Topological indices values

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

Electron Level Position. One essential condition of spectral sensitization by electron transfer is that the LUMO of the dye be positioned above the bottom of the conduction band, eg, > —3.23 eV in AgBr or > —4.25 eV in ZnO (108). To provide the desired frontier level position respectively to the valence and conduction bands of the semiconductor, it is necessary to use a polymethine with suitable electron-donor abiHty (Pq. Increasing the parameter (Pq leads to the frontier level shift up, and vice versa. Chain lengthening is known to be accompanied by a decrease of LUMO energy and hence by a decrease of sensitization properties. As a result, it is necessary to use dyes with high electron-donor abiHty for sensitization in the near-ir. The desired value of (Pq can be provided by end groups with the needed topological index Oq or suitable substituents (112). 

This chapter focuses on step 3. For step 1, descriptors may include property values, biological properties, topological indexes, and structural fragments. The performance of these descriptors and forms of representation have been analyzed by Brown and Brown and Martin. Similarity searching for step 2 has been discussed by Downs and Willett characteristics of various similarity measures have been discussed by Barnard, Downs, and Willett. " For step 4, little has been published specifically about visualization and analysis of results for chemical data sets. Flowever, most publications that focus on implementing systems that utilize clustering do provide details of how the results were displayed or analyzed. 

Pyka and Sliwiok separated six esters of nicotinic acids methyl nicotinate, ethyl nicotinate, isopropyl nicotinate, butyl nicotinate, hexyl nicotinate, and benzyl nicotinate by adsorption HPLC on a LiChrospher Si 60 column. The mixtures containing benzene and methanol in volume proportions (O-i-lO, 1h-9, 2h-8, 3h-7, 4-1-6, and 5-1-5) were used as the mobile phases. The (min) values of esters investigated have been correlated with the dipole moments (/imph) of the mobile phases apphed, with numerical values of one topological index from among those based on the distance matrix (A, W, °7J, B) or the... 

Djakovic-Sekulic et al. " separated eight anilides of 2,2-dimethylpropanoic acid, nine anilides of benzoic acid, and nine anilides of ot-phenyl acetic acid by RP-18 HPLC using mixtures containing methanol and water in volume proportions 6h-4, 6.5h-3.5, and 7-1-3 as the mobile phases. The log k values of investigated anilides have been correlated with the dipole moments ( raph) or permittivities (Emph) of the mobile phases applied, with numerical values of one topological index from among those based on the distance matrix R, W, A, B, B) or on the adjacency matrix (M, M, x with... 

Djakovic-Sekulic, T. Perisic-Janjic, N. Pyka, A. Correlation or retention of anilides and some molecular descriptors. Application of topological indexes for prediction of log k values. Chromatographia 2003, 58 (1/2), 47-51. Pyka, A. Sliwiok, J. Chromatographic separation of tocopherols. J. Chromatogr., A 2001, 935, 71-76. 

A topological index defined as the absolute value of the determinant of the orbital interaction matrix of linked atoms (OIMLA) [Xu et al, 1992a Xu et al, 1992b Xu, 1992] ... 

The E-state topological parameter, denoted as TI , is derived by applying the Ivanciuc-Balaban operator to the —> Estate index values used to characterize molecule atoms [Voelkel, 1994] ... 

Generalized topological indices represent a special class of variable descriptors since each value of the variable exponent generates a different topological index however, this value is usually a priori chosen and not optimized during the modeling phase. 

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. 

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 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. 

Another index in the topological state formalism has been developed. The total topological index t, has been defined, based on a summation of the topological state T, values. 

The average relative error is 3.9%, and no observation has a relative error greater than 10%. These results are significantly better than those given by the Hansch model. Hansch and Lien > found it necessary to delete two observations to achieve r - 0.911,5 = 0.22. When the full data set is used, the statistics are even worse r = 0.878, s = 0.24. The potential value of this total topological index x is yet to be explored. Because it is a very highly discriminating index, there may be a useful role for it in QSAR. 

---