Electron configurations INDEX

Information on the electronic configuration of each nonhydrogen atom is incorporated in the second order atomic index (S ) of the atom. 

Its counterpart, the first-order ( y") valence molecular connectivity index, is also calculated from the non-hydrogen part of the molecule and was suggested by several authors [103,276,277]. In the valence approximation, non-hydrogen atoms are described by their atomic valence <5 "values, which are calculated from their electron configuration by the following equation ... 

It is generally believed then that with metals the electronic configuration, in particular the catalytic activity [21], In this theory it is believed that in the absorption of the gas on the metal surface, electrons are donated by the gas to the d-band of the metal, thus filling the fractional deficiencies or holes in the d-band. Obviously, noble metal surfaces are particularly best for catalytic initiation or ignition, as they do not have the surface oxide layer formation discussed in the previous sections. 

Define the functional U(Q [v[/])=q integration over the electronic configuration space is indicated as a sub-index. The variational principle applied [6] to the (spin-free) function space v /(q) leads to the Euler-Lagrange equation ... 

Anatomic is dependent on the total number of atoms of given types, with electronic configurations specified by appropriate pairs of atomic indexes. The terms on the right-hand side of Eq. (18) not been defined earlier are as follows ... 

As can be seen, this index attains its maximal value of unity for two identical structures (9 = 9,

monotonously decreases. The use of this index for the formulation of the least motion principle arises from the following simple idea. Let us assume that we are on a reaction path at point characterised by the wave function P(, q> ) and we are looking for such an infinitesimally close structure (9, (p) for which the transformation (9,

requires minimal change in electronic configuration. This condition is equivalent to a search of the direction along which the derivative of K at the point = 9 and q> = q> attains its minimum. This directional derivative can be mathematically described as (27),... 

The second atomic index [Figure 2.2(b)] is the valence connectivity index 8V, incorporating information on details of the electronic configuration of each non-hydrogen atom. Its value for the lowest oxidation states of the elements will generally be assigned by Equation 2.1 [2], where Zv is the number of valence electrons of an atom, NH is the number of hydrogen atoms bonded to it, and Z is its atomic number (i.e., Z equals Zv plus the number of inner shell electrons). 

The recent interest in electronic factors in catalysis has produced two significant theories. The first is that with the metals the electronic configuration, in particular of the d-band, is an index of catalyst activity. The second is that with the oxides, activity may be controlled by the semiconducting property. Hitherto, these theories have been regarded as unrelated to one another. 

Whereas the index r characterizes the electron reorganization by one value expressing the total difference of electron configurations of the reactant and the product, the index J expresses the same difference not by the total but by the mean value along the concerted reaction path. 

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