Structural information electron propagation

The micrograph or the image obtained on an EM screen, photographic film, or (more commonly today) a CCD is the result of two processes the interaction of the incident electron wave function with the crystal potential and the interaction of this resulting wave function with the EM parameters which incorporate lens aberrations. In the wave theory of electrons, during the propagation of electrons through the sample, the incident wave function is modulated by its interaction with the sample, and the structural information is transferred to the wave function, which is then further modified by the transfer function of the EM. 

The interference effects resulting from electron propagation are responsible for providing the desired structural information in all the techniques discussed here. The extraction of structural information, therefore, requires a knowledge of the electron wavelengths and of any phase shifts that may occur in electron emission and electron-atom scattering. Failure to understand these processes can result in quite erroneous results. 

As the X-ray energy is increased beyond that required for promotion of the core electron, ejection of core electrons into the continuum occurs. This ejected electron propagates from the Mn center until it encounters another atom from which it can be back-scattered. The interference of back-scattered waves with propagating waves leads to an interference pattern that is manifested as an oscillation in the X-ray absorption pattern. Fourier transformation of this oscillating spectrum from the frequency domain to the distance domain gives a new spectrum whose abscissa contains information on the distance between the target atom (i.e., the Mn center) and the back-scattering atoms. This second technique is called Extended X-ray Absorption Fine Structure, EXAFS, and has been the only spectroscopic tech-... 

While this review discloses the kinetic and stereochemical features of soluble Ziegler-Natta catalysts, we have little information on the structure of the active center. The steric environments of active centers must be very important in determining the monomer reactivity, regiospecificity and stereospecificity of soluble catalyst. The influence of ligands such as the aluminum components on the rates of chain propagation and chain-terminating steps should be correlated to the electronic structure of... 

Reflection at a surface of a beam of linearly polarized photons alters the direction and amplitude of the electric and magnetic vectors. It is these differences between incident and reflected beams that give information concerning surface structure, as they depend on the interaction of the beam with the electronic distribution and with the associated local electric and magnetic fields on the surface. The phase and amplitude change for the vectors is different for the component parallel to the plane of incidence than for the component perpendicular to it. The result is a vector that follows a spiral during its propagation, and is referred to as elliptically polarized, Fig. 12.2. A deeper treatment of these optical properties can be found in Ref. 9. Such measurements are referred to as specular reflectance. 

In empirical force-fields calculations, the information about the electronic system is entirely contracted in the data of the ground state potential energy surface and forces acting on the nuclei. Model potentials and forces are then used to propagate the ionic dynamics, instead of performing an electronic structure calculation. This on the fly quantum calculation is the challenging part of first-principle Molecular Dynamics simulations. 

Electronic structure calculations of the type described above, provide the energy and related properties of the system at the absolute zero of temperature and do not account for any time-dependent effect. In some cases, temperature and/or time scale effects may be important and must be included. The appropriate theoretical approach is then molecular dynamics (MD) either in the classical or ab initio implementations. In the first approach, Newton s motion equations are solved in the field of a potential provided externally, which constitutes the main limitation of this approach. To overcome this problem, ab initio Molecular Dynamics (AIMD)94,95 solves Newton s motion equations using the ab initio potential energy surface or propagating nuclei and electrons simultaneously as in the Car-Parrinello simulation.96 The use of AIMD simulations will increase considerably in the future. In a way they furnish all the information as in classical MD, but there are no assumptions in the way the system interacts since the potential energy surface is obtained in a rather crude manner. 

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