The excited state antiaromatic benzene ring: a molecular Mr Hyde?

On the notion of strong correlation in electronic structure theory

Strong correlation has been said to have many faces, and appears to have many synonyms of questionable suitability. In this work we aim not to define the term once and for all, but to highlight one possibility that is both rigorously defined and physically transparent, and remains so in reference to molecules and quantum lattice models. We survey both molecular examples - hydrogen systems (Hn, n = 2, 4, 6), Be2, H-He-H, and benzene - and the half-filled Hubbard model over a range of correlation regimes. Various quantities are examined including the extent of spin symmetry breaking in correlated single-reference wave functions, energetic ratios inspired by the Hubbard model and the Virial theorem, and metrics derived from the one- and two-electron reduced density matrices (RDMs). The trace and the square norm of the cumulant of the two-electron reduced density matrix capture what may well be defined as strong correlation. Accordingly, strong correlation is understood as a statistical dependence between two electrons, and is distinct from the concepts of "correlation energy" and more general than entanglement quantities that require a partitioning of a quantum system into distinguishable subspaces. This work enables us to build a bridge between a rigorous and quantifiable regime of strong electron correlation and more familiar chemical concepts such as anti-aromaticity in the context of Baird's rule.

Excited-state aromaticity reversals in norcorrole

Aromaticity reversals between the electronic ground state (S0) and the lowest triplet (T1) and singlet (S1) excited states of NiII norcorrole (NiNc) and norcorrole (H2Nc) are investigated by comparing the HOMA (harmonic oscillator model of aromaticity) values at the optimized S0, T1 and S1 geometries, and by analysing the changes in the nucleus-independent chemical shift (NICS) values and in the isotropic magnetic shielding distributions between the S0 and T1 states. The results strongly suggest that the antiaromatic features of the S0 states of the NiNc and H2Nc molecules, two very similar antiaromatic "internal crosses", undergo aromaticity reversals upon excitation to T1 or S1 and merge with the aromatic peripheries to produce Baird-aromatic systems with 24 π electrons each. Somewhat counterintuitively, the geometries of the fully aromatic T1 and S1 states of NiNc and H2Nc turn out to have larger bowl depths and so are more non-planar than the corresponding S0 geometries at which both molecules display antiaromatic features.

Aromaticity and Antiaromaticity Reversals between the Electronic Ground State and the Two Lowest Triplet States of Thiophene

It is shown, by examining the variations in off-nucleus isotropic magnetic shielding around a molecule, that thiophene which is aromatic in its electronic ground state (S0) becomes antiaromatic in its lowest triplet state (T1) and then reverts to being aromatic in T2. Geometry relaxation has an opposite effect on the aromaticities of the ππ* vertical T1 and T2: The antiaromaticity of T1 is reduced whereas the aromaticity of T2 is enhanced. The shielding picture around T2 is found to closely resemble those around certain second singlet ππ* excited states (S2), for example, those of benzene and cyclooctatetraene, thought to be "strongly aromatic" because of their very negative nucleus-independent chemical shift (NICS) values. It is argued that while NICS values correctly follow the changes in aromaticity along the potential energy surface of a single electronic state, the use of NICS values for the purpose of quantitative comparisons between the aromaticities of different electronic states cannot be justified theoretically and should be avoided. "Strongly aromatic" S2 and T2 states should be referred to simply as "aromatic" because detailed comparisons between the properties of these states and those of the corresponding S0 states do not suggest higher levels of aromaticity.

The n,π* States of Heteroaromatics: When are They the Lowest Excited States and in What Way Can They Be Aromatic or Antiaromatic?

Heteroaromatic molecules are found in areas ranging from biochemistry to photovoltaics. We analyze the n,π* excited states of 6π-electron heteroaromatics with in-plane lone pairs (nσ, herein n) and use qualitative theory and quantum chemical computations, starting at Mandado's 2n + 1 rule for aromaticity of separate spins. After excitation of an electron from n to π*, a (4n + 2)π-electron species has 2n + 2 πα-electrons and 2n + 1 πβ-electrons (or vice versa) and becomes πα-antiaromatic and πβ-aromatic. Yet, the antiaromatic πα- and aromatic πβ-components seldom cancel, leading to residuals with aromatic or antiaromatic character. We explore vertically excited triplet n,π* states (3n,π*), which are most readily analyzed, but also singlet n,π* states (1n,π*), and explain which compounds have n,π* states with aromatic residuals as their lowest excited states (e.g., pyrazine and the phenyl anion). If the πβ-electron population becomes more (less) uniformly distributed upon excitation, the system will have an (anti)aromatic residual. Among isomers, the one that has the most aromatic residual in 3n,π* is often of the lowest energy in this state. Five-membered ring heteroaromatics with one or two N, O, and/or S atoms never have n,π* states as their first excited states (T1 and S1), while this is nearly always the case for six-membered ring heteroaromatics with electropositive heteroatoms and/or highly symmetric (D2h) diheteroaromatics. For the complete compound set, there is a modest correlation between the (anti)aromatic character of the n,π* state and the energy gap between the lowest n,π* and π,π* states (R2 = 0.42), while it is stronger for monosubstituted pyrazines (R2 = 0.84).

