Topological Ring-Currents Research Articles

Topological Ring Currents and Bond Currents in Neutral and Dianionic Altans and Iterated Altans of Benzene, Naphthalene, and Azulene.

In previous studies, the Hückel-London-Pople-McWeeny (HLPM) method was used to calculate the "topological" ring currents and bond currents that are associated with the mono-altans, and the doubly and triply iterated altans, of corannulene and coronene and their respective dianions. This gave rise to some intriguing patterns in these currents, which were partially rationalized by a detailed examination of the lone nonbonding orbitals that each of these structures possesses. In the present work, the same HLPM approach is used to investigate whether analogous changes in bond-current patterns are observed when going from the neutral species to the dianions of the iterated altans derived from some other, simpler, "parents" having molecular graphs with a nullity of zero. The altans and iterated altans of three of the simplest parents are studied: the neutral species (altan)n-benzene, (altan)n-naphthalene, and (altan)n-azulene, with n = 1, 2, and 3, together with their corresponding dianions. Analogous bond-current patterns are indeed encountered, some of which are likewise rationalized by a detailed consideration of the nonbonding orbitals.

Topological Ring-Currents and Bond-Currents in Hexaanionic Altans and Iterated Altans of Corannulene and Coronene.

Previous studies of the Hückel-London-Pople-McWeeny (HLPM) ring-currents and bond-currents associated with the neutral and the dianionic altans, and iterated altans, of corannulene and coronene, are here extended to the hexaanions of (altan)n-corannulene and (altan)n-coronene, with n = 1, 2, and 3. The magnetic properties of some of these species were originally studied by Monaco and Zanasi using the ipso-centric approach, which is ab initio in nature. The "topological" HLPM method, by contrast, constitutes a parameter-free, quasi graph-theoretical model requiring knowledge only of the molecular graph of the conjugated system being considered and the areas assumed for its constituent rings. The HLPM calculations are partially presented by means of a novel illustrative device that we call "difference diagrams". One aim of this work is to compare predictions of this very rudimentary HLPM formalism with those of the much more sophisticated ipso-centric ab initio approach when they are both applied to the calculation of ring-current properties in this family of neutral and anionic (especially, hexaanionic) conjugated systems. For those altans and iterated altans for which ab initio calculations are available for comparison, encouraging qualitative, and even quantitative, agreement is found between the predictions of the ab initio and HLPM approaches. Other structures for which HLPM calculations are reported here but which have not yet been studied by ab initio means are offered with some confidence for possible subsequent evaluation using the ipso-centric (or any other ab initio) formalism.

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".

Some Observations on Triplet Ground-States in the Context of ‘Topological’ (HLPM) Ring-Currents in Conjugated Systems

When the quasi graph-theoretical Hückel–London–Pople–McWeeny (HLPM) approach is used to calculate ‘topological’ π-electron ring-currents and bond-currents in conjugated hydrocarbons, a problem is identified that occurs whenever application of the Aufbau process gives rise to a π-electronic ground-state configuration that is a triplet. This circumstance seems to occur only occasionally and, even when it does, the generally somewhat outré molecular graphs in question appear unlikely to represent extant or viable conjugated systems. The molecular graphs of four examples are used to illustrate this ‘triplet ground-state problem’, only one of which represents a hydrocarbon that has actually been synthesised. It is pointed out that the ‘triplet ground-state problem’ does constitute an intrinsic limitation of the HLPM approach. It is, though, a limitation that is also necessarily inherent in other equivalent (though ostensibly different) methods of calculating magnetic properties due to π-electron ring-currents — methods that are likewise founded on the Hückel molecular-orbital conventions. When a triplet ground-state arises, topological ring-currents and bond-currents cannot be calculated by the HLPM method and its equivalents. Infinite paramagnetism is formally to be predicted in such situations.

Topological Ring-Currents and Clar Sextets in Fully Benzenoid Hydrocarbons. II. Large Structures Containing More than 18 Rings.

