Selected energy levels

Dr Irwin Wieder, Dr R.R. Neiman Dr A.P. Rodgers of Interphase Corporation-West, Palo Alto, Calif studied the IR and UV radiation emitted by excited species in low-pressure gaseous C2H2/O2 explosions in order to establish the population distribution in selected energy levels. In the UV they used cavity techniques, and found a relative enhancement of several electronic transitions in CH and OH radicals. In the IR the emission from excited CO2 molecules which form behind a fast detonation... 

Energy analysis of the photoelectrons is carried out by a spectrometer of which there are two types cylindrical and spherical sector. In both cases, they are in the form of a capacitor that focuses electrons with the same selected energy level to a detection point, spectrum acquisition is carried out sequentially by scanning the selected energy. 

Fig. 19. Selected energy levels in the oxygen and sulfur systems, as determined from isoelectronic sequences...

Table 9 Selected energy level parametrizations of M2ALnX6 and M2AM X6 Ln3+ systems ...

Fig. 4 shows selected energy levels of the He /He systems. The Is3s4s state of He is situated just below the He (3 S) threshold. This state, which is excited with laser (O, rapidly autodetaches via the 2 Sks and 2 Pk.p channels. Following the decay, the residual He atom will be left in either the or 2 P excited states. Two different laser frequencies and a" were applied separately in the resonance ionization scheme used to monitor the population of the 2 8 and 2 states. The frequency 0)2 was chosen to induce a transition between the 2 S and the 24 P states of the He atom, when photodetachment into the 2 Sks channel was studied. The frequency co" induced a resonance transition between the 2 P and 26 D states of He, when photodetachment into the 2 Pkp channel was studied. The population of both the high lying Rydberg states were efficiently depleted by the electric field of the second quadrupole deflector and He+ ions thus produced were recorded as a function of frequency of laser m,. The output of laser w, was attenuated to avoid... 

A resonance ionization mass spectrometer (RIMS) uses a tunable, narrow bandwidth laser to excite an atom or molecule to a selected energy level that is then analyzed by MS. The selective ionization often is accomplished by absorption of more photons from the exciting laser, but can also be effected by a second laser or a broadband photon source. Multiple photon absorption can result in direct ionization or in production of excited species that can then be ionized with a low-energy photon source (IR laser) or by a strong electric field. Resonance ionization methods have been applied to nearly all elements in the periodic table and to many radionuclides, including Cs (Pibida et al., 2001), Th (Fearey et al., 1992), U (Herrmann et al., 1991), Np (Riegel et al., 1993), Pu (Smith, 2000 Trautmann et al., 2004 Wendt et al., 2000), radioxenon and radiokrypton (Watanabe et al., 2001 Wendt et al., 2000), and 41Ca (Wendt et al., 1999). 

Figure 8.15 HBN radical potential energy surfaces and selected energy levels of 2 and II symmetry. Adiabatic (red, black) and diabatic (violet, magenta) PES. 2D cut at linear geometries, crossing seam shown as a green line ID cuts along BN stretching coordinate for / BH and 6 fixed at 2.1A and 150°, respectively. The component of the A" symmetry of the 11 state shown as a blue line. Assignment based on plots and expansion coefficients of vibrational part of wavefunctions. AU values in cm levels showing resonances are marked.

If the experunental technique has sufficient resolution, and if the molecule is fairly light, the vibronic bands discussed above will be found to have a fine structure due to transitions among rotational levels in the two states. Even when the individual rotational lines caimot be resolved, the overall shape of the vibronic band will be related to the rotational structure and its analysis may help in identifying the vibronic symmetry. The analysis of the band appearance depends on calculation of the rotational energy levels and on the selection rules and relative intensity of different rotational transitions. These both come from the fonn of the rotational wavefunctions and are treated by angnlar momentum theory. It is not possible to do more than mention a simple example here. 

Before presenting the quantum mechanical description of a hannonic oscillator and selection rules, it is worthwhile presenting the energy level expressions that the reader is probably already familiar with. A vibrational mode v, witii an equilibrium frequency of (in wavenumbers) has energy levels (also in... 

Av = 1 hannonic oscillator selection mle. Furthennore, the overtone intensities for an anhannonic oscillator are obtained in a straightforward maimer by detennining the eigenfiinctions of the energy levels in a hannonic oscillator basis set, and then simnning the weighted contributions from the hannonic oscillator integrals. 

Experimental. The vibrational spectrum of an ideal harmonic oscillator would consist of one line at frequency v corresponding to A = hv, where A is the distance between levels on the vertical energy axis in Fig. 10-la. In the harmonic oscillator, AE is the same for a transition from one energy level to an adjacent level. A selection rule An = 1, where n is the vibrational quantum number, requires that the transition be to an adjacent level. 

Once you have calculated an ab initio or a semi-empirical wave function via a single point calculation, geometry optimization, molecular dynamics or vibrations, you can plot the electrostatic potential surrounding the molecule, the total electronic density, the spin density, one or more molecular orbitals /i, and the electron densities of individual orbitals You can examine orbital energies and select orbitals for plotting from an orbital energy level diagram. 

The rotational energy levels for a prolate and an oblate symmetric rotor are shown schematically in Figure 5.6. Although these present a much more complex picture than those for a linear molecule the fact that the selection mles... 

Figure 6.7(a) illustrates the rotational energy levels associated with two vibrational levels u (upper) and il (lower) between which a vibrational transition is allowed by the Au = 1 selection rule. The rotational selection rule governing transitions between the two stacks of levels is... 

As in Section 5.2.4 on rotational spectra of asymmetric rotors, we do not treat this important group of molecules in any detail, so far as their rotational motion is concerned, because of the great complexity of their rotational energy levels. Nevertheless, however complex the stack associated with the v = 0 level, there is a very similar stack associated with each excited vibrational level. The selection mles for transitions between the rotational stacks of the vibrational levels are also complex but include... 

Figure 11-3. Electron energy level diagram of PPV and work functions of selected contael metals used in polymer LEDs.

With the advent of modern high-speed computers, this is not difficult to do for diatomic molecules, and it is the procedure followed when energy level information is available to perform the summation. Similar procedures have been followed for some nonlinear molecules, although as we have noted earlier, Table 10.4 gives reliable values for these molecules under most circumstances. References can be found in the literature to formulas and tables for calculating corrections for selected nonlinear molecules.12... 

Prediction of the energy level structure for Pu2+ (5f ) is of particular interest since no spectra for this valence state of Pu have been reported. On the basis of what is known of the spectra of Am2+ (26), Cf2" (27), and Es2+ (28), there appears to be evidence for a very small crystal-field splitting of the free-ion levels. Such evidence encourages use of a free-ion calculation in this particular case. The parameter values selected are indicated in Table V. Based on the systematics given by Brewer (19), the first f- d transition should occur near 11000 cm-, so the f- -f transitions at higher energies would be expected to be at least partially obscured. A... 

It would thus seem that promotion of a given electron in a molecule could result either in a singlet or a triplet excited state depending on the amount of energy added. However, this is often not the case because transitions between energy levels are governed by selection rales, which state that certain transitions are forbidden . There are several types of forbidden transitions, two of which are more important than the others. 

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