J. Phys. Chem. 1993, 97, 128-133
128
Cross Sections and Energy Disposal for CN(X) Produced in the H kcal mol-’ Collision Energies
+ HCN Reaction at 53 and 58
H. M. Lambert, Tucker Carrington, S. V. Filseth,’ and C. M. Sadowski Department of Chemistry, York University, Toronto, Ontario, Canada M3J 1 P3 Received: April 28, 1992; In Final Form: October 8, 1992
Energy disposal in the CN(X) product of the H + H C N reaction has been studied by the method of timeresolved laser-induced fluorescence. Translationally hot H atoms were formed by photodissociation of H2S and HBr at 193 nm, leading tocenter-of-mass collision energies of 53 and 58 kcal mol-’. The rotational distributions for CN(X,u=O,l) can be well described by single Boltzmann temperatures of 1400 and 1600 K, respectively, and correspond to 12% of the H atom energy above an apparent threshold of about 30 kcal mol-I. Between 3% and 5% of the energy above this threshold is found in the CN(X) vibration. Cross sections for the production of CN(X) at the two H atom energies have been measured as 0.007 f 0.002 and 0.009 f 0.002 A2, respectively.
1. Introduction
One of the most basic notions of chemical kinetics is that the rates of elementary endoergic processes increase dramatically with temperature. The simplest formal expression of this generality is the exponential temperature dependence of the reaction rate constant. The corresponding physical model is that of a system in which an exponentially rising proportion of encounters possess center-of-mass translational energy above some threshold. Quite apart from the purely kinematic factors which distinguish different reactions from one another, it has been the details of the potential energy surface controlling reaction dynamics that have most interested kineticists. Until comparatively recently, information on the effect of reactant translational energy on the reaction probability and energy disposal in endoergic reactions has been obtained primarily through experimental and theoretical studies of the reverse reactions. The study of X + H2 reactions (X = I, Br, C1, CN, F) has been especially fruitful in this regard. In this series of reactions, the kinematic factors are largely unchanged because of the favorable light-light-heavy (LLH) mass combination, while the potential energy surfaces and thermochemistry vary considerably from one member of the series to the next. It has been through the study of these and other reactions by experimental and theoretical means1 that the role of barrier height and position and reactant energy has been explored. Recently, interest in the experimental study of the forward H HX reactions has been encouraged by the availability of sources of hydrogen atoms with fairly narrow energy distributions at a number of different energies.2 In this work, energy disposal and, in some cases, cross sections have been measured for hydrogen abstraction as well as for reactive and nonreactive T-V,R energy transfer (ET) in the processes,
+
-
H + H’X H + H’X
H + H’X
HH’ + X
+H H X + H’
H’X
H atom abstraction
(1)
nonreactive T-V,R ET (2) reactive T-V,R E T
(3)
where Hsignifies a hydrogen atom with substantial kinetic energy. In the most recent work, abstraction reactions have been studied for X = 1,394Br,4 Cl,4q5and CN63’ and ET has been observed for X = I,8 Br,* Cl,53899and F.10 References to earlier studies are given in these articles and in a 1986 review article.2 Investigations of the abstraction reaction and its reverse have been supported and interpreted by trajectory calculations on a 0022-3654/58/2097-0128S04.00/0
number of surfaces computed at various levels of theory. The most accurate surfaces are those for the much-studied H2F system;]’ however, H atom abstraction has not been observed for this system and is predictedI2 to be unimportant for H atom kinetic energies up to 70 kcal mol-] unless reactant H F possesses two or more vibrational quanta. H2 production by abstraction has been observed direztly for X = 1,394Br,4 and C14,5and inferred6,’ by the direct observation of C N when X = CN. In all cases, the minimum energy path passes through a collinear saddle point for the best available surfaces for each reaction. There is a monotonic progression in the propertiesI3 of the surfaces for the X = I, Br, C1, and F reactions such that the H2F surface is characterized by a high barrier and endoergicity, while the H2I surface has a low barrier and high exoergicity. Similarly, the