ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

On the predictive power of Sombor indices: from diamond lattices to polychlorinated biphenyls

Song Tingting, Sadia Noureen, Amna Maryam, and Adnan Aslam

School of Information Technology, Concord University College Fujian Normal University, Fujian, People’s Republic of China

E-mail: 45445906@qq.com

Received: 2 July 2025  Accepted: 14 August 2025

Abstract:

Topological indices, particularly the Sombor index, have emerged as powerful tools for quantifying molecular structure–property relationships. This study investigates the predictive capacity of Sombor indices across two distinct systems: a tetrahedral diamond lattice (TDL) and twenty-eight polychlorobiphenyl (PCB) compounds. For the diamond lattice, we derived exact closed-form polynomial expressions for the Sombor index (SO) and its variants (\(SO_3\)–\(SO_6\)) as functions of the lattice dimension r, revealing their sensitivity to geometric regularity. For PCBs, Sombor indices were calculated and correlated with key physicochemical properties (melting point, relative retention time, log P, heat of formation, Henry’s constant). Remarkably strong linear relationships were observed, with correlation coefficients (\(R^2\)) exceeding 0.95 for relative retention time (RTT). Remarkably strong linear relationships were observed for relative retention time (RTT), with \(SO, SO_3\), and \(SO_4\) achieving \(R^2>0.93\) (\(p<0.001\)) exceeding 93% variance explanation while \(SO_6\) yielded \(R^2=0.873\). In contrast, correlations with melting point, log P, and Henry’s constant were significant for \(SO, SO_3\), \(SO_4\), and \(SO_6\) (\(R^2=0.875-1.000\)) but weaker for \(SO_5\) (\(R^2 =0.319\)). These results underscore the versatility of Sombor-type descriptors in bridging molecular topology with experimental behavior, offering a computationally efficient strategy for property prediction in materials design and environmental risk assessment.

Keywords: Molecular descriptors; Tetrahedral diamond lattice; Polychlorinated biphenyls; Quantitative structure–property relationship (QSPR)

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04406-9

Chemical Papers 80 (1) 501–515 (2026)