Superposition of waves or densities: Which is the nature of chemical resonance?

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.

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.

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.

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.

Comment on "Superposition of Waves or Densities: Which Is the Nature of Chemical Resonance?" [J. Comput. Chem. 2021, 42, 412-417]

We reply to specific criticisms and misrepresentations of natural resonance theory (NRT) in a recent article [Y. Wang, J. Comput. Chem. 2021, 42, 412-417] and argue that it presents a false dichotomy with respect to theoretical efforts to comprehend the nature of resonance-type phenomena.

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

Due to methodological difficulties and limitations of applicability, a quantitative bonding analysis based on the theory of resonance is presently not as convenient and popular as that based on the molecular orbital (MO) methods. Here, we propose an efficient quantitative resonance theory by expanding the DFT wave function in terms of a complete set of Lewis structures. By rigorously separating the resonance subsystem represented by a set of localized MOs, this approach is able to treat large molecules, nonplanar π-conjugate systems, and bonding systems mixing both σ and π electrons. Assessment in 2c-2e systems suggests a new projection-weighted symmetric orthogonalization method to evaluate the weights of resonance contributors, which overcomes the drawbacks of other weighting schemes. Applications to benzene, naphthalene and chlorobenzene show that the present method is insensitive to the basis set employed in the DFT calculations, and to the choices of the independent Lewis set determined by Rumer's rule. Advanced applications to diverse chemical problems provide unique and valuable insights into the understanding of hydrogen bonding, the π substituent effect on benzene, and the mechanism of Diels-Alder reactions.

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.