Collisions and energy transfer

In an actual experiment, it is frequently not possible to work under conditions where there are no relaxation effects. The usual reason for this is that the intensity of the fluorescence becomes too weak to observe as the concentration of excited molecules is reduced. The lowest pressures which can be used are defined by a number of parameters the strength of the transition, the power of the laser and the detection efficiency of the system are among the most important. It therefore follows that, in interpreting the results of lifetime measurements, one must consider carefully the possible effects of rotational and vibrational redistribution in the excited state. In a regular unperturbed state where there is little or no change in radiative lifetime with changes in rotational and vibrational level, the effects of relaxation are not observable so long as the fluorescence is still detected with the same efficiency. However, if the excited state is perturbed, for example by predissociation, then the effects of redistribution must be carefully studied. 

Some interesting examples of the effects of rotational and vibrational relaxation on the fluorescence decay profile of levels near and above a predissociation are provided by the studies by Clyne and McDermid [37—40], and Clyne and Heaven [41, 42] on the B—X systems of the hetero- and homo-nuclear diatomic inter halogens. 

To take one example, let us consider the effects of rotational relaxation in BrF. The excited 53FI(0+) state in BrF is crossed by another 0+ state which leads to predissociation of the B state in vibrational levels 7 and 6. The initial study of the dynamics of the B state was carried out in a discharge flow system where the minimum operating pressure was 50 m Torr. The gas-kinetic collision rate coefficient at 298 K for He + BrF(B) collisions is 4.4 x 10-10 cm3 molecule-1 s-1. Thus, at the minimum pressure of 50 m Torr, the average time between collisions of excited BrF molecules and helium buffer gas is 1.5/us. This time is short compared with the radiative lifetime of BrF (42—56/ns [43]) and therefore significant redistribution in the excited state can occur before it radiates. 

The experimental results for v = 7 [37] showed that the lowest ( 15) rotational levels exhibited single exponential decay with a decay constant that was essentially independent of J. These levels were then assumed to be stable and unaffected by the predissociation. For much higher initial rotational states, J 28, the observed lifetime was dramatically shortened. A very rapid initial decay was observed followed after a few microseconds by a slower decay. On increasing the pressure, the initial fast decay was hardly affected but the intensity of the longer-lived decay component increased as more molecules were transferred by rotational relaxation out of the initially formed predissociated state into lower-lying stable states. 

The fluorescence decay curves for initial rotational states 17 28 

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Abstract Classical trajectory calculations provide useful information about molecular collisions in the gas phase. Various energy transfer quantities such as the average energy transferred per collision , the lifetime of the collision complex and then-dependence on temperature, pressure and intermolecular potential can be calculated by this method and clues as to the mechanism of collision and energy transfer may come to light as a result of these calculations. Examples from our work are provided below for energy transfer between Ar and benzene and toluene and between Li" and Ceo under a variety of experimental conditions. 

Although such systems have been extensively studied at higher collision energies over the last few deeades, the new experimental breakthroughs in creating dense samples of cold and ultracold molecules have provided unprecedented opportunities to explore elastic, inelastic, and reactive collisions at temperatures close to absolute zero. These studies have revealed unique aspects of molecular collisions and energy transfer mechanisms that are otherwise not evident in thermal energy collisions. 

Figure 4.12 shows the primary quantum yields for the production of NO in reaction (12). The quantum yield is within experimental error of 1 up to 395 nm, declining slightly to 0.82 at the theoretical threshold for dissociation at 397.8 nm. This has been attributed to the formation of a nondissociative excited state of N02. In ambient air, electronically excited NOz which does not dissociate to form O P) is collisionally deactivated. When 02 is the collision partner, energy transfer may occur a fraction of the time to form 02( Ag) (Jones and Bayes, 1973a) ... 

Figure 2. Schematic of the energy levels for the OH molecule. The collision-induced energy-transfer transitions are denoted by double-line arrows. The rotational quantum number is denoted by K or K". Both spin doubling and lambda doubling have been suppressed for clarity.

