Two novel temperature-based topological indices with strong potential to predict physicochemical properties of polycyclic aromatic hydrocarbons with applications to silicon carbide nanotubes
Sakander Hayat, Seham J. F. Alanazi, Jia‐Bao Liu
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 & 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 & 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 & 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 & 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 >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.