Topological Resonance Energy Research Articles

A study of the global and local aromaticity of hetero[8]circulenes

AbstractThe topological resonance energy (TRE) method was used to investigate the aromaticity of hetero[8]circulenes in both their neutral and doubly charged ion states. The compounds varying stabilities in different charged states were explained in terms of the topological charge stabilization rule. The TRE‐based aromaticity indices were compared with those obtained by the gauge‐including magnetically induced currents (GIMIC) method. However, the lack of correlation between the TRE and GIMIC aromaticity indices, as well as the contradictory trends observed, suggest that further investigation is necessary to fully understand the aromaticity of hetero[8]circulenes. We employed the circuit resonance energy (CRE) method to assess local aromaticity. Our CRE results indicate that individual benzene or heterocyclic five‐membered units within the molecule maintain their strong aromatic character and serve as the primary source of global aromaticity, both in their neutral and doubly charged ion states. Although our CRE results provide valuable insights, it is important to note that there are cases where the magnitude of local aromaticity predicted by the nucleus‐independent chemical shift (NICS[0] and NICS[1]) indices does not align with our CRE results.

A study on the aromaticity and main conjugation pathways of triphyrin(2.1.1) and its heteroanalogues

The Topological Resonance Energy method was used to investigate the aromaticity of triphyrin(2.1.1) and its heteroanalogues. The calculations from indices of local aromaticity, such as Bond Resonance Energy (BRE) and Circuit Resonance Energy (CRE), enabled us to identify the origins of the aromaticity as well as the main conjugation pathways. The BRE and CRE results revealed that the macrocyclic delocalization pathways corresponding to the 14π-electron aromatic systems are not major contributors to global aromaticity. Instead, the five-membered rings show themselves to be the main contributors to the aromaticity of these molecules.

A study of the aromaticity of thia[7]circulene isomers

In this study, the TRE (topological resonance energy) method was used to determine the degree of aromaticity of [7]circulene and its isomers with two or more carbon atoms on benzene rings replaced by sulphur atoms. The aromaticity based on the TRE index has been compared with that reported by Gauge using the magnetically induced current (GIMIC) method. According to the GIMIC method, thia[7]circulene isomers must be antiaromatic with a negative ring-current susceptibility (I tot). However, they are aromatic with positive TREs. Thus, I tot values cannot always be used as indicators of global aromaticity. By the calculation of the local aromaticity indices, such as BRE (bond resonance energy) and CRE (circuit resonance energy), we explored the mechanism behind the decreased aromaticity for thia[7]circulene isomers. BRE and CRE results demonstrated that the local aromaticity of benzene unit(s) is dominant, and the contribution of the thiophene unit is small in the thia[7]circulene isomers. The Hückel–London model was used to estimate the intensity of ring currents. We found that general trends of the local aromaticity or antiaromaticity obtained from BRE and CRE indices can also be reproduced properly with the diatropic or paratropic ring current direction calculated from the Hückel–London model.

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.

A study on the aromaticity and ring currents of polycyclic neutral oxocarbon isomers

AbstractIn this study, topological resonance energy (TRE) methods and ring current (RC) methods were used to describe the global aromaticity of a series of polycyclic neutral oxocarbon isomers. The observed trends in aromaticity are explained. Our results obtained using the TRE method are compared with those obtained using the nucleus independent chemical shift (NICS) method as reported in the literature. The bond resonance energy (BRE) and circuit resonance energy (CRE) indices were applied to study the local aromaticity of oxocarbons. The aromaticity of the individual rings of each of the polycyclic neutral oxocarbon isomers studied was assessed using the Hückel–London ring current (RC) model. The results regarding the local aromatic and antiaromatic states of the individual rings as obtained using the BRE and CRE indices show direct correspondence with the RC results, which indicate the strength of the diatropic and paratropic currents within those rings.

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.

