Electronic Approach

Another example of the difficulty is offered in figure B3.1.5. Flere we display on the ordinate, for helium s (Is ) state, the probability of finding an electron whose distance from the Fie nucleus is 0.13 A (tlie peak of the Is orbital s density) and whose angular coordinate relative to that of the other electron is plotted on the abscissa. The Fie nucleus is at the origin and the second electron also has a radial coordinate of 0.13 A. As the relative angular coordinate varies away from 0°, the electrons move apart near 0°, the electrons approach one another. Since both electrons have opposite spin in this state, their mutual Coulomb repulsion alone acts to keep them apart. 

It should be stated that eqs. (3) through (21) are general in that they do not require a rr-electron approximation and do not represent directly any specific computational method. In the rr-electron approach with Pople s approximations, the F matrix elements become those below. 

Using the ab initio EM method, the steric ratio is taken as the calculated cross section for electron approach along the molecular axis towards the positive end of the dipole divided by that for approach towards the negative end of the dipole. The model predicts a steric ratio of 1.41 for the total ionization of CH3C1 that is, both the sign and magnitude are in accord with the experimental measurements. The... 

Figure 11. Ionization surfaces for CH3CI (a) for an electron approaching the Cl-end of the molecule (b) for an electron approaching the Cbb-end of the molecule.

It can be shown, from wave-mechanical calculations, that the Is orbital (quantum numbers n = 1, Z = 0, m = 0, corresponding to the classical K shell) is spherically symmetrical about the nucleus of the atom, and that the 2s orbital (quantum numbers n = 2, Z = 0, m = 0) is similarly spherically symmetrical, but at a greater distance from the nucleus there is a region between the two latter orbitals where the probability of finding an electron approaches zero (a spherical nodal surface). 

When a gamma produces an electron, the electron moves rapidly toward the positively charged central wire. As the electron nears the wire, its velocity increases. At some point its velocity is great enough to cause additional ionizations. As the electrons approach the central wire, the additional ionizations produce a larger number of electrons in the vicinity of the central wire. 

The operation voltage causes a large number of ionizations to occur near the central electrode as the electrons approach. 

An important difference between classical and quantum particles is the way they interact with potential barriers. It is a principle of classical mechanics that the only way to overcome a potential barrier is with sufficient energy. Quantum-mechanically this is not always the case. The effect is illustrated by a beam of particles (e.g. electrons) approaching a potential barrier. 

In neither the mechanical nor the electronic approaches is the beam perfectly sharp. This is inevitable since the aperture of the system is finite in extent. In the case of the electronic array, this problem is compounded by the fact that the array has discrete elements, rather than a continuum. However, in the latter case it is controllable. As a result of this imperfection, again the scene is blurred in this case... 

A third approach within the newly defined physical chemistry was to prove crucial to dealing with the old problems of affinity and reaction mechanisms. Like thermodynamics and radiation theory, it promised and eventually delivered a conceptual framework that constituted a truly theoretical chemistry. At the same time, this new ionic and electronic approach to chemical explanation served as an important testing ground for theoretical physicists primarily concerned with the physics tradition of ether- and electrodynamics. Helmholtz,... 

Whereas the one-electron exponential form Eq. (5.5) is easily implemented for orbital-based wavefunctions, the explicit inclusion in the wavefunction of the interelectronic distance Eq. (5.6) goes beyond the orbital approximation (the determinant expansion) of standard quantum chemistry since ri2 does not factorize into one-electron functions. Still, the inclusion of a term in the wavefunction containing ri2 linearly has a dramatic impact on the ability of the wavefunction to model the electronic structure as two electrons approach each other closely. 

This set of first-order differential equations can be solved, approximately or numerically, for a specific system. The theory has been applied to Li scattered from Cs/W, and gives more satisfactory agreement with experiment than does the one-electron approach. 

Nevertheless, the one-electron approach does have its deHciencies, and we believe that a major theoretical effort must now be devoted to improving on it. This is not only in order to obtain better quantitative results but, perhaps more importantly, to develop a framework which can encompass all types of charge-transfer processes, including Auger and quasi-resonant ones. To do so is likely to require the use of many-electron multi-configurational wavefunctions. There have been some attempts along these lines and we have indicated, in detail, how such a theory might be developed. The few many-electron calculations which have been made do differ qualitatively from the one-electron results for the same systems and, clearly, further calculations on other systems are required. 

When a neutral molecule interacts with an electron of high kinetic energy, the positive radical ion is generated by El. If the electrons have less energy than the IE of the respective neutral, El is prohibited. As the electrons approach thermal energy, EC can occur instead. Under EC conditions, there are three different mechanisms of ion formation [65,75-77]... 

As the electron approaches the molecule, an electric field is established that is described in terms of a Coulomb potential, (()(-. It is assumed that when the Coulomb potential reaches the electron transition energy (the ionization potential, Eq) the orbital electron involved in the transition absorbs energy from the field, the efficiency of the ionization depending on the transition probability, F, .. When the electron-induced dipole contribution is neglected, a cross section, which will be an underestimate, can be calculated from the interparticle separation when (()(- = Eq. In order to deduce the maximum ionization cross section, a., the transition probability P,. must be taken into account ... 

The results of the electron theory as developed for semiconductors are fully applicable to dielectrics. They cannot, however, be automatically applied to metals. Contrary to the case of semiconductors, the application of the band theory of solids to metals cannot be considered as theoretically well justified as the present time. This is especially true for the transition metals and for chemical processes on metal surfaces. The theory of chemisorption and catalysis on metals (as well as the electron theory of metals in general) must be based essentially on the many-electron approach. However, these problems have not been treated in any detail as yet. 

The possibility of adsorption on a virtual exciton was indicated by E. L. Nagayev (.14) on the simplest example of the adsorption of a one-electron atom. This problem is an example of the many-electron approach in chemisorption theory. Recently, V. L. Bonch-Bruevich and V. B. Glasko (16) have treated adsorption on metal surfaces by the many-electron method. 

In the absence of an external field, electrons in the metal are confronted by a semi-infinite potential barrier (upper solid line in Fig. la), so that escape is possible only over the barrier. The process of thermionic emission consists of boiling electrons out of the Fermi sea with kinetic energy > x + M- The presence of a field F volts/cm. at and near the surface modifies the barrier as shown. It follows from elementary electrostatics that the potential V will not be noticed by electrons sufficiently far in the interior of the metal. However, electrons approaching the surface are now confronted by a finite potential barrier, so that tunneling can occur for sufficiently low and thin barriers. 

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