Aromaticity and Electron Delocalization

The macrocycles 1-3 were prepared by Nwachukwu and Tykwinski. Their 1H NMR spectra were studied and the X-ray structure of 2 was determined.
The ortho protons chemical shifts are 5.935, 8.4 and 10.2 ppm for 1, 2 and 3, respectively, indicating paratropic ring current in 1 and diatropic ring current in 2 and 3.

Geometry optimizations were carried out using B3LYP and CAM-B3LYP with and without D3 dispersion corrections. NMR and NICS calculations were carried out with these functionals and with BLYP35. OX-BLYP was also attempted. The wave functions of three systems are unstable as a closed shell singlets. There is no correlation between the experimental data and a specific computational method. Thus, for example, the best geometrical description for 2 is obtained at the open-shell CAM-B3LYP, while the NMR chemical shift fits the calculated ones at BLYP35//B3LYP-D3 for 1, CAM-B3LYP//CAM-B3LYP-D3 for 2 and BLYP35//CAM-B3LYP-D3 for 3, all in their (wrong) closed shell wave function. It is concluded that, unless optimized for specific systems, DFT methods yield, at best, qualitative results for systems such as 1-3.

for the performance of organic electronic devices. As previously shown, the gas-phase aromaticity of a molecule strongly influences both the nature and strength of its interaction with a metal surface. Upon adsorption, however, aromaticity can change significantly. Understanding these changes is not only of fundamental interest but may also provide insights beyond conventional interface descriptors and help explain degradation processes.
Using density functional theory with periodic boundary conditions, we applied geometric, electronic, and magnetic aromaticity indices to investigate adsorbed π-systems. We studied 11 alternant and 11 non-alternant PCHs on Cu(111), covering interactions from physisorption to strong chemisorption. The adsorption-induced changes in aromaticity showed no clear correlation with established interface properties, indicating that aromaticity captures complementary aspects of the metal-organic interaction.
Furthermore, we confirmed aromaticity-driven charge transfer for a corrole adsorbed on Ag(111), extending previous evidence based only on comparisons with charged gas-phase species. The methodology established here enables the direct evaluation of aromaticity under periodic boundary conditions and is broadly applicable, even beyond metal-organic interfaces.

Electron delocalization error is one of the most pervasive deficiencies of modern density-functional approximations (DFAs). It leads to an inaccurate description of molecular electron distributions and, in turn, to a severe overestimation of electron delocalization and aromaticity. These effects can be mitigated by employing DFAs with a sufficiently large fraction of Hartree–Fock exchange (HFX). Yet, despite extensive analyses of this problem, the literature still contains routine studies of molecules prone to delocalization errors that rely entirely on functionals such as B3LYP. Other works adopt an intermediate strategy, evaluating properties with a DFA less susceptible to delocalization error but using geometries optimized with functionals containing low HFX.

In this work, we analyze the extent to which delocalization error affects molecular geometry and electronic properties, and how these two effects become intertwined, leading to a spurious description of chemical bonding. By examining delocalization and aromaticity descriptors of different nature, we identify which combinations of geometries and property-evaluation functionals, as well as which classes of molecules, are most prone to large delocalization errors. Our results also show how these errors can be substantially minimized through a judicious choice of DFA.

Few concepts in chemistry have been as influential, and as stretched, as aromaticity. The classical circle in benzene was meant to express an exceptional ground-state bonding pattern: a coherent system of cyclically delocalized π bonds. Yet it is now frequently read together with another circle — the arrowed loop of a magnetically induced ring current. This overlap is not, by itself, a problem. Magnetic aromaticity has a legitimate role in describing spectroscopic response properties. The difficulty begins when magnetic finger-prints are treated as structural evidence: when ring-current maps are used to assign Clar patterns, draw dashed Lewis bonds, or extend Hückel and Baird arguments to polycyclic and macrocyclic systems.
We revisit this shortcut from the common ground of molecular orbital (MO) theory. Cumulative MO-resolved spectral decompositions of induced currents reveal the orbital excitations responsible for magnetic response, whereas BDF-type approaches recover the coherence, or loss of coherence, of conjugated bonding in the unperturbed electronic state. We argue that separating these complementary descriptions is essential for restoring aromaticity as a predictive chemical concept: not merely a controversial label, but a tool for explaining the stability, experimental isolability, and optical/electronic properties of exceptional conjugated molecules.

Aromaticity and antiaromaticity are twin concepts, where the first leads to compounds with exceptionally high stability relative to nonaromatic isomers while the second, in its original form by Breslow, leads to compounds with exceptionally low stability. Yet, the concepts are fuzzy and have been debated for decades. We find that analyzing the limitations in excited states is revealing. For the lowest pp* triplet states, Baird showed in 1972 that 4np-electron cycles are aromatic and those with 4n+2 are antiaromatic, opposite to Hückel’s rule for the closed-shell singlet ground state (S0). It has been found through computations that Baird’s rule in several cases also can be extended to the lowest pp* singlet state. Yet, how does this translate to the lowest excited states of species which are s-aromatic in their S0 states? We revealed that H3+ (Figure 1), which is s-aromatic in S0 and the most abundant aromatic species in the Universe, is s-antiaromatic in first 1ss* states. This leads to an extensive destabilization and a lowest vertical excitation energy of 19.3 eV. We have now also explored the nonclassical vinyl and ethyl cations, having similar 3-center 2-electron bonding as H3+, and find similarities in the aromaticity of the S0 state and antiaromaticity of some of the ss* states. Conversely, we will also discuss the tentative Baird s-aromaticity of the hypothetical H4 molecule in its first ss* states.

Delocalization is one of the foundational principles of modern chemical theory. From resonance structures to band theory, it provides the framework for how we understand conjugated systems. Yet delocalization also carries an implicit assumption: that a molecule’s electronic behavior is an emergent, holistic property—not reducible to the sum of its parts.

And yet… what if it is?

In this talk, I explore the surprising success of additivity in predicting magnetic properties of conjugated molecules. Through a series of studies on NICS-XY-Scans,1,2 bond currents, and current densities,3 we show that even large polycyclic systems can be modeled accurately using only a small set of mono-, bi-, and tricyclic subunits. This is not merely a computational convenience—it is also a window into the behavior of polycyclic aromatic systems.

Strikingly, this pattern of locality also emerges from an entirely different direction: deep learning. Using graph neural networks trained only on small molecules, we achieve accurate predictions of magnetic behavior in systems many times larger.4 That these models succeed reinforces a central point: delocalization, at least in its magnetic manifestation, behaves as though it is fundamentally local.

This rethinking opens new avenues for how we understand, predict, and ultimately design π-conjugated systems—not by ignoring delocalization, but by redefining its scope.