This article develops and validates a novel graph energy-based computational framework for
Quantitative Structure-Property Relationship (QSPR) modeling of polycyclic aromatic
compounds. Our methodology leverages the energies of molecular graphs and their topological
indices to predict key physicochemical properties. To comprehensively evaluate this approach,
we applied it to two distinct classes of aromatic systems: five standard polycyclic aromatic
hydrocarbons (PAHs)—naphthalene, anthracene, phenanthrene, pyrene, and chrysene—and a
series of quinolone antibiotics representing complex heteroaromatic structures.
We computed ten different topological indices, including the Zagreb, Harmonic, Randić, and
Atom-Bond Connectivity indices, along with their corresponding energies for all compounds.
Linear regression models were developed to correlate these descriptor energies with
fundamental physicochemical properties: melting point, boiling point, molar refractivity, and
topological polar surface area.
The results demonstrate statistically significant correlations across both compound classes.
Notably, for melting point and molar refractivity, several models achieved high predictive
accuracy with R² values exceeding 0.8. Among the investigated indices, the First Zagreb,
Randić, and Geometric-Arithmetic indices exhibited the strongest predictive performance.
The successful application of this methodology to both simple PAHs and complex
pharmaceutical heteroaromatic systems confirms the predictive power and generalizability of
the proposed framework. This study establishes the graph energy-based approach as an
efficient, cost-effective, and reliable computational tool for predicting the properties of
aromatic compounds in drug design and materials science.