Electron Density Based Characterization of π Bonds in Planar Molecules

Abstract

A new method has been developed to detect and analyze molecular π systems. The concept of bonding critical point is generalized to electronic π systems, and it is shown how a π bond can be characterized via the corresponding bond critical point (BCP) in planar molecules. In this context, charge density and its Laplacian at the BCP(π) of a strongly delocalized π system can be distinguished from that of a localized one. The presented formalism is applied to three types of nanoconductors as conjugated polyenes, which revealed the alternative pattern of the double bonds. Also, several cyclic conjugated molecules are considered to explore their π electronic structure and aromaticity.

Electron Density Analysis of Hyperconjugation

“…However, the molecule in Figure b is identified as a transition structure (TS) with one imaginary frequency, for which the π molecular graph is depicted in Figure c. Although the presence of a CP in a TS does not necessarily imply a stabilizing interaction, the CP properties are still helpful to obtain an insight into the interaction . Several TS systems have also been evaluated previously through π CPs in antiaromatic rings …”

“…To calculate the charge density distribution owing to the molecular electronic π system, the columns of the MO coefficients matrix ( ) are first rearranged into Equation , those columns responsible for the π system are extracted as , and the electron density owing to the π system is computed as Equation : …”

“…As the hyperconjugation phenomenon is closely related to π electron density, the hyperconjugative BCP cannot be detected through conventional QTAIM. However, in a recent work by the present author, electron density analysis is generalized to π‐type electron density topology, which enables the detection of a hyperconjugative interaction. This approach is also used for the characterization of several concepts and interactions including aromaticity, antiaromaticity, heteroaromaticity, metal–π interaction, and van der Waals complexes …”

From Cyclopropenes to Tetrasubstituted Furans: Tandem Isomerization/Alkenylation Sequence with Cu/Pd Relay Catalysis

“…The QTAIM48–50 has been widely and successfully applied to the study of the properties of a variety of conventional and unconventional HBs6, 51 as well as the LB 43. It is known that σ and π orbitals are strictly unmixed in a planar molecule and can be partitioned by their contribution to single‐particle properties 52. To confirm that LiX molecules interact with the π orbitals of benzene, σ and π orbitals of benzene were separated from the total orbitals by using the GTA‐2010 program 40.…”

The Role of π Electrons in the Formation of Benzene‐Containing Lithium‐Bonded Complexes

“…[43] It is known that s and p orbitals are strictly unmixed in a planar molecule and can be partitioned by their contribution to single-particle properties. [52] To confirm that LiX molecules interact with the p orbitals of benzene, s and p orbitals of benzene were separated from the total orbitals by using the GTA-2010 program. [40] Herein, C 6 H 6 ···LiX complexes refer to those that include the total electrons of benzene and those of LiX molecules, pC 6 H 6 ···LiX complexes that include only p electrons of benzene and the total electrons of LiX molecules, and sC 6 H 6 ···LiX complexes that include only s electrons of benzene and the total electrons of LiX molecules.…”