Atom Indices

B Mohney and L B Kier 1991. The Electrotopological State An Atom Index for QSAR. ntitative Structure-Activity Relationships 10 43-51. 

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

The E-state indices may define chemical spaces that are relevant in similarity/ diversity search in chemical databases. This similarity search is based on atom-type E-state indices computed for the query molecule [55]. Each E-state index is converted to a z score, Z =(% -p )/0 , where is the ith E-state atomic index, p is its mean and O is its standard deviation in the entire database. The similarity was computed with the EucHdean distance and with the cosine index and the database used was the Pomona MedChem database, which contains 21000 chemicals. Tests performed for the antiinflamatory drug prednisone and the antimalarial dmg mefloquine as query molecules demonstrated that the chemicals space defined by E-state indices is efficient in identifying similar compounds from drug and drug-tike databases. 

H2 = difference = 1 pair of hydrogen atoms Index of hydrogen deficiency = 1... 

PA pseudo-atom index to the lower left atomic number... 

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 ... 

Takacs and co-workers (3,4) calculated the Kovats index for paraffins, olefins, cyclic hydrocarbons, and homologs of benzene on the basis of molecular structures. The index was divided into three additive portions atomic index, bond index, and samplestationary phase index components. 

Fig.4 Response to 120° rotation of the middle bond, a Average change, (A0/), in bond rotation angles as a function of location relative to the central bond, b Mean angular spatial reorientation of backbone bonds as a function of location relative to the central bond, c Mean spatial displacements of backbone atoms as a function of atom index along the chain for rotating chains of 25 bonds. The length of each bond is taken as 1 A (From [15])...

Figure 13-1. The eight most stable structures of guanine in the order or decreasing stability, with the corresponding terminology. A, Im, O and H stand for amino, imino, oxo and hydroxy (see text). The atom indexation of the purine frame is given on the first tautomer. The H atoms are not drawn...

L. H. Hall, B. Mohney and L. B. Kier, The electrotopological state-an atom index for QSAR., Quantitative Structure-Activity Relationships, 1991, 10, 43-51. 

Hall, L.H., Mohney, B. and Kier, LB. (1991a) The electrotopological state an atom index for QSAR. Quant. Struct. -Act. Rdat., 10, 43—48. 

We now reintroduce the atomic index, /, and include the atomic cross section, a. Then, for the scattering intensity contribution to a given spectral band, that arising from the atom is. 

The CANON algorithm derives a ligand ranking by assigning an atomic index based on the atomic number, s.g., the higher the atomic number, the lower the atomic index (see Figure 8). 

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). 

Figure 17.5. Hydrogen-suppressed graph of the a-naphthyl group in (a) poly(a-vinyl naphthalene) and (b) poly(a-naphthyl methacrylate). The simple atomic index 8 (see Chapter 2) is shown at the vertices. The products of pairs of 8 values are shown along the edges. The two graphs differ slightly because the vertex outside the box has 8=3 in (a) and 8=2 in (b), resulting in a small difference between the contributions of the a-naphthyl unit to the first-order connectivity index Both graphs make the same contribution to the zeroth-order index °x-...

Figure 17.6. Hydrogen-suppressed graph of polyoxynaphthoate, with the value of the simple atomic index 5 indicated at selected vertices. The lack of periodicity at the boundaries of the box, which contains a subunit smaller than the full repeat unit, causes different values to be calculated for the contribution of the group enclosed in the box to 1 % if only one of the two bonds linking it to the rest of the repeat unit is considered. One of these bonds contributes (1/60.5) o.4082, and the other bond contributes (l/9°-5)=0.3333. The correct contribution of these two bonds to is the average of these two numbers, i.e., 0.5-[(l/60-5) + (l/9°-5)]=O.3708. 

Figure 11.2 Sample output from phpPgAdmin showing how coordinates and atom indexes are stored as arrays.

These topological indexes, based on the molecular connectivity approach, include three types the ""Xr molecular connectivity chi indexes that characterize the structural attributes of molecules, the ""k kappa indexes of molecular shape, and the topological equivalence state T values that individually characterize atoms and groups in the molecular skeleton and are used primarily to determine chemically equivalent atoms within a molecule. A further development of this approach has led to the electrotopological state atom indexes, which will not be discussed here but will be presented elsewhere. Molecular connectivity chi indexes are discussed in the first part of this paper along with illustrative applications. Then kappa shape indexes are discussed. The topological state index is discussed in the final section. 

V( ) represents the three components of the atom in the A th normal mode eigenvector (the atom index is omitted for simplicity)... 

Molecular control over EHS as well as performance properties were attained through a design strategy that started with the creation of a chemical library composed of 239 potential solvent candidates. Relevant platform molecnles were selected in order to fulfil a diversity of design criteria inclnding a high renewable atom index, moderate to low vapour pressure and a cost-effective synthetic accessibility (see Table 10.4). 

Molecular structure derived from renewable platform molecules (e.g. glycerol, carboxylic acids and derivatives thereof). Environmental Renewable Atom Index... 

Being the actual numerical model mainly a rationalization of the experimental facts, let s involve other estimable quantities. The IP, closely related also with the actual absolute electronegativity (4.253) definition, is a quite accessible spectral atomic index, either theoretical from the limit frequency from which the continuum spectmm is achieved, or experimentally by a Franck-Hertz experiment. Nevertheless, as far as all the valence... 

Hall and Kier investigated the possible relationship between topological indices and the partial charge computed by semiempirical MO methods The following model was obtained in a comparison of atomic indices from MO theory (partial charge) and a modified version of the chi indices. In this case the chi indices were partitioned into atomic contributions. Of course, the index is already defined as an atom index the others are given the strike-through symbol, x (equation 24) ... 

VIII. ELECTROTOPOLOGICAL STATE GRAPH-INVARIANT ATOM INDEX... 

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