J . Phys. Chem. 1988, 92, 18-27
18
note that the TPID/chloroform photochemical system is a system involving two consecutive photochemical reactions. Such a scheme is similar, in its structure, to biphotonic photophysical processes. A simple photoionization kinetic scheme involving the successive absorution of two photons was studied some time ago by one of us.” It was then ihown that this type of system c&ldbecome bistable, under appropriate conditions.
Acknowledgment. J.P.L. acknowledges the financial support from CRAD Grant 3610-644:F4120. J.C.M. acknowledges a contribution from Centre National de la Recherche Scientifique, C N R S AIP 0693 1. (1 1) Micheau, J. C.; Boue, S.;VanderDonckt, E. J . Chem. SOC.,Faraday Trans. 2 1982, 78, 39.
FEATURE ARTICLE On the Dynamics of Abstraction, Insertion, and Addition-Elimination Reactions in the Gas Phaset J. J. Sloant National Research Council of Canada, 100 Sussex Drive, Ottawa, Canada K I A OR6, and Department of Chemistry, Carleton University, Ottawa, Canada iYlS 5B6 (Received: April 13, 1987; In Final Form: September I , 1987)
The dynamics of elementary abstraction, insertion, and addition-elimination reactions are discussed. For the case where the newly formed bond involves a light atom, special dynamical behavior occurs, and this is explored in depth. Following a brief outline of some early results on triatomic light-atom abstraction reactions, three examples of recent work, the F/HCO, F/NH3, and O(’D,)/H, reactions, are discussed. Although the mass combinations for the first two reactions are similar, their dynamics appear to be different. Furthermore, the dynamics of the third are dramatically different from those of the first two.
I. Introduction A fundamental advance in the study of physical chemistry occurred about 30 years ago with the introduction of two experimental techniques: molecular beam reactive scattering, which dates from 1954,’ and infrared chemiluminescence, introduced in 1958., The former permits the measurement of the kinematic and geometrical aspects of reactive collisions, and the latter gives the excitation in the products’ internal degrees of freedom. Together these techniques shifted the focus of physical chemistry from macroscopic kinetics and thermodynamics to the physics of chemical reactions at a molecular level, thereby creating the field of molecular reaction dynamics. This achievement was recognized by the award of the 1986 Nobel Prize in Chemistry to the founders and principal developers of the field, Professors J. C. Polanyi, D. R. Herschbach, and Y . T. Lee. In an exhaustive review of molecular beam reactive scattering published in 19663 it was reported that 20 reactions had been studied using that technique in the first decade of its existence. Less than half that number had been studied by infrared chemiluminescence at the time. A single 1979 review of molecular reaction dynamics: however, listed more than lo00 publications which had been generated during the field’s second decade. This explosive growth has placed the subject beyond comprehensive reportage in any but the most heroic format; therefore, the following discussion will deal with only that part of the field which is concerned with information drawn from measurements of internal energy distributions made by infrared emission spectroscopy. Since the results of current measurements are usually interpreted in terms of the simpler, triatomic reactions studied during Issued as NRCC No. 28300. *Present address: Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
0022-3654/88/2092-0018$01.50/0
the development of the field, I shall first refer to a few of these historically significant measurements to provide a basis for the subsequent discussion. Following this, I shall present detailed descriptions of three problems that exemplify work presently under way. When J. C. Polanyi and co-workers introduced the technique of infrared chemiluminescence, the first result that they published2 was the unresolved HCl emission produced by the H + C1, reaction. Although not vibrationally resolved, this first emission spectrum demonstrated that chemical reactions are capable of releasing very large amounts of energy as product internal excitation. Later studies of this same reaction5showed that it releases 37% of the total available energy as HCl vibration and causes the excitation of a broad distribution of vibrational levels, which extends up to the maximum energetically accessible level. Broadly similar results were found for the other H X2 (X = halogen atom) reactions as ell.^,^ All H + X2 reactions create total vibrational inversion. This refers to a vibrational distribution in which the population of at least one vibrational level, P(u), is greater than that of a lower level, P(u - n ) . (This may be distinguished from partial inversion, for which the vibrational excitation is greater than that appropriate to a Boltzmann distribution at the ambient temperature of the other degrees of freedom.’) Exploitation of vibrational inversion led to the chemically
+
(1) Bull, T. H.; moon, P. B. Discuss. Faraday SOC.1954, 17, 54. (2) Cashion, J. K.; Polanyi, J. C. J . Chem. Phys. 1958, 29, 455. (3) Herschbach, D. R. Adu. Chem. Phys. 1966, 10, 319. (4) Levy, M. R. Prog. React. Kinet. 1979, 10, 1 . (5) Anlauf, K. G.; Horne, D. S.; MacDonald, R. G.; Polanyi, J . C.; Woodall, K. B. J . Chem. Phys. 1962, 57, 1561. (6) (a) Polanyi, J. C.; Sloan, J. J. J . Chem. Phys. 1972, 57, 4988. (b) Jonathan, N . ; Okuda, S.;Timlin, D. Mol. Phys. 1972, 24. 1143. (c) Sung, J. P.;Malins, R. M.; Setser, D. W. J . Phys. Chem. 1979, 83, 1007. ( 7 ) Polanyi, J. C. J . Chem. Phys. 1961, 34, 347.