In previous work, π-electron ring currents in several fully benzenoid hydrocarbons were calculated by means of the quasi-graph-theoretical, parameter-free Hückel-London-Pople-McWeeny (HLPM) method. It was found that for fully benzenoid hydrocarbons formed from fewer than about 17 rings all ring currents in full rings are larger in intensity than the ring current in benzene, while ring currents in the empty rings are smaller than the benzene value. There was an indication that this distinction might break down when larger systems are considered. Accordingly, these studies are here extended to a selection of fully benzenoid hydrocarbons containing up to 43 rings. It is still found that all full rings in all structures bear ring currents that are greater than the ring current in benzene but, in several of the larger systems, empty rings are found to bear ring currents greater than the benzene value. In the very largest structures examined, the ring currents in some of the empty rings are greater than the currents in as many as half of the symmetrically nonequivalent full rings. Despite this, because every full ring bears a ring current of intensity greater than that of any of the empty rings that are immediately adjacent to it, all of the full rings are regions of diatropic circulation; there is also strong diamagnetic circulation around the perimeters of each of the fully benzenoid systems studied. Both of these observations, based on the topological HLPM approach, are qualitatively in agreement with the predictions of sophisticated ab initio calculations, earlier performed on some of these fully benzenoid structures by Steiner et al.

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

It is well-known that the very special family of conjugated systems described as "fully benzenoid hydrocarbons" have a unique Clar structure that causes all of their rings to be classified as either "full" or "empty". In this work, π-electron ring-currents in more than two dozen such structures are calculated by means of the quasi-graph-theoretical, parameter-free Hückel-London-Pople-McWeeny (HLPM) method. In the case of benzenoid hydrocarbons, the calculated values of such "topological" ring-currents depend on only the carbon-carbon connectivity of the system in question. It is found that, until a certain fully benzenoid hydrocarbon comprising 17 rings is examined, all ring currents in full rings are seen to be larger in intensity than the ring current in benzene, while such currents in empty rings are smaller than the benzene value. There is an indication that this distinction might break down when "giant" fully benzenoid structures are considered. These conclusions are consistent with chemical intuition, with earlier studies examining Clar aromatic sextets by means of NICS calculations, and with previous qualitative ab initio predictions of the patterns of π-electron current-flow in the fully benzenoid hydrocarbons.

Topological Ring Currents and Bond Currents in Some Neutral and Anionic Altans and Iterated Altans of Corannulene and Coronene

The novel series of conjugated systems called altans, defined nearly a decade ago, was subsequently extended to multiple ("iterated") altans, and their magnetic properties were calculated by Monaco and Zanasi using the ab initio ipso-centric formalism. Such properties of the single ("mono") altans of corannulene and coronene, calculated by this sophisticated ab initio approach, had earlier been compared with those calculated via the rudimentary Hückel-London-Pople-McWeeny (HLPM) method-a parameter-free topological, quasi graph-theoretical approach requiring knowledge only of the conjugated system's molecular graph and the areas of its constituent rings. These investigations are here extended to double and triple altans. HLPM bond currents in several neutral mono altans are found to differ from those in the corresponding dianion only in those bonds that lie on the structures' perimeters, while the HLPM bond currents in all bonds in the neutral double and triple altans of corannulene and coronene are precisely the same as in the respective dianions. Some rationalization of these unexpected phenomena is offered in terms of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) nature of the role played by the lone nonbonding orbital in each of the neutral species and its respective dianion.

Topological ring-currents and bond-currents in the altan-[r,s]-coronenes.

π-Electron ring-currents for the altans of the four regular [r,s]-coronenes are calculated by the topological HLPM approach. The bond-current pattern of the parent structure is generally preserved in the core of the corresponding altan. Altan-[10,5]-coronene appears to support an anomalous diamagnetic current in its [4n]-periphery. This invites further investigation.

