A Vector-Based Representation of the Chemical Bond for the Substituted Torsion of Biphenyl

Abstract

We use a new interpretation of the chemical bond within QTAIM. The bond-path framework set $\mathbb{B}=\{p,q,r\}$ with associated linkages with lengths ${\mathbb{H}}^{\ast },m\mathbb{H}$ and the familiar bond-path length is used to describe a torsion $\theta$, $0.0^{\circ }\le \theta <22.0^{\circ }$ of \emph{para}-substituted biphenyl, ${\mathrm{C}}_{12}{\mathrm{H}}_{9-x}$, $x=\mathrm{N}({\mathrm{CH}}_3{)}_2$, ${\mathrm{NH}}_2$, ${\mathrm{CH}}_3$, CHO, CN, ${\mathrm{NO}}_2$. We include consideration of the H---H bonding interactions and find that the lengths $\mathbb{H}>{\mathbb{H}}^{\ast }$ that we explain in terms of the most and least preferred directions of charge density accumulation. We also consider the fractional eigenvector-following path lengths ${\mathbb{H}}_f$ and ${\mathbb{H}}_{f{\theta }_{\min }}$.

manuscript+supplementary materials. arXiv admin note: text overlap with arXiv:1804.00776, arXiv:1804.00780, arXiv:1804.01525