Partitioning Hückel–London Currents into Cycle Contributions

Abstract

Ring-current maps give a direct pictorial representation of molecular aromaticity. They can be computed at levels ranging from empirical to full ab initio and DFT. For benzenoid hydrocarbons, Hückel–London (HL) theory gives a remarkably good qualitative picture of overall current patterns, and a useful basis for their interpretation. This paper describes an implemention of Aihara’s algorithm for computing HL currents for a benzenoid (for example) by partitioning total current into its constituent cycle currents. The Aihara approach can be used as an alternative way of calculating Hückel–London current maps, but more significantly as a tool for analysing other empirical models of induced current based on conjugated circuits. We outline an application where examination of cycle contributions to HL total current led to a simple graph-theoretical approach for cycle currents, which gives a better approximation to the HL currents for Kekulean benzenoids than any of the existing conjugated-circuit models, and unlike these models it also gives predictions of the HL currents in non-Kekulean benzenoids that are of similar quality.

Tuning (Anti)Aromaticity: Variations on the [8]‐Circulene Framework

“…Geometry is taken into account by using explicit coordinates or idealised areas for each ring, and the HL method exists in versions based on finiteperturbation theory, [72,75] bondbond polarisability [73] or cycle contributions. [74,76] It has been found to give physically reasonable schematic maps of total π current for many benzenoids and related systems, [77,78] though without the clear hierarchy of orbital contributions that is characteristic of an ipsocentric method (See e. g. Ref. [76], Section 5.1).…”

Revisiting the superaromatic stabilization energy as a local aromaticity index for excited states

“…[29,30] However, due to the Pauli exclusion principle, if the degenerate orbitals in question are occupied with electrons of the same spin, then the magnetic dipole transitions between them are forbidden and the infinite paramagnetism avoided. [28] In fact, the algorithm by Myrvold et al [20] that we are using requires that the high-spin state is calculated. For example, triplet benzene would have three electrons in a shell with twofold degenerate orbitals and one electron in a twofold degenerate shell (Figure 3).…”

“…In the case of degenerate orbitals and heteroatoms, Equation (6) has to be replaced by a more complicated expression. In particular, higher orders of polynomial derivatives are needed, and in COULSON, we have used the algorithm of Myrvold et al [20] for this purpose.…”

“…After the recent death of Aihara in 2018, his methods have been sparsely used. Notable exceptions include studies by Dias [ 19 ] and Myrvold et al [ 20 ] We have recently implemented all of Aihara's methods in the COULSON Python package. In connection with the work on this package, we have developed an implementation of the m‐SSE for local aromaticity of individual rings.…”

Current Density and Spectroscopy—A Themed Issue in Honor of Professor Riccardo Zanasi on the Occasion of His 70th Birthday

“…Other papers present theoretical and methodological advances in the calculation of the magnetic response: a topological analysis of the magnetically induced current density in strong magnetic fields [13], the partitioning of Hückel-London currents into cycle contributions [14], and decomposition in spatial contributions to 1H NMR chemical shifts [15].…”