No abstract

Elements of Bader's theory of atoms in molecules are combined with density-functional theory to provide an electron-preceding perspective on the deformation of materials. From this perspective, a network of atoms is changed by moving the bonds that connect them; the nuclei then follow. The electronic stress tensor is the key to understanding this process. Eigenvectors of the electronic stress tensor at critical points of the electron density provide insight into the "normal electronic modes" that accompany structural dynamics and rearrangements. Eigenvectors of the second-derivative matrix of the electron density emerge as effective approximations to the eigenvectors of the stress tensor; this makes it possible to apply our results to experimentally and computationally determined electron densities. To demonstrate the usefulness of our analysis, we show that (a) the low-frequency modes of ice Ic can be predicted from the eigenvectors of the second-derivative matrix and (b) the eigenvectors of the second-derivative matrix are associated with the direction of structural change during the pressure-induced phase transition from ice XI to a ferroelectric ice VIII-like structure. We conclude that the eigenvectors of the second-derivative matrix of the electron density are the key ingredient for constructing a dynamical theory of atoms in molecules.

New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S0 and S1 states follow the 'biradical' torsion model, but the double bond is stiffer in the S0 state; by contrast, the S2 state follows the 'zwitterionic' torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated -CH2 methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.

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.