3,4-Dimethylenecyclobutene: A Building Block for Design of Macrocycles with Excited State Aromatic Low-Lying High-Spin States

3,4-Dimethylenecyclobutene (DMCB) is an unusual isomer of benzene. Motivated by recent synthetic progress to substituted derivatives of this scaffold, we carried out a theoretical and computational analysis with a particular focus on the extent of (anti)aromatic character in the lowest excited states of different multiplicities. We found that the parent DMCB is non-aromatic in its singlet ground state (S0), lowest triplet state (T1), and lowest singlet excited state (S1), while it is aromatic in its lowest quintet state (Q1) as this state is represented by a triplet multiplicity cyclobutadiene (CBD) ring and two uncoupled same-spin methylene radicals. Interestingly, the Q1 state, despite having four unpaired electrons, is placed merely 4.8 eV above S0, and there is a corresponding singlet tetraradical 0.16 eV above. The DMCB is potentially a highly useful structural motif for the design of larger molecular entities with interesting optoelectronic properties. Here, we designed macrocycles composed of fused DMCB units, and according to our computations, two of these have low-lying nonet states (i. e., octaradical states) at energies merely 2.40 and 0.37 eV above their S0 states as a result of local Hückel- and Baird-aromatic character of individual 6π- and 4π-electron monocycles.

Excited-state antiaromaticity relief drives facile photoprotonation of carbons in aminobiphenyls

A combined computational and experimental study reveals that ortho-, meta- and para-aminobiphenyl isomers undergo distinctly different photochemical reactions involving proton transfer. Deuterium exchange experiments show that the ortho-isomer undergoes a facile photoprotonation at a carbon atom via excited-state intramolecular proton transfer (ESIPT). The meta-isomer undergoes water-assisted excited-state proton transfer (ESPT) and a photoredox reaction via proton-coupled electron transfer (PCET). The para-isomer undergoes a water-assisted ESPT reaction. All three reactions take place in the singlet excited-state, except for the photoredox process of the meta-isomer, which involves a triplet excited-state. Computations illustrate the important role of excited-state antiaromaticity relief in these photoreactions.

Theoretical investigation on regulating photophysical properties and proton transfer behavior by electronegativity for near-infrared emitting styryl dyes

Our main focus is to explore the atomic electronegativity-dependent photoinduced behavior of styryl derivatives (HBO, HBS, and HBSe). The results of structural parameter calculation by the DFT method show that the intramolecular hydrogen bonds of normal and tautomer form are strengthened and weakened, respectively, in an excited state (S1), which is conducive to the excited intramolecular proton transfer (ESIPT) process. The enhancement of excited hydrogen bond is beneficial to the ESIPT process from the aspects of infrared vibration frequency (IR), Mulliken's charge analysis, and density gradient reduction (RDG). Additionally, by determining the bond energy with the band critical point (BCP) parameter, we found that the lower the electronegativity of the atom, the larger the hydrogen bond strength at the excited state and the more likely ESIPT reaction occurs. Meanwhile, the intramolecular H-bonds O-H…N in HBO, HBS, and HBSe are enhanced with the weakened electron-withdrawing capacity of the atom (from O to S and Se). Subsequently, frontier molecular orbital (FMOs) and charge density difference (CDD) analyses essentially revealed that electron redistribution induces the ESIPT process. Low atomic electronegativity exhibits the high chemical activity of the excited state. Furthermore, to demonstrate the electronegativity-dependent ESIPT behavior of the system, we built potential energy curves (PECs) and located the transition states (TS) of proton transfer processes.

Small is Beautiful: Electronic Origin and Synthetic Evolution of Single-Benzene Fluorophores

ConspectusSingle-benzene fluorophores (SBFs) are small molecules that produce visible light by using only one benzene ring as the sole aromatic core. This Account centers around the chemistry of a new class of SBF that we accidentally discovered but rationally developed and refined afterward. In a failed experiment that took an unintended reaction pathway, we encountered the bright green fluorescence of ortho-diacetylphenylenediamine (o-DAPA). Despite its uninspiring look, reminiscent of textbook examples of simple benzene derivatives, this molecule had neither been synthesized nor isolated before. This discovery led to our studies on the larger DAPA family, including isomeric m-DAPA and p-DAPA. Remarkably, p-DAPA is the lightest red fluorophore, with a molecular weight of only 192. While o- and p-DAPA are emissive, m-DAPA rapidly undergoes internal conversion, facilitated by sequential proton transfer reactions in the excited state.Leveraging the synthetic utility of the amine group, we carried out straightforward single-step modifications to create a full-color SBF library from p-DAPA as the common precursor. During the course of the investigation, we made another fortuitous discovery. With increasing acidity of the N-H group, the excited-state intramolecular proton transfer reaction is promoted, opening up additional pathways for emission to occur at even longer wavelengths. Tipping the balance between the two excited-state tautomers enabled the first example of a single-benzene white-light emitter. We demonstrated the practical utility of these molecules in white light-emitting devices and live cell imaging.According to the particle-in-a-box model, it is difficult to expect a molecule with only one small aromatic ring to produce long-wavelength emission. SBFs rise to this challenge by exploiting electron donor-acceptor pairs around the benzene core, which lowers the energy of light absorption. However, this answers only half of the question. Where do the exceptionally large spectral shifts in the light emission of SBFs originate from? Chemists have long been curious about the molecular mechanisms underlying the dramatic spectral shifts observed in SBFs. Prevailing paradigms invoke the charge transfer (CT) between electron donor and acceptor groups in the excited state. However, without a large π-skeleton for effective charge separation, how could benzene support a CT-type excited state? Our experimental and theoretical studies have revealed that large excited-state antiaromaticity (ESAA) of the benzene core itself is responsible for this remarkable phenomenon. The core matters, not the periphery. With appropriate molecular design, large and extended π-conjugation is no longer a prerequisite for long-wavelength light emission.

