Distance indices and their hyper-counterparts: intercorrelation and use in the structure-property modeling

Area of Science:

• Quantitative Structure-Property Relationships (QSPR)
• Cheminformatics
• Organic Chemistry

Background:

• Molecular descriptors are crucial for predicting chemical properties.
• Various distance-based topological indices exist, including Wiener, Harary, and detour indices.
• Their hyper-counterparts represent extended versions of these indices.

Purpose of the Study:

• To investigate the intercorrelation of several distance-based topological indices and their hyper-variants.
• To evaluate the utility of these indices in modeling the structure-boiling point relationship of alkanes and cycloalkanes.
• To identify optimal descriptor combinations for accurate property prediction.

Main Methods:

• Calculation of Wiener, hyper-Wiener, Harary, hyper-Harary, detour, and hyper-detour indices.
• Analysis of intercorrelations across three distinct sets of aliphatic and cyclic hydrocarbons (39, 139, and 178 molecules).
• Development and evaluation of quantitative structure-property models, particularly for boiling points, using individual and composite descriptors.

Main Results:

• High intercorrelations were observed between pairs of distance indices and their hyper-counterparts for all tested molecular sets.
• Individual distance and hyper-distance indices showed limited success in structure-boiling point modeling.
• Composite models incorporating these indices along with descriptors like carbon atom count, Hosoya Z index, or total walk count yielded significantly improved predictive accuracy.

Conclusions:

• Distance and hyper-distance indices are highly correlated, suggesting potential redundancy.
• While not optimal alone, these indices enhance predictive models when combined with other molecular descriptors.
• The best models achieved standard errors of estimate of 2.1°C (S-39), 4.4°C (S-139), and 4.1°C (S-178), outperforming existing literature models.