsfor thereactions between OH and CO and OD and CO show little change when the temperature is decreased, to 80 K in the case of O H CO and to 178 K in the case of OD + CO. The lack of any large change in the low pressure rate constants for reaction of either O H or OD implies, of course, that the isotope effect, expressed as the ratio of rate constants ( ~ I , H / ~ I , D )retains , approximately the samevalue of ca. 2.7 as the temperature is lowered from room temperature to 178 K. The size of this isotope effect was one of the kinetic features of the reaction which was least satisfactorily explained by the calculations of Brunning et 0 1 . ~For ~ this reason and also because of the discrepancy between the observed and calculated30rate constants at low temperatures, we have carried out calculations similar to those undertaken p r e v i o ~ s l y but ~~.~~ this time have incorporated the possibility of quantum mechanical tunneling through the well-defined barrier associated with TS2. These calculations are described next. (a) Quantum Mechanical Tunneling in the OH(0D) CO Reaction. In terms of the reaction mechanism and rate constants given in eq 1,the second-order rate constant for loss of O H radicals by reaction with CO, kobJ= (-d[OH]/dt)/[OH][CO], is given by
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Under conditionsof low [MI, which we shall concentrate on here, this expression simplifies to (iii) In the treatment described fully by Brunning et a1.,15standard transition-state theory was used to estimate k,,while microcanonical transition-state theory was used to calculate the branching ratio, k,/(k, kp). The choice of parameters for the two transition states TS1 and TS2 was influenced both by the experimental kinetic data and by the ab initio results of Schatz et Thus, for TS1, the rotational constants and vibrational frequencies were taken to be those given by the ab initio calculations, whereas the vibrationally adiabatic energy barriers were chosen with reference to experimental data. First, was adjusted until the transition state theory rate constant for formation of energized H O C 0 complexes from OH(u= 1) and CO matched the rate constant, k,,, = 1.O X lei2 cm3moleculci S-I, which Brunning et al.Is measured for the relaxation of OH-
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The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12257
OH (OD) Radicals and CO Reaction (u=l) by CO. Considering the ~ a l c u l a t e dchange ~ ~ in the OH bond-stretching frequency between OH CO and TSl gave a vibrationally adiabatic barrier for OH(u=O) (30 of (AEfOlhc) cm3 molecule-’ s-I. The = 280 cm-I and kc,u=~ = 7.5 X calculations which we report in this section retain most of the same properties for T S l . However, if one calculates the electronic-rotational partition function of OH accurately by summation over the rotational energy levels of the X211i(u=O) spin-orbit terms, rather than by the approximate separation of electronic and rotational partition functions, one obtains a significant difference, even a t room temperature. This procedure becomes essential at lower temperatures30and requires that (mol hc) is adjusted to have a value of 210 cm-I. Brunning et al.’sI5procedure for estimating the relative values of k, and k,, that is, the ratio of rate constants for the breakdown of energized HOC0 complexes to OH CO and to H + C02, respectively, and hence the branching ratio k,/(k, k,), was based on the fundamental expression of microcanonical transition state theory, according to which the rate constant for reaction of a species of defined E,J is
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+
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k(E,J) = N*(E,J)/hP(E,J) (iv) where P ( E , J ) is the number of internal states in the transition state which are accessible a t energy E and angular momentum J, and p(E,J) represents the density of reagent states at E,J. When, as in the present case, there are two competing dissociation channels from the same species, the ratio of specific rate constants is simply the ratio of the numbers of accessible states in TS2 and TSl:
kp(E~J)/k-c(~,J) = N*TS2(E,J)/N*TS1(E,J)
It was necessary, as b e f ~ r e lto ~ ,allow ~ ~ for differences in the actiue energies a t TS 1 and TS2 and then to average and sum over E and J. The need to preserve angular momentum was taken into account by defining the adiabatic, J-dependent energies a t the two transition states as
+
where E, is a zero-point energy (Le., with J = 0) and BJ(J 1) is the conserved adiabatic rotational energy, B being the mean of the two smallest rotational constants in each transition state. Taking (viiia) from (viiib) yields ETS,(J) = ETSl(J)
+ hEz + (BTS2 - BTSI)J(J + l )
(viiic)
