Biphenyl: A stress tensor and vector-based perspective explored within the quantum theory of atoms in molecules

Abstract

We use quantum theory of atoms in molecules (QTAIM) and the stress tensor topological approaches to explain the effects of the torsion φ of the C-C bond linking the two phenyl rings of the biphenyl molecule on a bond-by-bond basis using both a scalar and vector-based analysis. Using the total local energy density H(rb), we show the favorable conditions for the formation of the controversial H–H bonding interactions for a planar biphenyl geometry. This bond-by-bond QTAIM analysis is found to be agreement with an earlier alternative QTAIM atom-by-atom approach that indicated that the H–H bonding interaction provided a locally stabilizing effect that is overwhelmed by the destabilizing role of the C-C bond. This leads to a global destabilization of the planar biphenyl conformation compared with the twisted global minimum. In addition, the H(rb) analysis showed that only the central torsional C-C bond indicated a minimum for a torsion φ value coinciding with that of the conventional global energy minimum. The H–H bonding interactions are found to be topologically unstable for any torsion of the central C-C bond away from the planar biphenyl geometry. Conversely, we demonstrate that for 0.0° < φ < 39.95° there is a resultant increase in the topological stability of the C nuclei comprising the central torsional C-C bond. Evidence is found of the effect of the H–H bonding interactions on the torsion φ of the central C-C bond of the biphenyl molecule in the form of the QTAIM response β of the total electronic charge density ρ(rb). Using a vector-based treatment of QTAIM we confirm the presence of the sharing of chemical character between adjacent bonds. In addition, we present a QTAIM interpretation of hyperconjugation and conjugation effects, the former was quantified as larger in agreement with molecular orbital (MO) theory. The stress tensor and the QTAIM H atomic basin path set areas are independently found to be new tools relevant for the incommensurate gas to solid phase transition occurring in biphenyl for a value of the torsion reaction coordinate φ ≈ 5°. © 2015 Wiley Periodicals, Inc.