Published 1988 by the American Chemical Society
Feature Article
The Journal of Physical Chemistry, Vol. 92, No. 1, 1988 19
pumped infrared laser, the first example of which was based on the H2-C12 reaction system.' The entire family of triatomic reactions among hydrogen and halogen atoms and molecules has been particularly important to the development of the fundamental concepts on which molecular reaction dynamics is based. These reactions have been discussed extensively in articles, reviews, and book^,^-'^ and the results of experimental measurements on them have been exhaustively catalogued.I4-l6 Their potential energy surfaces are simple and ~e1l-known.l~ In~the ~ ~ exoergic direction, these are characterized by small energy barriers in the reagent approach coordinate and monotonically repulsive energy release (most of the reaction energy is released during the product separation phase of the reaction). Several simple rules have been postulated, based on the observed behavior of these reactions. These rules are largely intuitive, are generally based on classical mechanics, and have a surprisingly wide range of applicability. These are discussed at length in ref 12 and 13, and I shall mention only two of them here, as these will be useful in the interpretation c some of the results to be discussed later. First, for the case of an atom-molecule reaction on a repulsive surface, the product vibrational excitation is less (and hence the translational excitation is greater) if the reagent atom is light than if it is heavy, because at comparable energies, the high velocity of the light atom brings it close to the bonding distance before a substantial increase in the internuclear separation of the reagent molecule can occur. This has the consequence that subsequent repulsive energy release imparts translation to the newly formed product molecule as a whole, rather than to one of its atoms. For example, the fraction of the available energy which becomes product vibration cf,') in the direct abstraction, F IC1 I F C1, is 0.5919whereasf,' in the direct CI abstraction by H, H + IC1 I, is only 0.36.20This holds true even though in the former reaction, a bound F-I-C1 intermediate exists,21which might be expected to reduce the product excitation (vide infra). This rule has the corollary that translational excitation of the reagent atom will cause the vibrational excitation of the product molecule to be reduced and its translation to be increased.6%22 Second, more product vibrational excitation is created by the transfer of a light atom between two heavier ones than for the transfer of a heavy atom because in the former case, repulsive energy release creates a higher relative velocity between the approaching atoms in the nascent product molecule. For example, HCI I reaction is 0.64,22b the value off;,' for the C1 H I and thef,' values for all reactions having the H LH HL H ( H = heavy; L = light) mass combination are high. The validity of these rules also depends upon the angular properties of the surface (they are strictly true only for reactions preferring linear
geometry). Where the surfaces allow significant deviations from linearity, the same rules are valid, but they must be modified in the obvious ways to include the participation of product rotation as well as vibration. Many other unusual properties have been noted for the case of reactions in which a light atom is transferred between two heavier masses. Many of these have been the subject of theoretical to which the interested reader is referred for further information. There are many more generalizations" which may be derived from the behavior of reactions with simple repulsive energy release, but the essence of those just mentioned is that any influence which enhances the relative motion of the atoms in the nascent product molecule enhances the product vibrational excitation at the expense of product translational energy. A closely related set of inverse rules has been d e r i ~ e d , ~which ~ ~ ' , relate ~ ~ the dynamics (and probability) of a reaction to the reagent translation and vibration. These are based on the thesis that any influence which contributes motion perpendicular to the reaction barrier on the potential energy surface increases the reaction probability. Thus, for example, reagent vibrational excitation will enhance the rate of thermoneutral reactions, which have the energy barrier in the region of closest approach,24or endothermic reactions, for which the energy barrier occurs as the products separate.2s It will do very little, however, to the rate of a reaction that must surmount a barrier before the reagents can approach each other. Reagent translational energy is most efficient in the latter case.26 These generalizations find application in helping to choose reactions suitable for selective rate enhancement by, for example, laser excitation of a specific bond. It is clear that only reactions for which the energy barrier is in the exit channel will be useful for this purpose. Similar rules may be derived from the behavior of reactions characterized by attractive energy release (those for which the major energy release occurs in the reagent-approach coordinate of the potential energy surface). Because the energy of reaction is released in the bond that is being formed, the vibrational excitation created by these reactions can be very high, if the product separation occurs in a time that is short with respect to that of IVR processes which would lead to its loss from that bond. The extraordinarily high OH excitation created by the reaction H + 0, OH(u? O2 results from this. About 93% of the total available energy appears as internal excitation of the OH in this ca~e.~',~~ The precise nature of the energy flow induced by the atomic rearrangements in a chemical reaction has always been a subject of principle importance to reaction dynamics. Product energy distributions, especially vibrational distributions, give detailed information about the energy migration in ways that will be discussed shortly. First, however, it is worth noting that the absolute time scales for these processes are just now becoming measurable by subpicosecond laser technique^.^^ Information about the characteristic times of the important reaction steps is complementary to the energy distribution information derived from asymptotic measurements. For example, if a long-lived intermediate is formed and if all modes of that species participate equally in product formation, then statistical energy partitioning is expected. Nonstatistical energy partitioning, however, may be due to a rapid, direct process (as described above) or to a long-lived
t-
+
-
+
-
+
-
+
+
-
+
(8) Parker, J. V. V.; Pimentel, G. C. Phys. Rev. Lett. 1965, 14, 352. (9) Polanyi, J. C. Acc. Chem. Res. 1972, 5, 161. (10) Carrington, T.; Polanyi, J. C. MTP Int. Rev. Sci. Phys. Chem. Ser. 1 1972, 9, 135. (1 1) Polanyi, J. C.; Schreiber, J. L. In Physical Chemistry, An Advanced Treatise; Jost, W., Ed.; Academic: New York, 1974; Vol. 6, 383. (12) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths: London, 1980. (13) Bernstein, R. B. Chemical Dynamics via Molecular Beam and Laser Techniques; Clarendon: Oxford, 1982. (14) Bogan, D. J.; Stetser, D. W. In Fluorine Containing Radicals; Root, J., Ed.; ACS Symposium Series 66; American Chemical Society: Washington, DC, 1978. (15) Holmes, B. E.; Setser, D. W. In Physical Chemistry of Fast Reactions; Smith, I. W. M., Ed.; Plenum: New York, 1980; Vol 2. (16) Agrawalla, B. S.; Setser, D. W. In Gas Phase Chemiluminescence and Chemiioniration; Fontijn, A,; Ed.; North-Holland, Amsterdam, 1985. (17) Parr, C. A,; Truhlar. D. G. J Phys. Chem. 1971, 75, 1844. (18) Baer, M.; Last, I. In Potential Energy Surfaces and Dynamics Calculations; Truhlar, D. G . , Ed.; Plenum: New York, 1981. (19) Trickl, T.; Wanner, J. J . Chem. 1985, 78, 6091. (20) Polanyi, J. C.; Skrlac, W. J. Chem. Phys. 1977, 23, 168. (21) Valentini, J. J.; Coggiola, M. J.; Lee, Y. T. Faraday Discuss. Chem. SOC.1977, 62, 232. (22) (a) Ding, A. M. G.; Kirsch, L. J.; Perry, D. S.; Polanyi, J. C.; Schreiber, J. L. Faraday Discuss. Chem. Soc. 1973, 55, 252. (b) Maylotte, D. H.; Polanyi, J C . ; Woodall, K. B. J . Chem. Phys. 1972, 57, 1547.
