A stress tensor and QTAIM perspective on the substituent effects of biphenyl subjected to torsion

Abstract

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.

Quinone‐based switches for candidate building blocks of molecular junctions with QTAIM and the stress tensor

“…A recent review by Zhang et al gives an overview of the breadth of the field. For the purposes of electronic components, molecular junctions are of particular interest, which have been reviewed by Komoto et al Major breakthroughs have recently been reported, but a workable strategy remains elusive.…”

“…We propose to do this with the scalar and vector‐based aspects of the quantum theory of atoms in molecules (QTAIM) and the stress tensor formalism. In particular, we will use the QTAIM and stress tensor trajectory T σ ( s ) formalisms in the stress tensor trajectory space U σ to understand the functioning of the switch, previously used for benzene to present a new characterization of normal modes …”

A vector-based representation of the chemical bond for the substituted torsion of biphenyl

“…The black plots; the relative energy ∆E for the undecorated biphenyl 19 and the BPLs were previously published by some of the current authors 4 but we include here as the BPL is the length of the r path that comprises the bond-path framework set = {p, q, r}. It can be seen that the form of the variation of the relative energy ∆E with the torsion θ is closer to that of the eigenvector-following path lengths than that of the corresponding variation of the BPL, compare The length exceed that of the BPL (path r) and can be seen from of the form of the path q i = r i + ε i e 2,i , where non-zero ellipticity ε values of the C4-C7 BCP result in values of the length > BPL.…”

“…This is due to the presence of both the strong torsion bond that links the phenyl rings and the associated weak H---H bonding interactions. Recently, some of the current authors used the quantum theory of atoms in molecules (QTAIM) 2 and the stress tensor topological approaches to add to the long standing discussion about both the biphenyl 3 and substituted biphenyl molecule 4,5 . We explained the effects of the torsion θ of the C-C bond linking the two phenyl rings of the biphenyl molecule and demonstrated the favorable conditions for the formation of the H---H bonding interactions for a planar biphenyl geometry.…”

Next generation QTAIM for the design of quinone-based switches

“…Recently developed "next-generation" QTAIM (quantum theory of atoms in molecules) 9 has provided a set of tools to study the bond structure of molecular systems [4][5][6][7] , which can be used to improve our understanding of molecular switches. A recent investigation by some of the current authors 8 focussed on 3-imino-6methylenecyclohexa-1,4-diene-1,4-diamine that we referred to as the quinone switch, with F substituted in two locations (UP or DOWN) for the ring hydrogens and with and without a coordinated Fe atom above the ring, see Scheme 1.…”