π-Electron currents in fixed π-sextet aromatic benzenoids

In view of different patterns of π-electron density currents in benzenoid aromatic compounds it is of interest to investigate the pattern of ring currents in various classes of compounds. Recently such a study using a graph theoretical approach to calculating CC bond currents was reported for fully benzenoid hydrocarbons, that is, benzenoid hydrocarbons which have either π-sextets rings or “empty” rings in the terminology of Clar. In this contribution we consider π-electron currents in benzenoid hydrocarbons which have π-electron sextets and C=C bonds fully fixed. Our approach assumes that currents arise from contributions of individual conjugated circuits within the set of Kekulé valence structures of these molecules.     

Modeling the Supramolecular Properties of Aliphatic-Aromatic Hydrocarbons with Convex–Concave Topology

The molecular tweezers 1 a and 1 b have an electrostatic potential on the concave sides of the molecule which is surprisingly negative for hydrocarbons. According to semiempirical calculations this is a general phenomenon in nonconjugated π-electron systems with concave–convex topology, and it explains the receptor properties of 1 a and 1 b .     

Graph theory and molecular orbitals. The loop rule

Graph theory is applied to the study of the dependence of total π-electron energy, π-electron charge distribution and free valency indices of conjugated hydrocarbons on molecular topology. It is shown that the number of loops in the molecular graph determines these quantities.     

Silicon-containing formal 4π-electron four-membered ring systems: antiaromatic, aromatic, or nonaromatic?

Density functional theory calculations (B3LYP) have been carried out to investigate the 4π-electron systems of 2,4-disila-1,3-diphosphacyclobutadiene (compound 1) and the tetrasilacyclobutadiene dication (compound 2). The calculated nucleus-independent chemical shift (NICS) values for these two compounds are negative, which indicates that the core rings of compounds 1 and 2 have a certain amount of aromaticity. However, deep electronic analysis reveals that neither of these two formal 4π-electron four-membered ring systems is aromatic. Compound 1 has very weak, almost negligible antiaromaticity, and the amidinate ligands attached to the Si atoms play an important role in stabilizing this conjugated 4π-electron system. The monoanionic bidentate ligand interacts with the conjugated π?system to cause π-orbital splitting. This ligand-induced π-orbital splitting effect provides an opportunity to manipulate the gap between occupied and unoccupied π?orbitals in conjugated systems. Conversely, compound 2 is nonaromatic because its core ring does not have a conjugated π?ring system and does not fulfill the requirements of a Hückel system.     

Bounds For Total π-Electron Energy

Upper and lower bounds for the total π-electron energy of conjugated hydrocarbons in the Hockel approximation are presented.     

Graph theoretical approach to the topological spin hamiltonian applied to conjugated molecules

Approximate formulae for the total π-electron energy calculated within the topological spin Hamiltonian are derived using the connected moments expansion (CMX) technique up to the third order. This provides the first reported graph theoretical approach to the topological Hamiltonian other than the Hückel one. The formulae, valid for alternant, singlet ground state hydrocarbons, are used to estimate the total π-electron energy of some large molecules     

Dynamical screening by Σ-electrons in π-electron transitions: Treatment in the equations-of-motion method

Dynamical screening in π-electron systems is studied by the equations of motion method. By using a partitioning technique on the equations of motion we can obtain simple expressions for the effect of dynamical screening directly on the transition energies and transition moments in π-electron systems. These results are used to study the effect of such screening in the N → V transition in ethylene. This procedure can be used to extend the equations-of-motion method to larger π-electron systems.     

Correlation between the out-of-plane components of magnetizability and central magnetic shielding in unsaturated cyclic molecules

A simple classical model of magnetic-field induced π-electron flow is discussed, showing that the contribution to the σ(∥) out-of-plane component of the virtual magnetic shielding provided by π-ring currents, at points P along the C(n) axis of cyclic planar unsaturated hydrocarbons C(n)H(n) with D(nh) symmetry, in the presence of a magnetic field B(ext) at right angles to the σ(h) plane, is, with good approximation, connected with the π-electron contribution to the out-of-plane component of the magnetizability, ξ(∥). The relationship is σ(∥)(h) = -(μ(0)/2π)(s(2) + h(2))(-3/2)ξ(∥), where s is the distance of a C nucleus from the center of the carbon ring, and h is the distance of P from σ(h). The ring current susceptibility, that is, the strength of the π currents, expressed in nA/T (nano ampe?re per tesla) within the SI system of units, is given by ?I/?B(ext) = -ξ(∥)/(πs(2)), which can be used as a reliable virtual measure of magnetotropicity and relative π-electron mobility in isoelectronic systems. Criteria for the practicality of the proposed ring current model are discussed.     

Bond orders in 1,5-benzodiazepinium cations compared to those in biphenylenes. Another example of bonds of low bond order which isolated π-electron systems.

