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

TL;DR

This paper introduces a new vector-based interpretation of chemical bonds using the eigenvectors of the electronic stress tensor within the quantum theory of atoms in molecules, applied to ethene torsion, revealing preferred bond motion directions.

Contribution

It develops a bond-path framework set based on stress tensor eigenvectors, extending QTAIM to better understand electronic structure changes during reactions.

Findings

Most preferred bond motion direction is the most compressible, not least compressible.

Eigenvector-based approach captures directional stress information beyond scalar measures.

Application to ethene torsion demonstrates the method's effectiveness in structural deformation analysis.

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.