location of the barrier moves from the entrance channel for H HI to the exit channel for H HF. Weanticipate, therefore, that translational energy in the reactants will become increasingly less effective at facilitating the abstraction reaction in the sequence I, Br, Cl, F. Indeed, as mentioned, abstraction is not expected to be significant in the case of H H F and has not been reported. The C N free radical displays a chemistry sufficiently similar to that of the halogens that it has been called a pseudo-halogen. With respect to several properties of the HzCN ~ u r f a c e , ~such ~*l~ as thermochemistry, barrier height, and barrier position, it lies naturally in sequence between H2F and H2Cl. The saddle point is collinear and, within the measure of uncertainty in each, adheres to the exponential relationship between barrier height and AH established by the other halogens. In view of the similarity in these aspects of the HzCN and H2F surfaces, it is not expected that H atom kinetic energy will be effective at promoting H atom abstraction in the H + HCN reaction. Rather, it is expected on the basis of theoretical study of the reverse reaction16J7that only vibrational excitation of reactant HCN would be effective in promoting abstraction. In view of this, it may prove difficult to investigate the nascent H2(v, j ) distribution by thesame techniques which have proven successful in the study of the analogous H + HI, HBr, and HC1 reacti0ns.39~ In the present work, we report measurements of the nascent internal energy distribution of the C N product of the abstraction reaction and its dependence upon H atom kinetic energy. By a calibration procedure involving ClCN photolysis, we report measurements of the cross section for abstraction and its energy dependence. We find, in agreement with expectation, that the cross sections are low, less than 1% of the cross sections for the abstraction reactions for H + HI, HBr, and HCI. The results are compared with a statistical energy-conserving prior model.
+
+
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0 1993 American Chemical Society
Cross Sections and Energy Disposal for CN(X)
2. Experimental Section The experiments were conducted in an anodized aluminum gas cell, and a block apparatus diagram has been given previously.'* Hydrogen atoms are generated by photolysis of H2Sand HBr by the radiation from an unpolarized ArF excimer laser passed through 0.5 m of air. As shown in a previous initial account of a portion of this work: the CN(X,u,N) product of the H + H C N reaction is produced on a time scale of a few tenths of a microsecond at total pressures between 10 and 20 mTorr. The time scale of this production step reflects transport of the rapidly moving H atoms away from the observation volume defined by the overlap between the 5-mm-diameter 193-nm photolysis beam and the 4-mm-diameter probe dye laser beam which intersect at a right angle in the gas cell. The probe is delayed in time relative to the photolysis beam by 300-500 ns such that the product of total pressure and delay (reaction) time is < 5 Torr ns. Under these conditions, relaxation of the nascent CN(X,u,N) distribution will not be significant.6 Similarly, loss of product C N from the observation volume will not be significant on this time scale. Product CN(X,u,N) populations are determined from the intensity of laser-induced fluorescence in the Au = 0 sequence of the CN(B-X) violet system near 388 nm with excitation in the (O,O), (1,1), and (2,2) bands. Measurements were made on 1:l H2S/HCN mixtures at 10 mTorr at delays of 460 ns and on HBr/HCN mixtures which varied between 4: 1 and 2: 1 at pressures from 15 to 20 mTorr at a delay of 270 ns. LIF spectra were scanned in sections, normalized to variations in photolysis laser and saturation-corrected probe laser energies, corrected for the development of window deposits arising during photolysis, and joined together with the aid of repetitive scans over selected lines taken at the beginning and end of individual sections. The probe laser was a nitrogen-laser-pumped tunable dye laser providing several microjoules of radiation with a 0.3-cm-I bandwidth. Fluorescence was collected at a right angle to the plane of intersection of the two laser beams with anf/2.7 Si02 lens, passed through a Au = 0 interference filter (peak wavelength = 385.5 nm, FWHM = 10.7 nm) and detected with an EM1 6256 photomultiplier tube. The signal was integrated, averaged, and