The application of aromaticity and antiaromaticity to reaction mechanisms

Aromaticity, in general, can promote a given reaction by stabilizing a transition state or a product via a mobility of π electrons in a cyclic structure. Similarly, such a promotion could be also achieved by destabilizing an antiaromatic reactant. However, both aromaticity and transition states cannot be directly measured in experiment. Thus, computational chemistry has been becoming a key tool to understand the aromaticity-driven reaction mechanisms. In this review, we will analyze the relationship between aromaticity and reaction mechanism to highlight the importance of density functional theory calculations and present it according to an approach via either aromatizing a transition state/product or destabilizing a reactant by antiaromaticity. Specifically, we will start with a particularly challenging example of dinitrogen activation followed by other small-molecule activation, C-F bond activation, rearrangement, as well as metathesis reactions. In addition, antiaromaticity-promoted dihydrogen activation, CO2 capture, and oxygen reduction reactions will be also briefly discussed. Finally, caution must be cast as the magnitude of the aromaticity in the transition states is not particularly high in most cases. Thus, a proof of an adequate electron delocalization rather than a complete ring current is recommended to support the relatively weak aromaticity in these transition states.

Non-adiabatic dynamics simulations of the S1 excited-state relaxation of diacetyl phenylenediamine

The small molecule built around the benzene ring, diacetyl phenylenediamine (DAPA), has attracted much attention due to its synthesis accessibility, large Stokes shift, etc. However, its meta structure m-DAPA does not fluoresce. In a previous investigation, it was found that such a property is due to the fact that it undergoes an energy-reasonable double proton transfer conical intersection during the deactivation of the S₁ excited-state, then returns to the ground state by a nonradiative relaxation process eventually. However, our static electronic structure calculations and non-adiabatic dynamics analysis results indicate that only one reasonable non-adiabatic deactivation channel exists: after being excited to the S₁ state, m-DAPA undergoes an ultrafast and barrierless ESIPT process and reaches the single-proton-transfer conical intersection. Subsequently, the system either returns to the keto-form S₀ state minimum with proton reversion or returns to the single-proton-transfer S₀ minimum after undergoing a slight twist of the acetyl group. The dynamics results show that the S₁ excited-state lifetime of m-DAPA is 139 fs. In other words, we propose an efficient single-proton-transfer non-adiabatic deactivation channel of m-DAPA that is different from previous work, which can provide important mechanistic information of similar fluorescent materials.

Quadripartite bond length rule applied to two prototypical aromatic and antiaromatic molecules

CONTEXT

In 2000, a remarkably simple relationship was introduced, which connected the calculated geometries of isomolecular states of three different multiplicities. These encompass a ground single state, the first excited triplet state, as well as related radical anion and radical cation. The rule allows the prediction of the geometry of one of the species if the three remaining ones are known. Here, we verify the applicability of this bond length rule for two small planar cyclic organic molecules, i.e., benzene and cyclobutadiene, which stand as prototypical examples of, respectively, aromatic and antiaromatic systems. We see that the rule works fairly well to benzene, and it works independently for quinoid as well as for anti-quinoid minima, despite the fact that radical anion species poses challenges for correct theoretical description.

METHODS

To obtain chosen electronic state equilibrium geometries, three types of computational approaches were utilized: fast and efficient density functional theory DFT, the coupled cluster method CC2, the complete active space self-consistent field (CASSCF) approach, and the most accurate but also resource-consuming perturbation theory with multireference wavefunction (CASPT2) with a default value and without IPEA-shift. Dunning and co-workers correlation-consistent basis sets (aug-)cc-pVXZ (X = D, T, Q) were employed. Gaussian 16 revision A.03, Turbomole 7.1, and Molcas 8.0 computational software were used.

How Different are the Diamagnetic and Paramagnetic Contributions to Off-Nucleus Shielding in Aromatic and Antiaromatic Rings?

The spatial variations in the diamagnetic and paramagnetic contributions to the off-nucleus isotropic shielding, σ i s o r = σ i s o d r + σ i s o p r ${\ {{\sigma }_{{\rm i}{\rm s}{\rm o}}\left({\bf r}\right)=\ \sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm d}}\left({\bf r}\right)+{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm p}}\left({\bf r}\right)}$ , and to the zz component of the off-nucleus shielding tensor, σ z z r = σ z z d r + σ z z p r ${{{\sigma }_{zz}\left({\bf r}\right)=\sigma }_{zz}^{{\rm d}}\left({\bf r}\right)+{\sigma }_{zz}^{{\rm p}}\left({\bf r}\right)}$ , around benzene (C₆ H₆ ) and cyclobutadiene (C₄ H₄ ) are investigated using complete-active-space self-consistent field wavefunctions. Despite the substantial differences between σ i s o r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}\left({\bf r}\right)}$ and σ z z r ${{\sigma }_{zz}\left({\bf r}\right)}$ around the aromatic C₆ H₆ and the antiaromatic C₄ H₄ , the diamagnetic and paramagnetic contributions to these quantities, σ i s o d r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm d}}\left({\bf r}\right)}$ and σ z z d r ${{\sigma }_{zz}^{{\rm d}}\left({\bf r}\right)}$ , and σ i s o p r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm p}}\left({\bf r}\right)}$ and σ z z P r ${{\sigma }_{zz}^{{\rm P}}\left({\bf r}\right)}$ , are found to behave similarly in the two molecules, shielding and deshielding, respectively, each ring and its surroundings. The different signs of the most popular aromaticity criterion, the nucleus-independent chemical shift (NICS), in C₆ H₆ and C₄ H₄ are shown to follow from a change in the balance between the respective diamagnetic and paramagnetic contributions. Thus, the different NICS values for antiaromatic and antiaromatic molecules cannot be attributed to differences in the ease of access to excited states only; differences in the electron density, which determines the overall bonding picture, also play an important role.

