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.

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.

Structural and chemical properties of the small water clusters W(4), W(5) and W(6) are investigated with the theory of atoms and molecules (QTAIM). For the W(4), W(5) and W(6) clusters, nine, fourteen and twenty-seven conformers, respectively, have been analyzed. For the W(4), W(5) and W(6) clusters one, two and three of these structures, respectively, have not been reported before. We then proceed to extend the W(4), W(5) and W(6) water cluster topology space using QTAIM; the Poincaré-Hopf topological sum rules are applied to create rules to identify the spanning set of conformer topologies, this includes finding three, ten and eight new distinct topologies that satisfy the Poincaré-Hopf relation for W(4), W(5) and W(6) respectively. The topological stability of degenerate solutions to the Poincaré-Hopf relation is compared by evaluating the proximity to rupturing of critical points of the gradient vector field of the charge density. We introduce a QTAIM topology space to replace the inconsistent use of Euclidean geometry to determine whether a cluster is 1-, 2- or 3-D. We show from the topology of the charge density that the conformers of the W(4), W(5) clusters are more energetically stable in less compact, planar forms, conversely the conformers of W(6) are more energetically stable with compact 3-D topologies. Quantifying the degree of covalent character in the hydrogen bonding for the W(4), W(5) and W(6) clusters independently verifies this finding. Differences in simple rules for the number of hydrogen bonds obeying the Bernal-Fowler ice rules between W(4), W(5) and W(6) reflect the transition from 2-D to 3-D structures being more energetically stable. In addition, we identify a new class of O-O bonding interactions that are up to 48% longer than the inter-nuclear separation and appear to be failed hydrogen bonds.