-
+
(23) (a) Mantz, J.; Meyer, R.; Pollak, E.; Romelt, J. Chem. Phys. Lett. 1982, 93, 184. (b) Manz, J.; Schor, H. H. R. Chem. Phys. Lett. 1984, 107, 549. (c) Manz, J. Comments A t . Mol. Phys. 1985, 17(2), 91. (24) Blackwell, B. A,; Polanyi, J. C.; Sloan, J. J. Chem. Phys. 1977, 24,
25. (25) (a) Douglas, D. J.; Polanyi, J. C.; Sloan, J . J. J . Chem. Phys. 1973, 59, 6679. (b) Douglas, D. J.; Polanyi, J. C.; Sioan, J . J. Chem. Phys. 1976,
13, 15.
(26) Polanyi, J. C.; Sloan, J. J.; Wanner, J . Chem. Phys. 1976, 13, 1. (27) (a) Charters, P. E.; Macdonald, R. G . ; Polanyi, J. C. J . Appl. Opt. 1971, I O , 1747. (b) Polanyi, J. C.; Sloan, J. J. Int. J . Chem. Kinet. 1974, 7 , 51. (28) Klenerman, D.; Smith, I . W. M. J . Chem. Soc., Faraday Trans. 2 1987, 83, 229. (29) (a) Zewail, A. H. Faraday Discuss. Chem. Soc. 1983, 75, 315. (b) Scherer, N. F.: Khundkar, L. R.: Bernstein, R. B.; Zewail, A. H . J . Chem. Phys. 1987, 87, 1451.
The Journal of Physical Chemistry, Vol. 92, No. 1, 1988
Sloan
reaction in which specificity is imposed by features in the exit channel of the potential energy surface. An important part of current reaction dynamics research is concerned with distinguishing between these two processes, and direct time scale measurements provide one means to make the distinction. Measurements made in this laboratory some time ago on the reactions of F atoms at selected sites on polyatomic molecules illustrate these ideas. Isotopic labeling of the reactive sites in the F HCOOH system shows that reaction at the C-H bond creates an inverted vibrational distribution resembling that of the F/CH4 reaction, whereas the reaction at the carboxyl group gives a vibrationally cold distribution which is identical, within the experimental uncertainty, with that expected from the statistical decomposition of a long-lived intermediate.’O The dramatic differences between these distributions suggests that they sample not only separate but isolated parts of the system’s phase space. The application of these ideas in current molecular reaction dynamics research will be the subject of later sections. Before discussing the results, however, it is necessary to describe the most common experimental techniques used to obtain them. This will be done in the next section.
dation will be given in order to illustrate their operation. In the low-pressure e ~ p e r i m e n tthe , ~ ~reagents are introduced through tubes (often concentric) at one end of a large reaction chamber. The width of the latter is comparable to or larger than its length, and it is furnished with pumps having adequate throughput to maintain the average pressure well below that for free molecular flow. In practice, this requires diffusion pumps having a rated speed of 6000-10000 l / s at 104-10-3 Torr. The Knudsen number at the highest pressure point, the outlet of the reagent tubes, is in the range 10-’-10-*, and the mean free path at this point is a few millimeters. At the lower end of the reaction chamber, the mean free path is typically several meters and the Knudsen number is 10-100. At some location close to the reagent inlet tubes, therefore, the expanding gases cease to have collisions and the energy distribution in the products “freezes in”. Since the relaxation of the products ceases during the expansion, the technique is called “arrested relaxation”. The major uncertainty in the operation of the low-pressure apparatus stems from the fact that the reagent gas streams have poor directionality and the absolute pressure at any given point is poorly known. As a result, in the limit of very low reagent flow, the mean free path may become so large that vibrationally excited product molecules can diffuse back into the reagent inlet tubes, increasing the probability for their deactivation in collisions with the incoming reagents or with the tube surfaces themselves. Under normal operation, the observed product excitation increases with decreasing reagent flows, as gas-phase relaxation by incoming reagents decreases. Under conditions of extremely low flow, however, this back-diffusion can cause anomalous relaxation by increasing the number of collisions with incoming reagents or with the walls of the reagent inlet assembly, with the result that the observed product excitation decreases with decreasing flows. We believe this to be the of the unusual behavior of the F/HBr reaction, in which the observed H F vibrational distribution is vibrationally cold at very low reagent f l o ~ s , j ’ -although ~~ the initial distribution is generally agreed to be strongly inverted.4s43 Clearly, this is a potential problem only for those reactions having extremely high rates, as it is only in these cases that the reagent flows can be reduced sufficiently to induce the effect, while still producing observable signal. There are also potential difficulties with the flowing afterglow technique, arising from the conflicting requirements of having a high buffer