Ultrafast Excited State Aromatization in Dihydroazulene

Excited-state aromatization dynamics in the photochemical ring opening of dihydroazulene (DHA) is investigated by nonadiabatic molecular dynamics simulations in connection with the mixed-reference spin-flip (MRSF)-TDDFT method. It is found that, in the main reaction channel, the ring opening occurs in the excited state in a sequence of steps with increasing aromaticity. The first stage lasting ca. 200 fs produces an 8π semiaromatic S₁ minimum (S_1, min) through an ultrafast damped bond length alternation (BLA) movement synchronized with a partial planarization of the cycloheptatriene ring. An additional ca. 200 fs are required to gain the vibrational energy needed to overcome a ring-opening transition state characterized by an enhanced Baird aromaticity. Unlike other BLA motions of ππ* state, it was shown that their damping is a characteristic feature of aromatic bond-equalization process. In addition, some minor channels of the reaction have also been discovered, where noticeably higher barriers of the S₁ non/antiaromatic transition structures must be surmounted. These anti-Baird channels led to reformation of DHA or other closed-ring products. The observed competition between the Baird and anti-Baird channels suggests that the quantum yield of photochemical products can be controllable by tipping their balance. Hence, here we suggest including the concept of anti-Baird, which would expand the applicability of Baird rule to much broader situations.

Aromaticity controls the excited-state properties of host-guest complexes of nanohoops

π-Conjugated organic molecules have exciting applications as materials for batteries, solar cells, light-emitting diodes, etc. Among these systems, antiaromatic compounds are of particular interest because of their smaller HOMO-LUMO energy gap compared to aromatic compounds. A small HOMO-LUMO gap is expected to facilitate charge transfer in the systems. Here we report the ground and excited-state properties of two model nanohoops that are nitrogen-doped analogs of recently synthesized [4]cyclodibenzopentalenes - tetramers of benzene-fused aromatic 1,4-dihydropyrrolo[3,2-b]pyrrole ([4]DHPP) and antiaromatic pyrrolo[3,2-b]pyrrole ([4]PP). Their complexes with C60 fullerene show different behavior upon photoexcitation, depending on the degree of aromaticity. [4]DHPP acts as an electron donor, whereas [4]PP is a stronger electron acceptor than C60. The ultrafast charge separation combined with the slow charge recombination that we found for [4]PP⊃C60 indicates a long lifetime of the charge transfer state.

A Benchmark Study of Aromaticity Indexes for Benzene, Pyridine, and the Diazines - II. Excited State Aromaticity

In this work, one geometrical aromaticity index and four electron sharing indexes are benchmarked for their application in excited state aromaticity calculations. Two computationally feasible and reliable procedures are identified, namely, CAM-B3LYP/cc-pVTZ and ωB97X-D/cc-pVTZ. Topological effects on the first excited singlet and triplet electronic manifold were investigated, and the latter was in general found to display more aromatic character compared to the S₁ surface. Besides, geometrical relaxation on each of the manifolds was observed to hamper the aromaticity, thereby resulting in more antiaromatic character. The relative order of excited state aromaticity within the studied molecules was noted to resemble the reversed version of the relative order of ground state aromaticity. Thereby, the following generalization was postulated: The more aromatic a molecule is in its ground state, the more antiaromatic it will be in its electronic first excited manifolds.

Baird's rules at the tipping point

This year marks the 50th anniversary of Baird’s rules of aromaticity — a set of perturbational molecular orbital theory analyses that has garnered considerable attention in the past ten years in light of its many real-world applications in photochemistry.

Localized Antiaromaticity Hotspot Drives Reductive Dehydrogenative Cyclizations in Bis- and Mono-Helicenes

We describe reductive dehydrogenative cyclizations that form hepta-, nona-, and decacyclic anionic graphene subunits from mono- and bis-helicenes with an embedded five-membered ring. The reaction of bis-helicenes can either proceed to the full double annulation or be interrupted by addition of molecular oxygen at an intermediate stage. The regioselectivity of the interrupted cyclization cascade for bis-helicenes confirms that relief of antiaromaticity is a dominant force for these facile ring closures. Computational analysis reveals the unique role of the preexisting negatively charged cyclopentadienyl moiety in directing the second negative charge at a specific remote location and, thus, creating a localized antiaromatic region. This region is the hotspot that promotes the initial cyclization. Computational studies, including MO analysis, molecular electrostatic potential maps, and NICS(1.7)_ZZ calculations, evaluate the interplay of the various effects including charge delocalization, helicene strain release, and antiaromaticity. The role of antiaromaticity relief is further supported by efficient reductive closure of the less strained monohelicenes where the relief of antiaromaticity promotes the cyclization even when the strain is substantially reduced. The latter finding significantly expands the scope of this reductive alternative to the Scholl ring closure.

Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D?

Several fully π-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored hitherto should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for tetrahedral or octahedral molecules, an aromatic closed-shell electronic structure with 6n + 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel’s 4n + 2 rule for each macrocyclic path, yet their π-electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., with π-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic π-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite the fact that these molecules show substantial π-electron delocalization, they cannot be classified as true 3D-aromatics.

