CDL descriptors | Topological charge index

Topological charge index

Descriptor Category : charge descriptors
c++ entity: functor

Description

The topological charge index were proposed to evaluate the charge transfer between a pair of atoms, and therefore, the global charge transfer in the molecule.
The Galvez matrix M is obtained by multiplying the adjacency matrix by the reciprocal square distance matrix. In order to avoid division by zero, the diagonal entries of the distance matrix remain the same.
An unsymmetric charge term matrix CT is derived from the matrix M. Its terms are calculated as:

CTij = delta(i) if i=j

and

CTij = mij - mji if i!=j

where mij are the elements of the M matrix, delta(i) is the vertex degree of the ith atom. The charge terms CTij are graph invariants that are related to the charge transfer between the pair of considered vertices. The diagonal elements of the CT matrix represent the the topological valence of the atoms; the off diagonal entries CTij represent a measure of the net charge transfer between atom j and i. For each path of lenght k, a topological charge index Gk is defined as:

**Equation 1:**Topological charge index

Where delta(k, dij) indicates the Kronecker delta: 1 if dij = k, zero otherwise.

Prototype

  template <class Molecule>
  struct topological_charge_index_lag0 : std::unary_function<Molecule,typename Molecule::calc_type> {

    result_type operator()(const Molecule& m);

  };

Where defined

morpho/cdl/descriptors/charge_descriptors.hpp

Namespace

morpho::cdl

Inherits from

std::unary_function<Molecule,typename Molecule::calc_type>

Arguments

Argument	Model of
`Molecule`	`cdl::molecule`