gas pressure to provide adequate pumping and prevent the too-rapid diffusion of the products to the tube walls, while at the same time having low enough pressures to provide for adequate lateral diffusion, reagent mixing, and reaction in the short time available before the observation. These difficulties are accentuated for very fast reactions, since in this case, the primary (molecular) reagent will be extensively converted to radicals in situ as it is injected into the flow; and subsequent diffusion of atoms into the radical-rich stream can lead to an increased probability for secondary reactions between the atomic reagent and the radical. The last difficulty, secondary reactions, is also a potential problem for the low-pressure techniques. To illustrate its effect under typical operating conditions, simple numerical models of both experiments have been written. These models are identical in all respects except that of the gas expansion. The low-pressure (LP) model assumes the reagents mix instantaneously at the outlets of two concentric tubes and that the pressure thereafter is inversely
20
+
11. Experimental Techniques
Two experimental techniques that have contributed substantially to our knowledge of reaction dynamics are low-pressure infrared chemiluminescence and flowing afterglow measurements. These will be described to the exclusion of the various implementations of laser-induced fluorescence, although the latter has become one of the most widely applied methods for obtaining state-resolved dynamical inf~rmation.~’There are many excellent reviews of the LIF technique, however, and in the interest of brevity, no further description will be presented here. Low-pressure infrared chemiluminescence is a direct descendent of the technique used in the first internal energy distribution measurements.’* The flowing afterglow experiment is a variant in which the reagents are entrained in a higher pressure carrier gas.33 In both cases, the observations are made directly by recording the infrared emission spectra of the internally excited products, and the populations of the observed states are calculated by using the known Einstein transition probabilities for the observed transitions. Aside from the pressure regime in which they operate, the essential difference between these two techniques lies in the way in which they deal with the problem of relaxation of the newly formed reaction products in collisions with the unused reagents. In the lowing afterglow technique, the reagent-mixing region is located as close as possible to the observation window. Although the pressure of the carrier gas is on the order of 1 Torr, the very rapid flow (1 80-200 m/s)34 carries the products past the observation window before collisional relaxation of the vibrational distribution. Rotational relaxation, however, is usually almost complete. In the low-pressure experiment, the reagents are mixed while expanding rapidly into a low-pressure region. Low reagent flows and very high pumping speeds are used in order to ensure that, after the initial reactive collision, the mean free path increases so fast that the newly formed products suffer a negligible number of collisions with other molecules. These techniques should, in prinicple, yield the same results, and in the great majority of cases, they do. There are, however, a small number of reactions for which they have given different results, and the causes of these discrepancies give information about the techniques themselves as well as the chemical systems involved. In the remainder of this section, some important details of the two experiments will be described; then a computer sim(30) Macdonald, R. G.; Sloan, J. J. Chem. Phys. 1987, 13, 165. (31) Jackson, W. M.; Harvey, A. B., Eds.; Lasers as Reactants and Probes in Chemistry; Howard University Press: Washington DC, 1985. (32) Polanyi, J. C.; Woodall, K. B. J . Chem. Phys. 1972, 57. 1574. (33) (a) Smith, D. J.; Setser, D. W.; Kim, K. C.; Bogan, D. J. J . Phys. Chem. 1977, 81, 898. (b) Wickramaaratchi, M. A,; Setser, D.W. J . Phys. Chem. 1983,87, 64. (34) Agrawalla, B. S.; Setser. D. W. J. Phys. Chem. 1986, 90, 2450.
(35) (a) Macdonald, R. G.; Sloan, J. J. Chem. Phys. Lett. 1979,61, 137 (b) Donaldson, D. J.; Wright, J. S.; Sloan, J. J. Can. J . Chem. 1983, 61, 912. (36) Aker, P. M.; Donaldson, D. J.; Sloan, J. J. J . Phys. Chem. 1986, 90, 3110. (37) Brandt, D.; Dickson, L. W.; Kwan, L. N. Y.; Polanyi, J. C. J . Chem. Phys. 1979, 39, 189. (38) Tamagake, K.; Setser, D. W.; Sung, J . P. J . Chem. Phys. 1980, 73, 2203. (39) Dill, B.; Heydtmann, H. Chem. Phys. 1983, 81, 419. (40) Sung, J. P.; Setser, D. W. Chem. Phys. Lett 1977, 48, 413. (41) Beadle, P.; Dunn, M. R.; Jonathan, N. B. H.; Liddy, J. P.; Naylor, J. C . J . Chem. Soc., Faraday Trans. 2 1978, 74, 2170. (42) Jonathan, N. B. H.; Sellers, P. V.; Stace, A. J. Mol. Phys. 1981, 43. 215.
(43) Duewer, W . H.: Setser, D. W . J . Chem. Phys. 1973, 58. 2310.