where hE, = E,,TS~-E~,TSI was treated as an adjustable parameter and varied to bring the calculated thermal branching ratio into agreement with the value of 0.2, which is the ratio of the observed value of the rate constant for reaction of OH CO at low total pressure and the value inferred for k, from the value of the rate constant for relaxation of OH(u=l) by C0.15 Averaging over a thermal energy spread was carried out first to yield values of k,(J)/k,(J). In this first stage, P T S I ( E , J )in eq vii was replaced by a partition function, which was calculated as a product of partition functions associated with one active external rotation, four vibrations and one motion going over from a torsion to an internal rotation at higher energies.I5 For each J-dependent state in TS2, a thermally averaged transmission coefficient was calculated by multiplying expression vi by a Boltzmann factor exp(-E/kBT) and integrating the result over all total energies relative to ETSI(J)as zero. Having found k,(J)/k,(J) for specified adiabatic rotational states, a weighted sum of the values of the branching ratio k,(J)/{k,(J) + UJ)} was taken to find kp(T)/Wp(n + k-dT)l the branching ratio for a given temperature. The weighting factors f J were estimated assuming a Boltzmann distribution of J states in TSl, so that
+
(v) To simulate the results of thermal experiments, it is necessary to take weighted sums of the ratio on the right-hand side of this equation over E and J. Equations iv and v arise because, in classical transition-state theory, passage through each internal energy state in the transition state makes a contribution of l/hp(E,J) to the specific rate constant. Summation over the P ( E , J ) classically accessible levels then yields eq iv. Miller3’ has suggested a simple and approximate method whereby allowance can be made for the f j = { (2J + 1) exP [ J ( J + 1 / &,TS I 1/ QJ,TS I 1 (ix) effects of quantum mechanical tunneling. The number of states, where QJ,TSI = ( k T / h ~ B ~ is s lthe ) partition function associated P ( E , J ) , is replaced by a summation, over all the internal energy with adiabatic rotations in TS1. states in the transition state, of the transmission factors, K(E,J). The results of the calculations that have just been described In our calculations, we have used Miller’s method to treat suggest that quantum mechanical tunneling has a strong influence passage through TS2 but retained N+T~~(E,J) in the equivalent on the magnitude of the rate constant k, and hence on the of eq v. The barrier in T S l is low and presumably the reaction branching ratio, k,/(k, k,). To obtain a branching ratio of coordinate mainly involves the relative motion of OH and CO. 0.2 at 298 K for thereaction between OH and CO, it was necessary On the other hand, the a b initio calculations of Schatz et ~ 1 . ~ ~ to increase AE,/hc from its classical value of -30 cm-l I s to +640 yield an imaginary frequency a t TS2 of 26491 cm-I, indicating cm-1. This latter value was then used in calculations at that at this point the reaction coordinate motion essentially temperatures down to 45 K to investigate the temperature corresponds to departure of the H atom from C02. Schatz et dependence of the branching ratio through the range covered by ~ 1do .not~give~the imaginary frequency at TS2 for the OD + the present experiments. The results of these calculations are CO system. We have assumed that it has the value of 1950i compared with those for the classical calculations in Table 111. cm-I. As the method for including tunneling is necessarily To show the magnitude of the quantum tunneling effect, we also approximate, we have further assumed that the adiabatic barrier include values of the branching ratio calculated on the surface at TS2 can be approximated by an inverted parabola, so that the used by Brunning et al.I5 but including tunneling. tunneling probability is given by” The variation of the branching ratio with temperatureis almost independent of whether or not tunneling through TS2 is included K(E,,J) = exp(2~E,/hv*,)/( 1 exp(2?rEX/hv*,)) (vi) in the calculations indicating that the explanation for the small where Y * ~is the imaginary frequency associated with motion decrease of rate constant between 300 and 80 K must be sought along the reaction coordinate (x) and E, is the energy along x, elsewhere. On the other hand, the inclusion of tunneling does i.e., the difference between the total energy in the complex and lead to an estimate of AE, which is in much better agreement that in the particular level in the transition state. with the estimates made by Schatz et Allowing for the When tunneling through TS2 is allowed for, then eq v should difference in the zero-point energies in TSl and TS2, our be replaced by calculations indicate that the classical potential barrier a t TS2 exceeds that in TS1 by ca. 1250 cm-I. The ab initio calculations kp(E,J)/k-c(E,J) = CKTS2(E,J)/N*T?jl (vii) gave a value of 2500 cm-’ and Schatz et aLZ4quoted a best estimate of this quantity corresponding to ca. 1300 cm-I. where the summation is over all the actiue internal states at TS2.
