Ionization limit

In contrast to the ionization of C q after vibrational excitation, typical multiphoton ionization proceeds via the excitation of higher electronic levels. In principle, multiphoton ionization can either be used to generate ions and to study their reactions, or as a sensitive detection technique for atoms, molecules, and radicals in reaction kinetics. The second application is more common. In most cases of excitation with visible or UV laser radiation, a few photons are enough to reach or exceed the ionization limit. A particularly important teclmique is resonantly enlianced multiphoton ionization (REMPI), which exploits the resonance of monocluomatic laser radiation with one or several intennediate levels (in one-photon or in multiphoton processes). The mechanisms are distinguished according to the number of photons leading to the resonant intennediate levels and to tire final level, as illustrated in figure B2.5.16. Several lasers of different frequencies may be combined. 

Figure 7. Several of the ionization schemes employed in various pump-probe experiments of ammonia clusters the energy levels correspond to those of the ammonia monomer. The upper hatched region denotes the ionization limit. Taken with permission from ref. 68.

The conclusions derived from the preceding experiments may be summarized with the aid of the reaction mechanism illustrated in Scheme II. The ester undergoes a rapid, reversible association with the cycloamylose, C—OH. An alkoxide ion derived from a secondary hydroxyl group of the cycloamylose may then react with an included ester molecule to liberate a phenolate ion and produce an acylated cycloamylose. This reaction is characterized by a rate constant, jfc2(lim), the maximal rate constant for the appearance of the phenolate ion from the fully complexed ester in the pH range where the cycloamylose is completely ionized. Limiting rates are seldom achieved, however, because of the high pK of cycloamylose. 

Following Platzman (1967), Magee and Mozumder (1973) estimate the total ionization yield in water vapor as 3.48. The yield of superexcited states that do not autoionize in the gas phase is 0.92. Assuming that all of these did autoion-ize in the liquid, we would get 4.4 as the total ionization yield. This figure is within the experimental limits of eh yield at 100 ps, but it is less than the total experimental ionization yield by about 1. The assumption of lower ionization potential in the liquid does not remove this difficulty, as the total yield of excited states in the gas phase below the ionization limit is only 0.54. 

Moore, C. E. Ionization potentials and ionization limits Natl. Stand. Ref. Data Ser. (U.S. Natl. Bur. Stand.) NSRDS-NBS, 1970, 34... 

Electronic levels are spaced more closely together at higher quantum numbers as the ionization limit is approached, vibrational levels are evenly spaced, while rotational and translational levels are spaced further apart at high energies. The classical principle assumes continuous variation of all energies. 

The HFS program [79] was modified especially for this purpose. The general response is the same as for hydrogen, except that all occupied levels are now also affected at the same time. The highest levels are the most sensitive, but even the deepest core levels show an increase. As for hydrogen, the valence level eventually reaches the ionization limit, but this cannot be interpreted directly as an ionization event, as was done for hydrogen. 

The valence-electron wave functions of atoms, compressed beyond their ionization limits are Fourier sums of spherical Bessel functions corresponding to step functions (Compare 6.3.1) of the type... 

It is apparent from Table IV that with nitrobenzene as the oxidation catalyst the ionization-limited rate was not reached even at a nitrobenzene concentration of 2.7M (0.02M fluorene, 0.02M potassium terf-butoxide). The rate of oxidation at the low nitrobenzene concentrations is first-order in nitrobenzene, fluorene, and base. This is consistent with an oxidation rate determined by Reaction 12 and involving an equilibrium concentration of the fluorene anions. 

Moore, C. E. Ionization Potentials and Ionization Limits Derived from the Analyses of Optical Spectra, NSRDS-NBS 34 National Bureau of Standards Washington. DC, 1970, except for the data on the actinides, which are from The Chemistry ofthe Actinide Elements, Katz, J. J. Seaborg, G. T. Morss, L. R., Eds. Qiapman and Hall New York, 1986 Vol. 2. 

Going further up the energy scale the molecule will reach its ionization limit where the impact of electromagnetic radiation is so strong that an... 

In some molecules there are orbitals of very large volume known as Rydberg orbitals which can be populated below the ionization limit. In the example of the nitrogen molecule, N2, the average distance from the nuclei is so large that the (N-N)+ ion looks like a single positive point charge for the excited electron. 

In Chapter 3 we considered briefly the photoexcitation of Rydberg atoms, paying particular attention to the continuity of cross sections at the ionization limit. In this chapter we consider optical excitation in more detail. While the general behavior is similar in H and the alkali atoms, there are striking differences in the optical absorption cross sections and in the radiative decay rates. These differences can be traced to the variation in the radial matrix elements produced by nonzero quantum defects. The radiative properties of H are well known, and the radiative properties of alkali atoms can be calculated using quantum defect theory. 

Finally, it is useful to extend the definition of oscillator strength above the ionization limit using... 

Fig. 4.1 Oscillator strength distribution from the H Is state to the excited p states. Below the ionization limit the area of each block corresponds to the average oscillator strength...

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