Rydberg convergence limits

FlO. 4. Vacuum-ultra violet absorption spectrum of oxygen gas. The positions at which Rydberg series convergence limits occur are marked X—X. (We are indebted to Professor W. C. Price for this photograph.)... 

Three methods are being used to obtain Ip (a) the spectroscopic determination of the convergence limit of a Rydberg series1 (b) the measurement of the spectral threshold for the appearance of an electron current in the irradiated gas2-4 (c) the direct identification of the positive molecular ion by mass spectrometry with the determination of the spectral threshold of its appearance. 

The investigation of Rydberg states in the far UV spectra of molecules may. also contribute to the interpretation of PE spectra. From the quantum defects and the number of Rydberg series that converge on a given limit, the ionized molecular orbital can be deduced. The convergence limit of a series corresponds to an ionization energy in the PE spectrum. 

Because the ionization potentials obtained from Rydberg convergence limits are much more accurate, the photoionization thresholds served mainly to limit the search range to find Rydberg series. The praseodymium threshold value is an exception because no Rydberg series were obtained for that element. The photoionization threshold of 5.464+0 012 eV t ie only experimental value available for praseodymium. 

Figure 3. Photoionization threshold spectra for neodymium. The excitation scheme used in each case is shown on the figure. The scanned laser wavelength calibration is shown at the top of each spectrum. In (a) the 20 300.8 cm 1 level is populated and in (b) the 21 572.6 cm 1 level is populated. The threshold wavelengths indicated yield the same ionization limit value of 5.523 eV. The arrows labeled R. L. indicate the position of the Rydberg convergence limit (3).

The convergence limits were obtained from the series data using the criteria that the quantum defect (n-n ) is a constant (.27) for the correct limit. To do this we determine the effective quantum number n of each observed Rydberg level using the relation... 

Some lanthanide Rydberg convergence limits derived from observed series by this method are given in Table II. The excitation wavelengths and levels from which the series were observed and the ion levels that they converge to are indicated in the table. Information on ionic states was obtained from the literature for Dy, t and where... 

The photoionization threshold values listed in column 4 are all lower by some 0.002 to 0.005 eV (15-30 cm l). Similar differences were found in uranium and neptunium and remain unexplained. Electric fields from the ion optics (field ionization) and collisional effects are possible explanations. In all cases, the Rydberg convergence limits are the most accurate and they are the preferred values. 

Ionization potentials can be, naturally, obtained from the absorption spectra themselves. Indeed, until this day, the most accurately known IPs are obtained from the convergence limits of Rydberg series. This is, however, limited to well resolved spectra of small molecules and radicals. In most cases such high quality electronic spectra cannot be obtained for the larger molecules which are of prime interest to the chemist. Even if instrumental conditions would make it possible the bands usually remain broad for physical reasons (dissociation, predissociation) and the coincidence and mutual overlap of bands. Therefore an independent source of ionization potentials was badly needed. It is enough to have another look at the Rydberg formula to understand this ... 

The 1415 A. group of bands is the first member of a Rydberg series of CH2, of which three others at shorter wavelengths were also found.63 Extrapolation to the series limit led to an ionization potential for CH2 of 10.4 e.v. It is believed that the series converges to the ground state of the CH2+ ion, and is therefore the lowest CH2 ionization potential. 

Fig. 20.1 A three channel, three limit problem. Three levels of the ion, shown by the bold lines, have Rydberg series converging to them from below and continua above them. The interactions between the series are shown by the horizontal arrows. Bound-continuum interactions are shown by single headed arrows while bound interactions are shown by...

---