The hidden aromaticity in borazine

The aromaticity of borazine (B3N3H6), also known as the inorganic benzene, is a controversial issue since this compound has several characteristics that could qualify it as an aromatic compound. However, recent studies using magnetic criteria indicate that this compound should be considered as a non-aromatic system. This assignment is mainly due to diatropic currents in the nitrogen atoms without observation of ring currents. The present work shows by means of the magnetic criteria that borazine has a ring current hidden by the local contributions of degenerate orbitals π1 and π2. Additionally, the study of borazine's first triplet state antiaromaticity using the magnetic and energetic criteria by means of isomerization stabilization energies (ISEs) together with Baird's and Hückel's rules suggests that borazine is best described as an (weakly) aromatic system.

A benchmark study of aromaticity indexes for benzene, pyridine and the diazines - I. Ground state aromaticity

Five different aromaticity indexes are benchmarked for benzene, pyridine and the diazines in their ground states. A basis set study was performed using the Pople style, Karlsruhe and Dunning's correlation consistent basis sets. Ten different DFT functionals, including LSDA, PBE, PBE0, B3LYP, CAM-B3LYP, wB97XD, M06-2X, SOGGA11X, M11 and MN15 were benchmarked by comparison with CCSD, CASSCF and MP2. Large out-of-plane imaginary frequencies were observed for some of the optimized structures at the correlated wavefunction level of theory. It was found that the DFT functionals in general predict the para-delocalization index, multicenter index and aromatic fluctuation index to be approximately 70%, 50% and 45% larger, respectively, compared to the CCSD method. Comparisons of the DFT functionals showed that the wB97XD, CAM-B3LYP and M06-2X functionals performed the best. Furthermore, the basis set dependence of the DFT functionals was found to be large for the electron sharing indexes. Based on these findings, it is recommended to perform ground state calculations of aromaticity indexes at the wB97XD, CAM-B3LYP or M06-2X level of theory utilizing a simple basis set of triple-ζ quality.

Five different aromaticity indexes are benchmarked for benzene, pyridine and the diazines in their ground states.

Structure, bonding and adaptive aromaticity in rhenium-oxo complexes: a DFT study

The concept of adaptive aromaticity has been extended to a rhenium-oxo complex, introducing a new member into this novel family.

Revival of Hückel Aromatic (Poly)benzenoid Subunits in Triplet State Polycyclic Aromatic Hydrocarbons by Silicon Substitution

By employing density functional theory (DFT) calculations we show that mono- and disilicon substitution in polycyclic aromatic hydrocarbons, having two to four benzene units, quenches their triplet state antiaromaticity by creating Hückel aromatic (poly)benzenoid subunit(s) and weakly antiaromatic, or almost nonaromatic silacycle. Therefore, such systems are predicted to be globally aromatic in both the ground state and the first excited triplet state. Putting the silicon atom(s) into various positions of a hydrocarbon provides an opportunity to tune the singlet-triplet energy gaps. They depend on the global aromaticity degree which, in turn, depends on the type of aromatic carbocyclic subunit(s) and the extent of their aromaticity. On the basis of the set of studied compounds, some preliminary rules on how to regulate the extent of global, semiglobal and local aromaticity are proposed. The results of this work extend the importance of Hückel aromaticity concept to excited triplet states which are usually characterized by the Baird type of (anti)aromaticity.

Porphyrinoids, a unique platform for exploring excited-state aromaticity

Recently, Baird (anti)aromaticity has been referred to as a description of excited-state (anti)aromaticity. With the term of Baird's rule, recent studies have intensively verified that the Hückel aromatic [4n + 2]π (or antiaromatic [4n]π) molecules in the ground state are reversed to give Baird aromatic [4n]π (or Baird antiaromatic [4n + 2]π) molecules in the excited states. Since the Hückel (anti)aromaticity has great influence on the molecular properties and reaction mechanisms, the Baird (anti)aromaticity has been expected to act as a dominant factor in governing excited-state properties and processes, which has attracted intensive scientific investigations for the verification of the concept of reversed aromaticity in the excited states. In this scientific endeavor, porphyrinoids have recently played leading roles in the demonstration of the aromaticity reversal in the excited states and its conceptual development. The distinct structural and electronic nature of porphyhrinoids depending on their (anti)aromaticity allow the direct observation of excited-state aromaticity reversal, Baird's rule. The explicit experimental demonstration with porphyrinoids has contributed greatly to its conceptual development and application in novel functional organic materials. Based on the significant role of porphyrinoids in the field of excited-state aromaticity, this review provides an overview of the experimental verification of the reversal concept of excited-state aromaticity by porphyrinoids and the recent progress on its conceptual application in novel functional molecules.

Investigation of a Series of 2-(2'-Hydroxyaryl)benzazole Derivatives: Photophysical Properties, Excited-State Intramolecular Proton-Transfer Reactions, and Observation of Long-Lived Triplet Excited States

Excited state intramolecular proton transfer (ESIPT) has drawn much attention for its important applications in a variety of areas. Here, the steady-state and time-resolved absorption spectroscopic experiments as well as DFT/TD-DFT calculations are employed to study the photophysical properties and photochemical reaction mechanisms of 2-(2'-hydroxyphenyl) benzoxazole (HBO) and selected derivatives (compounds 1-3). Because of their larger π-conjugation framework, compounds 1-3 display red-shifted absorbance but blue-shifted fluorescence compared with HBO. A fast ESIPT process is observed directly for HBO while compound 3 has an enol/keto equilibrium type of ESIPT that exhibits dual emission. Interestingly, only the emission of the enol form is observed for compounds 1 and 2 which suggests that the ESIPT process is strongly inhibited. These results indicate the decoration with electron-withdrawing groups such as thiadiazol and pyrazine on the hydroxyphenyl ring (compounds 1 and 2) apparently suppresses the proton-transfer processes in their excited states. Whereas the ESIPT process is rarely increased for compound 3 that modified with the phenanthrol ring, because the effective conjugation is reduced for compound 3 compared with HBO. The work here provides fundamental insights that may be useful for designing novel ESIPT molecules in the future.

