A reliable and efficient resonance theory based on analysis of DFT wave functions

Generalized kekulenes and clarenes as novel families of cycloarenes: structures, stability, and spectroscopic properties

Cycloarenes constitute a captivating class of polycyclic aromatic hydrocarbons with unique structures and properties, but their synthesis represents a challenging task in organic chemistry. Kekulenes and edge-extended kekulenes as classic types of cycloarenes play an important role in the comprehension of π electron distribution, but their sparse molecular diversity considerably limits their further development and application. In this work, we propose two novel classes of cycloarenes, the generalized kekulenes and the clarenes. Using density functional theory, we carry out a comprehensive study of all possible isomers of the generalized kekulenes and clarenes with different sizes. By applying a simple Hückel model, we show that π delocalization plays a crucial role in determining the relative stability of isomers. We also discover that π-π stacking is commonly present in certain larger clarenes and provides a considerable additional stabilization effect, making the corresponding isomers the lowest-energy ones. Among all considered typical looped polyarenes, generalized kekulenes and/or clarenes are revealed to be the energetically most stable forms, suggesting that these novel cycloarenes proposed here would be viable targets for future synthetic work. The simulated 1H NMR spectra and UV-vis absorption spectra provide valuable information about the electronic and optoelectronic properties for the most stable generalized kekulene and clarene species and may support their identification in future synthesis and experimental characterization.

Enumeration, Nomenclature, and Stability Rules of Carbon Nanobelts

With recent breakthroughs and advances in synthetic chemistry, carbon nanobelts (CNBs) have become an emerging hot topic in chemistry and materials science. Owing to their unique molecular structures, CNBs have intriguing properties with applications in synthetic materials, host-guest chemistry, optoelectronics, and so on. Although a considerable number of CNBs with diverse forms have been synthesized, no systematic nomenclature is available yet for this important family of macrocycles. Moreover, little is known about the detailed isomerism of CNBs, which, in fact, exhibits greater complexity than that of carbon nanotubes. The copious variety of CNB isomers, along with the underlying structure-property relationships, bears fundamental relevance to the ongoing design and synthesis of novel nanobelts. In this paper, we propose an elegant approach to systematically enumerate, classify, and name all possible isomers of CNBs. Besides the simplest, standard CNBs defined by chiral indices (n, m), the nonstandard CNBs (n, m, l) involve an additional winding index l. Based on extensive quantum chemical calculations, we present a comprehensive study of the relative isomer stability of CNBs containing up to 30 rings. A simple Hückel-based model with a high predictive power reveals that the relative stability of standard CNBs is governed by the π stabilization and the strain destabilization induced by the cylindrical carbon framework, and the former effect prevails over the latter. For nonstandard CNBs, a third stability factor, the H···H repulsion in the benzo[c]phenanthrene-like motifs, is also shown to be important and can be incorporated into the simple quantitative model. In general, lower-energy CNB isomers have a larger HOMO-LUMO gap, suggesting that their thermodynamic stability coincides with kinetic stability. The most stable CNB isomers determined can be considered the optimal targets for future synthesis. These results lay an initial foundation and provide a useful theoretical tool for further research on CNBs and related analogues.

Fusion Position-Dependent Aromatic Transitions of Ligand Backbone Rings for Controlling the Redox Energetics of Photoredox Catalysts

To reveal, quantify, and rationalize the effect of backbone π-extension on ligand redox activity, we studied the ground- and excited-state reduction potentials of eight ruthenium photoredox catalysts with the formula Ru(ppy)2L (L is the redox-active ligand of the bipyridine family) using density functional theory. Our research underlines the profound importance of the fusion position of backbone aromatic C6 rings on the redox activity of ligands in transition metal photoredox catalysts. Namely, certain fusion positions lead to the dearomatization of C6 rings in ligand-centered electron transfer events, resulting in a thermodynamic penalty equivalent to a half-volt negative shift in the reduction potential. Contrarily, the extent of backbone delocalization shows a minimal impact on redox energetics, which can be explained by the charge concentration at the nitrogen contact atoms in ligand-centered reductions. Grounded in Caulton's conceptual framework, we reaffirm the predictive potency of Lewis structures in ligand-centered redox energetics with qualitative and quantitative data. Our hypothesis regarding the effect of backbone ring dearomatization on redox energetics is further corroborated using magnetic and structure-based aromaticity indicators. Highlighting fusion-dependent dearomatization as a determining factor of ligand-centered electron transfer energetics, our findings hold implications for molecular-level design in advanced electroactive materials and catalysts.

