Molecular electronic states derivation

The correlation rules for determining what types of molecular electronic states result from given electronic states of the separated atoms were derived quantum mechanically by Wigner and Witmer [1] and are discussed in great detail by Herzberg [2], These correlation rules hold for the adiabatic potential curves of the electronic states1 when Russell-Saunders coupling is valid for the separated atoms as well as the molecule. 

In principle all the X-ray emission methods can give chemical state information from small shifts and line shape changes (cf, XPS and AES in Chapter 5). Though done for molecular studies to derive electronic structure information, this type of work is rarely done for materials analysis. The reasons are the instrumental resolution of commercial systems is not adequate and the emission lines routinely used for elemental analysis are often not those most useftil for chemical shift meas-ure-ments. The latter generally involve shallower levels (narrower natural line widths), meaning longer wavelength (softer) X-ray emission. 

Nonomura, Y. et al., Spectroscopic properties of chlorophylls and their derivatives. Influence of molecular structure on the electronic state, Chem. Phys., 220, 155, 1997. 

For linear molecules or ions the symbols are usually those derived from the term symbols for the electronic states of diatomic and other linear molecules. A capital Greek letter E, n, A, O,... is used, corresponding to k — 0,1,2,3,..., where A. is the quantum number for rotation about the molecular axis. For E species a superscript + or - is added to indicate the symmetry with respect to a plane that contains the molecular axis. 

The Time Dependent Processes Section uses time-dependent perturbation theory, combined with the classical electric and magnetic fields that arise due to the interaction of photons with the nuclei and electrons of a molecule, to derive expressions for the rates of transitions among atomic or molecular electronic, vibrational, and rotational states induced by photon absorption or emission. Sources of line broadening and time correlation function treatments of absorption lineshapes are briefly introduced. Finally, transitions induced by collisions rather than by electromagnetic fields are briefly treated to provide an introduction to the subject of theoretical chemical dynamics. 

As chemists, much of our intuition concerning chemical bonds is built on simple models introduced in undergraduate chemistry courses. The detailed examination of the H2 molecule via the valence bond and molecular orbital approaches forms the basis of our thinking about bonding when confronted with new systems. Let us examine this model system in further detail to explore the electronic states that arise by occupying two orbitals (derived from the two Is orbitals on the two hydrogen atoms) with two electrons. 

Beyond such electronic symmetry analysis, it is also possible to derive vibrational and rotational selection rules for electronic transitions that are El allowed. As was done in the vibrational spectroscopy case, it is conventional to expand i j (R) in a power series about the equilibrium geometry of the initial electronic state (since this geometry is more characteristic of the molecular structure prior to photon absorption) ... 

---