Electron levels, free molecules/solids

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

Calculations for C6o in the LDA approximation [62, 60] yield a narrow band ( 0.4--0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes arc indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo molecule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

In the case of a metal substrate, the experimental evidence shows that metal excitation is dominated by surface photon absorption. Optical radiation excites surface charge carriers, usually free or sub-vacuum-level electrons that can efficiently couple to the adsorbate. This often leads to enhanced photolysis cross sections or altered product distributions. Excitation localized on the adsorbed molecule in close proximity to a metallic solid may efficiently couple to the electronic states of the surface, leading to excitation quenching. When light-absorbing molecules are separated from the surface by spacer molecules, the influence of the surface on molecular excitation and relaxation decreases [4,21],... 

The first equation represents the equilibrium between hydrated Ag+ ions and Ag atoms in a single-crystal configuration. Alternatively, we may say that there is a heterogeneous thermodynamic equilibrium between Ag+ ions in the solid phase (where they are stabilized by the gas of free electrons) and Ag+ ions in the liquid phase (stabilized by interaction with water molecules). The forward reaction step corresponds to the anodic dissolution of a silver crystal. On an atomic level, one may say that a Ag" " core ion is transferred from the metallic phase to the liquid water phase. In an electrochemical cell, an electron flows from the Ag electrode (the working electrode) to the counter electrode each time that one Ag+ ion is transferred from the solid to the liquid phase across the electrochemical double layer. Although the electron flow is measured in the external circuit between the working... 

Conduction heating occurs via two different mechanisms. The first mechanism is accomplished by molecular interaction where molecules at a higher energy level impart energy to molecules at a lower energy level. The second mechanism takes place through free electrons. The ability of different solids to conduct heat... 

---