stored in a microcomputer for analysis. Although the excimer laser was unpolarized, generation of H atoms may still be characterized by a residual anisotropy. In a single experiment with 10 mTorr of an equimolar mixture of H2S and H C N and a delay of 270 ns, the LIF for the P(8) line of the (0,O)band was scanned alternately with about 50 nJ of probe laser radiation of orthogonal polarizations. No difference in LIF intensity was observed. Since H C N is itself photodissociated at 193 nm,18a correction was required for its contribution to the CN(X,u,N) signal. The nascent CN(X,u,N) distribution from the 193-nm H C N photolysis was remeasured and found to be in agreement with that reported previously.'8 For purposes of the correction, pure H C N was dissociated at a pressure of 50 mTorr and measurements were made of the LIF intensity for selected lines. The H C N pressure was then reduced to about 5 mTorr, a comparable amount of HBr or H2S was added through a separate calibrated flowmeter, and measurements were repeated of the LIF intensity for the same selected lines. A correction to the populations of CN(X,u,N) measured for the mixture was determined on the basis of the known population distribution from the photodissociation of pure H C N and the ratio of the two H C N pressures used. This correction varied with u and N a n d with H atom precursor and is shown in detail in the following section where the population results are reported. The magnitude of the correction varied from 5% to 10% for CN(u = 0) for 53 kcal mol-' atoms and from 15% to 60% for CN(u = 1) for 58 kcal mol-' atoms. Absolute cross sections for production of CN(X,u,N) in the H + H C N reaction were measured according to a procedure
The Journal of Physical Chemistry, Vol. 97, No. 1. 1993 129 described by Kleinermanns and W01frum.l~LIF signals for the P(64) line in the CN(X,u,N) product distribution from the 193nm photodissociation of 4.7 mTorr of ClCN measured at a delay of 310 ns following the photolysis laser pulse are compared with those for the R(4) line in the H + H C N product distribution produced at a 300-11s delay time in a 1:l mixture of H2S/HCN at 9.6 mTorr and in a 3:2 mixture of HBr/HCN at 16.8 mTorr. Allowance is made for differing 193-nm absorption cross sections of H2S, HBr, and ClCN which are taken as 6.4 X 10-18 cm2,20 17.7 X 10-19cm2,21 and 2.3 X 10-19cm2,22respectively. Similarly, allowance is made for the difference between the distributions from the 193-nm ClCN photodi~sociation~~ and those for the H atom reactions. In this work, H C N was prepared as discussed previously18and H2S and HBr were obtained from Matheson a t stated purities of 99.5% and 99.8%. HBr was further purified by trapto-trap distillation to remove H2 and Br2 impurities.
3. Results and Discussion 3.1. Reaction Thermochemistryand Potential Energy Surface. The thermochemistry for the abstraction reaction is not known to high precision. This isdue to thecomparatively high uncertainty in the standard 0 Kenthalpy of formation of H C N or, equivalently, to the corresponding uncertainty in the HCN bond dissociation energy. A value of 19.7 f 3.1 kcal mol-' may be calculated for AH(0 K), the endothermicity of the reaction, from the JANAFz4 table values of the standard enthalpies of formation at 0 K of CN, H , and HCN, which are 104.4 f 2.4, 51.63 f 0.001, and 33.1 f 2.0 kcal mol-', respectively. Somewhat lower values are obtained when more recent measurements are employed. Thus, utilizing a 1990 measurement of &(CN) = 179.2 f 1.2 kcal a value of AH(0 K) = 18.2 f 2.3 kcal mol-' is obtained, and a 1992 measurement of AHf,o(CN) = 104.2 f 0.5 kcal mol-) 26 yields a value of AH(0 K) = 19.5 f 2.1 kcal mol-'. The activation energy for the reverse reaction has been measuredZ7 over a temperature interval from 259 to 396 K to be 5.3 f 0.6 kcal mol-'. Thus, the activation energy for the forward reaction may be computed to lie between 23.5 and 25.0 kcal mol-' depending upon the choice of values for the endothermicity. These values may be compared with the results of the ab initio calculation of Bair and Dunning,14which predicted an endoergicity of 24 kcal mol-) with a barrier of 31 kcal mol-' in the forward direction. A recent semiempirical three-dimensional surface17 predicts values of 20.5 and 24.6 kcal mol-' for the endoergicity and barrier height, respectively. Reactants and productscorrelate through a collinear H2CN saddle point on a 