The bonds which link separate stablishing π-electron systems in 1,5-benzodiazepinium cations are shown from X-ray analysis and MNDO calculations to be of very low bond order, like the bridging bonds in biphenylenes, thereby inhibiting destabilising interaction between the π-electron systems.     

Applications of Hückel-Su-Schrieffer-Heeger method

Structural Chemistry - The equilibrium carbon-carbon (C-C) bond lengths in π-electron hydrocarbons are very sensitive to the electronic ground-state characteristic. In the recent two papers by...     

Macrocyclic π-systems with C2-symmetry as the sum of π-systems with hückel and möbius topology

The π-system of a macrocycle with twofold rotation symmetry and 2N conjugated π-electron can conveniently be regarded as the sum of two cyclic N π-electron systems having Hückel and Möbius topology, respectively.     

Solute-Solvent Interactions : Vol. 2. Editors J.F. Coetzee and C.D. Ritchie. Marcel Dekker Inc., New York, 1976, xii + 459 pages,Sfr. 125.

The photoelectron spectra of eight 4 π-electron hydrocarbons and their tricarbonyl complexes have been measured. From these spectra the perturbation energies of the π orbitals introduced by the tricarbonyliron moiety have been determined. These perturbation energies are 0.89 ± 0.07 and 0.22 ± 0.06 eV for the first and second π orbitals, respectively. Given these perturbation energies and the photoelectron spectra of the tricarbonyliron complexes of cyclobutadiene and trimethylenemethane, π-ionization energies for the two transients, cyclobutadiene (8.29 and 11.95 eV) and trimethylenemethane (8.36 and 11.79 eV), have been predicted.     

Semiempirical Hamiltonians for spatially confined π-electron systems

A study of π-electron systems confined by impenetrable surfaces is presented. The study results in a nonempirical-based approach to obtain confinement-adapted semiempirical π-Hamiltonians including repulsive terms (PPP or Hubbard). The impenetrable surface confinement of a physical system involves changes in the boundary conditions that the eigenvectors of its differential Hamiltonian operator have to fulfill, while the Hamiltonian itself remains unchanged. However, if this Hamiltonian is written in second quantization language, then confinement only involves changes of the Hamiltonian scalar factors (integrals). Semiempirical Hamiltonian integrals are replaced by parameters; therefore, confinement involves only changes of these parameters. It is shown that confinement changes Coulomb (α_i) and exchange (β_ij), while repulsion (γ_ij) parameters remain unaffected. Next, the influence of confinement upon the electron correlation of (i) π-electron molecular systems, (ii) atoms, and (iii) an electron gas is discussed. The behaviour of the correlation energy vs. the confinement size is found to be different for each type of system. A neat explanation of this variety is given in terms of the Coulomb attractive fields of the systems. Some chemical confinement effects such as an increase in the reactivity of π-electron systems is also outlined. © 1996 John Wiley & Sons, Inc.     

On total π-electron energy of benzenoid hydrocarbons

Hall's observation that the total π-electron energy E of benzonoid hydrocarbons is a linear functions of the number of Kukule structures is supported by theoretical arguments and extensive numerical work. A rather accurate topological formula for E is obtained.     

Synthesis and properties of azobenzocrown ethers with π-electron donor, or π-electron donor and π-electron acceptor group(s) on benzene ring(s)

New azobenzocrown ethers of differentiated size and with substituted benzene residues have been synthesized. These crown ethers possess π-electron donor, or π-electron donor-π-electron acceptor pair of functional group(s) in benzene ring(s) in the para position to azo-grouping. Their metal ion complexation abilities in solution were studied using UV-vis spectrophotometry. The X-ray structure of a 19-membered crown ether with 4-dimethylamino-4′-nitroazobenzene fragment has been solved.     

High-resolution electron spectroscopy, preferential metal-binding sites, and thermochemistry of lithium complexes of polycyclic aromatic hydrocarbons

Polycyclic aromatic hydrocarbons are model systems for studying the mechanisms of lithium storage in carbonaceous materials. In this work, Li complexes of naphthalene, pyrene, perylene, and coronene were synthesized in a supersonic metal-cluster beam source and studied by zero-electron-kinetic-energy (ZEKE) electron spectroscopy and density functional theory calculations. The adiabatic ionization energies of the neutral complexes and frequencies of up to nine vibrational modes in the singly charged cations were determined from the ZEKE spectra. The metal-ligand bond energies of the neutral complexes were obtained from a thermodynamic cycle. Preferred Li∕Li(+) binding sites with the aromatic molecules were determined by comparing the measured spectra with theoretical calculations. Li and Li(+) prefer the ring-over binding to the benzene ring with a higher π-electron content and aromaticity. Although the ionization energies of the Li complexes show no clear correlation with the size of the aromatic molecules, the metal-ligand bond energies increase with the extension of the π-electron network up to perylene, then decrease from perylene to coronene. The trends in the ionization and metal-ligand bond dissociation energies of the complexes are discussed in terms of the orbital energies, local quadrupole moments, and polarizabilities of the free ligands and the charge transfer between the metal atom and aromatic molecules.