CHAPTER 1
Reactive and Inelastic Collisions involving Molecules in Selected Vibrational States
BY I. W. M. SMITH
1 Introduction
State Selected Kinetics and Reaction Dynamics. — For many years chemical kineticists have sought to observe and understand the processes that bring about macroscopic chemical and physical changes at the level of individual molecular events. Unfortunately, the detailed microscopic information that can be extracted from the results of conventional 'bulb' experiments is necessarily limited, since the parameters that characterize the intermolecular collisions, such as relative translational energy, impact parameter, orientation, etc., have, under these conditions, a full spread of values in accordance with statistical laws. Over about the past 15 years therefore, increasing use has been made of experimental techniques which provide results whose connection with fundamental molecular collision dynamics is less obscured by the many 'layers' of averaging [see Section 2 below and Figure 1 in ref. l(a)] that play their part in determining the magnitude of the thermal rate constant for a chemical reaction, k(T), and its dependence on temperature. For example, molecular beam and 'hot atom' experiments can yield information about the excitation function, i.e. how the cross-section for reaction varies with collision energy, whilst i.r. chemiluminescence, chemical laser, and molecular beam techniques allow the experimenter to investigate how the energy that is released in an exoergic chemical reaction is distributed among the degrees of freedom of the separating products.
The experiments referred to in the second half of the previous sentence reveal something about the specificity of energy disposal in elementary exoergic reactions. The other side of this coin is the selectivity of energy consumption; for example, whether a reaction with a high activation energy is promoted more effectively by providing the reactants with excess translational energy or by providing the same energy to an internal degree of freedom. A measure of these selective energy requirements may be obtained by comparing the results of experiments which yield an excitation function with those where the rate of reaction is determined for selected internat quantum states of the reactants.
In practice, the Boltzmann laws actually impose some degree of state selection on a molecular system at thermodynamic equilibrium. This is because the separation of electronic and vibrational states is usually much greater than kT at low temperatures, so that the great majority of intermolecular collisions under these conditions must involve molecules in their lowest vibronic states. Photochemical methods provide the simplest means of disturbing the Boltzmann distribution over states and hence of studying the kinetics of processes involving species in excited states. The photochemical investigation of electronically excited species has, of course, been carried on for many years. However, the process of excitation alters the electronic structure of the atom or molecule that has absorbed light and the results of collisions involving these species cannot be directly related to those of the corresponding ground-state species since the chemical forces controlling the collision dynamics will be quite different. In relatively large molecules, for example cycloheptatriene, the energy supplied initially as electronic excitation can rapidly be transformed into vibrational excitation via a process of internal conversion. In this way, unimolecular processes can be studied as a function of internal energy supplied via photochemical activation. Such experiments are considered in Chapter 5.
Vibrational Photochemistry. — In contrast to electronic photochemistry, direct vibrational photochemistry has really only become possible quite recently with the development of powerful i.r. lasers capable of exciting molecules in their relatively weak vibration–rotation bands. The commonest such application has been to the study of vibrational energy transfer.' Molecules are promoted to excited vibrational levels by the absorption of pulsed laser radiation The requirement that frequencies emitted by the laser correspond with lines in the absorption spectrum of the molecule is most easily satisfied when the laser oscillates on lines in the (1,O) fundamental band of the molecule that one wishes to excite, although chance coincidences and tunable laser radiation have also been used. The rate of relaxation of molecules that have been excited in this way is followed by observing how the intensity of the vibrational fluorescence (Ifl) decays with time. In the simplest case, where relaxation occurs predominantly via collisions with a single component (Q) of the gas mixture,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where kQ1, 0 is the rate constant for
BC(υ = 1) + Q -> BC(υ = 0) + Q (2)
The method of laser-induced vibrational fluorescence has yielded a great many results on the transfer of energy from molecules such as the hydrogen and deuterium halides, CO, NO, CO2, and other triatomic molecules to chemically stable collision partners. This subject has been reviewed more than once recently and will not be considered here. However, the technique is now being used in several laboratories to investigate the result of collisions between vibrationally excited molecules and potentially reactive species, particularly atomic free radicals such as H, N, 0, and halogen atoms. In many such cases chemical reaction, as well as energy transfer, is energetically possible. These alternative channels for removal of the excited molecules, which may be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3a)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3b)
are not distinguished in a laser-induced vibrational fluorescence experiment, since this only provides a direct measure of the total rate constant for removal of BC(υ), i.e. k3 = k3a + k3b. To determine k3b it is necessary to observe one or other product directly and to relate its concentration to the initial concentration of the excited reactant. These three-atom systems are clearly the simplest in which one can study the effect of enhancing the vibrational energy of a molecular reactant and are amenable to the most detailed theoretical interpretation.
