Representation of electron

Guide to the Collection and Representation of Electronic, Sensing Component, and Mechanical Equipment Reliability Data for Nuclear Generating Stations. IEEE Standard 500-1984, Institute of Electrical and Electronics Engineers, New York, 1984. 

Optimize these three molecules at the Hartree-Fock level, using the LANL2DZ basis set, LANL2DZ is a double-zeta basis set containing effective core potential (ECP) representations of electrons near the nuclei for post-third row atoms. Compare the Cr(CO)5 results with those we obtained in Chapter 3. Then compare the structures of the three systems to one another, and characterize the effect of changing the central atom on the overall molecular structure. 

In representations of electron densities, the presence or lack of boundaries plays a crucial role. A quantum mechanically valid electron density distribution of a molecule cannot have boundaries, nevertheless, artificial electron density representations with actual boundaries provide useful tools of analysis. For these reasons, among the manifold representations of molecular electron densities, manifolds with boundaries play a special role. 

Figure 1.7 A schematic representation of electron transfer between Fe(H20) + and a metal electrode. The figure represents (i) the total electronic energy of the Fe(H20)3 + ion together with the energy of the electron at the Fermi level of the metal (ii> the total electronic energy of the Fc(H20)jr + ion, plotted vs. the Fe-O bond distance in the hydrates.

Scheme 29. Schematic Representation of Electron Charge Flow in 3-Methylsydnone (60) As Suggested in Ref 78...

Figure 2. Schematic representation of electron transfer from an aromatic compound to O2 with a Cu-exchanged clay as the catalyst and the formation of polymers (Reaction A) and hydrogen peroxide (Reaction B).

Half-cell reaction A conceptual representation of electron transfer in which the number of electrons gained by a molecule or atom is indicated. Eor example, the half-cell reduction of Mn to Mn ... 

The qualitative study of electronic structure through the electron (number) density p(r) relies heavily on linecut diagrams, contour plots, perspective plots, and other representations of the density and density differences. There is a review article by Smith and coworkers [302] devoted entirely to classifying and explaining the different techniques available for the pictorial representation of electron densities. Beautiful examples of this type of analysis can be seen in the work of Bader, Coppens, and others [303,304]. 

Fig. 24 Schematic representation of electron injection from a metallic electrode into a semiconductor (a) via Schottky emission, (b) via Fowler-Nordheim tunneling, and (c) via hopping in a disordered organic solid.

Figure 1. Schematic representation of electron transfer sensitization. 1 photo-oxidation of sensitizer 2 forward electron transfer (fluorescence quenching) 3 back electron transfer 4 product formation...

However, not all minima and saddle points are satisfactory representations of electronic states. The decision as to whether a stationary point is a good approximation to an electronic state must be based on other criteria. 

Atomic-orbital models, like that shown for benzene, are useful descriptions of bonding from which to evaluate the potential for electron delocalization. But they are cumbersome to draw routinely. We need a simpler representation of electron delocalization. 

Figure 9-17 Schematic representation of electronic, vibrational, and rotational energy levels. The vertical scale is greatly distorted rotational energy levels are normally 10 4-10-2 kcal mole-1 apart, vibrational energy levels are 1-10 kcal mole-1 apart, while electronic transitions involve 10-1000 kcal mole-1.

Figure 28-7 Representation of electron configuration changes in dissociation of tetramethyldioxacyclobutane, 8, to T-, and S0 2-propanone. Spin-orbit coupling of the nonbonding and the cr-bonding orbital on oxygen (shaded) produces one molecule of ketone in the triplet (7,) state.

Fig. 7.1. Schematic illustration of indirect photodissociation for a one-dimensional system. The two dashed potential curves represent so-called diabatic potentials which are allowed to cross. The solid line represents the lower member of a pair of adiabatic potential curves which on the contrary are prohibited to cross. The other adiabatic potential, which would be purely binding, is not shown here. More will be said about the diabatic and the adiabatic representations of electronic states in Chapter 15. The right-hand side shows the corresponding absorption spectrum with the shaded bars indicating the resonance states embedded in the continuum. The lighter the shading the broader the resonance and the shorter its lifetime.

