Randić index

The Randić index is a topological descriptor that summarizes aspects of the topology of a chemical molecule in a number. It is named after Milan Randić (* 1930). The Randić index is also known as the attachment index or connectivity index . It correlates with physicochemical parameters such as boiling point, enthalpy of formation or chromatographic retention time. For example, the boiling point of n-alkanes is a linear function of the index, and the boiling point of the isomers of a particular alkane is also a linear function of the index.

definition

The Randić index is defined by ${\displaystyle ^{0}\chi }$

${\displaystyle ^{0}\chi =\sum _{i=1}^{N_{B}}{v(i)^{-0,5}}}$

With

• ${\displaystyle N_{B}}$: Number of bonds in the molecule
• ${\displaystyle v(i)}$: Product of the number of neighbors of the two bound atoms. Hydrogen atoms are not taken into account.

Examples

To determine the index one draws the skeletal formula, i. H. the molecule without the hydrogen atoms. In the following, the indices of the atoms indicate the number of their neighboring atoms.

For 1-butanol (four relevant bonds, hence four summands) one obtains :

${\displaystyle \mathrm {C_{1}-C_{2}-C_{2}-C_{2}-O_{1}} }$

${\displaystyle ^{0}\chi ={\frac {1}{\sqrt {2}}}+{\frac {1}{\sqrt {4}}}+{\frac {1}{\sqrt {4}}}+{\frac {1}{\sqrt {2}}}=2{,}414}$,

for 1-pentanol (five relevant bonds, therefore five summands):

${\displaystyle \mathrm {C_{1}-C_{2}-C_{2}-C_{2}-C_{2}-O_{1}} }$

${\displaystyle ^{0}\chi ={\frac {1}{\sqrt {2}}}+{\frac {1}{\sqrt {4}}}+{\frac {1}{\sqrt {4}}}+{\frac {1}{\sqrt {4}}}+{\frac {1}{\sqrt {2}}}=2{,}914}$

and for 3,4-dimethylpentanol:

${\displaystyle \mathrm {C_{1}-{\overset {\displaystyle C_{1} \atop |}{C_{3}}}-{\underset {| \atop \displaystyle C_{1}}{C_{3}}}-C_{2}-C_{2}-O_{1}} }$

${\displaystyle ^{0}\chi ={\frac {1}{\sqrt {3}}}+{\frac {1}{\sqrt {3}}}+{\frac {1}{\sqrt {9}}}+{\frac {1}{\sqrt {3}}}+{\frac {1}{\sqrt {6}}}+{\frac {1}{\sqrt {4}}}+{\frac {1}{\sqrt {2}}}=3{,}681}$.

See also

• Wiener index
• Balaban J index

Individual evidence

1. ↑ ^{a b c} Milan Randic: On Characterization of Molecular Branching . In: American Chemical Society ACS (Ed.): Journal of the American Chemical Society . tape 97 , no. 23 , November 12, 1975, ISSN  0002-7863 , pp. 6609-6615 , doi : 10.1021 / ja00856a001 .
2. ↑ Joachim Braun: Topological indices and their computer-aided application in chemistry . September 1999 ( uni-bayreuth.de - Diploma thesis University of Bayreuth, Prof. Kerber).
3. ↑ ^{a b} Milan Randić: The connectivity index 25 years after . In: Journal of Molecular Graphics and Modeling . tape 20 , no. 1 , December 2001, p. 19-35 , doi : 10.1016 / S1093-3263 (01) 00098-5 .
4. ^ ^{A b} Lemont B. Kier, Lowell H. Hall, Wallace J. Murray, Milan Randic: Molecular Connectivity I: Relationship to Nonspecific Local Anesthesia . In: Journal of Pharmaceutical Sciences . tape 64 , no. December 12 , 1975, p. 1971–1974 , doi : 10.1002 / jps.2600641214 .