Transition intensities electronic spectroscopy

In the great majority of molecules, of course, no elements of symmetry exist at all. The point group is Ci. Similarly, in most reactions no useful elements of symmetry are conserved. How can one then decide which reactions are forbidden and which are allowed Actually the situation is very analogous to that of forbidden transitions in electronic spectroscopy. Reduction in symmetry can make such transitions allowed. However there will still be an inherent forbiddeness which shown up as a low intensity of absorption. 

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. 

A related measure of the intensity often used for electronic spectroscopy is the oscillator strengdi,/ This is a dimensionless ratio of the transition intensity to tliat expected for an electron bound by Hooke s law forces so as to be an isotropic hanuonic oscillator. It can be related either to the experimental integrated intensity or to the theoretical transition moment integral ... 

In much the same way as Stevens operators, the summation in Equation 1.15 is limited to well-defined values for f-electrons, the restriction k <7 holds, while q is limited to those values consistent with the point symmetry of the site. Finally, the even part k = 0, 2,4,6) is responsible for the CF splitting, while the odd part k = 1,3, 5,7) is responsible for the intensity of induced electric dipole transitions in optical spectroscopy [5b, 26]. 

The other form of optical activity in vibrational transitions is known as Raman optical activity (ROA). Here, also, one measures an intensity difference for left compared to right circularly polarized incident radiation however, optical activity in light scattering has no direct analog in electronic spectroscopy. ROA was first measured by Laurence Barron, A. D. Buckingham, and M. P. Bogaard in 1973 (9) and several reviews of the subject have since appeared (10-14). 

In electronic spectroscopy, one wants to know not only the energy difference between distinct electronic states but also the probability that a transition between them will take place under appropriate circumstances. Thus, in the recording of a classic UV/Vis spectrum for a molecule, the wavelengths of absorptions indicate the energetics of the transition, while the intensities of the absorptions indicate their aliowedness , or probability. 

Thus far, this contribution has been concerned mainly with the energies of vibrational transitions. Intensities were considered only in connection with Fermi resonance and RR spectroscopy. In this section a few short comments about the intensity of vibrational bands in normal IR and Raman spectra are presented. The intensity depends on the electronic stnicture of the species, since changes in the dipole moment (dfi) and in the polarizability (da) during a vibration are caused by changes in the electron density. 

There are also properties for which the magnitude is dependent upon transition intensity and for which accurate results can be obtained only with perturbation theory examples occur in currently much studied areas like NMR spectroscopy (described in Chapter 2), but also involve other properties like magnetic susceptibilities and refractive indices, which are not much studied from an electronic structure point of view (although we would argue that, due to advances in theory, such experimental techniques are ripe for further exploration). Within a Hartree-Fock approach the perturbation of a molecule by electric or magnetic fields can be calculated at a number of levels of theory. Coupled Hartree-Fock perturbation theory (Lipscomb, 1966 Ditchfield, 1974), which arrives at a self-... 

The observed shakedown is analogous to the satellites observed in photoelectron spectroscopy and can be treated in a similar manner [25]. This analysis enables us to quantify the intensity of the Is —> 4p + LMCT shakedown feature as a percentage of the total Is > 4p transition intensity. Comparison of the shakedown intensity to that of the Is > 3d(+4p) pre-edge transition (at 8,979 eV) then allows for quantitation of the amount of 4pz mixing into the 3d orbital. Within the sudden approximation [28-30], the creation of the core hole occurs rapidly, before the electron adjusts to the new potential. Here, the intensity /j of a given transition corresponding to either the main (Is —> 4p ) or shake down (Is —> 4p + LMCT) final state can then be given by the Sudden approximation... 

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