Wiener-Index

The Wiener index - named after Harry Wiener - is the oldest topological descriptor, which maps the structure of a molecule in a number.

Formulation

  • W: Wiener index
  • N: number of non- hydrogen atoms in the structure
  • Dij: number of bonds in the shortest path between atoms i and j

The factor 1/2 states that every path is received only once in the index.

Use

The Wiener index is used in the methods of quantitative structure - activity relationship ( QSPR ) to such as to correlate material properties of the saturation vapor pressure with the molecular structure. Since the Wiener index does not distinguish between different atoms, it can be used only useful within a homologous series.

Example calculation

The Wiener index for 3- ethyl hexane is W = 72 It is calculated as the sum of the distances

Example values

In these four examples, with identical molecular formula ( C6H14 ) is clear that the Wiener- index is highest without branching, and becomes smaller as the branching in the molecular structure; with the same number of branches become smaller with increasing Molekülsymetrie.

Calculation of the maximum values ​​for W

The current for each unbranched molecule maximum Wiener index can be calculated from the total number of " non-H " atoms (s) readily calculated as follows:

Examples of

As a simplified calculation formula can be used.

Table of maximum values ​​for W

To n = 21:

Topological index Digital Object Identifier
819523
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