Core electrons coordinate

Flere we distinguish between nuclear coordinates R and electronic coordinates r is the single-particle kinetic energy operator, and Vp is the total pseudopotential operator for the interaction between the valence electrons and the combined nucleus + frozen core electrons. The electron-electron and micleus-micleus Coulomb interactions are easily recognized, and the remaining tenu electronic exchange and correlation... 

XAS data comprises both absorption edge structure and extended x-ray absorption fine structure (EXAFS). The application of XAS to systems of chemical interest has been well reviewed (4 5). Briefly, the structure superimposed on the x-ray absorption edge results from the excitation of core-electrons into high-lying vacant orbitals (, ] ) and into continuum states (8 9). The shape and intensity of the edge structure can frequently be used to determine information about the symmetry of the absorbing site. For example, the ls+3d transition in first-row transition metals is dipole forbidden in a centrosymmetric environment. In a non-centrosymmetric environment the admixture of 3d and 4p orbitals can give intensity to this transition. This has been observed, for example, in a study of the iron-sulfur protein rubredoxin, where the iron is tetrahedrally coordinated to four sulfur atoms (6). 

Fig. 2. The potential energy surface for the electron motion from a donor to an acceptor in a condensed medium. U,t(r) and Ut, (r) are the potentials of the cores of the donor and the acceptor, the rest of the potentials are created by the molecules of the medium r is the electron coordinate, and R is the distance between the donor and the acceptor. The broken horizontal line corresponds to the under barrier electron motion from the donor to the acceptor. I is the height of the barrier for tunneling.

First, valence and core electrons are formally identical however, the separation of valence and core electron density is dictated by the standard view of atomic physics. Thus for an ion at j, coordinates r-hi are assigned to the z z electrons designated as core electrons, the understanding being that the states of the system are such that < r , >1/2 is a small quantity (< a0). 

Here Z is the core charge on A (e. g. the nuclear charge less the number of inner core electrons), Pu is the total charge on atom A, is the cartesian coordinate of atom A, and Z x is the Slater orbital exponent for 2 s and 2 p orbitals of atom A. 

At energies above the edge, core electrons are excited to continuum states, and the spectrum becomes dominated by scattering phenomena, similarly as in EXAFS. Flence, in a qualitative sense, the shape of the XANES spectrum depends straightforwardly on the states that are available to the excited electron. These depend on several factors, such as the coordination of the atom (octahedral, tetrahedral, etc.), its mode of bonding, oxidation state, the density of states in the electron band, etc., which give XANES its great chemical sensitivity. 

The LCAO tight-binding (Hartree-Fock) method and its successor, the density-functional theory (DFT), were used originally to solve electronic structure problems. More recently, both have been applied to the calculation of total energy, which includes contributions due to core-core, core-electron, and electron-electron interactions. By varying the coordinates of the core, the dependence of the total energy on the core coordinates can be examined. This is referred... 

The locations of the preedge absorptions and of the shape resonances of both spectra on the energy scale are very similar to those found in triphenylphosphite and triphenylphosphate, respectively. This illustrates that transistions of core electrons are mainly influenced by effects of the first coordination shell. In general, the location of the white line is characteristic for the local environment of the atom under consideration. 

To incorporate these qualitative ideas into a quantitative account of covalent binding the Heitler-London (HL) prescription is most effective. It must be formulated in terms of two monopositive cores at coordinates and X, and two electrons of which the coordinates are represented by ri and r2. The Coulombic interaction between these particles is expressed as... 

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