Free-electron model aromatic molecules

For the purposes of this review it is convenient to focus attention on that class of molecules in which the valence electrons are easily distinguished from the core electrons (e.g., -n electron systems) and which have a large number of vibrational degrees of freedom. There have been several studies of the photoionization of aromatic molecules.206-209 In the earliest calculations either a free electron model, or a molecule-centered expansion in plane waves, or coulomb functions, has been used. Only the recent calculation by Johnson and Rice210 explicitly considered the interference effects which must accompany any process in a system with interatomic spacings and electron wavelength of comparable magnitude. The importance of atomic interference effects in the representation of molecular continuum states has been emphasized by Cohen and Fano,211 but, as far as we know, only the Johnson-Rice calculation incorporates this phenomenon in a detailed analysis. 

Section 6.2 Free-Electron Model for Aromatic Molecules... 

If the particle in a box model is used in two dimensions for electrons that are assumed to be freely mobile in the k system of a planar aromatic molecule, the excitation energies (E - E ) are obtained, which agree quite well with the energy of spectral lines in the visible or UV part of the spectrum. It is certainly not to be expected that a perfect agreement is obtained, since V = 0 can only hold in a very approximate way. Anyway, this free-electron model is a rather good model for k systems. The electrons are not really free, but bound to the molecule, since V = oo outside. 

In the following 20 years, a group of physicists in the Ukraine [2] studied a series of other aromatic crystals spectroscopically. It developed that there are also very characteristic differences from the spectra of free molecules. In the year 1948, A. S. Davydov [3] formulated the basic theoretical explanation for the observable interaction processes in the crystal spectra, between the molecules in electronically excited states within the crystal. He made use of the model of Frenkel excitons [4] and was able in particular to give a quantitative explanation of a characteristic line splitting, the Davydov splitting, as a fundamental property of organic molecular crystals. Fig. 6.1 shows as an example the splitting of the 0,0-transition in the Ti So absorption spectrum of anthracene at room temperature. 

Very recently we have communicated on the role of the 5f orbitals in bonding, aromaticity, and reactivity of planar isocyclic and heterocyclic uranium clusters [185]. Using electronic structure calculation methods (DFT) we demonstrated that the model planar isocyclic cjc/o-U X (n = 3, 4 X = 0,NH) and heterocyclic cjc/o-U (/u.2-X) (n = 3, 4 X = C, CH, NH) clusters are thermodynamically stable molecules with respect to their dissociation either to free U and X moieties or to their monomeric UX species. The equilibrium geometries of the cyclo- J X and cyclo-U iJ,2-X) clusters are shown in Fig.42. 

---