Collisional complexes

A collisional complex interacts with radiation for short times only, roughly 10-13 s, the duration of a molecular fly-by encounter. We may say that collisional complexes exist for short times only. Nevertheless, supermolecules are a physical reality. Spectra of other species having... 

Interaction-induced absorption (as the new features were called early on [353]) has stimulated considerable interest. For a long time, explanations were attempted in terms of weakly bound (02)2 polarization molecules (that is, van der Waals molecules), but some of the early investigators argued that unbound collisional pairs might be responsible for the observed absorption. More recently, a study of the temperature dependence of the induced intensities has provided evidence for the significance of collisional complexes. The idea of absorption by collisionally interacting, unbound molecular pairs was, however, not widely accepted for decades. 

It is of interest to compare the half-widths at half-intensity of the spectral functions of the three systems shown in Fig. 3.2. These amount to roughly 140, 80 and 50 cm-1 for He-Ar, Ne-Ar and Ar-Kr, respectively, which are enormous widths if compared to the widths of common Doppler profiles, etc. The observed widths reflect the short lifetimes of collisional complexes. From the theory of Fourier transforms we know that the product of lifetime, At, and bandwidth, A/, is of the order of unity, Eq. 1.5. The duration of the fly-by interaction is given roughly by the range of the induced dipole function, Eq. 4.30 (1/a = 0.73 a.u. for He-Ar), divided by the mean relative speed, Eq. 2.12. We obtain readily ... 

Symmetry-adapted perturbation theory applied to interaction-induced properties of collisional complexes. Molec. Phys., 89 81, 1996. 

An excited aryl halide may also transfer charge to oxygen and thereby become activated towards attack by nucleophiles. The photoamination of 1-amino-2,4-dibromoan-thraquinone by rc-butylamine, in which the 4-Br atom is replaced, is supposed to proceed via direct interaction between the triplet state and the amine when the reaction is performed under nitrogen. In air atmosphere, however, it proceeds via both the T7, and SY states. From the singlet excited state and oxygen, an exciplex or collisional complex [AQ ()/ ] is formed which undergoes the animation639. 

Potential energy surfaces of weakly bound dimers and trimers are the key quantities needed to compute transition frequencies in the high resolution spectra, (differential and integral) scattering cross sections or rate coefficients describing collisional processes between the molecules, or some thermodynamic properties needed to derive equations of state for condensed phases. However, some other quantities governed by weak intermolecular forces are needed to describe intensities in the spectra or, more generally, infrared and Raman spectra of unbound (collisional complexes) of two molecules, and dielectric and refractive properties of condensed phases. These are the interaction-induced (or collision-induced) dipole moments and polarizabilities. 

During a collision between two molecules the intermolecular interaction leads to distortions of their charge distributions, so that a collisional complex possesses a... 

In Ref. (163) the techniques introduced above were illustrated for He-He and He-H2 collisional complexes. In Refs. (316,317) the property functions were applied in full quantum-statistical calculations of the dielectric second virial coefficient and of the polarized and depolarized Raman spectrum of the He gas. Some further applications were reported by Rizzo and collaborators318- 322. 

The most important process for the formation of the initial polyatomic species is radiative association. Upon collision, a large unstable molecule in an excited state ( collisional complex ) may form, which is stabilized with a low probability by the emission of a photon (e.g. Bates 1951 Williams 1972 Herbst Klemperer 1973). For example, the formation of light hydrocarbons starts with radiative association of C+ and H2, leading to excited CH ( o = 4.0 10-16 cm-3 s-1 and = —0.2, Herbst 1985). Despite their importance, rates of many radiative association processes remain unknown because they are difficult to measure in the laboratory or predict theoretically (Herbst Dunbar 1991). 

Here, (> and /> are initial and final states of the supermolecular complex, 11 is the induced incremental polarizability (a second-rank tensor), fio and fij are unit vectors in the direction of the electric polarization of incident and scattered waves, which are often specified in the form of subscripts V and H, for vertical and horizontal, (aif = (Ej- — Ei)lh is the energy difference of initial and final state in units of angular frequency, Pi T) is the population of the initial state (a function of temperature), <5 (to) is Dirac s delta function, and the summation is over all initial and final states of the collisional complex. 

The collision-assisted predissociation in iodine B O + state merits a detailed discussion. It is well known that B state is weakly coupled to the dissociative A 1m state by rotational and hyperfine-structure terms in the molecular Hamiltonian. The natural predissociation rate strongly depends on the vibrational quantum number (pronounced maxima for o=5 and u = 25, a minimum for u= 15), this dependence being due to a variation of the Franck-Condon factor. " The predissociation rate is enhanced by collisions. In absence of a detailed theoretical treatment of the colhsion-assisted 12 predissociation, one can suppose that the asymmetric perturbation (breakdown of the orbital symmetry) in the collisional complex affects electronic and rotational wavefimctions but does not change the nuclear geometry. 

Linear (44) and triangular (45) collisional complexes have been proposed for the CH3 H formation process. The cleavage of the R—CH3 bond should be the ratedetermining step for the Me abstraction in the linear complex 44 while the triangular... 

Not all PESs are of the type shown in Figure 20.6 for example. Figure 20.8 displays a different PES in which a potential well is encountered in the intermediate region, instead of a maximum as in Figure 20.6. The potential well provides the existence of a collisional complex (ABC) that might even be detected experimentally, as it may survive for an average duration of the order of picoseconds. In contrast, when the well is not present. 

In the above expressions is the elementary charge, the Avogadro constant, Sq the permittivity of vacuum, % and s are the refractive index and the static dielectric constants of the solvent, respectively, / the ionic strength of the solution and r the distance between the centres of the reactants in the collisional complex, assumed to be equal to 2 -av = ( ox + and/jg are the stretching vibrations for the two reactants in the oxi-... 

The metallic centres in the collisional complex are well separated, by at least rp p = 13.6 A, due to the size of the ligands. In contrast, for the Fe(OH2)6 complexes the corresponding distance is much smaller, and an electron can easily jump between the two iron atoms leading to a nearly adiabatic reaction, as illustrated in Figure 16.8. In Fe(phen)3 + + complexes the distance is too large for a nearly adiabatic electron jump from one metal centre... 

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