Can Aromaticity Be Evaluated Using Atomic Partitions Based on the Hilbert-Space?

Aromaticity is a fundamental concept in chemistry that explains the stability and reactivity of many compounds by identifying atoms within a molecule that form an aromatic ring. Reliable aromaticity indices focus on electron delocalization and depend on atomic partitions, which give rise to the concept of an atom-in-the-molecule (AIM). Real-space atomic partitions present two important drawbacks: a high computational cost and numerical errors, limiting some aromaticity measures to medium-sized molecules with rings up to 12 atoms. This restriction hinders the study of large conjugated systems like porphyrins and nanorings. On the other hand, traditional Hilbert-space schemes are free of the latter limitations but can be unreliable for the large basis sets required in modern computational chemistry. This paper explores AIMs based on three robust Hilbert-space partitions - meta-Löwdin, Natural Atomic Orbitals (NAO), and Intrinsic Atomic Orbitals (IAO) - which combine the advantages of real-space partitions without their disadvantages. These partitions can effectively replace real-space AIMs for evaluating the aromatic character. For the first time, we report multicenter index (MCI) and Iring values for large rings and introduce ESIpy, an open-source Python code for aromaticity analysis in large conjugated rings.

Understanding Aromaticity in [5]Helicene-Bridged Cyclophanes: A Comprehensive Study.

This study explores the aromaticity of doubly [5]helicene-bridged (1,4)cyclophane and triply [5]helicene-bridged (1,3,5)cyclophane via calculations of the magnetic response and of electronic aromaticity indices. The primary objective is to assess the π-electron delocalization to determine whether they sustain global ring currents associated with π aromaticity. The molecules show local ring currents in the presence of an external magnetic field. The ring currents flow diatropically in the stacked six-membered rings and in the helicene arms. However, these π currents are not interconnected due to the discontinuity of the π delocalization at the C-C single bonds connecting the central six-membered rings to the helicene arms. Electronic indices suggest that the helicene-arm systems have significantly smaller electron delocalization than benzene. The reduction in the delocalization does not compromise their ability to exhibit ring currents in the presence of an external magnetic field. The analysis provides further evidence that the magnetic criteria yield a different degree of aromaticity for the helicene arms than obtained in the calculation of the electronic aromaticity indices. However, both approaches confirm that the studied molecules are not globally aromatic.

From (Sub)Porphyrins to (Sub)Phthalocyanines: Aromaticity Signatures in the UV-Vis Absorption Spectra.

The development of novel synthetic methods has greatly expanded the toolbox available to chemists for engineering porphyrin and phthalocyanine derivatives with precise electronic and optical properties. In this study, we focus on the UV-vis absorption characteristics of substituted phthalocyanines and their contracted analogs, subphthalocyanines, which feature nonplanar, bowl-shaped geometries. These macrocycles, which are central to numerous applications in materials science and catalysis, possess extensive π-conjugated systems that drive their unique electronic properties. We explore how the change from a metalloid (B) to a metal (Zn) and the resulting coordination environments influence the aromaticity and, consequently, the spectroscopic features of these systems. A combined computational and experimental approach reveals a direct correlation between the aromaticity of the external conjugated pathways and the Q bands in the UV-vis spectra. Our findings highlight key structural modifications that can be leveraged to fine-tune the optical properties of porphyrinoid systems, offering new pathways for the design of advanced materials and catalysts with tailored functionalities.

Unveiling the quantum secrets of triel metal triangles: a tale of stability, aromaticity, and relativistic effects.

Low lying electronic states of Al3-, Ga3-, In3-, and Tl3- have been characterized using high level multiconfigurational quasi degenerate perturbation theory on the multiconfigurational self-consistent field. Among these species, the singlet states emerge as the predominant energy minima, displaying remarkable stability. However, within the Tl3- series, our investigation leads to the identification of the high-spin , as the most stable spin state, a result corroborated by previous experimental detection via photoelectron spectroscopy. Similarly, we have also identified the singlet state of In3- as the signal detected previously experimentally. By applying Mandado's rules and an array of aromaticity indicators, it is conclusively demonstrated that both the singlet and quintet states exhibit multiple-fold aromaticity, while the triplets exhibit conflicting aromaticity. Furthermore, this investigation highlights the significant impact of relativistic effects, as they enhance the stability of the state relative to its singlet counterpart. These findings shed new light on the electronic structures and properties of these ions, offering valuable insights into their chemical behavior and potential applications.

