Two novel temperature-based topological indices with strong potential to predict physicochemical properties of polycyclic aromatic hydrocarbons with applications to silicon carbide nanotubes

Abstract

Abstract For a vertex x ∈ V G , the temperature T x of x is defined as T x = d x / n − d x . A topological/graphical index G I is a map <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">GI</mml:mi> <mml:mo>:</mml:mo> <mml:mo>∑</mml:mo> <mml:mo>→</mml:mo> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:math> , where ∑ (resp. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:math> ) is the set of chemical graphs (resp. real numbers). Graphical indices are employed in structure-property &amp; structure-activity modeling to predict physicochemical/thermodynamic/bilogical characteristics of a compound. A temperature-based graphical index of a chemical graph G is defined as GI T ≔ ∑ edges f ( T x , t y ), where f ( T x , T y ) is a symmetric 2-variable map. In this paper, we introduce two new novel temperature-based indices known as the reduced reciprocal product-connectivity temperature ( RRPT ) index and the geometric-arithmetic temperature ( GAT ) index. The predictive potential of these indices have been investigated by employing them in structure-property modeling of physicochemical properties of polycyclic aromatic hydrocarbons (PAHs). The normal boiling point ( bp ) and the standard enthalpy of formation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> are selected as representatives of physicochemical characteristics. Intermolecular &amp; van der Waals kind of interactions have been represented by bp , whereas, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> advocates for thermal characteristics of a compound. In order to validate the statistical inference, the lower 22 PAHs have been opted as test molecules as their experimental data is also publicly available. We propose a computational method to compute all temperature indices in literature and employ it to compute them for the lower 22 PAHs. Besides all the existing temperature indices, both RRPT &amp; GAT are used in a quality testing to predict bp and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> for lower PAHs. Our statistical analysis asserts that both RRPT &amp; GAT outperformed all the existing temperature indices for correlating bp and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> for lower PAHs. Most appropriate data-fitting regression models have been suggested to be linear. Since RRPT has the both of correlation coefficients &gt;0.95, the study implicates its further employability in structure-property modeling. Importantly, our research contributes towards countering proliferation of graphical indices. Applications to well-performing temperature indices to correlate physicochemical characteristics of silicon carbide nanotubes are presented.