Three-body association

Association reactions, in particular, seem to present a severe problem for structural determination. In these reactions, an ion and a neutral species form a complex which is stabilized either by collision with a third body or, at especially low pressures, by the emission of radiation. The radiative mechanism, prominent in interstellar chemistry, is discussed below. Although some studies of radiative association have been performed in the laboratory,30,31 90 most association reactions studied are three-body in nature. It is customarily assumed that the product of three-body association is the same as that of radiative association, although this assumption need not be universally valid. 

Ion-molecule radiative association reactions have been studied in the laboratory using an assortment of trapping and beam techniques.30,31,90 Many more radiative association rate coefficients have been deduced from studies of three-body association reactions plus estimates of the collisional and radiative stabilization rates.91 Radiative association rates have been studied theoretically via an assortment of statistical methods.31,90,96 Some theoretical approaches use the RRKM method to determine complex lifetimes others are based on microscopic reversibility between formation and destruction of the complex. The latter methods can be subdivided according to how rigorously they conserve angular momentum without such conservation the method reduces to a thermal approximation—with rigorous conservation, the term phase space is utilized. 

Thermal reaction techniques enable a quantification of the influence of solvation on reactivities.1,2,19 One particular reaction which is a good example of how solvation can affect the nature of a core ion reaction site comes from a study118 of the interaction of OH with C02. The gas-phase reaction between the individual species is quite exothermic and can only take place by a three-body association mechanism. The reaction proceeds very slowly in the liquid phase and has been calculated119 to have a barrier of about 13 kcal mol-1. In biological systems, the reaction rate is enhanced by about 4 orders of magnitude through the enzyme carbonic anhydrase. Recent studies carried out in our laboratory provide detailed... 

The reactions of the bare sodium ion with all neutrals were determined to proceed via a three-body association mechanism and the rate constants measured cover a large range from a slow association reaction with NH3 to a near-collision rate with CH3OC2H4OCH3 (DMOE). The lifetimes of the intermediate complexes obtained using parameterized trajectory results and the experimental rates compare fairly well with predictions based on RRKM theory. The calculations also accounted for the large isotope effect observed for the more rapid clustering of ND3 than NH3 to Na+. 

The HO + CH2F2 reaction has been studied by selected ion flow tube (SIFT) experiments and ab initio calculations. SIFT experiments at 300 K showed that a bimolecular process [leading to CHF2 (86%), F (11%), and HF2 (3%)] competes with a three-body association leading to HO. CH2F2. The bimolecular rate coefflcient... 

However, it cannot convert atomic to molecular hydrogen under interstellar conditions. Nor is the three-body associative process possible because the density of a dense molecular cloud involves, say, 104 particles/mL the chance that a third body strikes the H2 collision complex before it dissociates so as to stabilize it, is zero under considered conditions. There is, however, a finite but exceedingly small possibility that a molecule of hydrogen can be formed in the gas phase in interstellar conditions the rate constant is in fact extremely low K = 10-31 s not sufficient to explain the amount of molecular hydrogen present in the Universe (Pirronello and Avema 1988). 

The modified thermal and phase space theories reproduce most three body association data equally well, including the inverse temperature dependence of the rate coefficient (Herbst 1981 Adams and Smith 1981), and are capable of reproducing experimental rate coefficients to within an order of magnitude (Bates 1983 Bass, Chesnavich, and Bowers 1979 Herbst 1985b). They should therefore be this accurate for radiative association rate coefficients if kr is treated correctly. 

Applications of this reaction will be specifically discussed for the carbon chain molecules, (ii) the radiative association of larger molecules has been studied by measurements of analogous three body associations (McEwan et al. 1980). 

The metal atoms of the neutral metal layers are subject to charge transfer ionization by the principal molecular ions of the ionospheric E-region, NO+ and 02" . The highly stable atomic metal ions are either transported to higher altitudes, where they can undergo electron-ion recombination, or they can be removed by three-body association reactions with atmospheric molecules at lower altitudes, such as N2 ... 

The product cluster ions can rapidly dissociatively recombine with electrons to produce excited neutrals. Three-body association reactions (10) become increasingly important as one descends from 90 km. Simultaneously, the electron density declines, increasing the lifetimes of the cluster ions. Below 80 km, positive and negative cluster ions become the most abundant charged species." ... 

Information about the complex lifetime x and the rate constant for vibrational predissociation k p can be obtained from the study of three-body association reactions by Ferguson (1984, 1986),... 

Fig. 15. Correlation between vibrational quenching and three-body association for 0 (r) and NO+(r) with some neutrals (Ferguson, 1986).

Some polyatomic ions, such as CH, were found to form very long-lived complexes (t > 10 s) even at room temperature. Three-body association rate constants for CH with a variety for diatomic and triatomic molecules, as measured by the SIFT technique (Adams and Smith, 1981), are given in Fig. 

Bohringer, H. Arnold, R, Temperature dependence of three-body association reactions... 

If /C3 and can be taken as Langevin collision rate constants, then to the extent that t (= V3 ) can be taken from (7) (or other, more refined expressions) and p can be assumed constant (or otherwise approximated), one has a theory for three-body association reactions. If and/or deviate from Langevin rate constants, the factor p must absorb this effect also. Variations in third-body efficiency are commonly observed, although not generally very large ones. This establishes that k j) cannot be equal to /cl for the third-body collisions, i.e., either k ki ov p 1. 

A rather striking correlation of three-body association rate constants and D has been obtained in the recent work of Adams et From the occurrence of reactions of the type... 

Under normal circumstances, this occurs by collisions with a third-body species and the reaction rate therefore depends on total pressure. Such a mechanism is impossible in the super-rarified environment of interstellar space. However, the kinetics of such reactions are of indirect interest to astrochemists on two counts. First, treatments of radiative association [22], which is implicated in the formation of molecular species in interstellar clouds, have much in common with those of three-body association [23]. Second, the rate constants for radical association in the limit of high pressure correspond to those for formation of the energised associated molecule, since all such species are collisionally stabilised in the limit of high pressure. Consequently, the values of kggg and how they vary with temperature provide an important test of theories of reactions occurring over attractive potential energy surfaces [6]. 

More complex hydrocarbons can be built by three-body associations such... 

The SOf anion, which is more accurately described as the electrostatically bonded complex S03 02, has been generated [12] by the three-body association of S03 with O2 as well as the ligand switching reaction SO3" (H2O) + O2 -> SO5--h H2O = 5 X 10"" cm s ). 

Three body association, the low pressure limit of an association reaction, as discussed in Sect. 3.4.4, is not an efficient reaction in the ISM because of the very low pressures that pertain. An alternative process is radiative association, in which the adduct is stabilised by emission of radiation rather than by collision. An... 

Reactions of N2H with H2 and with N2 to form the ion clusters N2H H2 and (N2)2H, respectively, were observed to proceed via a three-body association [1 to 4]. 

The radiative association N2H -f H2N2H H2 +hv was estimated to proceed with a rate constant of the order of 10" cm molecule" s at temperatures around 20 to 70 K (this estimate is based on the rate constant for the three-body association N2H +2 H2) [2]. 

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