Fig. 16 Schematic representation of electronic changes due to photostimulated electron transfer.

Fourier representation of electron density suggests the possibility of direct structure analysis. If all structure factors, F(hkl), are known, p(xyz) can be computed at a large number of points in the unit cell and local maxima in the electron-density function are interpreted to occur at the atomic sites. A typical single-crystal diffraction pattern of the type used for measuring structure factor amplitudes is shown in Figure 6.12. 

Where appropriate, increased-valence structures [2-5] will be used to provide qualitative VB representations of electronic structure. Increased-valence structures involve localised one-electron and fractional electron-pair bonds, as well as "normal" electron-pair bonds [2-5]. These features will be re-described by reference to HCNO. 

Figure 2.5. Schematic representation of electronic potential energy surfaces 1, consecutive conformational and solvatational equilibrium processes with the essential change in the nuclear coordinates Q and the standard Gibbs energy AG0 2, consecutive non-equilibrium processes with small changes in Q and AG0 3, 4, equilibrium (full line) and non-equilibrium (broken line) processes in the normal and inverted Marcus regions respectively. (Likhtenshtein, 1996) Reproduced in permission.

Figure 14-4 Schematic representation of electron transport in mitochondria.

In the past twenty years, there has been increasing interest in the calculation of correlation energies and other properties of atomic and molecular systems by means of diagrammatic many-body perturbation theory techniques3-9 due to Brueckner10 and Goldstone.11 Diagrammatic many-body perturbation theory provides a simple pictorial representation of electron correlation effects in atoms... 

Because of the inclusion of Dewar-type as well as the Kekul6-type structures in the Lewis structure resonance scheme, the increased-valence structures are more stable than are the familiar Kekule-type Lewis structures from which they are derived, provided that the one-electron bond polarity parameters, are chosen variationally. Therefore as discussed already in Section 8, a better (i.e. lower energy) VB description of the bonding may be obtained when increased-valence structures rather than only the component Kekul6-type structures, are used to provide VB representions of electronic structure. 

Fig. 14. Schematic representation of electron redistribution from metal to dy ...

Roman letters are used for representations of electronic states and greek letters for vibrational modes... 

FIGURE 12.6 Schematic representation of electron impact (A) and electrospray (B) mass spectrometer ionization sources. 

Figure 2. Schematic representation oF electron, hole, and triplet energy transfer between the localized HOMO and LUMO orbitals of the donor and the acceptor. Note that the above diagram also applies to the exchange-mediated singlet excitation transfer if the spin of the electron in the LUMO orbital is reversed.

Figure 1.11 The logo of the International Atomic Energy Agency, which is based on a stylized representation of electron orbits in the Bohr model of a multielectron atom. (Courtesy, International Atomic Energy Agency.)...

Electron-density map A contour representation of electron density in a crystal structure. Peaks appear at atomic positions. The map is computed by a Fourier synthesis, that is, the summation of waves of known amplitude, periodicity, and relative phase. The electron density is expressed in electrons per cubic A. 

Figure 5.28. Frontier orbital representation of electron exchange in a) electron transfer, b) hole transfer, and c) triplet-triplet energy transfer (adapted from Closs etal., 1989).

Figure 12.4 Schematic representation of electronic transitions, including Shockley-Read-Hall processes for a deep-level state.

Figure 1.6. Schematic representation of electron promotion processes in ionic crystals. At the shortest wavelengths, electrons are promoted to the conduction band and photoconductivity is observed. Exciton formation occurs on promotion to levels below the conduction band, this energetic combination of electron and positive hole does not conduct electricity but may participate in decomposition processes. Electrons or positive holes may also be generated from impurities.

Figure 1.24 Schematic representation of electron transfer reaction to the conduction band for direct (1) and resonance tunneling (2).

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