Theory of ion-molecule reactions

Since the observation made in study of the formation HeH+ indicated that this product was not formed by reaction of He + with H2, it had been assumed that the exothermic heat of reaction of He+ ions with H2 is probably deposited in the product HeH + as internal energy, decomposing the product into H+ and He. This idea was cited by Light (16) in his phase space theory of ion-molecule reactions to account for the failure to observe HeH+ from reactions with He+ ions. The experimental difficulty in the mass spectrometric investigation of this process is that H + formed by electron impact tends to obscure the ion-molecule-produced H+ so that a sensitive quantitative cross-section measurement is difficult. 

Ton-molecule reactions are of great interest and importance in all areas of kinetics where ions are involved in the chemistry of the system. Astrophysics, aeronomy, plasmas, and radiation chemistry are examples of such systems in which ion chemistry plays a dominant role. Mass spectrometry provides the technique of choice for studying ion-neutral reactions, and the phenomena of ion-molecule reactions are of great intrinsic interest to mass spectrometry. However, equal emphasis is deservedly placed on measuring reaction rates for application to other systems. Furthermore, the energy dependence of ion-molecule reaction rates is of fundamental importance in assessing the validity of current theories of ion-molecule reaction rates. Both the practical problem of deducing rate parameters valid for other systems and the desire to provide input to theoretical studies of ion-molecule reactions have served as stimuli for the present work. 

The molecular beam technique, which was first applied to a chemical system in 1954 by Bull and Moon [165] and the first crossed beam study of Datz and Schmidt [123] in 1967, has reached maturity with the development by Greene and co-workers [373] in 1974 of a molecular beam apparatus for student teaching experiments. Future developments will probably be in the study of the reactions of beams of metals other than alkali and alkaline earths and atoms and radicals. Hopefully, the theories of such reactions will merge with the theories of ion—molecule reactions. 

In these volumes, we have attempted to present some information about the various methods and techniques for studying ion-molecule reactions together with a survey of the principal results obtained. One chapter is devoted to the rate theory of ion-molecule reactions, and consideration of reaction rates is necessarily of importance in discussions of all of the methods. In addition, chapters are included on ion-molecule reactions in flames, discharges, and radiation systems. While this book can hardly be considered as including all the information on ion-molecule reactions, we hope that it includes material representative of the broad field. 

A more detailed statistical theory of ion-molecule reactions [275, 345] allowing for a reverse process probability yields cross sections sometimes by an order lower than those obtained from Eq. (32.3). 

F ( D) with Ht and Dg ( ). The dashed curves give the corresponding results assuming the phase space theory of ion-molecule reactions. 

Much of the interest of this symposium centers on the effect of the kinetic energy of the reacting ion on the reaction cross-section. A detailed examination of the effect of energy variations is essential to the development of a comprehensive theory for the kinetics of ion-molecule reactions. 

TYoe, J. (1992). Statistical aspects of ion-molecule reactions, in State-Selected and State-to-State Ion-Molecule Reaction Dynamics, Part 2 Theory, ed. M. Baer and C.Y. Ng (Wiley, New York). 

The trajectory surface hopping model of ion-molecule reaction dynamics has realized an impressive agreement between theory and experiment in this reaction, i.e. H+ + H2, and it provides the experimentalist with a realistic and workable theory to use in the comparison with and interpretation of experimental results. As reliable potential energy surfaces become available for other ion-molecule systems, we can expect further tests of this theory and its applicability to more complicated reactions. 

Troe, J. Statistical aspects of ion-molecule reactions. In State-selected and state-to-state ion-molecule reaction dynamics theory Baer, M., Ng, C.-Y., Eds. John Wiley New York, 1992, 485. 

While having such limitations and difficulties in the actual calculation as described above, there seem to be no reasons why the theory should not apply to the dissociation of the ion—molecule reaction complex. Rather, some favourable ion—molecule reactions would be expected to provide more suitable tests of the equilibrium assumption. Although the problem of not knowing the normal frequencies of the molecular ion (ion-molecule complex in this case) and activated complex remains and a new problem arises concerning the structure of the reaction complex, it is to be expected that the problem of the unknown distribution of excitation energies can be avoided if reactant ions formed at very low electron energies are used. In this hope, Buttrill [84] carried out a calculation of ion—molecule reaction product distribution for the reactions... 

S. E. Buttrill, Jr., Calculation of ion-molecule reaction product distributions using the quasiequilibrium theory of mass spectra, J. Chem. Phys. 52, 6174-6183 (1970). 

The Hj" ion crystals produced in this way could be useful systems for exploring the chemistry of In particular, the study of state-specific reactions of via high-resolution infrared spectroscopy could provide valuable input for theories of ion-molecule gas-phase chemistry and precise calculations of molecular transition frequencies of this two-electton molecule. 

Langevin Theory The theoretical treatment of ion-molecule reactions is presented. This is a useful aid in understanding the collision dynamics of two species. The collision rate for an ion and a polarizable molecule having no permanent dipole moment is given by the Langevin theory [2,3] as follows. For an ion and a molecitle approaching each other with a relative velocity v and impact parameter b (Fig. 2.1), the Langevin theory describes the molecular interaction potential between an ion... 

With so many molecules now being observed in interstellar clouds, chemical reaction models which can explain how these molecules are produced and destroyed are becoming increasingly more valuable. The most modern chemical reaction networks that have been proposed involve following the concentration of several hundred atomic and molecular species as a function of time, and reliable temperature-dependent rate coefficients for several thousand reactions are a vital requirement in such simulations. The role of ion-molecule reactions has been shown to be of particular Importance in these networks as these reactions can have very large rate coefficients at the low temperatures of interstellar clouds [2]. Furthermore, a more limited number of neutral species, particularly radicals and open-shell atoms, can have large rate coefficients at low temperatures [3]. Since only a relatively small number of reactions have been studied in the laboratory at the temperatures relevant to Interstellar chemistry, theory plays an Important role in producing many of the required rate coefficients. 

While the behaviour of the majority of ion-molecule reactions can be adequately represented using capture theories, there are numerous reactions for which a more sophisticated treatment is required, namely those reactions which are slow at room temperature, that is whose reaction probability is much lower than unity. CRESU measurements have shown that, in several cases, the rate coefficients increase at lower temperatures, sometimes approaching kc when extrapolated towards OK. This has been shown for the reaction of -I-CH4, -I-O2, and of Ar+ with N2 and 2. Such... 

EXAMPLE 4. The study of ion-molecule reactions in flames is important in kinetic theory because a flame presents an environment where the pressure, temperature, and composition can be easily controlled furthermore, the average energy of an individual molecule (2000 K corresponds to a translational energy of 0.26 eV) in a flame is low in comparison with the cases cited above. The relative simplicity of charged and uncharged species in flames allows us to interpret processes from fundamental parameters and to obtain precise values of rate constants. 

The phase space theory in its present form suffers from the usual computational difficulties and from the fact it has thus far been developed only for treating three-body processes and a limited number of output channels. Further, to treat dissociation as occurring only through excitation of rotational levels beyond a critical value for bound vibrational states is rather artificial. Nevertheless, it is a useful framework for discussing ion-molecule reaction rates and a powerful incentive for further work. 

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