Feature Article
The Journal of Physical Chemistry, Vol. 92, No. 1, 1988 21
TABLE I: Parameters Used in the Numerical Models rate const, reagent flows, Torr-’ s-I X lo5 mol s-I x 10“ reactn deactvn atom source
signal-to-noise ratios comparable to the (single-pass) FA experiment. For this case of an extremely fast secondary reaction, this same effect also causes the creation of more secondary products in the FA configuration-about 10% in calculation A, as compared to about 3% for the LP experiment. This effect is not ameliorated by a small primary reaction rate, if the secondary rate is large (calculation C), because in this case, the fractional creation of the secondary product is the same. If the secondary rate constant is reduced by a factor of 10 (calculation D) or if both rate constants are small (calculation E), the interference by the secondary reaction becomes negligible. The distortion caused by the secondary reaction is much enhanced if higher reagent flows are used, as shown by calculations F and G. Comparison of calculations A and F shows, for the distributions in this model, the observed distribution becomes less excited when the reagent flow is decreased. This is not caused by the anomalous relaxation effects described previously for the LP experiment-these are not included in the present-and moreover, it occurs for both experiments. It is caused by the increasing contribution of the secondary reaction at higher reagent flows. An effect of this type has been found in previous work on the reaction of F atoms with NH3.43-50 The HF(u9 distribution for the primary F NH, reaction is P(u’ = 1:2) = 0.60:0.40, and the observed vibrational distribution becomes more inverted with increasing reagent flow. Using a model based on the hypothesis that a fast secondary reaction was leading to this observation, we extracted the following vibrational distribution for the F N H 2 reaction: P(u’= 1:2:3:4) = 0.23:0.68:0.08:0.01.48 Even if the reagent flows are extremely high and the rate constants are unfavorable, distortions of this kind can be eliminated by performing the experiment in a pulsed mode and gating the detection such that the observation has been completed before a substantial amount of the secondary reaction has occurred. We have recently developed a time-resolved Fourier transform spectrometer that is capable of measuring infrared emission spectra separated in time by a few microseconds. Although the first applications of this instrument have been to the observation of the reactions of transient species (we have used it to measure the energy partitioning in the reactions of O(’D2) atoms with H2,51 HQ5* and certain halogenated methanes5,), it can also be used to time resolve the emission spectra from the primary and secondary reactions in applications such as this. The expected behavior can be predicted by using the numerical model. If the observation is made after 5 1 s under conditions of calculation F, for example, the LP result would be P(u’= 1:2) = 0.88:0.12 and the FA result would be 0.86:0.14. Thus, direct time resolution can also retrieve essentially the exact primary energy distribution.
run
A B
c D E
F G
1 10 10
10
1 10 l
10 1 l
10
10 10
10
2
10
RHz, R H 10 0 10 10 10 10
10
A,R 1
0 1
1 1 1 1
RHz 10 10 10 10 10 100 10
(A21 10 10 10 10 10 100
25
proportional to the volume of a sphere that is expanding at the flow velocity of the gases. The initial diameter of the sphere is that of the larger reagent tube. The initial pressure and the expansion velocity are computed from the specified reagent flow, the pumping speed, and the dimensions of the inlet tube and the pumping outlet, which are assumed to be those of the apparatus described in ref 35. The flowing afterglow (FA) model also assumes instantaneous reagent mixing across the flow tube but ignores product deactivation on the tube walls. The flow velocity, tube dimensions, and pumping speed reported in ref 34 are used in the computation. It is assumed that the molecular reagent RH2 can give rise to both primary and secondary reactions with the atomic reagent A:
+ RH2 A + RH
A
-
---*
+ RH HA(v” I 2) + R
H A ( u ’ I 2)
(1) (2)
It is further assumed that each reaction populates two excited vibrational levels of the H A product. The relative population distributions used as input to the model are P(u’ = 0:1:2) = 0.0:0.9:0.1 and P(u”= 0:1:2) = 0.0:0.1:0.9-an example of a worst case situation in which two reactions populate the same product levels in different ways. After construction of these models, the rate equations were integrated during the time required for the products to flow past the observation regions of the experiments. The detection geometry of the typical Welsh optical cell used in the LP apparatus is taken into account by computing the overlap of the expanding sphere with the optical cell and including only the emission from those excited products within this volume. It was assumed that all excited products created in the FA experiment were observable and that the observation zone began just at the point of reagent mixing. The reagent flows and rate constants for reaction and product deactivation in collision with the various species present are listed in Table I. The corresponding results are listed in Table 11. The distributions of the primary and secondary reactions are separately normalized to C$=,P(u’)= 1.0, and the total excited ( u ’ > 0) population created by each reaction is also given. The composite distribution is the one that would be observed experimentally-the renormalized sum of the other two distributions, weighted by their respective total populations. Calculation A was carried out under conditions that are appropriate for a fairly difficult, but not atypical, energy distribution measurement. For calculation B, the deactivation rates were set to zero. In calculations C and D, the primary and secondary reaction rate constants (respectively) were set to 10% of their values in the reference calculation, while in calculation E, both reaction rate constants were set to 10% of their reference values. The rate constants all have their reference values in calculations F and G, but in the former, the flows of both reagents are increased by a factor of 10, and in the latter, the atom precursor flow is increased by a factor of 2.5. Table I1 shows that, for calculation A, both techniques give essentially the exact results for both the primary and secondary reactions individually, despite the extremely high vibrational deactivation rate constants. Although the total flows are the same, the confinement of the reagents by the buffer gas in the FA experiment creates about 10 times more product than in the AR experiment-a difference that normally necessitates the use of multipass light-collection optics in the LP apparatus to obtain
+
+
111. Current Research Problems
The reactions being investigated presently are more complex than the three-atom systems referred to in the Introduction, and much current work is designed to explore the effects resulting from this added complexity. The duration of the interaction may be used as a diagnostic for complexity, and in the following, deductions about the duration of the reaction will be based on the internal energy distributions of the products. Two extremes may be identified: reactions having internal energy distributions that (44) Douglas, D. J.; Sloan, J. J. Chem. Phys. 1980, 46, 307. (45) Sloan, J. J.; Watson, D. G.; Williamson, J. Chem. Phys. Lett. 1980, 74, 48 1. (46) Manocha, A. S.; Setser, D. W.; Wickramaaratchi, M. Chem. Phys. 1983. 76. 129. (47) Donaldson, D. J.; Parsons, J.; Sloan, J. J.; Stolow, A. Chem. Phys. 1984. 85. 47.
