Flexibility descriptors

The possibility of rotation of some groups of atoms around some chanical bonds is intuitively associated with molecular flexibility. Consequently, the number of rotatable bonds and the percentage of rotatable bonds are the simplest descriptors that measure the molecular flexibility. More complicated formulas calculate flexibility descriptors by weighting some topological descriptors therefore, they consider the shape and size of the molecules, the number of atoms, and the sum of bond orders (Tarko 2004c). 

W=Wiener topological index N=number of heavy atoms 

S=bond order sum (all bonds which bond heavy atoms) 

Much utilized is the Kier flexibility index (Kier 1990), defined as a weighted product of some shape indices of the molecules. 

Pt is the number of topological routes, of length equal to k steps, that can be taken on the graph of the molecule Pj (k= 1) is the number of chemical bonds in the molecule 

---

Flexible optimal descriptors have been defined as specific modifications of adjacency matrix, by means of utilization of nonzero diagonal elements (Randic and Basak, 1999, 2001 Randic and Pompe, 2001a, b). These nonzero values of matrix elements change vertex degrees and consequently the values of molecular descriptors. As a rule, these modifications are aimed to change topological indices. The values of these diagonal elements must provide minimum standard error of estimation for predictive model (that is based on the flexible descriptor) of property/activity of interest. 

Tarko, L., 2004c. Molecular flexibility descriptors for QSAR calculations. Rev. Chim. 

Flexible Descriptors Obtained via Optimization of Correlation Weights of Local Graph Invariants... 

Table 14 Statistical characteristics for models obtained using different definitions of flexible descriptors...

---