Frontier Electron Energy

In summary, the position of the frontier electron energy levels (HOMO and LUMO) of porphyrins and phthalocyanines can be finely tuned by the appropriate combination of central metal and substituted ligand as detected in photoelectron spectroscopy or in the redox potentials. A rich redox chemistry in interplay with a number of reactants and counterions has been estabhshed. A systematic consideration of the electrochemical and photoelectrochemical characteristics of porphyrins and phthalocyanines as individual molecules in solution, as molecules adsorbed at surfaces, and as molecular thin films serving to mimic the characteristics of molecular aggregates is of much relevance to the choosing or designing of optimized porphyrin or phthalocyanine sensitizers for DSSCs. 

The contribution of the frontier orbitals would be maximized in certain special donor-acceptor reactions. The stabilization energy is represented by Eqs. (3.25) and (3.26). Even in a less extreme case, the frontier orbital contribution maybe much more than in the expression of the superdelocalizability. If we adopt the approximation of Eq. (6.3), the intramolecular comparison of reactivity can be made only by the numerator value. In this way, it is understood that the frontier electron density, /r, is qualified to be an intramolecular reactivity index. The finding of the parallelism between fr and the experimental results has thus become the origin of the frontier-electron theory. The definition of fr is hence as follows ... 

The frontier orbital approach (Fukui et al., 1962, 1954b) has met with considerable success in so far as frontier orbital charges correlate well with experimental data. The performance of these indices is often superior to that of others, with the possible exception of localization energies. It is, however, difficult to give meaning to the correlation since physical interpretations of the role of the frontier electrons in reaction mechanisms are often obscure, and attempts to give substance to Fukui s hypothesis have frequently embodied questionable procedures or models. 

Fig. 2-4. Lattice potential energy and electron energy bands in crystals IB s inner band FB s frontier band.

Fig. 2-12. Electron energy band formation of silicon crystals from atomic frontier orbitals number of silicon atoms in crystal r = distance between atoms rg = stable atom-atom distance in crystals, sp B8 = bonding band (valence band) of sp hybrid orbitals sp ABB = antibonding band (conduction band) of sp hybrid orbitals.

Most metal oxides are ionic crystals and belong to either the class of semiconductors or insulators, in which the valence band mainly comprises the frontier orbitals of oxide ions and the conduction band contains the frontier orbitals of metal ions. In forming an ionic metal oxide ciTstal from metal ions and oxide ions, as shown in Fig. 2-21, the crystalline field shifts the frontier electron level of metal ions to higher energies to form an antibonding band (the conduction... 

The frontier electron level of adsorbed particles splits itself into an occupied level (donor level) in a reduced state (reductant, RED) and a vacant level (acceptor level) in an oxidized state (oxidant, OX), because the reduced and oxidized particles differ from each other both in their respective adsorption energies on the interface of metal electrodes and in their respective interaction energies with molecules of adsorbed water. The most probable electron levels, gred and eqx, of the adsorbed reductant and oxidant particles are separated from each other by a magnitude equivalent to the reorganization energy 2 >. ki in the same way as occurs with hydrated redox particles described in Sec. 2.10. 

Figure 8-1 shows the potential energy barrier for the transfer reaction of redox electrons across the interface of metal electrode. On the side of metal electrode, an allowed electron energy band is occupied by electrons up to the Fermi level and vacant for electrons above the Fermi level. On the side of hydrated redox particles, the reductant particle RED is occupied by electrons in its highest occupied molecular orbital (HOMO) and the oxidant particle OX, is vacant for electrons in its lowest imoccupied molecular orbital (LUMO). As is described in Sec. 2.10, the highest occupied electron level (HOMO) of reductants and the lowest unoccupied electron level (LUMO) of oxidants are formed by the Franck-Condon level sphtting of the same frontier oihital of the redox particles... 

Frontier orbital energies and coefficients for sydnone, calculated by the MINDO/3 method, and the predicted dominant frontier orbital interaction with an electron-deficient alkene. 

Fig. 1. -electron energy changes of the frontier orbitals of Ml2- effected by N-atoms and CN-groups (HMO/PMO treatment). 

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