Transition intensities applications

Direct printout of Mathematica commands to calculate and plot wavefunctions and electronic transition intensity factors for a diatomic molecule (I2) using harmonic and Morse oscillator wavefunctions. See text for discussion. A Maple version of this calculation can be found on the Maple applications website. 

Lanthanide compounds have attracted attention due to their potential applications as various materials. Their intra-4f electronic transition, the so-called f-f transition, is one of the most discriminative properties and used extensively for many optics, such as lasers, fibers, optical displays, and biosensors [1-3]. The probability of photo absorption is represented by oscillator strength, a dimensionless quantity. The oscillator strengths of f-f transitions are small, typically in the order of 10 , reflecting Laporte forbidden transitions, and their absorption and emission spectra have sharp peaks in visible, near infrared, and near ultraviolet regions. Despite the usefulness of these systems, there are only a few relevant ab initio studies of the f-f transition intensities that explicitly included ligand electrons [4—7] because these calculations are difficult due to the importance of both relativistic and electron correlation effects. 

The same integrals also appear in Problem 3.61, where they are needed to find spectroscopic transition intensities. In that case, a photon provides the applied electric field. This similarity allows polarizabilities to be determined in some applications (particularly for molecular ions and other molecules where dipole moments are hard to measure directly) by adding together transition intensities determined by spectroscopy. 

Magnetic measurements find intensive applications in the study of transitional metal 7r-complexes. Such data can give information that is useful for the elucidation of valency, bond type, and stereochemistry of such compounds. 

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

The applications to selection rules work as follows. Intensities depend on the values of the transition moment integral of equation (Bl.l.lT... 

Since no special ligand design is usually required to dissolve transition metal complexes in ionic liquids, the application of ionic ligands can be an extremely useful tool with which to immobilize the catalyst in the ionic medium. In applications in which the ionic catalyst layer is intensively extracted with a non-miscible solvent (i.e., under the conditions of biphasic catalysis or during product recovery by extraction) it is important to ensure that the amount of catalyst washed from the ionic liquid is extremely low. Full immobilization of the (often quite expensive) transition metal catalyst, combined with the possibility of recycling it, is usually a crucial criterion for the large-scale use of homogeneous catalysis (for more details see Section 5.3.5). 

As early as 1990, Chauvin and his co-workers from IFP published their first results on the biphasic, Ni-catalyzed dimerization of propene in ionic liquids of the [BMIM]Cl/AlCl3/AlEtCl2 type [4]. In the following years the nickel-catalyzed oligomerization of short-chain alkenes in chloroaluminate melts became one of the most intensively investigated applications of transition metal catalysts in ionic liquids to date. 

Moseley found that each K spectrum of Barkla contains two lines, Ka and K(3, and that the L spectra are more complex. Later important work, especially by Siegbahn,38 has shown that M, N, and O spectra exist and are more complex in their turn. Relatively numerous low-intensity lines are now known to exist in all series. Fortunately, the analytical chemist can afford to ignore most of these low-intensity lines in his practical applications of x-ray methods at present. It generally suffices for him to know that x-ray spectra at their most complex are enormously simpler than emission spectra involving valence electrons, and that most x-ratr lines are satisfactorily accounted for on the basis of the simple selection rules that govern electron transitions between energy states. 

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