Adaptive aromaticity in 16-valence-electron metallazapentalenes

According to Hückel's and Baird's rules, cyclic species are generally aromatic only either in the lowest singlet state (S₀) or in the lowest-lying triplet ππ* excited state (T₁). Thus, species with aromaticity both in S₀ and T₁ states (termed as adaptive aromaticity) are particularly rare. Herein, we carry out density functional theory (DFT) calculations to examine the aromaticity of 16e metallapentalenes containing heteroatoms (N, O). Interestingly, metallazapentalenes show adaptive aromaticity whereas metalloxapentalenes display nonaromaticity in the S₀ and T₁ states, which is supported by structural, magnetic, and electronic indices. In addition, a series of metallazapentalenes containing strong σ- or π-donor ligands are predicted to achieve adaptive aromaticity. Our findings expand the family of adaptive aromatics significantly, inviting experimental chemists to realize more hetero-metallapentalenes with adaptive aromaticity.

Visualizing electron delocalization in contorted polycyclic aromatic hydrocarbons

Electron delocalization in contorted polycyclic aromatic hydrocarbon (PAH) molecules was examined through 3D isotropic magnetic shielding (IMS) contour maps built around the molecules using pseudo-van der Waals surfaces. The resulting maps of electron delocalization provided an intuitive, yet detailed and quantitative evaluation of the aromatic, non aromatic, and antiaromatic character of the local and global conjugated cyclic circuits distributed over the molecules. An attractive pictural feature of the 3D IMS contour maps is that they are reminiscent of the Clar π-sextet model of aromaticity. The difference in delocalization patterns between the two faces of the electron circuits in contorted PAHs was clearly visualized. For π-extended contorted PAHs, some splits of the π system resulted in recognizable patterns typical of smaller PAHs. The differences between the delocalization patterns of diastereomeric chiral PAHs could also be visualized. Mapping IMS on pseudo-van der Waals surfaces around contorted PAHs allowed visualization of their superimposed preferred circuits for electron delocalization and hence their local and global aromaticity patterns.

An Element-Substituted Cyclobutadiene Exhibiting High-Energy Blue Phosphorescence

1,3,2,4-Diazadiboretidine, an isoelectronic heteroanalogue of cyclobutadiene, is an interesting chemical species in terms of comparison with the carbon system, whereas its properties have never been investigated experimentally. According to Baird's rule, Hückel antiaromatic cyclobutadiene acquires aromaticity in the lowest triplet state. Here we report experimental and theoretical studies on the ground- and excited-state antiaromaticity/aromaticity as well as the photophysical properties of an isolable 1,3,2,4-diazadiboretidine derivative. The crystal structure of the diazadiboretidine derivative revealed that the B₂ N₂ ring adopts a planar rhombic geometry in the ground state. Yet, theoretical calculations showed that the B₂ N₂ ring turns to a square geometry with a nonaromatic character in the lowest triplet state. Notably, the diazadiboretidine derivative has the lowest singlet and triplet states lying at close energy levels and displays blue phosphorescence.

Singlet/Triplet State Anti/Aromaticity of CyclopentadienylCation: Sensitivity to Substituent Effect

It is well known that singlet state aromaticity is quite insensitive to substituent effects, in the case of monosubstitution. In this work, we use density functional theory (DFT) calculations to examine the sensitivity of triplet state aromaticity to substituent effects. For this purpose, we chose the singlet state antiaromatic cyclopentadienyl cation, antiaromaticity of which reverses to triplet state aromaticity, conforming to Baird’s rule. The extent of (anti)aromaticity was evaluated by using structural (HOMA), magnetic (NICS), energetic (ISE), and electronic (EDDBp) criteria. We find that the extent of triplet state aromaticity of monosubstituted cyclopentadienyl cations is weaker than the singlet state aromaticity of benzene and is, thus, slightly more sensitive to substituent effects. As an addition to the existing literature data, we also discuss substituent effects on singlet state antiaromaticity of cyclopentadienyl cation.

Aromaticity in Phenyl Decorated closo-Monocarboranes. Planar-Spherical Aggregates Involving 7-12-Vertex Cages

The characterized phenyl decorated closo-monocarboranes with variable sizes from 7- to 12-vertex cages, [Ph-closo-CB_nH_n]^-, n = 6-11, allow us to address the role of the varying size and shape of the carborane cage in dual planar-spherical aromatic species. Our results show the formation of adjacent shielding cone characteristics enabled from both planar and spherical aromatic fragments, despite the different structures of the closo-monocarboranes. Under a field perpendicular to the phenyl ring, both shielding cones are enabled, which overlap at long-range regions, in contrast to other orientations leading to a short-range response from the planar aromatic fragment. Thus, a two- or one-aromatic circuit is enabled selectively within the same molecular unit, by controlling the orientation of the external field. Along with the series, a variable extension of the shielding cone from the carborane cage is observed, which is larger for the -CB₁₁H₁₁ case, decreasing toward -CB₆H₆, denoting a similar extension from both the planar and spherical aromatic regions at the [4-Ph-closo-4-CB₈H₈]^- (4) counterpart. The analysis of such multiple aromatic structures shows that, despite the different sizes and shapes of the closo cages, a similar aromatic behavior remains. In addition, the anisotropy of the induced magnetic field is given graphically, denoting a larger anisotropy for the planar aromatic moiety owing to its two-dimensional structure, which is suggested to discriminate between planar and spherical aromatic fragments within the same molecule.

