We use quantum theory of atoms in molecules (QTAIM) and the stress tensor topological approaches to explain the effects of the torsion u 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(r b ), 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(r b ) analysis showed that only the central torsional C-C bond indicated a minimum for a torsion u 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 0.08 < u < 39.958 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 u of the central C-C bond of the biphenyl molecule in the form of the QTAIM response b of the total electronic charge density q(r b ). 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 u % 58. V C 2015 Wiley Periodicals, Inc.
We
located the unknown chirality–helicity equivalence in
molecules with a chiral center, and as a consequence, the degeneracy
of the S and R stereoisomers of lactic acid was lifted. An agreement
was found with the naming schemes of S and R stereoisomers from optical
experiments. This was made possible by the construction of the stress
tensor trajectories in a non-Cartesian space defined by the variation
of the position of the torsional bond critical point upon a structural
change, along the torsion angle, θ, involving a chiral carbon
atom. This was undertaken by applying a torsion θ, −180.0°
≤ θ ≤ +180.0° corresponding to clockwise
and counterclockwise directions. We explain why scalar measures
can at best only partially lift the degeneracy of the S and R stereoisomers,
as opposed to vector-based measures that can fully lift the degeneracy.
We explained the consequences for stereochemistry in terms of the
ability to determine the chirality of industrially relevant reaction
products.
Left: The BCP trajectories T(s) for H2O for the bending (Q1) mode, the axes labels of the trajectory T(s). The green spheres correspond to the bond critical point (BCPs). Right: The corresponding T(s) for H2O for the symmetric-stretch (Q2) mode.
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