The regular [r, s]-Coronenes and the ‘Annulene-Within-an-Annulene’ rule

Regular [r,s]-Coronenes comprise a regular polygon of r sides each shared with a regular [s]-gon, resulting in an r(s − 3) outer-ring joined to an r-membered central-ring by ‘spokes’ bonds. Topological ring-currents indicate that the one [r,s]-Coronene with ‘decoupled’ inner and outer rings obeys the ‘Annulene-Within-an-Annulene’ rule, but the others do not.

An Analysis of Topological Ring-Currents and their Use in Assessing the Annulene-Within-an-Annulene Model for Super-Ring Conjugated Systems

An Analysis of Topological Ring-Currents and their Use in Assessing the Annulene-Within-an-Annulene Model for Super-Ring Conjugated Systems

Correlations between Topological Ring-Currents, π-Electron Partitions, and Six-Centre Delocalisation Indices in Benzenoid Hydrocarbons

Comparison is made between three different indices that characterise the individual rings of a wide range of condensed benzenoid hydrocarbons. Two of these (π-electron and the six-centre delocalisation-indices that have been called Δ6-values) have been introduced only recently as potential indicators of what might be called local aromaticity, whilst the third (topological π-electron ringcurrents) was suggested as a possible discriminator in this regard nearly fifty years ago. Whilst linear correlations between ring currents and π-electron partitions within certain restricted classes of ring types are good (with correlation coefficients of up to 0.998), agreement between the two indices over all classes of ring types is poor. Predictions arising from a consideration of π-electron partitions and Δ6-values seem, on the other hand, to be in somewhat better accord. It is therefore concluded that, despite its superficially intuitive appeal, the ring-current index is out of step both with π-electron partitions and Δ6-values as a general indicator of so-called local aromaticity. (doi: 10.5562/cca1846)

Topological Ring-Currents and Bond-Currents in Some Nonalternant Isomers of Coronene

The Hückel-London-Pople-McWeeny (HLPM) (topological) approach for calculating π-electron ring-currents and bond-currents in conjugated systems is applied to coronene and the 17 nonalternant isomers of it for which Balaban, Bean, and Fowler recently published ab initio ipso-centric π-electron current-density maps. In a parallel investigation to that conducted by Balaban et al., the key findings of their quantum-mechanical study are confirmed by this topological one: (a) all seven rings in all of the 18 structures studied are found to bear substantial diamagnetic ring-currents, greater than the benzene value; (b) all 18 conjugated systems have a pronounced, overall London diamagnetic-susceptibility, perpendicular to their respective molecular-planes; (c) a substantial diamagnetic current runs around the periphery of each of these structures; and (d) there is general agreement between the two studies as to which structures, of those treated, respect the annulene-within-an-annulene model for conjugated systems of this sort. The same ideas are also tested against ring-current and bond-current intensities recently calculated by Randić et al. using purely graph-theoretical methods that are based on circuits of conjugation. Considerable qualitative agreement is found, and when there is disagreement, arguments are offered as to why the HLPM topological ring-currents and bond-currents are to be preferred.

Topological Ring Currents in the “Empty” Ring of Benzo-Annelated Perylenes

Cyclic conjugation in benzo-annelated perylenes is examined by means of the topological π-electron ring currents calculated for each of their constituent rings, in a study that is an exact analogy of a recent investigation by Gutman et al. based on energy-effect values for the corresponding rings in each of these structures. "Classical" approaches, such as Kekulé structures, Clar "sextet" formulas, and circuits of conjugation, predict that the central ring in perylene is "empty" and thus contributes negligibly to cyclic conjugation. However, conclusions from the present calculations of topological ring currents agree remarkably with those arising from the earlier study involving energy-effect values in that, contrary to what would be predicted from the classical approaches, rings annelated in an angular fashion relative to the central ring of these perylene structures materially increase the extent of that ring's involvement in cyclic conjugation. It is suggested that such close quantitative agreement between the predictions of these two superficially very different indices (energy effect and topological ring current) might be due to the fact that, ultimately, both depend, albeit in ostensibly quite different ways, only on an adjacency matrix that contains information about the carbon-carbon connectivity of the conjugated system in question.