Geometry and Stability of Small Gold Cluster Ions by Graph Theory and Hückel model

Structure and stability of the gold cluster ions of which skeleton are synthesized as a complex were analyzed using the Hückel method based on graph theory. Hückel Energy (HE) and Topological Resonance Energy (TRE) were determined for neutral, positive ion, and negative ion clusters, where all the isomers of the gold cluster up to octamer were considered. Since some graphically designed isomers include bonds that cannot be realized in three- dimensional space, the screening was carried out by a molecular force field calculation with LAMMPS (lammps.sandia.gov/.). Among the isomers thus obtained, both HE and TRE were most stable when the tetramer was Au4 2 + with a tetrahedral structure, and with the hexamer, Au6 2+ with two tetrahedrons sharing one side. The complexes with these structures have actually been synthesized. On the other hand, the synthesis example of the most stable cluster for octamer Au8 has not been reported.

A study of the aromaticity and ring currents of azaacepentalenes

AbstractUsing the topological resonance energy (TRE) method, a computational study has been carried out on the aromaticity of an acepentalene (cyclopenta[cd]pentalene) molecule upon the replacement at different positions of some of its carbon atoms by two pyrrole‐like nitrogen atom isomers and by one or more pyridine‐like nitrogen atom isomers. The relative aromaticity of the isomers was explained by the topological charge stabilization rule. Each of the resultant azaacepentalene isomers shows lower aromaticity relative to the acepentalene dianion. We found that the magnitudes of the global aromaticity of these azaacepentalenes are solely determined by the position of the two substituted pyrrole‐like nitrogen atoms. Bond resonance energy (BRE) and circuit resonance energy (CRE) indices were used to evaluate the local aromaticity of each of the distinct azaacepentalenes. Our BRE and CRE results show that all of these compounds are primarily stabilized by the 6π electron conjugated system. Our global and local aromaticity results are compared with the other aromaticity indices as reported in the literature. Regarding the order of aromaticity, some discrepancies were found between the magnetic and energic criteria for aromaticity. The ring current (RC) analyses were made using the Hückel‐London model. The RC results revealed that all of the compounds were diatropic, and the quantitative differences in their degrees of diatropicity were quite consistent with the experimental data on 1H NMR chemical shifts.

A study on the aromatic conjugation pathways and the ring currents of bridged [18]annulenes.

In this article, the topological resonance energy (TRE) method was used to investigate the global aromaticity of a set of [18]annulene-derived compounds which were obtained by replacing either two, four, or all six of the inner hydrogen atoms of [18]annulene with bridges (oxygen, imino-, sulfur, or combinations of the three). Our TRE results show that all the mono-bridged, di-bridged, and tri-bridged [18]annulenes are globally aromatic systems with positive TREs and show relatively larger aromaticity in comparison with the [18]annulene. The aromaticity of each compound was explained using the topological charge stabilization (TCS) rule. The bond resonance energy (BRE) and circuit resonance energy (CRE) methods were used to evaluate local aromaticity. Our BRE and CRE results show that incorporation of five-membered heterocyclic rings changes the main conjugation pathway of the bridged [18]-annulenes. The local aromaticities arising from the five-membered heterocyclic rings (6π) contribute strongly to global aromaticity. However, the ring current (RC), which arises from the 18π annulene-like pathway structures, is the primary determinant of the magnetic properties of the molecule. Our RC results are in good agreement with available 1H-NMR chemical shift data.

A study of the aromaticity of heteroannelated cyclooctatetraene derivatives.

The aromaticity of the rings of thiophene, pyrrole, furan, and benzene annelated cyclooctatetraene (COT) derivatives and of their double charged ions was studied using the graph-theoretical theory of aromaticity. On the basis of topological resonance energy, it was found that the global aromaticity is dependent upon on the arrangement of heteroatoms in the given molecule. Relative stability of these molecules when in different charged states can been explained in terms of the topological charge stabilization rule. We expect that fusing the COT ring with an increasing number of aromatic rings will lead to an increase in the aromaticity of the molecule. According to the bond resonance energy (BRE) and circuit resonance energy (CRE) indices, local antiaromaticity of the COT ring is weakened as the number of fused rings increases, and these changes play a significant role in the global aromaticity of the molecule. For some compounds, our BRE and CRE indices do not predict the same order of magnitude of the local aromatic character of certain rings that the nucleus independent chemical shift (NICS(0) and (NICS(1)) methods predict. Finally, for the available compounds, correlations between the diatropic and paratropic chemical shifts of the protons and our ring current results were analyzed and good agreement was found.

