Valence delta value

The valence-delta value, 6V, is calculated from the atomic electron configuration as follows ... 

Kier, L.B. and Hall, L.H. (1983b). General Definition of Valence Delta-Values for Molecular Connectivity. J.Pharm.ScL, 72,1170-1173. 

For atoms beyond fluorine, the principal difference among family members is the number of core electrons. The valence delta value must explicitly take this factor, Z - Z, into account. (Z is the atomic number.)... 

The key to useful topological state values is an appropriate form for the r, values. Hall and Kier have shown that simple forms, such as the graph distance d,j, are not useful because they fail to indicate proper topological equivalence. To ensure representation of topological equivalence, two features of the paths must be encoded (1) atomic identity and (2) the sequence of atoms in each path. It has been shown that both these characteristics can be encoded as follows. Atomic identity can be encoded using the molecular connectivity valence delta value, 8. The discussions concerning chi indexes and related quantities have shown the validity of the valence delta value as a characterization of atoms. 

L.B. Kier, L.H. Hall, General definition of valence delta-values for molecular connectivity, J. Pharm. Sci. 1983, 72, 1170- 3. 

Many of the descriptors which can be calculated from the 2D structure rely upon the molecular graph representation because of the need for rapid calculations. Kier and Hall have developed a large number of topological indices, each of which characterises the molecular structure as a single number [Hall and Kier 1991]. Every non-hydrogen atom ir the molecule is characterised by two delta values, the simple delta Si and the valence delta SJ ... 

MCIs are calculated from the hydrogen suppressed skeleton of a molecule. First, each non-hydrogen atom is assigned a delta value (8). For simple indices, 8 is equal to the number of atoms to which it is bonded for valence indices, 8 values are based upon the number of valence electrons not involved in bonds to hydrogen atoms. Simple and valence indices of different orders and types can be calculated for a given molecule. 

The perturbation delta value was defined in terms of the valence vertex degree 5 modified by the atomic environment as [Gombar, Kumar et al, 1987]... 

With these considerations as a general background, let us summarize our approach. In the molecular connectivity approach, the molecule is represented by the hydrogen-suppressed graph. The key feature in the quantitation of the graph is the characterization of the atom in the molecular skeleton. The molecular connectivity method explicitly introduces the electronic character of atoms into the graphic representation of molecules. Atom identity is specified through the molecular connectivity delta values the simple delta, 6, and the valence delta,... 

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. 

The Feynman diagram for the simplest annihilation event shows that annihilation is possible when the two particles are Ax h/mc 10 12 5 m apart, and that the duration of the event is At h/mc2 10-21 s. The distance is the geometric mean of nuclear and atomic dimensions, which is probably not significant. The distance is so much smaller than electronic wave functions that it may be assumed to be zero in computations of annihilation rates. The time is so short that, during it, a valence electron in a typical atom or molecule moves a distance of only ao/104, so that a spectator electron can be assumed to be stationary and the annihilating electron can be assumed to disappear in zero time. Thus the calculation of annihilation rates requires the evaluation of expectation values of the Dirac delta function, and the relaxation of the daughter system (post-annihilation remnant) can be understood with the aid of the sudden approximation [4], These are both relatively simple computations, providing an accurate wave function is available. 

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