Substituent-modulated adaptive aromaticity in NHC-pyrrolyl cations: a combined DFT and machine learning study

The stabilization of 4π-electron systems remains a fundamental challenge in chemistry, stemming from their intrinsic antiaromaticity and thermodynamic instability as dictated by Hückel's rule. A recent experimental study has demonstrated that rational molecular design using N-heterocyclic carbenes (NHCs) can surmount these limitations by inducing aromaticity. However, the issue of T₁ aromaticity in such systems remains unresolved. Elucidating the substituent-modulated behavior of T₁ (anti)aromaticity is crucial for deciphering the physicochemical properties of these systems. In this work, Density Functional Theory (DFT) was employed to investigate the (anti)aromaticity of NHC-substituted pyrrolyl cations and substituted pyrrolyl anions in both the singlet ground state (S₀) and triplet excited state (T₁). Our results reveal a clear correlation between substituents and adaptive aromaticity. Notably, within the reduced pyrrole framework (A-H), only the nitroso (NO) substituent (A) is capable of inducing adaptive aromaticity. In contrast, for the NHC-substituted pyrrolyl cations (I-P), two-state aromaticity is sequentially triggered by the substituent effects of NO, NO₂, CHO, and COCH₃. Spin density analysis reveals distinct electronic behaviors across the studied systems. In adaptively aromatic compounds, the major electron spin density localizes on the substituent, thereby preserving the aromatic character of the pyrrole ring. Conversely, for systems B-D, F-H, and M-P, the spin density is predominantly concentrated on the pyrrolyl ring moiety, which disrupts aromaticity. This conclusion is supported by computational analyses of multiple aromaticity descriptors, including the harmonic oscillator model of aromaticity (HOMA), nucleus-independent chemical shift (NICS(1)_zz), multicenter indices (MCI), anisotropy of the induced current density (ACID), and electron density of the delocalized π-bond (EDDB_π). Regression analysis (a supervised machine learning technique) indicates that the spin density on the substituent is strongly correlated with the T₁ aromaticity. Our findings highlight the pivotal role of substituents in regulating two-state aromaticity in heterocyclic systems, laying a solid theoretical foundation for advanced applications in molecular electronics and materials science.