Prediction of Spin Density, Baird-Antiaromaticity, and Singlet-Triplet Energy Gap in Triplet-State Polybenzenoid Systems from Simple Structural Motifs

Triplet-state aromaticity has been recently proposed as a strategy for designing functional organic electronic compounds, many of which are polycyclic aromatic systems. However, in many cases, the aromatic nature of the triplet state cannot be easily predicted. Moreover, it is often unclear how specific structural manipulations affect the electronic properties of the excited-state compounds. Herein, the relationship between the structure of polybenzenoid hydrocarbons (PBHs) and their spin-density distribution and aromatic character in the first triplet excited state is studied. Although a direct link is not immediately visible, classifying the PBHs according to their annulation sequence reveals regularities. Based on these, a set of guidelines is defined to qualitatively predict the location of spin and paratropicity and the singlet-triplet energy gap in larger PBHs, using only their smaller tri- and tetracyclic components, and subsequently tested on larger systems.

Excited state character of Cibalackrot-type compounds interpreted in terms of Hückel-aromaticity: a rationale for singlet fission chromophore design

The exact energies of the lowest singlet and triplet excited states in organic chromophores are crucial to their performance in optoelectronic devices. The possibility of utilizing singlet fission to enhance the performance of photovoltaic devices has resulted in a wide demand for tuneable, stable organic chromophores with wide S1-T1 energy gaps (>1 eV). Cibalackrot-type compounds were recently considered to have favorably positioned excited state energies for singlet fission, and they were found to have a degree of aromaticity in the lowest triplet excited state (T1). This work reports on a revised and deepened theoretical analysis taking into account the excited state Hückel-aromatic (instead of Baird-aromatic) as well as diradical characters, with the aim to design new organic chromophores based on this scaffold in a rational way starting from qualitative theory. We demonstrate that the substituent strategy can effectively adjust the spin distribution on the chromophore and thereby manipulate the excited state energy levels. Additionally, the improved understanding of the aromatic characters enables us to demonstrate a feasible design strategy to vary the excited state energy levels by tuning the number and nature of Hückel-aromatic units in the excited state. Finally, our study elucidates the complications and pitfalls of the excited state aromaticity and antiaromaticity concepts, highlighting that quantitative results from quantum chemical calculations of various aromaticity indices must be linked with qualitative theoretical analysis of the character of the excited states.

An unprecedented π-electronic circuit involving an odd number of carbon atoms in a grossly warped non-planar nanographene

The formation of π-aromatic circuits along a grossly warped nanographene, C₈₀H₃₀, containing five- and seven-membered rings inserted into a six-membered mesh, reveals global π-circuits at the edge of the backbone.

Triplet state (anti)aromaticity of some monoheterocyclic analogues of benzene, naphthalene and anthracene

By employing DFT calculations, we show the influence of heteroatom substitution on the triplet state (anti)aromaticity of benzene, naphthalene and anthracene.

Excited-State Aromaticity Reversals in Möbius Annulenes

It is suggested that Möbius annulenes follow a rule similar to Baird's rule such that the 4n and 4n + 2 criteria for Möbius electronic ground-state aromaticity and antiaromaticity are reversed in the lowest triplet and first singlet excited electronic states. Support comes from an investigation of aromaticity in the ground (S₀), lowest triplet (T₁), and first singlet excited (S₁) electronic states of the Möbius-aromatic cyclononatetraenyl cation, C₉H₉⁺, using isotropic magnetic shielding isosurfaces calculated with state-optimized complete-active-space self-consistent field wave functions constructed from gauge-including atomic orbitals. Examination of these isosurfaces demonstrates that while the S₀ state of C₉H₉⁺ is aromatic, the T₁ and S₁ states are antiaromatic.

Are Multicentre Bond Indices and Related Quantities Reliable Predictors of Excited-State Aromaticity?

Systematic scrutiny is carried out of the ability of multicentre bond indices and the NOEL-based similarity index d_AB to serve as excited-state aromaticity criteria. These indices were calculated using state-optimized complete active-space self-consistent field wavefunctions for several low-lying singlet and triplet states of the paradigmatic molecules of benzene and square cyclobutadiene and the inorganic ring S₂N₂. The comparison of the excited-state indices with aromaticity trends for individual excited states suggested by the values of magnetic aromaticity criteria show that whereas the indices work well for aromaticity reversals between the ground singlet and first triplet electronic states, addressed by Baird’s rule, there are no straightforward parallels between the two sets of data for singlet excited states. The problems experienced while applying multicentre bond indices and d_AB to singlet excited states are explained by the loss of the information inherently present in wavefunctions and/or pair densities when calculating the first-order density matrix.

How does excited-state antiaromaticity affect the acidity strengths of photoacids?

