Electron interactions with atoms

The fundamental mechanisms through which electrons interact with atoms and molecules have been reviewed is detail by several authors for additional details, see Mark et al. [19],... 

Kameta, K. Kouchi, N. Hatano, Y. In Landolt-Bomstein, New series volume I/17C, Photon and Electron Interactions with Atoms, Molecules and Ions — Photon- and electron-interactions with molecules Ionization and dissociation, Itikawa, Y., Ed. Springer-Verlag Berlin, 2003 4-1-4-61, Chapter 4. 

Thermal diffuse or phonon scattering. The incident electrons interact with atoms that are oscillating about their mean positions and lose or gain energy of the order of kT ( 0.025 eV at room temperature). This amount of energy is too small to be detected by any available electron spectrometer, and there is no evidence that these phonon-scattered electrons contain any microanalytical information. 

Scanning electron microscopy (SEM) is a widely available technique in which a fine electron beam is rastered across the sample surface. The electrons interact with atoms in the surface component of the sample, producing various signals (Fig. 2.13) that can be detected and that contain information about the sample s surface... 

Electrons interact with solid surfaces by elastic and inelastic scattering, and these interactions are employed in electron spectroscopy. For example, electrons that elastically scatter will diffract from a single-crystal lattice. The diffraction pattern can be used as a means of stnictural detenuination, as in FEED. Electrons scatter inelastically by inducing electronic and vibrational excitations in the surface region. These losses fonu the basis of electron energy loss spectroscopy (EELS). An incident electron can also knock out an iimer-shell, or core, electron from an atom in the solid that will, in turn, initiate an Auger process. Electrons can also be used to induce stimulated desorption, as described in section Al.7.5.6. 

Because the neutron has a magnetic moment, it has a similar interaction with the clouds of impaired d or f electrons in magnetic ions and this interaction is important in studies of magnetic materials. The magnetic analogue of the atomic scattering factor is also tabulated in the International Tables [3]. Neutrons also have direct interactions with atomic nuclei, whose mass is concentrated in a volume whose radius is of the order of... 

Computational solid-state physics and chemistry are vibrant areas of research. The all-electron methods for high-accuracy electronic stnicture calculations mentioned in section B3.2.3.2 are in active development, and with PAW, an efficient new all-electron method has recently been introduced. Ever more powerfiil computers enable more detailed predictions on systems of increasing size. At the same time, new, more complex materials require methods that are able to describe their large unit cells and diverse atomic make-up. Here, the new orbital-free DFT method may lead the way. More powerful teclmiques are also necessary for the accurate treatment of surfaces and their interaction with atoms and, possibly complex, molecules. Combined with recent progress in embedding theory, these developments make possible increasingly sophisticated predictions of the quantum structural properties of solids and solid surfaces. 

EELS is a direct result of the Coulombic interaction of a fast nearly monochromatic electron beam with atoms in a solid. As the incident probe propagates through the... 

Even if it is assumed that the reaction is ionic, Occam s Razor would lead to the conclusion that the system is too complex and that the effort to keep it ionic is too great. It is difficult to undersand why step 8c is slow and why a simple uncharged complex would not be equally reasonable. We prefer a mechanism in which the carbon monoxide molecule is adsorbed parallel to the surface and in which the oxygen orbitals as well as the carbon orbitals of C=0 bond electrons interact with the metal. It seems reasonable that hydrogenolysis occurs exclusively only because the oxygen is held in some way while the two bonds are broken and it finally desorbs as water. The most attractive picture would be (a) adsorption of CO and H2 with both atoms on the surface... 

Our catalog of atomic characteristics emphasizes electrons, because electrons determine the chemical properties of atoms. For the same reason, the next several chapters examine electrons and the way they influence chemical properties. First, however, we describe light and its interaction with atoms, because light is an essential tool for probing properties of electrons. 

The spin magnetic moment Ms of an electron interacts with its orbital magnetic moment to produce an additional term in the Hamiltonian operator and, therefore, in the energy. In this section, we derive the mathematical expression for this spin-orbit interaction and apply it to the hydrogen atom. 

Electronic interactions with the formation of bonding molecular orbitals (orbital energy) and the electrostatic attraction between the nuclei of atoms and electrons. These two contributions cause the bonding forces of covalent bonds. 

In these equations, (24)-(26), orthonormal orbits are denoted by indices Vs. Equation (26) means that the orbiting electron interacting with itself, that is self-interaction, exists. This is unphysical. In order to remove this unphysical term, the SIC is taken into account by the following procedure. The SIC for the LDA in the density functional method has been treated for free atoms and insulators [16], and found an important role in determining the energy levels of electrons. However, no established formula is known to take into account the SIC for semiconductors and metals. As a way of trial, in the present calculation, the atomic SIC potential is introduced for each angular momentum in a way similar to the SIC potential for atoms [17] as follows ... 

In this chapter we give a brief review of some of the basic concepts of quantum mechanics with emphasis on salient points of this theory relevant to the central theme of the book. We focus particularly on the electron density because it is the basis of the theory of atoms in molecules (AIM), which is discussed in Chapter 6. The Pauli exclusion principle is also given special attention in view of its role in the VSEPR and LCP models (Chapters 4 and 5). We first revisit the perhaps most characteristic feature of quantum mechanics, which differentiates it from classical mechanics its probabilistic character. For that purpose we go back to the origins of quantum mechanics, a theory that has its roots in attempts to explain the nature of light and its interactions with atoms and molecules. References to more complete and more advanced treatments of quantum mechanics are given at the end of the chapter. 