So far in this introduction, emphasis has been placed on the part that studies of state-selected processes can play in helping to elucidate the factors that control molecular collisions in cases where there is the possibility of 'chemical' interaction between the collision partners. However, the impetus for the recent upsurge of interest in this subject has not been entirely engendered by purely 'academic' motives. More mundane, or more important – depending on one's point-of-view – considerations have also been at work.
The desire to understand, and hence improve, the performance of chemical lasers has served as one such stimulant. If high laser powers are to be extracted from these devices it is necessary to tolerate high concentrations of reactive atoms in the reacting gas that constitutes the laser medium. Unfortunately, these species may deactivate the excited, laser-active molecules at an unusually rapid rate and these processes can then be a crucial factor in limiting the efficiency of the laser. This appears to happen in the laser fuelled by the H2-Cl2 chain reaction. Partly because the Cl + H2 + HCl + H reaction is not particularly fast, the concentration of Cl atoms is likely to be high and these atoms rapidly relax the vibrationally excited HCl formed in the laser pumping reaction, H + Cl2 -> HCl + Cl.
Laser-induced Chemistry. — There is a second 'practical' reason for interest in vibrational photochemistry which is generating a great deal of excitement at the present time. This concerns the possibility of inducing novel chemical reactions by means of selective vibrational excitation resulting from the absorption of i.r. laser radiation. The equivalent of the visible–u.v. dye laser is badly needed but no comparably powerful, and relatively cheap laser, providing tunable, narrow bandwidth, radiation in the i.r. yet exists. Nevertheless, a considerable amount has been achieved using the specific laser sources that are currently available, particularly the CO2 laser.
However, even where an absorption frequency in one of the potential molecular reagents in a gas mixture does coincide with a laser line, several factors may prevent the laser energy from being used effectively in promoting chemical reaction. The first of these factors is the fairly limited amount of energy that is acquired by a molecule when it absorbs a single photon in a fundamental vibrational band. For example, the P(30) line from the CO2 laser at 9.6 µm has a photon energy equivalent to 12.5 kJ mol-1, and the P1(6) line from an HF laser at 2.71 µm corresponds to 44.2 kJ mol-1. These energies are comparable with the activation energies of many thermoneutral or exothermic atom-transfer reactions involving a simple free radical and a 'stable' molecule, but it now seems clear (see below) that in most cases not all of the vibrational excitation energy can be used to lower the activation energy of the reaction. Consequently, the enhancement of the chemical reaction rate that is brought about by promoting molecules to the first excited level associated with a particular vibrational mode may be fairly small.
Another major problem may be that the high selectivity of the initial excitation is lost rapidly in inelastic collisions. This is certainly true, for example, of any rotational disequilibrium brought about by the excitation process. Consequently, there is rather little direct experimental information about the influence of rotational excitation on chemical reaction rates, although what evidence there is (see below p. 36) suggests that such effects are usually small. In contrast to rotational energy transfer, V–T energy transfer, that is, the transfer of energy between the vibration of a small molecule and the relative translation of it and a second species, is usually extremely slow, unless there are specific intermolecular forces between the colliding species. Thus, the probabilities 'per collision' of Ar deactivating HCl (υ = 1) and CO (υ = 1) at room temperature are 1.7 × 10-8 and < 1.8 × 10-8, respectively.
The fastest vibrational energy transfer processes are likely to be those involving near-resonant vibrational–vibrational (V–V) energy exchange. Thus for a diatomic molecule, processes such as
BC(υ = 1) + BC(υ = 1) [??] BC(υ = 2) + BC(υ= 0) (4)
occur on a timescale characteristic of about 1O-lOOO intermolecular collisions. For polyatomic molecules, similar exchange processes occur, the excitation being retained for some time within the levels associated with one or a limited number of vibrational modes, before 'leaking away' into other degrees of freedom.