2A' surface. Elsewhere on the surface of Bair and Dunning lies a well, corresponding to the ground state of H2CN (X 2B2) in geometry, which is bound by 19 kcal mol-) relative to H HCN. 3.2. Reaction Collision Energies. For each of the two H atom sources, C N reaction product is produced in collisions with a range of kinetic energies. While the center-of-mass speed is essentially that of the H atoms, that speed is determined by the precursor photodissociation distribution as modified by the effect of any moderating collisions and by the thermal motion of H C N and the H atom precursor. Products are formed under approximately single-collision conditions since at 5 Torr ns the nascent H atoms will experience only about 0.4 hard-sphere collision on average. The collision energy uncertainty due to the thermal motion of the HBr precursor and the H C N reactant can be calculated as described by van der Zande et a1.28and amounts to about 4 kcal mol-' at FWHM. Hydrogen atoms are produced by the 193-nm photodissociation of HBr and H2S. Dissociation of HBr has been found29to produce 85% Br(2P312) and 15% Br(2Pl/2), and there are thus two groups of H atoms coproduced with 62.0 and 51.5 kcal mol-' of translational energy, respectively. Hydrogen atoms produced by the 193-nm H2S photodissociation have lower energies with a
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130 The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
broader distribution due to the internal energy of the HS coproduct. The vibrational and rotational energy contents of the HS product have been studied several times. The most recent report of the results for the vibrational distribution30 contains references to earlier work with which there is some moderate disagreement. For the purpose of the present calculation, we employ the most recent result, which reports HS(u=O) to correspond to 72.8% of the product and decreasing for higher u, falling to about 2% for HS(u=5). Rotational distribution measurements for the HS fragment are limited to HS(u=O,1)31 and find only about 1% of the available energy in this degree of freedom. For the purpose of this calculation, we have ignored the rotational energy of the HS fragment, the contribution of H atoms coproduced with HS(u > 4)and the thermal internal energy of HIS. The distribution of translational energies in the reactive H atoms-thosecoproduced with HS(u-
0.006
-0
0004
4d
Q,
Q: 0 002
131
result from an isolated interaction between the two H atoms followed by dynamical scattering of Hzoff the remaining X species. This same picture can account qualitatively for the observation of substantial amounts of rotational energy in C N since energy release on a late barrier will be repulsive in nature. In this event, the newly formed H2 product rebounds from the C N fragment with considerable translational energy, and the process will resemble the impulsive dissociation of the bent H2CN intermediate. An aspect of impulsive dissociations from a fixed geometry is the observation of a nearly constant fraction of available energy as average rotational energy of the fragment as is observed here. At the H atom energies involved in this work, an encounter with H X can be described as rotationally impulsive. Even though the H2CN surface is strongly bound in CzUgeometry, it is unlikely at these total energies that an H2CN intermediate will have a lifetime sufficient to permit extensive IVR. In addition, the existence of the small exit channel barrier argues against the expectation that product energy disposal will be statistical. As a measure of the extent of departure from a purely statistical distribution, we have compared our experimental rotational and vibrational distributions to the simplest energy-conserving prior distribution. The prior distribution for the breakup of a four-atom complex of two diatomics, only one of which is observed for its rotational energy content at fixed vibrational energy, can be written in the rigid rotor harmonic oscillator approximation as
0.000 0
20
10
30
40
N
Figure 1. Rotational population distributions from the reaction of 58 kcal mol-’ H atoms with H C N . (a) Open circles, relative populations for CN(X,u=O) corrected for the contribution from the photodissociation of HCN; closed circles; the relative population correction for H C N photodissociation; solid line, fitted single boltzmann with T = 1626 K. (b) As above except for CN(X,u=I). The fitted Boltzmann is for T = 1645
K.