In recent years numerous experiments have been reported on the fluorescence and energy transfer processes of electronically excited atoms. However, for flame studies the rates of many possible collision processes are not well known, and so the fate of these excited atoms is unclear. An interesting example concerns the ionization of alkali metals in flames. When the measured ionization rates are interpreted using simple kinetic theory, the derived ionization cross sections are orders of magnitude larger than gas kinetic (1,2,3). More detailed analyses (4,5) have yielded much lower ionization cross sections by invoking participation of highly excited electronic states. Evaluation of these models has been hampered by the lack of data on the ionization rate as a function of initial state for the alkali metals. 

We have used trajectory calculations to calculate this quantity [26]. Our method distinguishes between effective trajectories that contribute to P(E ,E) and those with very large impact parameter which do not. The P(E ,E) thus found, obeys conservation of probability and detailed balance and is independent of the impact parameter. The method is demonstrated for benzene-Ar collisions at various temperatures and internal energies. With this method, it is possible to combine ab initio inter and intramolecular potentials with trajectory calculations, obtain P(E ,E) and use that in master equation calculations to obtain rate coefficients and population distributions without resorting to any a priori assumptions and energy transfer models. 

The sputtering process involves a complex series of collisions (the collision cascade) involving a series of angular deflections and energy transfers between many atoms in the solid. The most important parameter in the process is the energy deposited at the surface. 

Figure 2.3 Perturbations and predissociations affect absorption and emission line intensities in quite different ways. Two pairs of absorption and emission spectra are shown. The first pair illustrates the disappearance of a weakly predissociated line in emission without any detectable intensity or lineshape alteration in absorption. The second pair shows that emission from upper levels with slow radiative decay rates can be selectively quenched by collision induced energy transfer. The opposite effect, selective collisional enhancement of emission from perturbed, longer-lived levels, is well known in CN B2 +—X2 +(u = 0,v") emission spectra (see Fig. 6.14 and Section 6.5.5). (a) the CO B1S+—X1S+(1,0) band in emission (top) and absorption (bottom). The last strong lines in emission are 11(16) and P(18). Emission from levels with J > 17 is weak because the predissociation rate is larger than the spontaneous emission rate. (Courtesy F. Launay and J. Y. Roncin.) (6) The CO A ll—X1 + (0,0) band in emission (bottom) and absorption (top). The a 3 + —X1 +(8,0) band lines appear in absorption because the A1 FI a 3 + spin-orbit interaction causes a small amount of A1 character to be admixed into the nominal a 3 + levels. These a —X lines are absent from the emission spectrum because collisional quenching and radiative decay into a3II compete more effectively with radiative decay into X1 + from the long-lived a 3 + state than from the short-lived A1 state. In addition, collisions and radiative decay into a3II cause the P(31) extra line (E) (arising from a perturbation by d3A v = 4) to be weakened in emission relative to the main line (M). (Courtesy F. Launay, A. Le Floch, and J. Rostas.)...

The details of the location and perturbations of metastable states are important for understanding and possibly exploiting collision-induced energy transfer between metastable and short-lived, strongly radiating levels (see Section 6.5.5). 

Theoretical chemistry is the discipline that uses quantum mechanics, classical mechanics, and statistical mechanics to explain the structures and dynamics of chemical systems and to correlate, understand, and predict their thermodynamic and kinetic properties. Modern theoretical chemistry may be roughly divided into the study of chemical structure and the study of chemical dynamics. The former includes studies of (1) electronic structure, potential energy surfaces, and force fields (2) vibrational-rotational motion and (3) equilibrium properties of condensed-phase systems and macromolecules. Chemical dynamics includes (1) bimolecular kinetics and the collision theory of reactions and energy transfer (2) unimolecular rate theory and metastable states and (3) condensed-phase and macromolecular aspects of dynamics. 

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