Photoacids like substituted naphthalenes (X = OH, NH3+, COOH) are aromatic in the S0 state and antiaromatic in the S1 state. Nucleus independent chemical shifts analyses reveal that deprotonation relieves antiaromaticity in the excited conjugate base, and that the degree of "antiaromaticity relief" explains why some photoacids are stronger than others.

Impact of Excited-State Antiaromaticity Relief in a Fundamental Benzene Photoreaction Leading to Substituted Bicyclo[3.1.0]hexenes

Benzene exhibits a rich photochemistry which can provide access to complex molecular scaffolds that are difficult to access with reactions in the electronic ground state. While benzene is aromatic in its ground state, it is antiaromatic in its lowest ππ* excited states. Herein, we clarify to what extent relief of excited-state antiaromaticity (ESAA) triggers a fundamental benzene photoreaction: the photoinitiated nucleophilic addition of solvent to benzene in acidic media leading to substituted bicyclo[3.1.0]hex-2-enes. The reaction scope was probed experimentally, and it was found that silyl-substituted benzenes provide the most rapid access to bicyclo[3.1.0]hexene derivatives, formed as single isomers with three stereogenic centers in yields up to 75% in one step. Two major mechanism hypotheses, both involving ESAA relief, were explored through quantum chemical calculations and experiments. The first mechanism involves protonation of excited-state benzene and subsequent rearrangement to bicyclo[3.1.0]hexenium cation, trapped by a nucleophile, while the second involves photorearrangement of benzene to benzvalene followed by protonation and nucleophilic addition. Our studies reveal that the second mechanism is operative. We also clarify that similar ESAA relief leads to puckering of S₁-state silabenzene and pyridinium ion, where the photorearrangement of the latter is of established synthetic utility. Finally, we identified causes for the limitations of the reaction, information that should be valuable in explorations of similar photoreactions. Taken together, we reveal how the ESAA in benzene and 6π-electron heterocycles trigger photochemical distortions that provide access to complex three-dimensional molecular scaffolds from simple reactants.

Substituent Effect in the First Excited Triplet State of Monosubstituted Benzenes

The structure of 30 monosubstituted benzenes in the first excited triplet T₁ state was optimized with both unrestricted (U) and restricted open shell (RO) approximations combined with the ωB97XD/aug-cc-pVTZ basis method. The substituents exhibited diverse σ- and π-electron-donating and/or -withdrawing groups. Two different positions of the substituents are observed in the studied compounds in the T₁ state: one distorted from the plane and the other coplanar with a quinoidal ring. The majority of the substituents are π-electron donating in the first group while π-electron withdrawing in the second one. Basically, U- and RO-ωB97XD approximations yield concordant results except for the B-substituents and a few of the planar groups. In the T₁ state, the studied molecules are not aromatic, yet aromaticity estimated using the HOMA (harmonic oscillator model of aromaticity) index increases from ca. -0.2 to ca. 0.4 with substituent distortion, while in the S₁ state, they are only slightly less aromatic than in the ground state (HOMA ≈0.8 vs ≈1.0, respectively). Unexpectedly, the sEDA(T₁) and pEDA(T₁) substituent effect descriptors do not correlate with analogous parameters for the ground and first excited singlet states. This is because in the T₁ state, the geometry of the ring changes dramatically and the sEDA(T₁) and pEDA(T₁) descriptors do not characterize only the functional group but the entire molecule. Thus, they cannot provide useful scales for the substituents in the T₁ states. We found that the spin density in the T₁ states is accumulated at the C_ipso and C_p atoms, and with the substituent deformation angle, it nonlinearly increases at the former while decreases at the latter. It appeared that the gap between singly unoccupied molecular orbital and singly occupied molecular orbital (SUMO-SOMO) is determined by the change of the SOMO energy because the former is essentially constant. For the nonplanar structures, SOMO correlates with the torsion angle of the substituent and the ground-state pEDA(S₀) descriptor of the π-electron-donating substituents ranging from 0.02 to 0.2 e. Finally, shapes of the SOMO-1 instead of SOMO frontier orbitals in the T₁ state somehow resemble the highest occupied molecular orbital ones of the S₀ and S₁ states. For several planar systems, the shape of the U- and RO-density functional theory-calculated SOMO-1 orbitals differs substantially.

Structure-Property Relationships in Unsymmetric Bis(antiaromatics): Who Wins the Battle between Pentalene and Benzocyclobutadiene?†

According to the currently accepted structure–property relationships, aceno-pentalenes with an angular shape (fused to the 1,2-bond of the acene) exhibit higher antiaromaticity than those with a linear shape (fused to the 2,3-bond of the acene). To explore and expand the current view, we designed and synthesized molecules where two isomeric, yet, different, 8π antiaromatic subunits, a benzocyclobutadiene (BCB) and a pentalene, are combined into, respectively, an angular and a linear topology via an unsaturated six-membered ring. The antiaromatic character of the molecules is supported experimentally by ¹H NMR, UV–vis, and cyclic voltammetry measurements and X-ray crystallography. The experimental results are further confirmed by theoretical studies including the calculation of several aromaticity indices (NICS, ACID, HOMA, FLU, MCI). In the case of the angular molecule, double bond-localization within the connecting six-membered ring resulted in reduced antiaromaticity of both the BCB and pentalene subunits, while the linear structure provided a competitive situation for the two unequal [4n]π subunits. We found that in the latter case the BCB unit alleviated its unfavorable antiaromaticity more efficiently, leaving the pentalene with strong antiaromaticity. Thus, a reversed structure–antiaromaticity relationship when compared to aceno-pentalenes was achieved.