of-mass collision energy. We might thus anticipate an H atom translational energy threshold of some 50 kcal mol-I for a reaction with a 25 kcal mol-’ barrier located well within the exit channel. While on average only 12% of the collision energy above threshold is found in C N rotation, there is substantial population in quantum states corresponding to N = 40 and above. For these states, the C N rotational energy corresponds to over one-third of the available energy so that rotational energy disposal cannot be described as inefficient. The available energy is sufficient to permit formation of the unobserved H2 coproduct in rotational quantum states only as high as N = 12 in u = 0. Evidently, breakup of the H2CN intermediate must occur from geometries sufficiently bent that fragment impact parameters can reach values of 0.1-0.2 nm. Although the saddle-point geometry for the minimum energy path has been calculated as linear for all the H H X reactions, theenergy dependence of the bending potential will allow reaction from much lower angles of encounter at the translational energies of interest in this work. Indeed, a comparison with the steep H H F bending potential13 suggests that the barrier for the H H C N reaction will be lower than 40 kcal mol-’ for bending angles of up to 60’. Recently, Takada et al.34 found, on the basis of exact quantum mechanical calculations for J = 0 for the D + H2 = D H + H reaction, that noncollinear conformations in the reaction zone contribute significantly to the reaction probability, although both the saddle point and minimum energy path are located in the collinear configuration. Barclay et al.5 similarly found in a semiclassical trajectory study of the H + DCl reaction that the preferred geometry for abstraction corresponded to HDCl angles lying in the range 95-155O. It has been pr0posed3~that the detailed H2 internal state distributions in the analogous H + HI, HBr, and HCI reactions
+
+
+
where g/ is the nuclear spin degeneracy and the summation is taken over all the internal states of H2. As illustrated in Figure 3, the experimental data are in satisfactory accord with a distribution of the form
P(v,N) = ~ ( N C N I U C N Sex~[-ef(r)I ) (8) wheref(r) is the fraction of available energy which appears as rotational energy and 8 is an adjustable parameter, the surprisal. The data in this figure are for the production of CN(u=O) in the reaction of 53 kcal mol-’ H atoms with HCN, and the fittedvalue of the rotational surprisal parameter is 9.2 f 0.3. A similar analysis of the data for CN(u=l) yielded a surprisal parameter of 7.2 0.9. Analysis of the data shown in Figure l a and b for production of CN(u=O,l) in the reaction of 58 kcal mol-l H atoms gave surprisal parameters of 8.7 f 0.1 and 8.2 f 0.5, respectively. The C N rotational distributions measured in this work are thus found to be much colder than those characteristic of an energy-conserving statistical distribution. As indicated in Table I, the proportion of vibrationally excited product C N is higher at the higher H atom energies. Expressed as a percentage of the available energy above a 30 kcal mol-’ threshold energy, C N vibrational energy corresponds to 3.2 0.1% for 53 kcal mol-’ and 4.7 f 0.8% for 58 kcal mol-’ H atoms. As illustrated in Figure 4 for 53 kcal mol-l atoms, the distribution is markedly cooler than the energy-conserving prior distribution. 3.5. Comparisonwithother H + ABCSystems. There are still relatively few measurements of energy disposal in the “old bond” of reactions involving fast hydrogen atoms and triatomic molecules, and only H + H C N is an example of the LLHH mass combination. In those that are available for comparison, two proceed across nonlinear saddle points. These are H203*+2and C0243344 with reaction enthalpies of 15.0 and 25.6 kcal mol-I, respectively. Of these, the H + H20 reaction is the most similar to H + H C N energetically and kinematically, and it has also been studied as a function of H atom energy. H atom abstraction in the H + H20 reaction proceeds with a 20-fold higher cross section which is approximately independent of collision energy in the 34-58 kcal mol-’ interval. Rotational energy disposal in
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Lambert et al.
The Journal of Physical Chemistry, Vol. 97, No. 1 , 1993
TABLE I: Reaction Cross Section and Energy Disposal in the H + HCN Reaction. CN(X.u) rotational temp (K);C N ( X ) vibrational distribution hvdronen atom * source HI + 248 nm (ref 7) HIS 193 nm HBR 193 nm
enerw
u=o
u= 1
u=2
43 53 58
760 f 35; 1 1404 f 95;0.866 f 0.005 1626 f 40;0.8I f 0.03
1430 f 391;0.134f 0.005 1645 f 137;0.14f 0.01
0.05 f 0.03
+ +
0
reaction cross-section
(A2)
~
0.007f 0.002 0.009f 0.002
Energies are in kcal/mol. Temperature uncertainties are f95% confidence intervals. Cross-section uncertainties are f 1u.
