Stress Tensor Eigenvector Following with Next-Generation Quantum Theory of Atoms in Molecules

Abstract

The eigenvectors of the electronic stress tensor have been identified as useful for the prediction of chemical reactivity because they determine the most preferred directions to move the bonds that correspond to a qualitative change in the molecular electronic structure. A new 3-D vector based interpretation of the chemical bond that we refer to as the bond-path framework set $\mathbb{B} = \{p,q,r\}$ provides a version of the quantum theory of atoms in molecules (QTAIM) beyond the minimum definition for bonding that is particularly suitable for understanding changes in molecular electronic structure that occur during reactions. The bond-path framework set $\mathbb{B}$ is straightforwardly constructed and visualized from the eigenvalues and eigenvectors of QTAIM. This approach is applied to the structural deformations of ethene that occur during applied torsion ${\theta}$, -180.0{\deg} $\leq$ ${\theta}$ $\leq$ +180.0{\deg}. The corresponding stress tensor version is readily constructed as $\mathbb{B}_{\sigma} = \{p_{\sigma},q_{\sigma},r\}$ within the QTAIM partitioning making it possible to compare experimentally and computationally determined electronic charge densities. The bond-path framework set $\mathbb{B}$ or $\mathbb{B}_{\sigma}$ are the networks that comprise three strands: the least preferred ($p, p_{\sigma}$), most preferred ($q, q_{\sigma}$) and $r$ is the familiar QTAIM bond-path. We demonstrate that the most preferred direction for bond motion using the stress tensor corresponds to the most compressible direction and not to the least compressible direction as previously reported. We show the necessity for a directional approach constructed using the eigenvectors along the entire bond length and demonstrate the insufficiency of the sole use of scalar measures for capturing the nature of the stress tensor within the QTAIM partitioning.