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.
Modified ANO-RCC basis sets are used to determine twelve molecular graphs of the Ehrenfest force for H2, CH4, CH2O, CH3NO, C2H2, C2H4, C3H3NO, N4H4, H2O, (H2O)2, (H2O)4 and (H2O)6. The molecular graphs include all types of topological critical points and a mix of bonding types is chosen to include sigma-, π- and hydrogen-bonding. We then compare a wide range of point properties: charge density, trace of the Hessian, eigenvalues, ellipticity, stiffness, total local energy and the eigenvectors are calculated at the bond critical points (BCPs) and compared for the Ehrenfest, QTAIM and stress tensor schemes. QTAIM is found to be the only partitioning scheme that can differentiate between shared- and closed-shell chemical bond types. Only the results from the Ehrenfest force partitioning, however, are demonstrated to be physically intuitive. This is demonstrated for the water molecule, the water-dimer and the water clusters (H2O)4 and (H2O)6. In particular, both the stiffness and the trace of the Hessians of the appropriate quantities of the sigma-bond BCPs for the water clusters are found to depend on the quantum topology dimension of the molecular graph. The behavior of all the stress tensor point properties is found to be erratic. This is explained by the ambiguity in the theoretical definition of the stress tensor. As a complementary approach the Ehrenfest force provides a new indicator of the mixed chemical character of the hydrogen-bond BCP, which arises from the collinear donor sigma-bond donating a degree of covalent character to the hydrogen-bond. This indicator takes the form of the relative orientation of the shallowest direction of the Ehrenfest potential of the hydrogen-bond BCPs and the corresponding direction for the collinear sigma-bond BCP.
The Quantum Theory of Atoms in Molecules (QTAIM) defines quantities in 3D space that can be easily obtained from routine quantum chemical calculations. The present investigation shows that local properties can be related quantitatively to measures traditionally connected to experimental data, such as Hammett constants. We consider the specific case of substituted biphenyl to quantify the effects of a torsion φ, 0.0° ≤ φ ≤ 180.0°, of the C-C bond linking the two phenyl rings for C12 H9 -x, where x = N(CH3 )2 , NH2 , CH3 , CHO, CN, NO2, on the entire molecule. QTAIM interpreted Hammett constants, aΔH(rb ) are introduced and constructed using the difference between the H(rb ) value of C12 H9 -x and the C12 H9 -H, biphenyl which is the reference molecule, with a constant of proportionality a. This investigation unexpectedly yields very good or good agreement for the x groups with the Hammett para-, meta-, and ortho-substituent constants and is checked against para-substituted benzene. We then proceed to present the interpreted substituent constants of seven new biphenyl substituent groups, where tabulated Hammett substituent constant values are not available; y = SiH3 , ZnCl, COOCH3 , SO2 NH2 , SO2 OH, COCl, CB3 . Consistency is found for the QTAIM interpreted biphenyl substituent constants of the seven new groups y independently using the stress tensor polarizability Pσ . In addition, a selection of future applications is discussed that highlight the usefulness of this approach. © 2016 Wiley Periodicals, Inc.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.