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12258 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE III: Rate Constant and Branching Ratios Calculated with and without Allowance for Tunneling in the OH CO and OD + CO Systems
+
T/K 300
kc/cm3molecule-I s-I a & P / ( L + kP)ICI ( ~ P /+(~L P)IQM W ( k + +k p ) l ~ ~ (kckp/(k+ + kp)QM/Cm3 molecule-1 s-1
160
OH + CO 7.4 (-13)g
3.2 (-13)
0.22
0.34
0.47
0.65 0.33
0.195 1.45 (-13)
1.04 (-13)
80
6.8 (-14) 0.44
0.76 0.44 3.0 (-14)
OD + CO
k,/cm3 molecule-l s-l 1.1 (-1 2) 7.1 (-1 3) 4.4 (-1 3) (kp/(k+ + k p ) l ~ ~ f 0.037 0.067 0.113 (kckp/(k, + kp)QM/cm' 4.0 (-14) 4.8 (-14) 5.0 (-14) molecule-1 s-1 a Estimated using the standard TST expression with (hE'/hc) = 210 cm-I. Classicalvalues of branching ratio with (AEJhc) = -30 cm-1,15 Branching ratio allowing for tunneling with (AE,/hc) = -30 cm-I. Branching ratio allowing for tunnelling with ( A E J h c ) = 640 cm-I. 'Estimated by adjusting (hE'o/hc) = 93 cm-l in accordance with the estimated change in the zero-point energy in TSl and the actual change in OD. /Branching ratio allowing for tunnelling and with (AEJhc) = 1080 cm-I, a value consistent with estimated changes in the zero-point energies in TSl and TS2 on exchanging OD for OH. g 7.5 (-13) = 7.5 x 10-13.
Frost et al. between OH and CO may provide a precursor state for the formation of energized HOCO radicals via TS1. There are no reports in the literature of any experimental study of a OH--CO complex held together by a hydrogen bond. However, there have been several spectroscopic studies of complexes, formed in supersonic expansions, of hydrogen halides (HF, HCl, and HBr) with C0.3638 These three complexes have near linear X-H-structures with estimated dissociation energies equivalent to (De/hc)= 987 cm-' for X = F, 569 cm-I for X = C1, and 469 cm-' for X = Br. By plotting D, for XH--CO against dipole moments for HX,39940for X = F, C1, Br, and 0 we estimate that (De/hc)for OH--CO should be cu. 830 cm-I. This is in fairly good agreement with the ab initio value of cu. 600 cm-I estimated by Kudla et ul.24b Using similar interpolation procedures, it is possible to estimate rotational constants and the wavenumbers of the low-frequency modes in the O H 4 0 hydrogen-bonded complex. Making due allowance for zero-point energies, (DO/ hc) for OH--CO is estimated to be cu. 450 cm-I. This is significantly higher than the average thermal energy associated with reagents at the lowest temperatures in our experiments, suggesting that the formation and subsequent isomerization of OH--CO may play a role in the formation of HOCO complexes. To explore this matter further, estimates have been made of the relative rates at which energized O H 4 0 complexes might isomerize to HOCO and dissociate to OH + CO a t different temperatures, according to the scheme
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Calculations on OD CO including tunneling have been carried out, reducing the imaginary frequency at TS2 to 195Oicm-I. The value of hE, was adjusted to allow for the estimated15differences in the vibrational frequencies for HOCO and DOCO at TS 1 and TS2. This procedure increased AE,/hc from 640 cm-I in HOCO to 1080 cm-I in DOCO. The larger adiabatic barrier and the lower imaginary frequency a t TS2 in DOCO reduced the average tunneling probability and hence the branching ratio { k P / ( k ++ kp)] relative to their values in HOCO. The results of the