A study on the aromaticity and ring currents of dithienopyridines and dithienobenzene

The global aromaticity of dithienopyridine and dithienobenzene isomers was investigated using the topological resonance energy (TRE) and percentage topological resonance energy (%TRE) methods. The effect of variations in the positions of sulfur and nitrogen atoms on [Formula: see text]-electron delocalization is analyzed. The local aromaticity of these isomers is described based on the bond resonance energy (BRE) and circuit resonance energy (CRE) methods. Our BRE and CRE results show that structure of the central six-membered rings has a strong effect on global aromaticity. The aromaticity of these dithienopyridine isomers is enhanced when a complete pyridine unit exists in their middle ring structure, while the aromaticity of the dithienobenzene isomers is enhanced when a complete benzene unit exists in their middle ring structure. For dithienopyridines, our results obtained using the TRE method correlate well with the Bird aromaticity index as reported in the literature. Our ring-current results show that all these compounds are diatropic systems.

The Influence of Benzo‐Fusion on the Aromatic Pathways and Ring Currents of Cycl[3.2.2]azine

The effect of benzene ring fusion on the aromaticity of cycl[3.2.2]azine was studied by calculating topological resonance energy (TRE), the percentage topological resonance energy (%TRE), and magnetic resonance energy (MRE). The bond resonance energy (BRE) and circuit resonance energy (CRE) indices were used to estimate the local aromaticity. Our BRE and CRE results show that the central nitrogen atom plays a significant role both in the global and local aromaticity of the compounds in our study, and contrary to what has been reported in the literature, none of these compounds are peripheral π‐electronic systems. In the case of benzene ring‐fused derivatives, benzene ring(s) exhibit relatively larger local aromaticity and reduce the local aromaticity of the central portion of cycl[3.2.2]azine to a level comparable to a corresponding non‐benzene fused parent system. Ring current results predict that a strong diamagnetic current flows around the whole molecular perimeter. The diatropic bond current results, as computed here, are in good agreement with the observed 1H‐NMR chemical shifts of these compounds.

Aromaticity of Nonplanar Fully Benzenoid Hydrocarbons.

The Clar aromatic sextet theory can provide a qualitative description of the dominant modes of cyclic π-electron conjugation in benzenoid molecules and of the relative stability among a series of isomeric benzenoid systems. In a series of nonplanar fully benzenoid hydrocarbons, the predictions of the Clar theory were tested by means of several different theoretical approaches: topological resonance energy (TRE), energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six center delocalization index (SCI), and nucleus-independent chemical shifts (NICS). To assess deviations from planarity in the examined molecules, four different planarity descriptors were employed. It was shown how the planarity indices can be used to quantify the effect of nonplanarity on the local and global aromaticity of the studied systems.

Radialenes are minimally conjugated cyclic π-systems

ABSTRACTConjugation energy (CE) in benzene is larger than its aromatic stabilisation energy (ASE). A far-reaching conclusion offered by this work is that per π-electron, CE is energetically larger than aromaticity. If a diene has a doubly degenerate HOMO, then its Diels–Alder reaction will be kinetically faster than a similar diene with a nondegenerate HOMO. The topological conjugation energy (TCE) for the radialene, monocyclic, dendralene, and linear polyene series has quite different trends. Radialenes are minimally conjugated cyclic systems with the TCE/No. π-bond = 0.432 β; the members of the dendralene series approach this same value from smaller values with increasing size. With increasing size, the members of the monocyclic and linear polyene series have, respectively, decreasing and increasing TCE/No. π-bond values approaching 0.547 β. Topological resonance energy (TRE) for radialenes, dendralenes, and linear polyenes all have TRE = 0, and the TRE/π-electron for monocyclic polyenes has alternating declining values between antiaromatic (−0.3066 β, −0.07435 β, −0.03287 β, …) and aromatic (0.04543 β, 0.01594 β, 0.00807 β, …). For benzene, TRE/No. π-bond = 0.0909 β and TCE/No. π-bond = 0.576 β.