Infinitenes as the Most Stable Form of Cycloarenes: The Interplay among π Delocalization, Strain, and π-π Stacking

The recent successful preparation of infinitene has sparked widespread attention due to its aesthetic appeal and synthetic challenge. Spectroscopic measurements and follow-up computational investigations suggest that infinitene holds fundamental significance and potential applications in chiroptics, optoelectronics, asymmetric synthesis, and supramolecular chemistry. However, unlike other looped polyarenes enriched with sizes and shapes, the infinitene molecule seems, so far, the only known example of this fascinating new form of nanocarbons, whose further exploitation would be considerably limited because of the lack of molecular diversity. Here, we introduce a whole new family of generalized infinitenes with different sizes and topologies. Three types of infinitene structures are rationally designed by joining two units of coronene, kekulene, or their extended analogs. The constructed molecules of varying sizes, each with a large number of possible topoisomers, are systematically studied by DFT calculations. Comprehensive analysis using a simple energy decomposition model uncovers that the stability of infinitenes is governed by the interplay among π delocalization, steric strain, and π-π stacking. While the first two factors are crucial to the stability of smaller infinitenes, the latter is the primary stabilizing interaction for larger infinitenes. Most importantly, we show that larger-sized infinitenes are actually the energetically most favorable form among all known looped polyarenes; their substantial thermodynamic stability surpassing that of circulenes, various carbon nanobelts, and kekulene-like macrocycles renders them promising targets for synthesis. The simulated ¹H NMR, UV-vis, and circular dichroism spectra along with optical rotations for the most stable infinitene species may help their identification in future synthetic efforts.

Resonance-Enhanced Emission Effects toward Dual-State Emissive Bright Red and Near-Infrared Emitters

Resonance-enhanced emission (REE) effect was discovered and lead to a novel dye family of hydrostyryl pyridinium derivatives in our recent work. Herein, the REE effect was employed to design a red and near-infrared dual-state emissive fluorophore family of SW-OH-NO₂ derivatives which were easily synthesized by coupling an electron-withdrawing group (W) onto nitro(hydroxyl)styryl (S-OH-NO₂ ) through a C=C double bond as π-bridge. The deprotonation of a phenolic hydroxyl group promoted by a nitro group and the electron-withdrawing group (W) on the other side of the π-bridge triggered resonance, resulting in significantly red-shifted emission. All the resultant SW-OH-NO₂ compounds showed excellent dual-state emission behavior. Remarkably, hydrostyryl quinolinium (SQ-OH-NO₂ ) is one of the smallest NIR emitter molecular skeleton (λ_em =725 nm, MW<400) and showed dual-state emission characteristics and obvious viscosity-depended fluorescent behaviors. In addition to constructing electron donor-acceptor structures and prolonging π-bridges, the REE effect promises a reliable strategy toward novel fluorophores with small size, long emissive wavelength, and dual-emission characteristics, and importantly, feasible industrial manufactures and applications due to their easy and low-cost synthesis strategy.

Unusual In-plane Aromaticity Facilitates Intramolecular Hydrogen Transfer in Long-Bonded cis-Isonitrosyl Methoxide

The hydrogen-atom transfer from methoxy radical to nitric oxide, leading to the formation of formaldehyde and nitroxyl, represents a secondary reaction of photodissociation of methyl nitrite, which is used as rocket fuel. In this study, we explored the potential energy profile of the hydrogen-atom transfer using the electronic structure calculations at the DLPNO-CCSD(T)/aug-cc-pVTZ level of theory for two isomeric forms (cis and trans) of the pre-reaction complex. The cis-oriented pre-reaction complex has a weak elongated O─O bond, which gets further elongated in the hydrogen transfer transition state. This O─O bond stabilizes the pre-reaction complex by 32.9 kJ/mol. The O─O-induced stabilization is even greater for the transition state (48.2 kJ/mol), which was unexpected because of the larger O─O distance in the transition state structure. To address this paradox, we performed the electronic structure analysis of the reaction participants using the valence bond (VB) theory, natural resonance theory, topological analysis of the electron density and its derivatives, and analysis of the electron localization function distribution. This combined analysis led to the conclusion that the cis-transition state for hydrogen transfer, instead of being directly stabilized by the O─O interaction, gained substantial stabilization from the in-plane five-center six-electron aromaticity.

Electronic densities and valence bond wave functions

Valence bond (VB) wave functions are studied from the density point of view. The density is plotted as a difference with the quasi-state built on the same orbitals. The densities of the components of the VB wave function are also shown. The breathing orbital effect leads to small modifications of the density. It is shown that while the densities of ionic and covalent components are the same, their coupling ends-up in modifications of the electronic density.

