THE VALENCE REGION OF MOLECULES

The valence region of molecules and of the isolated ground-state atoms or ions are described by the same formula, Eq. (3.27). For isolated atoms, of course, we use = 0, = 0, and Fnn = 0- The description presented here for the molecules... 

The nature of the final state depends upon the energy, hv, of the exciting photons. In X-ray photoelectron spectroscopy (XPS) the exciting photons are provided by sources such as A1 Ka (1,486 eV) or Mg Ka (1,253 eV) and excitation of the core electrons of the molecules is observed. In UV photoelectron spectroscopy (UPS), Hel (21.2eV) or Hell (40.8 eV) radiation is used and excitation from the valence region of the neutral molecule is observed. XPS and UPS are surface-sensitive techniques, which are capable of providing extremely useful information on the chemical nature of a surface or interface and, in the case of the XPS, the conformational state of the molecules at the surface [64]. 

Z] is considered together with its core electrons Nl- This amounts to a corevalence partitioning of atom k in the molecule its valence region now consists of all the electrons except and of all the other nuclei. At this stage it is not taken into account that the other nuclei—those embedded in the valence region of atom k—may possess core electrons of their own. 

Consideration of the valence region of a ground-state molecule leads to a formula for the energy of atomization in an approximation akin to the Thomas-Fermi model. The final result, from Eq. (10.33), is... 

It is also possible, although not trivial, to define a local hardness. ° It has been shown that this local hardness can be approximated reasonably in the valence region of the atom or the molecule as ° ... 

G [H-Xe] Split valence 2 sets of functions in the valence region provide a more accurate representation of orbitals. Use for very large molecules for which 6-31G(d) is too expensive. 9 2 6D... 

We often refer to Heitler and London s method as the valence bond (VB) model. A comparison between the experimental and the valence bond potential energy curves shows excellent agreement at large 7 ab but poor quantitative agreement in the valence region (Table 4.3). The cause of this lies in the method itself the VB model starts from atomic wavefunctions and adds as a perturbation the fact that the electron clouds of the atoms are polarized when the molecule is formed. 

The hnal step considers all the nuclei with their own core electrons, meaning that all the remaining electrons shall be regarded as the valence electrons of the molecule. The idea is to hnd an expression for the energy of a molecule featuring the role of its electronic valence region. 

The first part of the right-hand side (RHS) of Eq. (4.17) represents the valence region energy of atom k embedded in the molecule, and the second term is the energy - VI )/jI of the ionic core k. The total energy E = E ... 

---