‘ E 1200
@
c
0.9 0.8
2
0.6
0
800
1
Experiment
1000
Prior Distribution
-I
600
400
E
0.2
200
20
30
50
40
60
0
70
Effective H Kinetic Energy (kcal mole-’)
Figure 2. Dependence of average CN(X,u=O) rotational energy on effective (defined in text) H atom kinetic energy. Open circles, this work; closed circle, ref 7. 0 10
I
I
I
I
I
0
0.08 0
Y
2
0.06
0 LL
.-p
1
o.l 0.0
0
.-0
i4
c
0.04
Y
0 a,
0.02
0.00 0
10
20
30
SO
40
N Figure 3. Rotational population distribution for CN(X,u=O) produced in the reaction of 53 kcal mol-’ H atoms with H C N . Open circles, relative populations corrected for the contribution from H C N photodissociation; closed circles, the relative population correction for H C N photodissociation; solid line, the surprisal parameter corrected prior distribution.
product O H decreases in efficiency from 8% to 3% of available energy over the same interval, whereas, in terms of available energy, C N rotational energy disposal becomes somewhat more efficient at higher collision energies, reaching 8% at 58 kcal mol-’. Energy disposal in CO rotation in the H + CO2 reaction has been investigated by LIF43and by diode laser absorptionu at 55 kcal mol-’ H atom energy. C O is found to be rotationally colder than expected on the basis of a phase space model. Schatz et al.45 have computed a global PES for the H C02 reaction and have performed a quasi-classical trajectory study on this surface at 44 and 55 kcal mol-’ H atom energies. They find the old bond product to be somewhat hotter at 55 kcal mol-’ than experiment does. They also find that the efficiency of disposal of available energy into the old bond decreases a t higher H atom energies. This is in agreement with the experimental results and, as mentioned above, was also observed for the H HzO reaction but is not the case for the H + H C N reaction reported here.
+
+
1
3
2
4
5
V Figure 4. Vibrational population distribution for CN(X) produced in the reaction of 53 kcal mol-I H atoms with H C N . Filled squares, the experimental distribution; open squares, the energy-conserving prior distribution uncorrected for the value of the vibrational surprisal parameter.
One other system where comparison is possible is the H + ClCN reaction which has been studied a t two different H atom e n e r g i e ~ . ~ This * ~ 6 is an exothermic reaction and can proceed by two reaction paths: H atom insertion into the C1-C bond and direct abstraction across a linear saddle point. The activation energy in the forward direction has been found7 to exceed 7 kcal mol-’. Although the barrier height for the forward reaction was calculated46as 3 1.3kcal mol-’, the same calculation overestimates Nl for the abstraction reaction by almost 20 kcal mol-’, and the actual barrier will be substantially lower. The C N rotational distributions can be described as single Boltzmann, and C N rotational energy disposal amounts to (two data points 0 n l y ~ 3 ~ ) 16% of the energy above a threshold H atom kinetic energy of about 13 kcal mol-’. This result is in agreement with the observation in the current work on H + H C N that the old bond average rotational energy is a fixed proportion of the energy available above a threshold H atom energy corresponding to a few kcal mol-’ greater than the best current estimates of the barrier height. Also in agreement with the current work on H H C N is the observation that the H ClCN abstraction cross section is quite small, less than 0.01 A2. Finally, we mention the studies of the reaction of fast H atoms with N 2 0 reported by Shin et aL4’ and by B6hmer et al.48 The internal energy distribution of the “new bond” N-H was observed by LIF at a number of different H atom energies. As has been found in the present work for the old bond CN, the rotational populations could be described by single Boltzmann temperatures and the average N H rotational energy was a linear function of the H atom kinetic energy above an intercept -lose to the endoergicity of the abstraction reaction.
+
+
4. Summary
We have reported measurements of the reaction cross sections and the nascent CN(X) internal energy distributions from the H + H C N reaction a t two different H atom kinetic energies. This is the only example available of the measurement of old bond energy disposal for the unique LLHH mass combination. The
Cross Sections and Energy Disposal for CN(X)
The Journal of Physical Chemistry, Vol. 97, No. I , 1993 133
very low cross sections measured and the absence of appreciable vibrational excitation in the C N fragment are not unexpected in view of a previous cal~ulation'~ of the structures and vibrational frequencies of the reactants, transition states, and products of this reaction. When combined with a previous study of the reaction with 43.3 kcal mol-' H atoms,' we find on average in C N rotation a constant 12% of the available energy above an H atom kinetic energy threshold of 30 kcal mol-'.
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Acknowledgment. This work has been supported by the Natural Sciences and Engineering Research Council of Canada and by York University. We thank the reviewers for useful comments. References and Notes ( I ) Polanyi, J. C. Arc. Chem. Res. 1972,5, 161. (2) Flynn, G.W.; Weston, R. E., Jr. Annu. Rev. Phys. Chem. 1986,37, 551.
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