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Molecular Connectivity

Chi Descriptors

The Molecular Connectivity Chi Indices

The molecular connectivity chi indices provide quantitative characterization of skeletal variation in a molecule [1,2,7]. These descriptors are based on substructure features in the molecular graph, such as bonds, clusters and rings. Each feature is weighted according to number of skeletal neighbors for each atom, the connectivity simple delta value, d. In the more general formalism, called valence molecular connectivity, the feature weights also include valence electron counts, using the valence delta value dv

The first order simple chi index is given as:

summed over all skeletal bonds.

A similar relation exists for chi indices of other orders and types [5,7].

(See the Methods and Descriptors Reference Page for a display of chi subgraphs and symbols)

The simplest and lowest level structure information is encoded in the low order chi indices, such as 1c and 2c (chi 1 and chi 2) Both structure descriptors encode degree of skeletal branching. The 1c (chi 1) index decreases with increased branching. The 2c index is more sensitive to degree of branching and also increases with increased skeletal branching. Both indices increase with atom count. More specific aspects of branching are encoded in the higher order indices. The 4cpc index characterizes adjacency of branch points in the skeleton and 6cCH (chi chain 6) characterizes six-membered rings. Chi indices that include valence state information are called valence chi indices and given a different symbol, such as in the examples below.

The first order simple and valence chi indices,  1c  and  1cv, example 1:

The 1c (chi 1) index gives identical values for each of the substituted 3-methyl pentanes shown. It does not differentiate among them. The 1cv (chi 1 valence) index gives a different value for the substituted and unsubstituted molecules as well as a different value for each type of non-H atom.

The first order simple and valence chi indices,  1c  and  1cv, example 2:

The 1c index gives an identical value for all three alcohols whereas the 1cv index gives a different value for the position of each alcohol group. Note that the 1cv value increases when the alcohol group is adjacent to a more highly saturated carbon.

The chi path cluster indices,  4cpcv

The Chi Cluster and Chi Path/Cluster Indices reflect patterns of adjacency in skeletal branching. The 4cpc (chi path/cluster 4) values for the tri-substituted benzenes in figure 4 increase as the adjacency of the substituents increases.

The chain chi indices,  6cCHv

The Chain Chi Indices encode aspects of the degree of ring substitution and cyclization in a molecule.  Phenyl rings and substituents shows the variation of  6cCH (chi chain 6) with variation of the number of substituents.

The second order simple chi index,  2c

The value for 2c (chi 2) increases with increases branching, as seen in the 2c values for the four branched hexanes.

(See references 1,4,5,7,12,21,29-31 on our Methods and Descriptors Reference Page for additional information)

The difference chi Indices, d2c

The chi descriptors tend to be dependent upon the size of the molecule. A modification of chi indices was developed to make them independent of size, called the difference chi indices [12]. To accomplish this modification, the index for the unbranched skeleton is subtracted from the chi index:

where n is for the number of atoms in the molecule.

Back to: ChemSilico Descriptors