Electron field gradients

Perhaps not so very well suitable Thus, semiconductor electrodes exhibit limiting currents that arise from the transport of the charge carrier inside the semiconductor. In practice, this means that it is difficult to get current densities above -1 mA cm-2 at moderately doped semiconductors. No such limitation occurs with metals that have roughly l electron per atom free to move under an electron field gradient. The limiting currents that arise with metals are due to the limitation in supply of materials in the solution. 

Values of R for free atoms have been calculated in Table 3 from the restricted Hartree-Fock functions by perturbation theory and are usually in the range 0.0-0.5. For molecules, however, the only satisfactory procedure is to introduce the dependence on m right from the start and indeed to include the m dependence as one of the parameters to be minimised in the var-ation method. In H - Cl the inner shell polarisation accounts for 17% of the electronic field-gradient l2)... 

The spatial part represents the two-electron field gradient integrals. Employing the notation for the Cartesian components... 

Aray, Y., Gatti, G. and Murgich, J. (1994) The electron field gradient at the N nuclei and the topology of the charge distribution in the protonation of urea, J. Chem. Phys., 101, 9800-9806. 

One has to note that the choice of z-axis, which determines the ZFS parameters D and E, depends on the molecule and on the symmetry of the triplet state. In our calculations of the free-base porphin molecule z-axis is along the N-H bonds and X-axis is out of plane. Numeration of atoms and orientation of axes is shown in Fig. 1.1. In that case, as follows from the present and from previous calculations [7, 28], Disnot determined by Eq. (1.5), but by D = — X, something that coincides with experimental findings [28], The ZFS tensor can be obtained by contracting two-electron field gradient integrals with a quintet two-electron density [47]... 

If the electrodes are moved closer together, the positive column begins to shorten as it moves through the Faraday dark space because the ions and electrons within it have a shorter distance through which to diffuse. Near the cathode, however, the electric-field gradient becomes steeper and electrons from the cathode are accelerated more quickly. Thus atom excitation through collision with electrons occurs nearer and nearer to the cathode, and the cathode glow moves down toward the electrode. 

Forces of Adsorption. Adsorption may be classified as chemisorption or physical adsorption, depending on the nature of the surface forces. In physical adsorption the forces are relatively weak, involving mainly van der Waals (induced dipole—induced dipole) interactions, supplemented in many cases by electrostatic contributions from field gradient—dipole or —quadmpole interactions. By contrast, in chemisorption there is significant electron transfer, equivalent to the formation of a chemical bond between the sorbate and the soHd surface. Such interactions are both stronger and more specific than the forces of physical adsorption and are obviously limited to monolayer coverage. The differences in the general features of physical and chemisorption systems (Table 1) can be understood on the basis of this difference in the nature of the surface forces. 

The primary photochemical act, subsequent to near-uv light (wavelengths <400 nm) absorption by Ti02 particles, is generation of electron—hole pairs where the separation (eq. 3) into conduction band electrons (e g ) and valence band holes (/lyB ) faciUtated by the electric field gradient in the space charge region. Chemically, the hole associated with valence band levels is constrained at... 

In a molecule, a given nucleus will generally experience an electric field gradient due to the surrounding electrons. The energy of interaction U between the nuclear quadrupole and the electric field gradient E is given by... 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

If the field gradient has no axial symmetry, then a more complicated expression is found, involving an asymmetry parameter which is often moderate. In particular, the study of this parameter has been useful for the determination of resonance structures and for the understanding of the bonding in solid iodine. The contribution of each of the molecular electrons to q is given by a relation of the form... 

Eckart, criteria, 264, 298 procedure, 267 Effective charge, 274, 276 Effective Hamiltonian, 226 Elastic model, excess entropy calculation from, 141 of a solid solution, 140 Electric correlation, 248 Electric field gradient, 188, 189 Electron (s), 200... 

Figure 4.54 The effect of an electric field gradient (EFG) creating asymmetry in the electron distribution round a gold nucleus, leading to a quadrupole splitting in the Mossbauer spectrum. (Reproduced with permission from Gold Bull., 1982,15, 53, published by World Gold Council.)...

Hinton, DP Johnson, CS, Diffusion Coefficients, Electrophoretic Mobilities, and Morphologies of Charged Phospholipid Vesicles by Pulsed Field Gradient NMR and Electron Microscopy, Journal of Colloid and Interface Science 173, 364, 1995. 

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