Electron-density surface

The most popular of the scanning probe tecimiques are STM and atomic force microscopy (AFM). STM and AFM provide images of the outemiost layer of a surface with atomic resolution. STM measures the spatial distribution of the surface electronic density by monitoring the tiumelling of electrons either from the sample to the tip or from the tip to the sample. This provides a map of the density of filled or empty electronic states, respectively. The variations in surface electron density are generally correlated with the atomic positions. 

Figure 1.2 A schematic view of an atom. The dense, positively charged nucleus contains most of the atom s mass and is surrounded by negatively charged electrons. The three-dimensional view on the right shows calculated electron-density surfaces. Electron density increases steadily toward the nucleus and is 40 times greater at the blue solid surface than at the gray mesh surface.

Based on the first-principles study of helium adsorption on metals (Zaremba and Kohn, 1977), Esbjerg and Nprskov (1980) made an important observation. Because the He atom is very tight (with a radius about 1 A), the surface electron density of the sample does not vary much within the volume of the He atom. Therefore, the interaction energy should be determined by the electron density of the sample at the location of the He nucleus. A calculation of the interaction of a He atom with a homogeneous electron distribution results in an explicit relation between the He scattering potential V r) and the local electron density p(r). For He atoms with kinetic energy smaller than 0.1 eV, Esbjerg and Nprskov (1980) obtained... 

The detailed data from He-scattering experiments provide information about the electron density distribution on crystalline solid surfaces. Especially, it provides direct information on the corrugation amplitude of the surface charge density at the classical turning point of the incident He atom, as shown in Fig. 4.13. As a classical particle, an incident He atom can reach a point at the solid surface where its vertical kinetic energy equals the repulsive energy at that point. The corrugation amplitude of the surface electron density on that plane determines the intensity of the diffracted atomic beam. 

The modification of an x-wave sample state due to the existence of the tip is similar to the case of the hydrogen molecule ion. For nearly free-electron metals, the surface electron density can be considered as the superposition of the x-wave electron densities of individual atoms. In the presence of an exotic atom, the tip, the electron density of each atom is multiplied by a numerical constant, 4/e 1.472. Therefore, the total density of the valence electron of the metal surface in the gap is multiplied by the same constant, 1.472. Consequently, the corrugation amplitude remains unchanged. 

Esbjerg, N., and Nprskov, J. K. (1980). Dependence of the He-scattering potential at surfaces on the surface-electron-density profile. Phys. Rev. Lett. 45, 807-810. 

The decrease of the electron density favours the hydrogenation processes of the double bonds, but in the case of the triple bonds, use of the catalysts with the higher surface electron density is more preferable (24). Zn is a donor related to Pd, so it is able to increase the electron density at the surface palladium atoms. So the modifier (Zn) introduction into the HPS catalyst leads to the higher selectivity (see Table 3). 

Since the electron density is a continuous function across the interatomic surface, the two atoms that form the surface must have the same distribution of electrons over this face. The most stable structures will be those which require the least amount of redistribution of electron density when the free atoms come together, that is, they will be formed between atoms that have similar surface electron densities. This idea is related to the valence matching principle (Rule 4.2) which states that the most stable bonds are formed between ions that have similar bonding strengths. The bonding strength is thus related to the surface electron density of the ion. 

The density of electrons at a particular energy for surface and bulk atoms can be calculated according to the Mulliken procedure outlined in Section 11.B.1. The data in Fig. 13 show a different electron distribution on surface and bulk atoms. The bulk electron density is split-the maximum in surface electron density occurs at the minimum in bulk density. This behavior indicates that the bulk electron distribution is different from the surface electron distribution. 

Metal nanoparticles have been used for many applications because of their unique characteristics, even before they were visualized as small particles of nano-meter order by using a transmission electron microscope [118]. For example, colored glasses, which gained in popularity in medieval times, contain nanoparticles of noble metals. These colors originate from the SPR of metal nanoparticles, which is the resonance phenomenon of surface electron density wave with incident light wave at the metal surface [119]. Since this resonance is sensitive to the dielectric constant of surrounding media, the phenomenon has... 

Using atomic densities calculated from tabulated atomic wave functions, the summation was found [214] to produce results equivalent to the most elaborate molecular Hartree-Fock calculations for a series of small molecules, at a fraction of the computing expense. Surface areas and volumes computed by the two methods were found virtually identical. The promolecule calculation therefore has an obvious advantage in the exploration of surface electron densities, surface areas and molecular volumes of macromolecules for the analysis of molecular recognition. 

Next we illustrate how electrode reactions differ fundamentally from regular heterogeneous reactions on account of the involvement of electron charge transfer, a process that can be directly modulated in its rate in an instrumen-tally controlled way (by means of a potentiostat and/or an on-line computer). Because of this possibility, the extent of coverage by adsorbed intermediates and the surface electron density of the electrode can also be correspondingly modulated in an experimentally determinable way through measurement of the interfacial double-layer capacitance (7). 

Almost a linear dependence between pore size and positrons lifetime can be observed which was not clearly obtained in previous studies. This relationship is expected because when the pores are wider the probability of interaction between the positrons and the surface electron density in the pore walls decreases. This results in a lower rate of positrons annihilation with the surrounding electrons and then a higher lifetime. A simple model for the annihilation process can be constructed assuming that the positron is trapped in a spherical pore of radius R of constant potential. The resolution of the Schroedinger equation shows that the lifetime of positrons is a function of R [5]. 

When intermediate surface bonding (Vnp = Vzp) occurs the adatom bonding and antibonding orbitals are not any more separate, but then overlap as broadened bands in the surface electron density regime (Fig. 4.3d). 

Both the intensity and the frequency of the -OH stretch in water are critically dependent upon the extent of hydrogen bonding to the immediate environment [40] and thus is a sensitive probe of the various types of water existing at the electrode-electrolyte interface. However, there are additional physical effects that may be detected by the phase-sensitive IR-ATR technique such as those derived from the variation of the electric field at the surface these electroreflectance effects are primarily due to changes in the surface electron density. 

One of the unsolved problems in the interaction of low-energy ions with surfaces is the mechanism of charge transfer and prediction of the charge composition of the flux of scattered, recoiled and sputtered atoms. The ability to collect spectra of neutrals plus ions and only neutrals provides a direct measure of scattered and recoiled ion fractions. SARIS images can provide electronic transition probability contour maps which are related to surface electron density and reactivity along the various azimuths. 

The situation is completely different in the case of sol-gel derived compact anatase Ti02 films where the extent of charge recombination is largely reduced due to the effect of anodic potential, E, applied through the space charge layer. The anodic bias causes the surface electron density, Ns, to decrease with the applied potential as [21]... 

In Eq. (10.1), Pjjj( ) is the surface electronic density of states. the interaction Hamiltonian, cp. the adsorbate atomic orbital, xp-g a metal surface orbital, and a the energy of an adsorbate orbital. The tight-binding overlap energy between adsorbate and surface atomic orbital is described as f and that between two metal atomic orbitals as f. As the adsorbate atomic orbital energy equals the Fermi level energy and metal orbitals are half-filled, a simple expression results for the interaction energy ... 

Schematic illustration of the electronic structure of the adsorption complex that consists of an adatom atomic orbital of energy cr that interacts with overlap energy p with a surface atom that is part of a simple cubic lattice. The surface electron density of states is represented by It has a...

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