Electronic level inversion

Investigation of excited states of polyatomic molecules in solution provides a good framework in order to study many classes of interactions. But their lifet ime is very short (10 s - 10 °s). So, in order to study such excited states we have built a picosecond absorption spectrometer which allowed us to study many types of molecular systems in solution. We present here two such studies. In the first one (1-4-diphenyl-butadiene) we have shown a solvent assisted electronic level inversion. In the second one we have studied interactions between an intramolecular charge transfer state and polar environment. Before discussing these results, we present the apparatus we have built in our lab. 

The determining feature by which laser action can be efficiently obtained from this type of active medium is the fact that the atoms that form the dimmer are only bound in the excited state. Figure 2.9 shows a schematic diagram of the laser energy levels in a molecule of excimer. The laser transition is produced between two molecular electronic levels in which the potential energy curve for the fundamental state is repulsive. This ensures the population inversion. 

Figure 10-23 shows the electron levels and the polarization curves for the transfer of anodic redox holes both at a photoexcited n-fype electrode and at a dark p-type electrode of the same semiconductor. The range of potential where the anodic hole current occurs at the photoexcited n-type electrode is more cathodic (more negative) than the range of potential for the anodic hole current at the dark p-type electrode. The difference between the polarizatitm potential aE(i) (point N in the figure) of the photoexcited n-type electrode and the polarization potential pE(i) (point P in the figme) of the dark p-type electrode at a constant anodic current i is equivalent to the difference between the quasi-Fermi level pej of interfacial holes and the Fermi level bEf of interior holes (electrons) in the photoexcited n-type electrode this difference of polarization potential, in turn, equals the inverse overvoltage rip.sc(i) defined in Eqn. 10-46 ... 

This chapter is devoted to photoemission spectroscopy and the related inverse photo-emission spectroscopy, which are well developed experimental tools to study occupied and empty electronic levels, respectively. Special emphasis is given to the 5f electrons and their localized or delocalized character. 

From various sources Dowden (27) has accumulated data referring to the density of electron levels in the transition metals and finds an increase from chromium to iron. The density is approximately the same from a-iron to /3-cobalt there is a sharp rise between the solid solution iron-nickel (15 85) and nickel, and a rapid fall between nickel-copper (40 60) and nickel-copper (20 80). From Equation (2), the rates of reaction can be expected to follow these trends of electron densities if positive ion formation controls the rates. On the other hand, both trends will be inversely related if the rates are controlled by negative ion formation. Where the rate is controlled by covalent bond formation, singly occupied atomic orbitals are deemed necessary at the surface to form strong bonds. In the transition metals where atomic orbitals are available, the activity dependence will be similar to that given for positive ion formation. In copper-rich alloys of the transition elements the activity will be greatly reduced, since there are no unpaired atomic d-orbitals, and for covalent bond formation only a fraction of the metallic bonding orbitals are available. 

Fig. 14 The inverse life-time (r/1) 1 as a function of A/cao at optimal electron level position eo = A2/2cjo for neutral state (thin solid line), and for the charged state (dashed line), and for the neutral state at other level position eo = A2/4cj0 (thick solid line).

It is noted [166] that the similarity in energy between metal and quinone electronic levels is responsible for shifts in charge distribution between metal and ligands. These shifts result from the change in the donor character of the ligand with reduction from SQ to Cat, and the consequential inversion in the order of localized metal and quinone electronic levels. 

However, transition from discrete to a continuous spectrum of levels does not mean full disappearance of quantum dimensional effects. It has been shown [14] that even in rather large metal nanocrystals in the size 5-10 nm it is necessary to take into account the direct influence of crystal boundaries on density of the crystal electronic levels that leads to the dependence of Fermi energy on the crystal size. The Fermi energy correction for a spherical crystal caused by crystal surface is inversely proportional to radius of crystal... 

Phosphorescence corresponds to one another relaxation process. After the absorption phase, corresponding to the transfer of an electron into the Sj level (singlet state), an electron spin inversion can occurs if the vibrational relaxation is slow enough, which leads to a slightly stable Tj (triplet state). From here return to the ground electronic state is slowed as it requires a new spin inversion for this electron. These radiative lifetimes can be up to several minutes duration (Figure 11.2). 

The total-energy eigenvalues of the electron are inversely proportional to the square of n. Each value of n is said to specify an energy level, and the energy of the electron remains the same while it stays at the same energy level, irrespective of the values of the other quantum numbers. Sub-levels with the same energy are known as degenerate states of the electron. 

Even without any theoretical derivation of the d term properties, it is clear that the intensity is not only dependent on the transition probabilities for left and right circularly polarized light but also on the Zeeman splitting and the bandwidth of electronic levels involved in the transition. The narrow peaks, typical for the lanthanides, will influence favourably the MCD signal. Indeed, the MCD signal for the d term is inversely proportional to the bandwidth (see Sect. 5.3 in Piepho and Schatz... 

The line width of the resonance-broadened adsorbate level is proportional to the square of the overlap energy and varies inversely as the bandwidth of the surface valence electron levels. The general form of the LDOS in the weak-adsorption limit... 

DiBella et al. (1993) performed SCF, CASSCF and CISD ealculations for LaFs and Lads- A relativistic effective-core potential of Hay and Wadt (1985b) was used for La, whereas F and Cl were treated at the all-electron level. LaFs was found to be slightly pyramidal (F-La-F bond angle 118.5°, inversion barrier 0.04kcal/mol), whereas LaCU was calculated to be planar. The increasing tendency towards a planar geometry in the... 

The principle of operation of atomic emission spectrometry (AES) (or optical emission spectrometry (OES)) is based on the measurement of photons emitted when electrons move from an excited electronic state to a lower state, rather that the inverse when radiation energy is absorbed, as in AAS. Thus, instead of measuring signal attenuation due to photon absorption, the photons emitted from excited atoms and ions are measured as they decay to lower electronic levels. Here, too, each element has its characteristic wavelengths that serve to identify the element and signal intensity is proportional to the concentration of the element in the sample. A comprehensive overview of ICP-AES techniques for measuranent of many different types of samples was published (TAMU 2000). The term ICP-OES for optical emission spectrometry is also used sometimes to describe the same technique. 

An efficient way to generate inversion is to use double pulses [510], where the first pulse heats and explodes a thin metal foil, producing a hot plasma. The second pulse further ionizes the plasma, generating highly charged ions, which can recombine with electrons creating inversion between two Rydberg levels (Fig. 5.111). 

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