Electrons kinetic energy

Figure Al.7.12 shows the scattered electron kinetic energy distribution produced when a monoenergetic electron beam is incident on an A1 surface. Some of the electrons are elastically backscattered with essentially...

Figure Al.7.12. Secondary electron kinetic energy distribution, obtained by measuring the scadered electrons produced by bombardment of Al(lOO) with a 170 eV electron beam. The spectrum shows the elastic peak, loss features due to the excitation of plasmons, a signal due to the emission of Al LMM Auger electrons and the inelastic tail. The exact position of the cutoff at 0 eV depends on die surface work fimction.

XPS is also often perfonned employing syncln-otron radiation as the excitation source [59]. This technique is sometimes called soft x-ray photoelectron spectroscopy (SXPS) to distinguish it from laboratory XPS. The use of syncluotron radiation has two major advantages (1) a much higher spectral resolution can be achieved and (2) the photon energy of the excitation can be adjusted which, in turn, allows for a particular electron kinetic energy to be selected. 

Since the electronic kinetic energy f= fj operator is also one-electron additive, so is the mean-field... 

Here, t is the nuclear kinetic energy operator, and so all terms describing the electronic kinetic energy, electron-electron and electron-nuclear interactions, as well as the nuclear-nuclear interaction potential function, are collected together. This sum of terms is often called the clamped nuclei Hamiltonian as it describes the electrons moving around the nuclei at a particular configrrration R. 

Note that the electronic kinetic energy operator does not depend on the nuclear configuration explicitly. Therefore, we can conclude that... 

The total energy in an Molecular Orbital calculation is the net result of electronic kinetic energies and the interactions between all electrons and atomic cores in the system. This is the potential energy for nuclear motion in the Born-Oppenheimer approximation (see page 32). 

The Auger electron kinetic energy is obtained from... 

Fig. 11. "Universal curve" of inelastic mean free path, X, as a function of electron kinetic energy. Solid line is universal curve, points are experimental data...

The CRR mode involves retarding the electron kinetic energies to a constant ratio of H /H where H is the energy passed by the analyzer. Thus, the energies are retarded by a constant factor. Spectra acquired in this mode ate less easy to quantify, but small peaks at low kinetic energies ate readily detected. This mode of operation results in spectra of constant relative resolution throughout. The relative resolution is improved in this mode by a factor of E. ... 

Figure 2 Experimental data from an early stage of CO adsorbed on Fe (001) known as the GC3 state polar scans (a) of the C 1s-0 Is Intansity ratio taken in two Fe (001) azimuthal planes, the (100) and the (ITO) (the C Is and O Is electron kinetic energies are 1202 aV and 955 aV, respectively) C Is azimuthal scan (b) taken at the polar angle of maximum intensity in (a) and geometry (c) deduced from the data.

Consider now the Hamilton operator. The nuclear-nuclear repulsion does not depend on electron coordinates and is a constant for a given nuclear geometry. The nuclear-electron attraction is a sum of terms, each depending only on one electron coordinate. The same holds for the electron kinetic energy. The electron-electron repulsion, however, depends on two electron coordinates. 

Electron kinetic energy = Photon energy - Binding energy E] ijietic( l ctron) = A v - A vq... 

Figure 2. Photoelectron chiral asymmetry factor, y, obtained as a function of electron kinetic energy at hv = 21.2 eV for the (R)- and (S)- enantiomers of glycidol. Also included is a moderate resolution photoelectron spectrum recorded under identical conditions. Data from Refs. [37, 38].

The individual terms in (5.2) and (5.3) represent the nuclear-nuclear repulsion, the electronic kinetic energy, the electron-nuclear attraction, and the electron-electron repulsion, respectively. Thus, the BO Hamiltonian is of treacherous simplicity it merely contains the pairwise electrostatic interactions between the charged particles together with the kinetic energy of the electrons. Yet, the BO Hamiltonian provides a highly accurate description of molecules. Unless very heavy elements are involved, the exact solutions of the BO Hamiltonian allows for the prediction of molecular phenomena with spectroscopic accuracy that is... 

We now need to discuss how these contributions that are required to construct the Kohn-Sham matrix are determined. The fust two terms in the parenthesis of equation (7-12) describe the electronic kinetic energy and the electron-nuclear interaction, both of which depend on the coordinate of only one electron. They are often combined into a single integral, i. e ... 

One knows, however, that the simple density-functional theories cannot produce an oscillatory density profile. The energy obtained by Schmickler and Henderson55 is, of course, lower than that of Smith54 because of the extra parameters, but the oscillations in the profile found are smaller than the true Friedel oscillations. Further, the density-functional theories often give seriously inexact results. The problem is in the incorrect treatment of the electronic kinetic energy, which is, of course, a major contributor to the total electronic energy. The electronic kinetic energy is not a simple functional of the electron density like e(n) + c Vn 2/n, but a... 

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

For a many-electron molecule, the Hamiltonian operator can thus be written as the sum of the electrons kinetic energy term, which in turn is the sum of individual electrons ... 

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