For some purposes the V-V processes can be extremely useful, since they provide a means of achieving significant excitation to levels high above the ground vibrational state without recourse to direct promotion from v = 0 in extremely weak overtone bands, or without relying on sequential (i.e. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] etc.) or multiphoton pumping. A simple example can be provided as an illustration of this. Consider a harmonic oscillator that is pumped sufficiently strongly on lines in its (1,O) band for 50% of the molecules to be raised 'instantaneously' to the first excited level. If then V–T energy transfer can be ignored, once the V–V relaxation has occurred ca. 1.2% of the molecules will be in levels with υ < 4. Furthermore, if some reaction removes molecules preferentially from these states, the reaction yield may be very much higher than is suggested by this 'equilibrium' figure, since molecules will continue to be excited to these higher levels (but at a continually decreasing rate) as the system attempts to establish a Boltzmann distribution over vibrational states.
The selective activation of a molecular reagent by V–V 'ladder-climbing' processes following primary excitation by powerful, singlephoton, optical pumping is one technique for inducing chemical reaction by i.r. laser irradiation. A number of reactions have been promoted in this way and some of these are discussed later. However, this method is, at best, only 'mode-selective' rather than 'state-selective', since the occurrence of V–V energy exchange prior to chemical reaction destroys the state selectivity of the initial photochemical act.
The rapidity of V–V energy exchange can make it extremely difficult to carry out highly selective experiments of two kinds. The first is measurements of reaction (or relaxation) rates out of specified vibrational levels. It is necessary that the reactive process occurs faster than the redistributim of vibrational quanta via V–V energy exchange if the rate of the former is to be determined. This problem is particularly severe when molecules are excited directly in an overtone absorption band for a study of the kinetics of processes involving species with υ > 1. The intrinsic feebleness of the absorption cannot be countered by using high concentrations of the absorbing species, since this will only accelerate relaxation via processes such as
BC(υ) + BC(υ = 0) + BC(υ - 1) + BC(υ = 1) (5)
Despite the difficulty caused by rapid V–V energy exchange (and the process
HCl(υ = 2) + HCl(υ= 0) -> 2HCl(υ = 1) (6)
occurs with a rate constant of 2.9 × 10-l2 cm3 molecule-1 s-1, corresponding to a probability of 1.4 × 10-2 Moore and his co-workers have succeeded in measuring directly the rates of a number of processes involving HCl(υ= 2), the excitation being provided by the tuned output from an optical parametric oscillator. Among their experiments is one showing that Br atoms remove HCl(υ = 2) 6.4 times more rapidly than HCl (υ = 1). In a particularly elegant experiment, Arnoldi, Kaufman, and Wolfrum have shown that this is primarily due to the 'opening up' of the reactive channel
Br + HCl(υ) -> HBr + Cl (7)
once HCl is excited as far as the υ= 2 level. These results confirm earlier observations made by Polanyi's group using a non-laser, 'i.r. chemiluminescence depletion' method (see p. 42). For reaction (7), ΔEo = +65.6 kJ mol-1, the energy of activation [??] 70 kJ mol-1, and the vibrational excitation energy of HCl(υ = 2) corresponds to 67.8 kJ mol-1. The efficient utilization of the vibrational excitation in overcoming the activation barrier appears to be characteristic of endoergic reactions and contrasts sharply with the results expected for exoergic reactions and, to a lesser extent, thermoneutral reactions. The reasons for this difference in behaviour are discussed in Section 3.
Isotope Separation. — Rapid V–V energy exchange also interferes with highly selective experiments which have a different objective and one which could be of immense technological value. These are experiments designed to separate isotopes via selective excitation with lasers. Several schemes have been suggested and the fundamental principles have been discussed by Moore and by Letokhov. These schemes have four basic requirements in common : (a) isotopically different starting materials that have some discrete spectral absorptions that do not overlap; (b) a laser that is sufficiently tunable and monochromatic to excite only one of these species; (c) a chemical or photochemical method that selectively removes the excited species; and (d) the elimination of processes that destroy the isotopic selectivity during excitation and subsequent reaction.
In the context of this article, we are principally concerned with the case where the laser causes selective vibrational excitation and (c) is a chemical reaction that occurs preferentially with vibrationally excited reactants. In order to achieve a useful isotopic enrichment it will be necessary that the rate of the thermal reaction, averaged over the time the reactants are together, must be appreciably less than that of the laser-enhanced – and therefore isotopically selective – reaction. The latter will depend on the average rate of photochemical excitation as well as on the relative values of the rate constants for reaction of the excited and unexcited molecules and for the competing processes of relaxation. One process that can clearly destroy the isotopic selectivity of a scheme of this kind is V–V energy exchange between species that differ only in their isotopic composition. Except for species that vary in their D and H atom content, vibrational transition energies for different isotopic species are quite similar. Consequently, V–V energy exchange between these species occurs almost as rapidly as between identical molecules.