Quest for the Most Aromatic Pathway in Charged Expanded Porphyrins.

Despite the central role of aromaticity in the chemistry of expanded porphyrins, the evaluation of aromaticity remains difficult for these extended macrocycles. The presence of multiple conjugation pathways and different planar and nonplanar π-conjugation topologies makes the quantification of global and local aromaticity even more challenging. In neutral expanded porphyrins, the predominance of the aromatic conjugation pathway passing through the imine-type nitrogens and circumventing the amino NH groups is established. However, for charged macrocycles, the question about the main conjugation circuit remains open. Accordingly, different conjugation pathways in a set of neutral, anionic, and cationic expanded porphyrins were investigated by means of several aromaticity indices rooted in the structural, magnetic, and electronic criteria. Overall, our results reveal the predominance of the conjugation pathway that passes through all nitrogen atoms to describe the aromaticity of deprotonated expanded porphyrins, while the outer pathway through the perimeter carbon atoms becomes the most aromatic in protonated macrocycles. In nonplanar and charged macrocycles, a discrepancy between electronic and magnetic descriptors is observed. Nevertheless, our work demonstrates AVmin remains the best tool to determine the main conjugation pathway of expanded porphyrins.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment.

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Electric-field induced second harmonic generation responses of push-pull polyenic dyes: experimental and theoretical characterizations.

The second-order nonlinear optical properties of four series of amphiphilic cationic chromophores involving different push-pull extremities and increasingly large polyenic bridges have been investigated both experimentally, by means of electric field induced second harmonic (EFISH) generation, and theoretically, using a computational approach combining classical molecular dynamics (MD) and quantum chemical (QM) calculations. This theoretical methodology allows to describe the effects of structural fluctuations on the EFISH properties of the complexes formed by the dye and its iodine counterion, and provides a rationale to EFISH measurements. The good agreement between experimental and theoretical results proves that this MD + QM scheme constitutes a useful tool for a rational, computer-aided, design of SHG dyes.

Three-centre electron sharing indices (3c-ESIs) as a tool to differentiate among (an)agostic interactions and hydrogen bonds in transition metal complexes.

The agostic bond plays an important role in chemistry, not only in transition metal chemistry but also in main group chemistry. In some complexes with M⋯H-X (X = C, N) interactions, differentiation among agostic, anagostic, and hydrogen bonds is challenging. Here we propose the use of three-centre electron sharing indices to classify M⋯H-X (X = C, N) interactions.

Excited state dynamics and conjugation effects of the photoisomerization reactions of dihydroazulene.

Herein, we present an investigation of the excited state dynamics of the dihydroazulene photoswitch and its photoinduced reaction to vinylheptafulvene. The focus is on how the introduction of a benzannulated ring in different sites of the structure can modify the excited state topology and thus the kinetics of the ring opening reaction of DHA by alteration of the excited state conjugation of the system. The dynamics of the systems is obtained utilizing ab initio density functional theory calculations in different solvents coupled with unimolecular reaction theory. To accompany these results, the electron delocalization is investigated using the quantum theory of atoms in molecules partitioning to follow the trends induced by the benzannulated ring. It is observed that the introduction of a benzannulated ring can both enhance and diminish the rate of the photoinduced ring opening of dihydroazulene and that certain patterns of conjugation are consistent with the rate constants. Lastly, we find good agreement with earlier experimental studies indicating that the chosen approach could be used to predict whether photochromic systems lose their photoswitchability upon being optimized for specific applications via functionalization.

Natural range separation of the Coulomb hole.

A natural range separation of the Coulomb hole into two components, one of them being predominant at long interelectronic separations (hcI ) and the other at short distances (hcII ), is exhaustively analyzed throughout various examples that put forward the most relevant features of this approach and how they can be used to develop efficient ways to capture electron correlation. We show that hcI , which only depends on the first-order reduced density matrix, can be used to identify molecules with a predominant nondynamic correlation regime and differentiate between two types of nondynamic correlation, types A and B. Through the asymptotic properties of the hole components, we explain how hcI can retrieve the long-range part of electron correlation. We perform an exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting the hole contributions into spin components. We also analyze the simplest molecule presenting a dispersion interaction and how hcII helps identify it. The study of several atoms in different spin states reveals that the Coulomb hole components distinguish correlation regimes that are not apparent from the entire hole. The results of this work hold out the promise to aid in developing new electronic structure methods that efficiently capture electron correlation.