calculations for OH + CO and OD C O at 300, 160, and 80 K are shown in Table 111. These data show that differences in the rates of tunneling through TS2 in the HOCO and DOCO systems do provide a reasonable explanation for the sizeable isotope effect on the rate of reaction 1. Indeed given theapproximations in the treatment, theagreement between the observed kinetic isotope effect at 300 K of ( k l , ~ / k l = , ~2.7 ) and the calculated value of 3.7 is remarkable. (b) Possible Role of H-Bonded Complexes in the Reaction between OH (OD)Radicals and CO. Our present experimental results, which show that the rate constants for reaction between OH (OD) and C O at low total pressure remain almost independent of temperature down to 80 K (1 78 K), make it still more difficult to find a reaction model which simultaneously explains the rather low value of the rate constant and its insensitivity to temperature. Lowering the value of ( A E + o , ~ s ~ / hfor c )OH + CO to 120 cm-I would reproduce the temperature dependence of kobs between 300 and 80 K but would increase k, by 5 0 4 0 % . However, as regards the overall valueof {k,kp/(kp+ k,)}, lowering ( h E t o , ~ s l / hc) will have relatively little effect since the increase in k, will be partly compensated by a smaller increase in k,. On the other hand, lowering ( A E + o , ~ s l / hand ~ ) consequently ( @ I , T s I / ~ c )will raise theestimated rateof formation of HOCO complexes from OH(u=l) + CO, and hence the estimated rate of relaxation of OH(u= 1) by CO to ca. 50% above its observed value.I5 Measurements of the temperature-dependence of the rate constants for relaxation of OH,OD(u= 1) by CO and for the association of OH (OD) with C O in the limit of high pressure would be extremely valuable in helping to establish the magnitude of the vibrationally adiabatic barriers in TSl. Another possible reason for the unusual kinetic behavior of the OH + CO reaction, and in particular the lack of temperature dependence down to 80 K, is that a hydrogen-bonded complex
+
ko
OH
+ CO e (OH--CO)* ka
k,'
(HOCO)*
Because TS1, limiting formation of (HOCO)*, is much tighter than that controlling the formation of (OH--CO)* from OH + CO, the branching ratio {k,'/(ka + k,')) is small and the isomerization of (HOCO)* back to (OH--CO)* can be ignored. The method used to estimate this branching ratio was, in principle, the same as that used to estimate the branching ratio for dissociation of energized (HOCO) * complexes. However, the assumption was made that the rate constants ko and k-0 are determined by the requirement that the systems must surmount centrifugal maxima on the long-range intermolecular potential. The electronic part of this potential was assumed to have the form V(r) = - 2 ~ ( r ~ / rwhere ) ~ E is the value of De estimated for theOH--COhydrogen bondandreis thedistance (3.89A) between the centers-of-mass of OH and C O similarly estimated for this complex. The values of ko estimated in this way, varied from 6.2 X lWocm3 molecule-' S-I a t 80 K to 8.2 X 1 W 0cm3 molecule-' s-l a t 300 K, although it should be noted that these represent upper limits as the value of E used corresponds to the specific hydrogen bonded O H 4 0 interaction rather than an intermolecular attraction averaged over all orientations. The main purpose of our calculations was to see whether the temperature variation and absolute magnitude of k, = kOkl(k-0 + k:) throughout this temperature