异质富勒烯C<sub>26</sub>N<sub>4</sub>的芳香性和动力学稳定性研究

采用拓扑共振能(Topological Resonance Energy, TRE)方法对氮原子插入在C30(D5h)异构体后形成的异质富勒烯的芳香性进行了研究，分析了氮原子的取代位置和稳定性之间的关系，解释了各种异构体的相对稳定性。最后，用最小键共振能(Minimum Bond Resonance Energy, Min BRE)方法对C30(D5h)和C26N4的动力学稳定性进行了研究。研究结果表明，C30(D5h)在中性状态下，因TRE为负值具有反芳香性，C24N4所有异构体TRE为正值具有芳香性。Min BRE方法研究结果证明了C30(D5h)和C26N4的动力学不稳定性与分子中具有较高反芳香性键直接有关。TRE和min BRE方法研究结果表明，C26N4各异构体在二价阴离子状态下不仅具有较高的芳香性而且也具有较高的动力学稳定性。 The aromaticity of heterofullerene C26N4 formed on the initial C30 cage of D5h symmetry have been systematically investigated by the topological resonance energy (TRE). The relationships between the stabilities of the C26N4 isomers and the sites where nitrogen atoms dope at the C30 cage have been discussed. The kinetic stability of C30(D5h), C26N4 isomers were examined by the minimum bond resonance energy (min BRE) model. The min BRE model results show that kinetic instability of these compounds are closely related to the existence of highly reactive substructures in the molecule. Both the TRE and min BRE results show that the C24N2-4 isomers were found to not only have aromaticity but also have large kinetic stability.

Excited-State Intramolecular Proton Transfer and Global Aromaticity

A general survey of excited-state intramolecular proton transfer (ESIPT) processes was made from the viewpoint of global aromaticity. For most ESIPT processes studied, a tautomeric product in the first excited electronic state was found to have a larger topological resonance energy (TRE) than the reactant in the same excited state. Conversely, if a transient tautomer is much less aromatic in the excited state than the reactant, an appreciable aromaticity-imposed energy barrier to the reaction will result. Thus, excited-state aromaticity is a very important factor, although not a definitive one, in determining the allowedness of ESIPT.

Graph Theory of Aromatic Stabilization

Aromaticity is very sensitive to the geometry of the π-system. Topological resonance energy (TRE), defined graph-theoretically, represents an aromatic stabilization energy (ASE) arising from cyclic...

Systematic investigation of the stability of all dihydro isomers of the more stable C38fullerene isomer with C2 symmetry

The local aromaticity of fullerene C[Formula: see text] ([Formula: see text] was studied using the bond resonance energy (BRE) method. The global aromaticity of all 349 possible isomers of C[Formula: see text]H2based on [Formula: see text] symmetry was investigated using the topological resonance energy (TRE) method. The TRE results show that most of the C[Formula: see text]H2isomers have greater stability than C[Formula: see text] ([Formula: see text]. Based on the BRE results, the preferred addition sites of hydrogen atoms are discussed. The relationship between the addition sites and BREs is analyzed and discussed. We found that the addition sites of hydrogen atoms are strongly dependent on the magnitude of the parent cage BRE values. The most stable isomers of C[Formula: see text]H2are often produced by diminishing of the [Formula: see text]-bonds from those sites in the parent cage at which are located the two carbon atoms with the lowest BRE values. Based on this rule, the preferred addition patterns for non-IPR fullerene cages can be easily predicted.

The tube length dependence of topological resonance energy in armchair carbon nanotubes

The effect of the tube length on the thermodynamic stabilities of finite-length (1,1)–(5,5) armchair carbon nanotubes (CNTs) were examined by means of topological resonance energy (TRE). In result, it was found that the topological resonance energy per electron (TREPE) values oscillate with the increase of the tube length. These oscillations of TREPE have the period 3. In this sense, these oscillations are very similar to the oscillations of the HOMO-LUMO gap found earlier.

A study on the aromaticity and kinetic stability of fullerene C38 isomers and their molecular ions

ABSTRACTThe aromaticity of the fullerene C38 isomers and their molecular ions is examined by the topological resonance energy (TRE) method. The aromaticity order obtained by the TRE method is compared with relative energies found in DFT calculation results reported in literature. It is found that all C38 isomers exhibit antiaromaticity when in the neutral state. However, they are highly aromatic in the hexaanionic states. The minimum bond resonance energy (min BRE) method is utilized to estimate the kinetically stability of the C38 isomers and their molecular ions. According to the min BRE method, C38 isomers are only have kinetic stability in penta- and hexavalent molecular anionic states.