Valence electrons INDEX

The values 1/V(dj dj) are for the atoms i and j, which make up this bond, and the connectivity index, x, is obtained as the sum of the bond connectivities. In molecules containing heteroatoms, the d values were considered to be equal to the difference between the number of valence electrons (E") and the number of hydrogen atoms (hi). Thus, for an alcoholic oxygen atom, d = 1, and d = 5. The valence connectivity-index, y can then be calculated the use of removes redundancies that can occur through the use of y alone. The calculation of connectivity indices and for the case of two isomeric heptanols is as follows. 

Kier and Hall noticed that the quantity (S -S) jn, where n is the principal quantum number and 5 is computed with Eq. (2), correlates with the Mulliken-Jaffe electronegativities [19, 20]. This correlation suggested an application of the valence delta index to the computation of the electronic state of an atom. The index (5 -5)/n defines the Kier-Hall electronegativity KHE and it is used also to define the hydrogen E-state (HE-state) index. 

The concept of the molecular connectivity index (originally called branching index) was introduced by Randic [266]. The information used in the calculation of molecular connectivity indices is the number and type of atoms and bonds as well as the numbers of total and valence electrons [176,178,181,267,268]. These data are readily available for all compounds, synthetic or hypothetical, from their structural formulas. All molecular connectivity indices are calculated only for the non-hydrogen part of the molecule [269-271]. Each non-hydrogen atom is described by its atomic 6 value, which is equal to the number of adjacent nonhydrogen atoms. For example, the first-order Oy) molecular connectivity index is calculated from the atomic S values using Eq. (38) ... 

Obviously, these values of the refractive index are not physically acceptable. Eor instance, a zero value for n leads to an infinite phase velocity (v = cjn). The physical meaning of this infinite phase velocity is that all valence electrons are oscillating in phase for frequencies below while for frequencies larger than oop this coherence is broken and the plasma is formed. 

Z and Hj are the number of valence electrons of the atom i, and, respectively, the number of hydrogen atoms attached to this atom. The resulted connectivity index "Xr is given by ... 

In non-polar, isotropic crystals or in glasses, there is no crystallographic direction distinguished and the linear electro-optic effect is absent. Nevertheless a static field may change the index by displacing ions with respect to their valence electrons. In this case the lowest non-vanishing coefficients are of the quadratic form, i.e. the refractive index changes proportionally to the square of the applied field Kerr effect . 

The relation between this definition and the mathematical expression of and IIP values (Equation 5.13 and Equation 5.14) can be easily seen. The simple represents the vertex valence (a number of skeletal neighbors for each vertex). It can be presented as both = = k - h, and = - h, after the substitution of the number of valence electrons k with the number of electrons assigned to sigma orbitals . It is evident from Equation 5.15 that the greater the number of skeletal neighbors, the larger the value and the lower the connectivity index. Recently, new arguments were evaluated in support of the thesis that the molecular connectivity indices represent molecular accessibility areas and volumes (Estrada, 2002). 

The superdelocalizability of an atom in a molecule provides another measure of the tendency of the molecule to be attacked by an electrophile or nucleophile. It is related to electron density on that atom. The electrophilic superdelocalizability for a given atom k in the molecule may be defined as a sum over occupied MOs (index i) and valence AOs (index r), Eq. [14]. 

These summarize topological information about a molecule with atomic properties [39]. A molecular E-state index is expressed as a sum of atomic E-state indices, which are composed of two parts. First is the intrinsic atomic part, and second is perturbation, which depends on its neighborhood (other atoms in the structure). The intrinsic part includes information about the a- and 7r-orbitals, lone pairs, hydrogen atoms attached to heavy atoms, and the principal quantum numbers of valence electrons. The perturbation part is a sum of all other atomic parts modified by fimction, which descends with distance. 

The Pariser-Parr-Poplc (PPP) method is based on three assumptions (a) Whenever the factor, (n), (n) (where i n is any electron index) appears in the integrand the integi al vanishes zero differential overlap approximation) (b) The resonance integrals between nearest neighbours are treated as empirical parameters those between non-neighbours are neglected (c) The one-centre Coulomb integrals ii, it) are taken to be equal to /, — E where I, and E, are the ionization potential and electron affinity, respectively, of the atomic orbital tpi, when the atom is in the appropriate valence state. 

Molecular descriptor proposed as the sum of atomic properties, accounting for valence electrons and extended connectivities in the H-depleted molecular graph using a Randic connectivity index-type formula [Lohninger, 1993] ... 

The intrinsic state of an atom can be simply thought of as the ratio of k and lone pair electrons to the count of the a bonds in the molecular graph for the considered atom. Therefore, the intrinsic state reflects the possible partitioning of non-o electrons influence along the paths starting from the considered atom the less partitioning of the electron influence, the more available are the valence electrons for intermolecular interactions. From the intrinsic state the -> Q polarity index was derived. 

ETA indices are an extension of the TAU indices (or Topochemically Arrived Unique indices) [Pal, Purkayastha et al, 1992 Pal, Sengupta et al, 1988,1989,1990], which were defined some years before in the framework of a previous version of the Valence Electron Mobile environment (VEM environment). TAU indices are calculated from previous definitions of core count and VEM count and include four indices the composite topochemical index, denoted by T (similar to the composite ETA index), the functionality index, denoted by F, the skeletal index, denoted by Tr, and the simple branching index, denoted by B. In QSAR studies, these indices were used in combination with —> STIMS indices, connectivity indices, and some information indices [Roy, Pal et al, 1999, 2001]. 

Unlike the index of hydrogen deficiency, the degree of unsaturation has the same value for any structural representation corresponding to a molecular formula and can be calculated for much variety of structure representations. In this approach, the valence electrons of an element are partitioned into bond electrons and electrons localized on an atom, as shown in Table M14. 

Moreover, the same index was also calculated from a variant of the matrix S, defined in terms of the total energies of valence electrons of vertices as [Yang, Wang et al, 2003a]... 

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). 

Combined descriptors attempt to put more than one type of information into the same descriptor. For instance, the electronic-topological descriptor, used by Katritzky and Gordeeva [83], is an electronic version of the valence connectivity index. The work by Stanton and Jurs [84] has produced over 25 combined descriptors based on charged partial surface areas. Other descriptors are mentioned in the review by Brown [1]. 

This pair of delta values is seen as a characterization of the atom in its valence state. The simple delta, 5, describes the role of the atom in the skeleton in terms of its connectedness and count of sigma electrons it could be called the sigma electron descriptor. The valence delta, 8, encodes the electronic identity of the atom in terms of both valence electron count and core electron count. It could be called the valence electron descriptor. The isolated, unbonded atom may be thought of as characterized by its atomic number, Z, and the number of valence electrons, Z. In its valence state, the bonded atom is characterized by 8 and 8. Embedded in the molecular skeleton, the full characterization of the atom in the environment of the whole molecule is given by the topological equivalence value, described in a later section, and the electrotopological state value, presented separately.A representation of the whole molecule is accomplished by the combination of chi, kappa, and topological state indexes. 

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