Electron particles Delocalized

A particle occupies a particular location, but a wave has no exact position. A wave extends over some region of space. Because of their wave properties, electrons are always spread out rather than located in one particular place. As a result, the position of a moving electron cannot be precisely defined. We describe electrons as delocalized because their waves are spread out rather than pinpointed. 

Figure 12.23 shows that, in small molecules, electrons occupy discrete molecular orbitals whereas in macroscale solids the electrons occupy delocalized bands. At what point does a molecule get so large that it starts behaving as though it has delocalized bands rather than localized molecular orbitals For semiconductors, both theory and experiment tell us that the answer is roughly at 1 to 10 nm (about 10—100 atoms across). The exact number depends on the specific semiconductor material. The equations of quantum mechanics that were used for electrons in atoms can be applied to electrons (and holes) in semiconductors to estimate the size where materials undergo a crossover from molecular orbitals to bands. Because these effects become important at 1 to 10 nm, semiconductor particles with diameters in this size range are called quantum dots. 

As an elementary particle, a few laws govern the electronic behavior. The uncertainty principle forbids the electron to be definitely located (on the nucleus) and have at the same time a definite energy level (or velocity). Therefore, the electron is delocalized in space and hovers over the nucleus. Thus, the uncertainty principle... 

Molecules with delocalized molecular orbitals are generally more stable than those containing molecular orbitals locahzed on only two atoms. The benzene molecule, for example, which contains delocalized molecular orbitals, is chanically less reactive (and hence more stable) than molecules containing localized C=C bonds, such as ethylene. Benzene is so stable because the energy of the pi electrons is lower when the electrons are delocalized over the entire molecule than when they are localized in individual bonds, much as the energy of the particle in a one-dimensional box is lowered when the length of the box is increased (see Section 1.3). 

Quantum size effects ( true size effects, which involve changes of local materials properties), hi metals and semiconductors (note cathode materials for lithium-ion batteries can be considered semiconductors for practical purposes) the electronic wave functions of condnction electrons are delocalized over the entire particle and there is a continnons size-dependence of various materials characteristics in the non-nano region. In nanomaterials, a discontinuous behavior of quantum size effects is observed, with the ionization potentials and electron... 

Carotenes are molecules with alternating C—C and C=C bonds in which the electrons are delocalized across the entire alternating bond system. As such, the electrons can be approximated as being a particle-in-a-box. Lycopene is a carotene found in tomatoes and watermelon. Assuming that the alternating carbon-carbon bond system is 2.64 nm wide ... 

We need ways to visualize electrons as particle-waves delocalized in three-dimensional space. Orbital pictures provide maps of how an electron wave Is distributed In space. There are several ways to represent these three-dimensional maps. Each one shows some important orbital features, but none shows all of them. We use three different representations plots of electron density, pictures of electron density, and pictures of electron contour surfaces. 

All models of this type have become known colloquially by the misnomer free-particle model. Diverse objects with formal resemblance to chemical systems are included here, such as an electron in an impenetrable sphere to model activated atoms particle on a line segment to model delocalized systems particle interacting with finite barriers to simulate tunnel effects particle interacting with periodic potentials to simulate electrons in solids, and combinations of these. 

Despite spectacular successes with the modelling of electron delocalization in solids and simple molecules, one-particle models can never describe more than qualitative trends in quantum systems. The dilemma is that many-particle problems are mathematically notoriously difficult to handle. When dealing with atoms and molecules approximation and simplifying assumptions are therefore inevitable. The immediate errors introduced in this way may appear to be insignificant, but because of the special structure of quantum theory the consequences are always more serious than anticipated. 

The fragmentation may occur due to favorable delocalization of the unpaired electron in the neutral particle forming. Again the rules of classic organic chemistry... 

Figure 2-41 compares the electron level diagram of intrinsic semiconductors with that of hydrated redox particles at the standard concentration. The two diagrams resemble each other in that the Fermi level is located midway between the occupied level and the vacant level. It is, however, obvious that the occupied and vacant bands for semiconductors are the bands of delocalized electron states, whereas they are the fluctuation bands of localized electron states for hydrated redox particles. 

This specific direction of protonation might be caused due to the inclusion of a proton in the chelate between the two oxygen atoms of NOy group. The negative charge of NOy group attracts a proton. Being included in the unpaired electron delocalization within the chelate, a proton seizes an electron and departs as a small radical particle H. 

The product of desorption in all the cases considered is a neutral particle C. As r increases, i.e., as particle C moves away from the surface, the level A in Fig. 10 can be shown 2) to approach the conduction band and to merge with it in the limit r = oo at the same time the level D in Fig. 10 descends to the valence band and merges with it at r = w. In other words, an electron localized on an acceptor level A (making an n bond) or a hole localized on a donor level D (making a p bond) becomes delocalized as r increases and in the limit (at r = ) returns to the conduction band or, respectively, to the valence band, that is, becomes again one of the free electrons or holes. 

The various forms of chemisorption can go over into one other i.e., the chemisorbed particle can change the character of its bonding with the surface during its lifetime in the adsorbed state. This is a result of the localization or delocalization of a free electron or hole near the particle (Sec. IV,A). 

---