(48) Donaldson, D. J.; Goddard, J. D.; Sloan, J. J. J. Chem. Phys. 1985, 82, 4524. (49) Wategaonkar, S.; Setser, D. W. J. Chem. Phys. 1987, 86, 4477. (50) Goddard, J. D.; Donaldson, D. J.; Sloan, J. J. Chem. Phys. 1987, 114, 321. (51) Aker, P. M.; Sloan, J. J. J. Chem. Phys. 1986, 85, 1412. (52) Kruus, E. J.; Niefer, B. I.; Sloan, J. J., accepted for publication in J . Chem. Phys. (53) Aker, P. M.; Niefer, B. I.; Heydtmann, H.; Sloan, J. J. J. Chem. Phys. 1987, 87, 203.
22
The Journal of Physical Chemistry, Vol. 92, No. I , 1988
Sloan
TABLE II: Numerical Results for Low-Pressure (LP) and Flowing Afterglow (FA) Models
computed population distribn primary reactn run/model
u' = 1
A/LP
0.900
A/FA
0.901 0.900 0.900 0.900 0.901 0.900 0.901 0.900 0.901 0.902 0.905 0.900 0.901
B/LP B/FA C/LP C/FA
D/LP D/ FA E/ LP E/FA F/LP €/FA G/LP G/FA
u'= 2 0.100 0.099 0.100 0.100 0.100 0.099 0.100 0.099 0.100 0.099 0.098
0.095 0.010 0.099
secondary reactn Prm
0.367 4.390 0.373 4.670 0.038
0.500 0.372 4.570 0.039 0.525 21.60 115.0 1.630 15.20
L"= 1 0.111 0.139 0.100 0.100 0.111 0.139 0.111 0.139 0.1 11 0.138 0.194 0.334 0.1 18 0.161
are strongly inverted and those having much lower levels of excitation. In the three-atom case, direct interactions giving inverted s. In product distributions have durations on the order of the latter case, the situation is more complicated, but one extreme can also be identified-that in which the populations of the product modes are strictly proportional to their state densities. The case of statistical partitioning of the reaction exoergicity has been extensively explored in the literature of unimolecular reactions as well as in early molecular beam54.55and infrared chemilum i n e s c e n ~ e work. ~ ~ - ~ ~(See ref 15 for an extended discussion of the early results.) The intermediate cases-those in which the product excitation cannot be described by statistical calculations but it is not as high as would be expected on the basis of direct interactions-will form the basis for the following discussion. As indicated above, the (qualitative) shapes of vibrational distributions are often diagnostic of the duration of the interaction. The behavior of reactions involving the transfer of a light atom (hydrogen or deuterium) is especially important in this respect, because the transfer of a light atom via a smoothly repulsive potential energy surface occurs in the shortest possible time-often less than one vibrational period of the bond being broken-and this provides the minimum-time reference point with which to compare other reactions. Direct hydrogen abstractions such as the X HY reaction family (X and Y = halogen atoms) and the F H2 reaction are examples of this behavior. For the opposite extreme-that of statistical energy partitioning-the products have monotonically decreasing vibrational populations with increasing vibrational excitation. In this case, the dynamics of the reaction have no influence on the product energy distribution and only thermochemical information about the reaction can be obtained, even from dynamical measurements. The consequences of this have been discussed extensively in the application of information theory to this s u b j e ~ t . ~ ~ - ~ * Closely related to the statistical case, but somewhat more complicated, is the case of reactions having a strongly bound, long-lived intermediate that must cross an energy barrier in the exit channel. In this case, the excess energy (the difference between the total available energy and that which is in the form of potential energy at the top of the barrier) is considered to be statistically distributed among the modes of the transition state
+
ut= 2 0.889 0.861 0.900 0.900 0.889 0.861 0.889 0.861 0.889 0.862 0.806 0.666 0.882 0.839
composite distribn PTOT
0.01 1 0.439 0.01 1 0.442
0.001 0.0511 0.001 0.052 0.0001 0.0061
0.050 70.60 0.224 6.580
1
u'= 2
PTOT
0.878 0.832 0.878 0.831 0.878 0.830 0.898 0.892 0.898 0.892 0.770 0.688 0.806 0.677
0.122 0.168 0.122 0.169 0.122 0.170 0.102 0.108 0.102
0.378 4.830 0.384
l;'=
5.1 I O 0.039
0.551 0.373 4.620 0.039 0.531 26.50 185.0 1.850 21.80
0.108 0.230 0.312 0.194 0.323
Y'
N 0
"'
FTP) + HCO('A') O
__ 25
-13
h
-20
-15
+
(54) Shobotake, K.; Lee, Y. T.; Rice, S. A. J . Chem. Phys. 1973,59, 1435. (55) Shobotake, K.; Lee, Y. T.; Rice, S. A. J . Chem. Phys. 1973, 59, 6104. (56) Chang, H. W.; Setser, D. W.; Perona, T. J. J . Phys. Chem. 1971, 75, 2070. (57) Kim, K. C.; Setser, D. W. J . Phys. Chem. 1974, 78, 2166. (58) (a) Holmes, B. E.; Setser, D. W.; Pritchard, G. 0. Int. J . Chem. Kinet. 1976.8, 215. (b) Holmes, B. E.; Setser, D. W. J . Phys. Chem. 1978, 82, 2450. (c) Holmes, B. E.; Setser, D. W. J . Phys. Chem. 1978, 82, 2461. (59) Zamir, E.; Levine, R. D. Chem. Phys. 1980, 52, 253. (60) (a) Bernstein, R. B.; Levine, R. D. Ado. At. Mol. Phys. 1975, 11, 216. (b) Levine, R. D.; Bernstein, R. B. In Modern Theoretical Chemistry; Miller, W. H., Ed.; Plenum: New York, 1976; Vol. 3. (61) Levine, R. D.; Ben-Shaul, A. Chemical and Biological Applications of Lasers; Moore, C . B., Ed.; Academic: New York, 1977; Vol. 3. (62) Levine, R. D. Anntr. Rel;. Phys. Chem. 1978, 29, 59.
