The Alkanes with Maximum Wiener Polarity Index

Area of Science:

• Chemical Graph Theory
• Molecular Structure-Property Relationships
• Computational Chemistry

Background:

• The Wiener polarity index ($$) is a topological index used in chemistry.
• It quantifies specific carbon-atom pair distances in alkanes and aids in predicting boiling points.
• Previous work established the maximum possible $$ value for alkanes with n carbons.

Purpose of the Study:

• To identify all alkane molecular structures that achieve the maximum Wiener polarity index ($$) for a given number of carbon atoms (n).
• To provide a complete characterization of alkanes exhibiting this maximal topological index.

Main Methods:

• Analysis of alkane molecular graphs.
• Determination of pairs of carbon atoms separated by exactly three bonds.
• Identification of structures satisfying the maximal $$ condition.

Main Results:

• The paper characterizes the specific branching patterns and carbon connectivity of alkanes that yield the maximum Wiener polarity index.
• Explicit enumeration or description of these maximal alkane structures is provided.

Conclusions:

• The study successfully identifies all alkanes that attain the maximum Wiener polarity index for a given n.
• This provides a deeper understanding of the relationship between molecular topology and physical properties like boiling point.