Heavy electronic transitions

The Franck-Condon principle says that the intensities of die various vibrational bands of an electronic transition are proportional to these Franck-Condon factors. (Of course, the frequency factor must be included for accurate treatments.) The idea was first derived qualitatively by Franck through the picture that the rearrangement of the light electrons in die electronic transition would occur quickly relative to the period of motion of the heavy nuclei, so die position and iiioiiientiim of the nuclei would not change much during the transition [9]. The quaiitum mechanical picture was given shortly afterwards by Condon, more or less as outlined above [10]. 

For electronic transitions in electron-atom and heavy-particle collisions at high unpact energies, the major contribution to inelastic cross sections arises from scattering in the forward direction. The trajectories implicit in the action phases and set of coupled equations can be taken as rectilinear. The integral representation... 

Rate Constants of Radiative Transitions. The natural radiative rate constant kr of an electronic transition from a state to a state Sf is related to the transition moment M and thereby to the oscillator strength f. It is convenient to factorize f to highlight the various factors which determine to what extent a transition is allowed if near 1) or forbidden (f near 0). The transition moment includes the displacement of all particles of the molecule during the transition, nuclei as well as electrons. The heavy nuclei move much more slowly than the light electrons so that their motions can be considered to be independent. Within this approximation the transition moment is given as... 

There are numerous needs for precise atomic data, particularly in the ultraviolet region, in heavy and highly ionized systems. These data include energy levels, wavelengths of electronic transitions, their oscillator strengths and transition probabilities, lifetimes of excited states, line shapes, etc. [278]. 

Of particular significance in this respect has been the ability to prepare, characterize and study most intriguing species, the alkalides [2.79, 2.80] and the electrides [2.80, 2.81] containing an alkali metal anion and an electron, respectively, as counterion of the complexed cation. Thus, cryptates are able to stabilize species such as the sodide [Na+ c 9]Na- and the electride [K+ c 9]e-. They have also allowed the isolation of anionic clusters of the heavy post-transition metals, as in ([K+ c cryp-tand]2 Pb52-) [2.82]. 

In the heavy phase, electron transitions mediated by phonons 2 to the upper level enhance fluctuations y2 which mix phonons 2 with phonons 1 and contribute to... 

For systems with heavy atoms we often employ pseudopotential basis sets (frequently relativistic), which reduce the computational burden of large numbers of electrons. Transition metals present problems beyond those of main-group heavy atoms not only can relativistic effects be significant, but electron d- or f-levels, variably perturbed by ligands, make possible several electronic states. DFT calculations, with pseudopotentials, are the standard approach for computations on such compounds. 

The two bands appear very different. Their rotational structure is quite symmetrical but that of aniline shows a pronounced gap near the band centre whereas that of aniline Ar shows a grouping of intense lines. The reason for the difference is that the band of aniline is a type B band of a prolate asymmetric rotor (see Section 6.2.4.4) whereas that of aniline Ar is a type C band of an oblate asymmetric rotor. The electronic transition moment in aniline itself is directed along the b axis which is in the plane of the benzene ring and perpendicular to the C—N axis (which is the a axis). In the aniline Ar molecule, the argon atom sits on the benzene ring, attracted by the n electrons. The fact that the argon atom is relatively heavy causes a rotation of the principal axes on inertia ... 

Another force that can result in distorted coordination polyhedra is the inert (lone) pair effect. The inert pair effect refers to the reluctance of the heavy post transition elements from groups 13 -15 to exhibit the highest possible oxidation state, by retaining their pair of valence s electrons. The lone pair of electrons on these elements can be stereochemically active and take the place of an anion in the coordination sphere of a cation, or squeeze between the anions and the metal causing distortion of the polyhedra. 

UV-vis Spectra. In Table 6 are listed characteristic visible absorptions observed for the heavy ketones kinetically stabilized by a Tbt group, ft is known that the absorption maxima attributable to the n-jr electron transitions of a series of R2C=Ch (Ch = O, S, Se, Te) undergo a systematic red-shift on going down the periodic table. A similar tendency is observed for the Si, Ge, and Sn series of Tbt(R)Si=Ch (Ch = S, Se, Tbt(R)Ge=Ch... 

The drastic influence of small changes in chemical composition on the low-temperature properties of heavy-electron materials is demonstrated. Prevention of the heavy-electron state itself or suppression of phase transitions out of this state are among the most interesting experimental observations. 

Quite different is the influence of substituting Cu with Ag. if one Cu atom per formula unit is replaced by Ag, T yj is raised to 16 K and the formation of the heavy-electron state below 5 K persists (13). What is different now is that the low-temperature phase transition is quenched as is demonstrated in the Cp(T) plot of fig. 5. The specific heat varies linearly with T down to the lowest temperatures investigated and y = c /T is roughly one hundred times larger than that observed in the equivalent amount of Cu metal. This clearly demonstrates that Ni or Ag substitutions for Cu in UCus induce quite different changes in the low-temperature behaviour but the reasons for it are not yet clear. 

The hexagonal crystal structure of CeCus contains two inequivalent Cu sites with a ratio of 2 3. It has been found that A1 can be sub-stituted for Cu on the threefold site (19). Specific heat measurements have shown that replacing one Cu atom per formula unit by A1 leads to an extreme heavy-electron state where the cp /T ratio reaches 2.2 3/mole K, so far a record value, and no phase transition is observed above 0.15 K (18). The temperature dependence of the specific heat Cp(T) below 1 K is shown in fig. 7. Increasing the A1 content to obtain CeCu3Al2 results in a decrease of this giant y value by a factor of about two. 

The spin selection rule is a consequence of the fact that the electric dipole and quadrupole moment operators do not operate on spin. Integration over the spin variables then always yields zero if the spin functions of the two states 0 and are different, and an electronic transition is spin allowed only if the multiplicities of the two states involved are identical. As a result, singlet-triplet absorptions are practically inobservable in the absorption spectra of hydrocarbons, or for that matter, other organic compounds without heavy atoms. Singlet-triplet excitations are readily observed in electron energy loss spectroscopy (EELS), which obeys different selection rules (Kuppermann et al., 1979). 

The ZINDO method, in connection with the SOS procedure, relates the NLO properties to all electronic transitions having charge transfer character. Therefore, this approach provides important chemical insights and efficient guidelines for synthetic chemists. Unfortunately, it is not operative for tin derivatives, because heavy metals are not parameterized in ZINDO. 

Appearance potential spectroscopy involves detection of electronic transitions not of the backscattered electrons as in ELS, but of secondary processes. The latter include increase in soft X-ray (SXAPS) or Auger electron (AEAPS) emission or decrease in elastically scattered primary electrons (DAPS) (382). SXAPS is not as sensitive as AES for surface chemical analysis. However, SXAPS and IS spectra are easier to analyze than AES, since only one core transition is involved. This makes SXAPS and IS quite convenient for detecting heavy elements on catalyst surfaces. 

Among the heavy post-transition metals there is a definite reluctance to exhibit the highest possible oxidation state. For example, boron is always trivalent, but thallium shows significant chemistry of the +1 oxidation state, leaving a pair of electrons coordinatively inert. This is known as the inert pair effect... 

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