Topological Indexes

Molecular Topological Index The molecular topological index (MTI) is derived from v, calculated as the sum of D and A premultiplied by the row vector v [11]  

---

An index with extremely low degeneracy (i.e., where no degenerate structures have been observed yet) [6], the Charge-related Topological Index (CTI), has been proposed by one of the authors (l.B.) (Figure 6-1). It has a potential-like form (Eq. (4)). 

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. 

Estimation of the influence of end groups by using their topological indexes, Oq and E, has been proposed. The first parameter, Oq, characterizes the shift of the MO modes and the level positions of a PMD containing end groups relative to unsubstituted polymethines. Thus it corresponds to the end-group basicity concept (7). The parameter Oq was found to be related directiy to the electron donor ability 1 = lim ( q. The other index, E,... 

The perturbation of the PMD symmetry is accompanied by a decrease in the charge alternation and by the appearance of bond alternation from one end group to another. The bond alternation ampHtude has been revealed to be proportional to the asymmetry degree, which can be calculated as the difference of topological indexes = 4>gj — 4>gg. The effect is maximum if Tgj > 45° and Tgg < 45°. If A4>j2 = 90°, the ideal polyene state is... 

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). 

Balaban, A. T. Highly discriminating distance-based topological index. Chem. Phys. Lett. 1982, 89. 399 04. 

Schultz MTI by valence vertex degrees Gutman Molecular Topological Index Gutman MTI by valence vertex degrees Xu index... 

Silica plates were activated at 120°C for 30 min then cooled in a desiccator. Separations were performed with dichloromethane-methanol mixed in various volume ratios. C18 plates were not pretreated and separation was carried out with mixtures of acetone-water. It was established that both adsortion and RP-TLC can be applied for the separation of tetraphenylporphyrin pigments. Topological indexes may help the better understanding the physicochemical procedures underlying the separation [309],... 

Junkes, B. S., Amboni, R. D. M. C., Yunes, R. A., Heinzen, V. E. F. Anal. Chim. Acta All, 2003, 29-39. Prediction of the chromatographic retention of saturated alcohols on stationary phases of different polarity applying the novel semi-empirical topological index. 

When we are truly clueless, we can nevertheless rely on intuition to propose an ad hoc set of structural and related property parameters for the correlation. We may be lucky and find the hidden variable by chance, and we may be inspired. An example is the topological index, which describes how carbon atoms are connected together, and was proposed in the hope that it would correlate a large range of molecular properties. 

This method is similar to the group contribution method (GCM) when the descriptor is the number of functional groups in a molecule. More often in the literature, the descriptors are based on the connectivity of the atoms in a highly elaborate manner. There are frequently no theoretical justifications to connect a topological index to a property, so they should be extrapolated with caution and vigilance. 

Balaban applied 47a b> a Randic-type formula (7) to distance sums instead of vertices and created thereby the most discriminating (least degenerate) topological index proposed so far ... 

For acyclic graphs only, if in the above formula only distances between endpoints are taken into account, the related endpoint mean square topological index Df1 results. 

A combined topological index, named superindex, SI, consisting of a number of topological indices was, proposed.88 Three versions of SI have been presented ... 

---