range was such that k,k,/(k, + kp) matched the experimentally observed rate constants for reaction. The value of the branching ratio (k,'/(kq + k,')) varied from 3.75 X exp(-uto,Tsl/kBT) at 300 K to 7.45 X exp(-@o,Tsl/kBT) at 80 K. With ( h E f o , ~ s l / h ~=) 210 cm-I and the values of ko given earlier, the model gives k, = 11.2 X lO-I3cm3molecule-I s-I at 300 K and 1.1 X lO-I3 cm3molecule-l s-I a t 80 K. The former is in reasonable agreement with experiment but the predicted dependence of k, on temperature is not greatly improved by the application of this admittedly rather crude model over that provided by application of the rate constant expression from standard transition-state theory. Summary The results reported in this paper extend the kinetic data base on the important and interesting reactions between OH (OD) radicals and CO. The observation that the low-pressure rate
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12259
OH (OD) Radicals and CO Reaction constants remain almost constant with temperature down to 80 K for O H CO and 178 K for OD CO requires the modification of previous kinetic models for this reaction. The observed temperature dependence is consistent with an adiabatic barrier at TSl which is lower than previous estimates,I5 but this adjustment leads to estimated rate constants for reaction and relaxation of OH(o-1) (OD(o=l)) that are somewhat higher than the observed values. The possible participation, at low temperatures, of the long-range, hydrogen-bond interaction between OH (OD) and CO is noted, but simplistic calculations designed to examine the role of the weakly bound OH--CO species as a precursor to formation of (HOCO)* are inconclusive. Tunneling through the well-defined adiabatic barrier at TS2 which separates H O C 0 (DOCO) from H(D) COZ has been treated in an approximate fashion. These calculations indicate that the great majority of reaction to H (D) COz occurs through tunneling processes. The results are able to explain the relatively large kinetic isotope effect in this reaction and to resolve, at least in part, the discrepancy between ab initio estimates of the barrier height at TS2 and the value indicated by previous rate calculationsIs which did not include tunneling.
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Acknowledgment. We are grateful for support from the CEC under the Science Plan (Contract SC'CT89-0261). References and Notes (1) Warnatz, J. Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: New York, 1984; p 197. (2) (a) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampon, Jr., R. F.; Kerr, J. A.; Troe,J. J . Phys. Chem. Ref.Dura 1989, 18,881. (b) DeMore, W. B.; Golden, D. M.; Hampson. Jr., R. F.; Howard, C. J.; Kurylo, M. J.; Molina, M. J.; Ravishankara, A. R.; Sander, S.P. JPL Publication, 1987,
8741. (3) Smith, I. W. M.; Zellner, R. J . Chem. Soc., Furuduy Truns. 2 1973, 69, 1617. (4) Smith, I. W. M. Chem. Phys. Lett. 1977, 49, 112. (5) Dryer, F.; Naegeli, D.; Glassman, I. Combust. Flume 1971,17,270. (6) (a) Milligan, D. E.; Jacox, M. E. J. Chem. Phys. 1971,54,927. (b) Jacox, M. E. J. Chem. Phys. 1988,88,4598. (7) Overend, R.; Paraskevopoulos, G. Chem. Phys. Lett. 1977,49, 109. (8) (a) Biermann, H. W.; Zetsch, C.; Stuhl, F. Ber. Bunsen-Ges. Phys. Chem. 1978, 82,633. Hofzumahaus, A.; Stuhl, F. Ber. Bunsen-Ges. Phys. Chem. 1984,88, 557. (9) Butler, R.; Solomon, I. J.; Snelson, A. Chem. Phys. Lett. 1978, 54, 19.