In this expression, the term hydrogen atoms A and B. The term interaction with the electrons interchanged. However, the term A2 represents both electrons 1 and 2 interacting with nucleus A. That means the structure described by the wave function is ionic, HA HB+. In an analogous way, the term B1 Bj2 represents both electrons interacting with nucleus B, which corresponds to the structure HA+ Hb . Therefore, what we have devised for a molecular wave function actually describes the hydrogen molecule as a "hybrid" (a valence bond term that is applied incorrectly) of... 

Only for a special class of compound with appropriate planar symmetry is it possible to distinguish between (a) electrons, associated with atomic cores and (7r) electrons delocalized over the molecular surface. The Hiickel approximation is allowed for this limited class only. Since a — 7r separation is nowhere perfect and always somewhat artificial, there is the temptation to extend the Hiickel method also to situations where more pronounced a — ix interaction is expected. It is immediately obvious that a different partitioning would be required for such an extension. The standard HMO partitioning that operates on symmetry grounds, treats only the 7r-electrons quantum mechanically and all a-electrons as part of the classical molecular frame. The alternative is an arbitrary distinction between valence electrons and atomic cores. Schemes have been devised [98, 99] to handle situations where the molecular valence shell consists of either a + n or only a electrons. In either case, the partitioning introduces extra complications. The mathematics of the situation [100] dictates that any abstraction produce disjoint sectors, of which no more than one may be non-classical. In view if the BO approximation already invoked, only the valence sector could be quantum mechanical9. In this case the classical remainder is a set of atomic cores in some unspecified excited state, called the valence state. One complication that arises is that wave functions of the valence electrons depend parametrically on the valence state. 

The interaction of even simple diatomic molecules with strong laser fields is considerably more complicated than the interaction with atoms. In atoms, nearly all of the observed phenomena can be explained with a simple three-step model [1], at least in the tunneling regime (1) The laser field releases the least bound electron through tunneling ionization (2) the free electron evolves in the laser field and (3) under certain conditions, the electron can return to the vicinity of the ion core, and either collisionally ionize a second electron [2], scatter off the core and gain additional kinetic energy [3], or recombine with the core and produce a harmonic photon [4]. 

In the case of iron, magnetism is due to the unpaired electrons in the 3d-orbitals, which have all parallel spin. These electrons interact with all other electrons of the atom, also the s-electrons that have overlap with the nucleus. As the interaction between electrons with parallel spins is slightly less repulsive than between electrons with anti parallel spins, the s-electron cloud is polarized, which causes the large but also highly localized magnetic field at the nucleus. The field of any externally applied magnet adds vectorially to the internal magnetic field at the nucleus. 

Now, to return to the orange stain, formed on the surface of a pan by adsorption of capsaicin from a solution (the curry). Such organic dyes are usually unsaturated (see the structure I above), and often comprise an aromatic moiety. The capsaicin, therefore, has a high electron density on its surface. During the formation of the adsorption bond, it is common for this electron cloud to interact with atoms of metal on the surface of the pan. Electron density flows from the dye molecule via the surface atoms to the conduction band of the bulk metal. The arrows on Figure 10.4 represent the direction of flow as electron density moves from the charge centroid of the dye, through the surface atoms on the substrate, and thence into the bulk of the conductive substrate. 

Figure 3. Spin levels for an electron interacting with the N atom (1=1) in the nitroxide radical. The three allowed transitions generate an ESR spectrum with hyperfine splitting, A.

With this technique, under an especially equipped electron microscope, high-energy electrons are focused on a fine probe and directed at the point of interest in the specimen. The electrons interacting with the sample atoms cause the emission of the characteristic X-rays, which are detected and identified for qualitative analysis and used, generally through suitable standardization, to perform also a quantitative analysis. 

The mechanism by which electrons interact with crystals is different from that of X-rays. X-rays detect electron density distribution in crystals, while electrons detect electrostatic potential distribution in crystals. Electron crystallography may be used for studying some special problems related to potential distribution such as the oxidation states of atoms in the crystal. 

Electron interacts with an atom by the Coulomb potential of the positive nucleus and electrons surrounding the nucleus. The relationship between the potential and the atomic charge is given by the Poisson equation ... 

In Auger transitions, incident electrons interact with the inner shell electrons E of the sample. The vacancy created by an ejected inner shell electron is filled by an outer shell electron (Ei), and a second outer shell electron ( 2) is ejected leaving the atom in a doubly ionized state. The electrons ejected from the outer shells are called Auger electrons, named after the Frenchman Pierre Auger, who discovered the effect. Thus, AES measures the energies of the Auger electrons ( a) emitted from the first 10 A of a sample surface. The energy equation is expressed as... 

By the time Bohr turned his attention to the problem, significant advances had been made. Physicists working with the old quantum theory had developed a number of rules about the manner in which electrons interacted with one another. Bohr realized that these rules could be used to confirm Kossel s hypothesis and to make informed guesses about the atomic structure of the elements. For example, hydrogen has one electron, placed in the innermost shell. Helium, having two electrons, has this shell filled up. Thus lithium, the third element, has to have two electrons in an inner shell and one with an... 

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