Topological Ring-Currents and Clar Sextets in Fully Benzenoid Hydrocarbons I. Structures with Fewer than 18 Rings

Assessment of the Performance of the Bond Resonance Energy, Circuit Resonance Energy, Magnetic Resonance Energy, Ring Currents, and Aromaticity of Anthracene, Biphenylene, Phenalenyl, and p-Terphenyl

This paper contributes to the further understanding of bond resonance energy (BRE), circuit resonance energy (CRE), and ring currents (RC = I) as indices for the measure of local ring aromaticity and topological resonance energy (TRE) and magnetic resonance energy (MRE) as indices for the measure of global molecular aromaticity. Calculations of ring currents in the 3-ring polycyclic hydrocarbons of anthracene, biphenylene, phenalenyl, and p-terphenyl are demonstrated. This comparative study provides new molecular insights. A number of shortcut techniques are briefly illustrated. p-Terphenyl is a benzenoid total resonant sextet (TRS) and biphenylene is shown to be a nonbenzenoid TRS, i.e., both obey Clar's sextet principle. p-Terphenyl has only ring circuits, whereas anthracene, biphenylene, and phenalenyl have ring circuits and larger circuits engulfing the ring circuits. The perimeter circuits of anthracene, biphenylene, and phenalenyl engulf all other circuits, thus leading to the definition of MRE. By these several aromatic indices, the monocation, monoanion, and monoradical of phenalenyl are equally aromatic. The agreement in the prediction of local ring aromaticity between the three indices of m-BRE, t-BRE, and CRE is evaluated.

Applications of Hückel-Su-Schrieffer-Heeger method

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 Stolarczyk and Krygowski (J Phys Org Chem, 34:e4154,e4153, 2021) a simple quantum approach, the Augmented Hückel Molecular Orbital (AugHMO) model, is proposed for the qualitative, as well as quantitative, study of this phenomenon. The simplest realization of the AugHMO model is the Hückel-Su-Schrieffer-Heeger (HSSH) method, in which the resonance integral β of the HMO model is a linear function the bond length. In the present paper, the HSSH method is applied in a study of C-C bond lengths in a set of 34 selected polycyclic aromatic hydrocarbons (PAHs). This is exactly the set of molecules analyzed by Riegel and Müllen (J Phys Org Chem, 23:315, 2010) in the context of their electronic-excitation spectra. These PAHs have been obtained by chemical synthesis, but in most cases no diffraction data (by X-rays or neutrons) of sufficient quality is available to provide us with their geometry. On the other hand, these PAHs are rather big (up to 96 carbon atoms), and ab initio methods of quantum chemistry are too expensive for a reliable geometry optimization. That makes the HSSH method a very attractive alternative. Our HSSH calculations uncover a modular architecture of certain classes of PAHs. For the studied molecules (and their fragments – modules), we calculate the values of the aromaticity index HOMA.

Finding the direct energy-structure correlations in intramolecular aromaticity assisted hydrogen bonding (AAHB)

A predictive model for intramolecular hydrogen bond energy (E_HB) calculation of polyaromatic ortho-hydroxyaldehydes based on a set of small, functionalized hydrocarbons is developed. The complete data set of 18 compounds was used for this study. The model is based on one of four optional categories of molecular descriptors: geometric, spectroscopic, bond order and topological indices. The model of Wiberg bond indices (WBIs) as descriptors of the CC involved bond based on stepwise regression has acceptable prediction abilities for 14 structures of ortho-hydroxyformylobenzo[a]pyrene derivatives already at the semiempirical level. The presented correlation enables a significantly more rapid and quantitative description of the hydrogen bonding strength than the much more time-consuming MTA method. Thus, WBIs are shown to provide a reliable means for fast prescreening of the energy of chelate hydrogen bonds potentially for any polyaromatic derivatives.