Quantitative Resonance Theory Based on the Clar Sextet Model

Despite its great explanatory power in understanding the chemistry of polycyclic aromatic hydrocarbons (PAHs) and related systems, the Clar sextet rule still remains an intuitive and qualitative model with notable exceptions in some cases. Here we develop a quantitative theory of chemical resonance based on semilocalized Clar-type resonance structures (named the Clar resonators) consisting of variable numbers of Clar sextets and C═C bonds. The constructed wave functions of the Clar resonators are used to expand the actual wave function of the π-conjugated system obtained from a DFT or Hartree-Fock calculation. The resultant weights and one-electron energies of the Clar resonators can serve as a quantitative measure of the importance of these resonators. Implementing the theory in our open-source python code EzReson and applying it to over a thousand PAH molecules of different sizes and shapes, we show that the weight of the Clar resonators increases exponentially with increasing number of sextets and that their energy decreases linearly with the latter, thus confirming the general validity of the Clar rule. On the basis of such a large-scale resonance analysis, we propose three extended Clar rules, along with a unified quantitative model, that are able to evaluate the importance of all Clar resonators and the ring aromaticity for PAHs. Using the present theories, we uncover the essential role that the minor Clar resonators may play in correctly understanding the resonance stabilization and local aromaticity of rings, which was totally overlooked in the original Clar model.

Electrostatic effects in N-heterocyclic carbene catalysis: revealing the nature of catalysed decarboxylation

Quantum chemistry is used to investigate the nature of protonated N-heterocyclic carbene (NHC·H⁺) catalysed decarboxylation recently reported by Zhang et al. (ACS Catal., 2021, 11, 3443-3454). Our results show that there are strong electrostatic effects within the NHC·H⁺ catalysed decarboxylation, and these dominate hydrogen bonding. At the same time, energy decomposition analyses and comparison between the original NHC·H⁺ catalyst and a truncated form reveal that stabilizing dispersion interactions are also critical, as is induction. We also show that the electrostatic effects and their associated catalytic effects can be further enhanced using charged functional groups.

An analysis of valence electronic structure from a viewpoint of resonance theory: Tautomerization of formamide and diazadiboretidine

The resonance theory is still very useful in understanding the valence electron structure. However, such a viewpoint is not usually obtained by general-purpose quantum chemical calculations, instead requires rather special treatment such as valence bond methods. In this study, we propose a method based on second quantization to analyze the results obtained by general-purpose quantum chemical calculations from the local point of view of electronic structure and analyze diazadiboretidine and the tautomerization of formamide. This method requires only the "PS"-matrix, consisting of the density matrix (P-matrix) and overlap matrix, and can be computed with a comparable load to that of Mulliken population analysis. A key feature of the method is that, unlike other methods proposed so far, it makes direct use of the results of general-purpose quantum chemical calculations.

Extension and Quantification of the Fries Rule and Its Connection to Aromaticity: Large-Scale Validation by Wave-Function-Based Resonance Analysis

The Fries rule is a simple, intuitive tool to predict the most dominant Kekulé structures of polycyclic aromatic hydrocarbons (PAHs), which is valuable for understanding the structure, stability, reactivity, and aromaticity of these conjugated compounds. However, it still remains an empirical hypothesis, with limited qualitative applications. Herein, we verify, generalize, and quantify the Fries rule based on the recently developed resonance analysis of the DFT wave functions of over 1500 PAH and fullerene molecules with over a billion Kekulé structures. The extended rules, counting the numbers of electrons within all rings (not just sextets), are able to rank the relative importance of all Kekulé structures for all considered systems. The statistically meaningful quantification also opens a way to evaluate ring aromaticity based on the resonance theory, which generally agrees well with conventional aromaticity descriptors. Furthermore, we propose a purely graph-based aromaticity indicator nicely applicable to PAHs and fullerenes, with no need of any quantum chemistry calculations, so that it can make valuable predictions for molecular properties that are related to local aromaticity.

Response to comment on "Superposition of waves or densities: Which is the nature of chemical resonance?"

I reply to the comment by Weinhold and Glendening on the article (J. Comput. Chem. 2021, 42, 412). I provide further explanation and an additional numerical example to support my previous assertion that the present form of natural resonance theory is fundamentally flawed, at least within the DFT framework.

DDQ dehydrogenative Diels–Alder reaction for the synthesis of functionalized spiro[carbazole-1,3′-indolines] and spiro[carbazole-1,5′-pyrimidines]

Reactive 3-vinylindoles were generated by in situ DDQ oxidative dehydrogenation of 3-(indol-3-yl)-1,3-diphenylpropan-1-ones, and underwent sequential Diels–Alder reaction to give novel heterocyclic spirocarbazoles.