Figure 1. Schematic minimum-energy path for the F(2P) reaction, showing the product vibrational energy levels.
+ HC0(2A')
and to remain thus during the decomposition. The partitioning of the remaining exoergicity, which is released in the exit channel, depends upon the details of the potential energy surface and the structure of the transition state. A large literature has been produced on this subject, based on simple "tight" and "loose" ~ ,behavior ~ ranges from the models of the transition ~ t a t e . ~The extreme case of the tight transition state in which the entire barrier is converted into translational energy,55 in a process analogous to the repulsive release of the exoergicity in a direct reaction (vide supra), to a range of intermediate cases in which exit channel coupling causes the conversion of part of the barrier into internal excitation of the p r o d ~ c t s . ~ ~In- ~ the~ remaining part of this (63) Marcus, R. A. J . Chem. Phys. 1977, 62, 1372. (64) Worry, G.; Marcus, R. A. J . Chem. Phys. 1977, 67, 1636. (65) Cheung, J. T.; McDonald, J. D.; Herschbach, D. R. J . A m . Chem. Soc. 1973, 95, 7889. (66) Parson, J. M.; Lee, Y. T. J . Chem. Phys. 1972, 56, 4658. (67) Farrar, J. M.; Lee, Y. T. J . Chem. Phys. 1976, 65, 1414. (68) Dagdigian, P. J. Chem. Phys. 1977, 21, 453. (69) Hsu, D. S. Y.; Lin, M. C. Chem. Phys. 1979, 38, 285. (70) Donaldson, D. J.; Sloan, J. J. J . Chem. Phys. 1985, 82, 1873. (71) (a) Morokuma, K.; Kato, S.; Hirao, K. J . Chem. Phys. 1980, 72, 6800. (b) Morokuma, K.; Kato, S. In Potential Energy Surfaces and Dynamics Calculations, Truhlar, D. G., Ed.; Plenum: New York, 1981; p 243.
(72) Setser, D. W., private communication. (73) Nazar, M. A,; Polanyi, J. C. Chem. Phys. 1981, 55, 299. (74) (a) Wickramaaratchi, M. A,; Setser, D. W.; Hildebrandt, B.; Korbitzer, B.; Heydtmann, H. Chem. Phys. 1985, 94, 109. (b) Chang, H . W.; Setser, D. W. J . Chem. Phys. 1973, 58, 2298.
Feature Article
The Journal of Physical Chemistry, Vol. 92, No. I , 1988 23
section, these ideas will be illustrated by three reaction systems recently studied in this laboratory (and elsewhere), each of which demonstrates one of these exit channel effects. 111.1. The F HCO Reaction. This reaction7’ creates H F and C O with a total exoergicity of 116 kcal/mol. The potential energy surface contains the strongly bound HFCO intermediate, which is separated from the exit channel by a barrier of approximately 60 k ~ a l / m o l . ’ ~A schematic correlation diagram showing some of the important energy levels, including the accessible product vibrational levels, is shown in Figure 1. The experimentally observed vibrational excitation in both reaction products decreases monotonically in conformity with the general expectation for a reaction with a prolonged interaction. The C O distribution is P(u’ = 1:2:3:4:5) = 0.53:0.24:0.12:0.08:0.02. (Only those product levels giving rise to emissions with signal-to-noise greater than one are quoted here; it is assumed that the shape of the population distribution in the observable levels is continued in the remaining energetically accessible levels.) The lowest four H F levels are obscured by emission from H F produced in the F H 2 C 0 reaction (used to make the H C O radicals) but the next six levels can be measured and have the following population distribution: P(u’= 5:6:7:8:9:10) = 0.35:0.26:0.19:0.12:0.07:0.01. Although both decrease monotonically with vibrational level, these distributions differ from the respective statistical distributions in a way that permits the extraction of detailed information about the decomposition of the enegetic H F C O intermediate. For comparison, the appropriate statistical populations were calculated, beginning with the customary assumption that the energy in excess of the barrier is statistically distributed among the modes of the HFCO transition state at the top of the barrier. A plausible model for the steps in the decomposition that follow this point must be based on what we know about the structure and ,vibrational frequencies of the transition state,71and it must be consistent with expectations based upon the behavior of the simpler systems alluded to in the Introduction. Since the overall reaction involves the transfer of a hydrogen atom between two heavier species, it is clear that this atom will move with a much higher velocity than the other atoms-an expectation which is borne out by the calculations reported in ref 7 l . The observed C O vibrational excitation is very low (has larger populations in the lower vibrational levels), much lower than that of the HF. If populated by a simple statistical decomposition in which the total reaction exoergicity is available, the C O vibrational = distribution would be P ( u ’ = 1:2:3:4:5) 0.28:0.23:0.19:0.16:0.14-much more excited than the experimental result. It must be concluded, therefore, that the C O product does not share fully in the partitioning of the reaction exoergicity in the exit channel. If it is assumed that the C O becomes isolated immediately upon passing through the transition state, then it would have access to only that energy in excess of the exit channel barrier (approximately 50 kcal/mol) and the calculated statistical C O vibrational distribution would be P(u’ = 1-5) = 0.44:0.28:0.17:0.08:0.04. This is very close to the experimental distribution, and in view of the uncertainty both in the experimental result (likely about f0.05 per u level) and in the height of