Electronic energy levels, crystalline

The physical concept of a single electrode potential has been also discussed in terms of the energy levels of ions in electrode systems. This concept may be usefirl in the cases where the system has no electronic energy levels in a range of practical interest, such as in ionic solid crystalline and electronically nonconductive membrane electrodes. "... 

To have free-electron energy levels, the potential in which the electrons move must be constant (V = - V0) in a crystalline metal there are ion cores arranged in a regular array or lattice, which... 

For electrodes which have no electron energy levels in the energy range of general interest, such as ionic crystalline sohd electrodes and membrane electrodes, only the concept of ionic electrode potential can be of practical significance. 

In principle, molecules can be either passive or active electronic components, either singly or in parallel as a one-molecule-thick monolayer array. This may lead to electronic devices with dimensions of 1-3 nm. Unimolecular electronics (UE) or molecular electronics sensu stricto, or molecular-scale electronics evolved from studies of organic crystalline metals, superconductors, and conducting polymers the idea is to exploit the electronic energy levels of a single molecule, and most importantly its HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital), which can be tuned, or modified by incorporation of electron-donating... 

Consider a sample of frozen crystalline helium with a large number of atoms arranged into a lattice (Figure 15.47). Six of them are labelled A to F, and each is assumed to have a set of four evenly spaced vibrational energy levels. (In reality the vibrational energy levels converge in a similar way to electronic energy levels (Chapter 2)). 

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. 

Fig. 10 Electrochemical energy level model for orbital mediated tunneling. Ap and Ac are the gas-and crystalline-phase electron affinities, 1/2(SCE) is the electrochemical potential referenced to the saturated calomel electrode, and provides the solution-phase electron affinity. Ev, is the Fermi level of the substrate (Au here). The corresponding positions in the OMT spectrum are shown by Ar and A0 and correspond to the electron affinity and ionization potential of the adsorbate film modified by interaction with the supporting metal, At. The spectrum is that of nickel(II) tetraphenyl-porphyrin on Au (111). (Reprinted with permission from [26])...

Metals are defined as materials in which the uppermost energy band is only partly filled. The uppermost energy level filled is called the Fermi energy or the Fermi level. Conduction can take place because of the easy availability of empty energy levels just above the Fermi energy. In a crystalline metal the Fermi level possesses a complex shape and is called the Fermi surface. Traditionally, typical metals are those of the alkali metals, Li, Na, K, and the like. However, the criterion is not restricted to elements, but some oxides, and many sulfides, are metallic in their electronic properties. 

Weak crystalline field //cf //so, Hq. In this case, the energy levels of the free ion A are only slightly perturbed (shifted and split) by the crystalline field. The free ion wavefunctions are then used as basis functions to apply perturbation theory, //cf being the perturbation Hamiltonian over the / states (where S and L are the spin and orbital angular momenta and. 1 = L + S). This approach is generally applied to describe the energy levels of trivalent rare earth ions, since for these ions the 4f valence electrons are screened by the outer 5s 5p electrons. These electrons partially shield the crystalline field created by the B ions (see Section 6.2). 

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