(10) Paraskevopoulos, G.; Irwin, R. S.Chem. Phys. Lett. 1982,93, 138. (11) DeMore, W. B. Int. J . Chem. Kinet. 1984, 16, 1187. (12) Paraskevopoulos, G.; Irwin, R. S . J . Chem. Phys. 1984,80, 259. (13) Hynes, A. J.; Wine, P. H.; Ravishankara, A. R. J. Geophys. Res. 1986, 91. 11815. (14) Ravishankara, A. R., personal communication. (15) Brunning, J.; Derbyshire, D. W.; Smith, I. W. M.; Williams, M. D. J. Chem. Soc., Furuduy Truns. 2 1988,84, 105. (16) Back, M. H.; Schon, A. H. Cun. J . Chem. 1960, 38, 1261. (17) Mearns, A. M.; Back, R. A. Can. J. Chem. 1963,41, 1197. (18) Ung, A. Y.-M.; Back, R. A. Can. J . Chem. 1964,42, 753. (19) Radford, H. E.; Sears,T. J.; Wei, W. J. Chem. Phys. 1992,97,3989. (20) (a) Sears,T.J.; Fawzy, W. M.; Johnson, P. M. J. Chem. Phys. 1992. 97. 3996. (b) Petty, J. T.; Moore, C. B. J. Chem. Phys. 1993, 99, 47. (21) Ruscic, B.; Schwarz, M.; Berkowitz, J. J . Chem. Phys. 1989, 91, 6780. (22) McLean, A. D.; Ellinger, Y . Chem. Phys. 1984, 94, 25. (23) Aoyagi, M.; Kato, S . J. Chem. Phys. 1988, 88, 6409. (24) (a) Schatz, G. C.; Fitzcharles, M.; Harding, L. B. Furuduy Discuss. Chem. Soc. 1988, 84, 359. (b) Kudla, K.; Koures, A. G.; Harding, L. B.; Schatz, G. C. J. Chem. Phys. 1992,96,7465. (25) (a) Kudla, K.; Schatz, G. C.; Wagner, A. F. J . Chem. Phys. 1991, 95, 1635. (b) Clary, D. C.; Schatz, G. C. J . Chem. Phys. 1993, 99,4578. (26) Mozurkewich, M.; Benson, S.W. J . Phys. Chem. 1984, 88, 6429, 6435. (27) Larson, C. W.; Stewart, P. H.; Golden, D. M. Int. J. Chem. Kinet. 1988,20, 27. (28) Hippler, H.; Forster, R.; Frost, M. J.; Schlepegrell, A,; Troe, J. XXth Informal Conference on Photochemistry, Atlanta, Apr 1992; abstract K4. (29) (a) Troe,J. J. Chem. Phys. 66,4745, 4758. (b) Troe, J. J . Phys. Chem. 1979.83, 114. (30) Smith, I. W. M. Mon. Not. R. Astron. Soc. 1988, 234, 1059. (31) Miller, W. H.J. Am. Chem. SOC.1979,101. 6810. (32j Frost, M. J.; Sharkey, P.; Smith, I. W. M. Furuduy Discuss. Chem. Sm. 1991, 91, 305. (33) Sharkey, P.; Smith, I. W. M. J . Chem. SOC.,Furrrduy Truns. 1993, 89. 63 1. (34) (a) Sims, I. R.; Smith, I. W. M. Chem. Phys. Lett. 1988,151,481. (b) Sims, I. R.; Smith, I. W. M. J . Chem. Soc., Furuduy Truns. 1993,89, 1. (35) Smith, I. W. M.; Williams, M. D. J . Chem. SOC.,Furuduy Truns. 1986, 82, 1043. (36) Soper, P. D.; Legon, A. C.; Flygare, W. H. J . Chem. Phys. 1981,74, 2138. (37) Keenan, M. R.; Minton, T.K.; Legon, A. C.; Balle, T.J.; Flygare, W. H. Proc. Nurl. Acud. Sci. U S A . 1980, 77, 5583. (38) Legon, A. C.; Soper, P. D.; Flygare, W. H. J . Chem. Phys. 1981.74, 4944. (39) Atkins, P.W. Physical Chemistry, 4th ed.; Oxford University Press: Oxford, 1990. (40) Huber, K. P.; Herzberg, G. Molecular Spectru and Molecular
Structure. IV. Constants ofDiutomic Molecules, Van Nostrand Reinhold: New York, 1979.
