A Vector-Based Representation of the Chemical Bond for the Normal Modes of Benzene

We introduce a vector-based interpretation of the chemical bond within the quantum theory of atoms in molecules (QTAIM), the bond-path framework set $\mathbb{B} = \{p, q, r\}$, to follow variations in the 3-D morphology of all bonds for the four infra-red (IR) active normal modes of benzene. The bond-path framework set comprises three unique paths $p$, $q$ and $r$ where $r$ is the familiar QTAIM bond concept of bond-path ($r$) while the two new paths $p$ and $q$ are formulated from the least and most preferred directions of electron density accumulation respectively. We find 3-D distortions including bond stretching/compression, torsion and curving. We introduce two fractional measures to quantify these variations away from linearity of the bond.