A study on the aromaticity and magnetic properties of N-confused porphyrins

In this paper, topological resonance energy (TRE) methods were used to describe the global aromaticity of nitrogen confused porphyrin (NCP) isomers. The TRE results show that all NCP isomers exhibit lower aromaticity than the normal porphyrins, and their aromaticity decreases as the number of confused pyrrole rings in the molecule increases. In the NCPs, global aromaticity decreases as the distance between the nitrogen atoms increases. The bond resonance energy (BRE) and circuit resonance energy (CRE) indices were applied to study local aromaticity and conjugated pathways. Both the BRE and CRE indices revealed that individual pyrrolic subunits maintain their strong aromatic character and are the main source of global aromaticity. Ring currents (RC) were analysed using the Hückel-London model. RC results revealed that the macrocyclic electron conjugation pathway is the main source of diatropicity. As the number of confused pyrrole rings in the molecule increases, its diatropicity gradually decreases. In the confused pyrrole rings of the NCP isomers, the diatropic RC passing through the β-positions is always weaker than that passing through the inner sections. This is unrelated to the location of the protonated or non-protonated nitrogen atom at the periphery of the molecule and must be ascribed to the unique properties of the confused pyrrole rings.

Magnetically Induced Current Density in Nonplanar Fully Benzenoid Hydrocarbons

In our recent paper, the effects of molecular planarity on the local aromaticity in several series of increasingly planar fully benzenoid hydrocarbons were examined. It was found that the Clar formulas can provide correct information on the local aromaticity distribution even in nonplanar fully benzenoid systems. In the present work, the influence of molecular planarity on the ab initio magnetically induced current densities was examined for the same sets of molecules. The planarity effects were rationalized by examining the origins of the induced current density through the virtual transitions between occupied and unoccupied molecular orbitals.

Electrostatic Topographical Viewpoint of π-Conjugation and Aromaticity of Hydrocarbons

A molecular electrostatic potential (MESP) topographical study has been conducted for a variety of conjugated hydrocarbons at B3LYP/6-311+G(d,p) level of theory to understand their π-conjugation features and aromaticity. The value of MESP minimum (V_m) is related to the localized and delocalized distribution of π-electron density. The V_m values are located interior to the rings in polycyclic benzenoid hydrocarbons (PBHs), whereas they lie outside the boundary of the rings in antiaromatic and in fused systems consisting of aromatic and antiaromatic moieties. The V_m points lie on top and bottom of the π-regions in linear polyenes and annulenes, while a degenerate distribution of CPs around the midpoint region of triple bonds is observed in alkynes. The eigenvalues λ₁, λ₂, and λ₃ of the Hessian matrix at V_m(MESP minima) are used to define the aromatic character of the cyclic structures. The eigenvalues follow the trend λ₁ ≫ λ₂ > λ₃ ≅ 0 in PBHs, λ₁ > λ₂ > λ₃ ≅ 0 in linear polyenes, and λ₁ > λ₂ > λ₃ ≠ 0 in antiaromatic systems. The difference in the aromatic character of PBHs from that of benzene is related to the deviations Δλ₁, Δλ₂, and Δλ₃. The total deviation ∑_i=1³Δλ_i is found to be ≤ 0.011 au for all aromatic systems and lies between 0.011 and 0.035 au for all nonaromatic systems. For antiaromatic systems, its value is found to be above 0.035 au. Further, ∑_i=1³Δλ_i gives a direct interpretation of Clar's aromatic sextet structures for PBHs. In summary, MESP topography mapping is a powerful technique to quantify the localized and delocalized π-electron distribution in a variety of unsaturated hydrocarbon systems.

Assessing the Extent of π-Electron Delocalization in Naphtho-Annelated Fluoranthenes by Means of Topological Ring-Currents

The extent of π-electron delocalization in the five-membered rings of 14 naphtho-annelated fluoranthenes has recently been assessed by means of several approaches, including application of the following indices: the energy effect (ef), bond resonance-energy (BRE), multicenter delocalization-energies (MCI), the index arising from the harmonic-oscillator model of aromaticity (HOMA), and nucleus-independent chemical shifts (NICS). The calculated Hückel-London-Pople-McWeeny (HLPM) ("topological") ring-current intensities (TRC) for the five-membered rings of these same structures are here compared with the above-named indices in order to assess how well TRC parallels these other criteria. The indices ef and BRE are the ones that correlate best with TRC, and it is suggested that this is because all three approaches are founded on the Hückel model. TRC does not, however, confirm the proposal that cyclic delocalization in the five-membered rings can be greater than in any of the six-membered rings in this series of conjugated systems. Certain ostensible shortcomings of the NICS approach are discussed, and some doubts are emphasized regarding the legitimacy of associating "ring currents" with "aromaticity".