the exit-channel barrier (calculated at the 6-31G** ), very level with CI, based on 4-31G S C F s t r ~ c t u r e s ~it~represents good agreement. Thus it may be concluded that the first step in the decomposition is the isolation of the C O molecule and its separation from the nascent HF, either at or immediately after passing through the transition state. On considering the partitioning of the exoergicity between the internal modes of the HF and relative translation, if it is assumed that the energy barrier is converted entirely into relative translation, the remaining energy would only be sufficient to create HF(u’5 4), whereas the observed distribution extends up to HF(u’ = 10). The converse assumption-that the entire exoergicity is available to the HF and is partitioned at the transition state, as in the C O case-leads to the predicted H F vibrational distribution P(u’ = 5:6:7:8:9:10) = 0.32:0.25:0.19:0.14:0.09:0.01 in good
agreement with the experiment. Thus the following self-consistent picture of the F H C O reaction emerges: first, a long-lived HFCO species is formed which eventually reaches a transition state characterized by the presence of an energy barrier caused by a substantial increase in the potential energy of the system as the C-H and C-F bonds break and the H-F bond begins to form (see Figures 6 and 7 of ref 71). The CO is decoupled from the system at (approximately) the top of the barrier, and its excitation is characteristic of the energy available at this point. The HF formation then proceeds after the CO elimination, and the potential energy released in this process is distributed approximately statistically between H F excitation and relative translation. 111.2. The F NH3 Reaction. The reaction F NH, HF(u’ 5 2) N H 2 moo = -30 kcal/mol (3)
+
+
(75) Kollman,
P. A.; Allen, L. C. J . Am. Chem. SOC.1970, 92, 753.
+
+
-
+
+
is more complex than the F/HCO system, and although it has been the subject of a large number of experiment^,^^-^^ some aspects of its behavior are still in doubt. In addition to the existence of complicated exit channel effects, to be discussed shortly, it can also undergo the fast secondary reaction AHoo = -43 kcal/mol F NH, HF(u’ I4) N H
+
-
+
(4)
This secondary reaction is a considerable experimental difficulty, inasmuch as it creates all of the H F vibrational levels that can be formed by the primary reaction. Its presence can be identified by the fact that it has sufficient exoergicity to create HF(u’ 1 3), whereas the primary reaction does not. As expected, emission from HF(u’+ 3) is observed from this system under conditions of high reagent densities, which favor the secondary reaction. We have previously r e p ~ r t e dan ~ ~estimate , ~ ~ of the vibrational distribution created by reaction 4 from an extensive series of measurements of the composite vibrational distributions from both reactions, combined with a numerical model based on the gas dynamics of the low-pressure experiment. The result, P(u’ = 1:2:3:4) = 0.25:0.68:0.08:0.01, has the characteristic inversion expected of a direct reaction. Ab initio computations of the lowest energy triplet potential surface for the reaction (3A”) showed the existence of a direct pathway having zero energy barrier for the abstraction reaction via an F-HNH reaction geometry.48 We concluded from all of these results that reaction 4-the F / N H 2 reaction which produces vibrationally excited H F and hence ground-state NH(3Z-)-is a simple abstraction having direct dynamics like reactions such as F/H2. The vibrational distribution created by the primary F / N H 3 reaction is P(u‘ = 1:2) = 0.60:0.40.47,49Also, it has been sugg e ~ t e d ~that ~ , ’this ~ distribution peaks in u’ = 1, and the complete result, estimated by extrapolation of the vibrational surprisal, is P(u’ = 0:1:2) = 0.18:0.47:0.35. The inverted vibrational distribution reported for the isotopically analogous reaction: F/ND3 in ref 49 is cited as additional evidence for this. The low-pressure technique obtains a less excited vibrational distribution for the latter reaction, however,47 and so the details in this regard are still in doubt. In any case, the F/NH3 distribution is considerably less vibrationally excited than would be expected of a light atom transfer reaction having simple, direct, dynamics. Even for the latter distribution above, the reaction partitions about 40% of the available energy into HF vibration, and if the u t = 0 population is high, this percentage would be much less. This is low by comparison with other reactions having this mass combination. The F/CH4 reaction, for example, partitions 63% of the energy into ~ i b r a t i o n ,and ~ ~ this . ~ ~ percentage varies from 55% to 60% for the F/HX reactions.16 The vibrational distribution created by the F/ND3 reaction also gives an unusually low diatomic product vibrational excitation. Measurements on this reaction are also subject to contamination by secondary reaction (which, as in the F / N H 3 case, has an inverted vibrational distribution). We have shown47that, at high reagent flows, the observed D F distribution from the F/ND3
24
The Journal of Physical Chemistry, Vol. 92, No. I , 1988
Sloan 0
C LO 0
0
N
FH
+ NH,
-(H-F)
F--NH3
Figure 2. Computed minimum-energy path for the F + NH, reaction showing the minimum due to hydrogen bonding. The zero point energies corresponding to the reagents, products, and potential minimum are also
shown.
inverted-P(u’ = 1:2:3:4) = 0.15:0.37:0.48:
