Triplet State Aromaticity: NICS Criterion,Hyperconjugation, and Charge Effects

Aromaticity, one of the most important concepts in organic chemistry, has attracted considerable interest from both experimentalists and theoreticians. It remains unclear which NICS index is best to evaluate the triplet‐state aromaticity. Here, we carry out thorough density functional theory (DFT) calculations to examine this issue. Our results indicate that among the various computationally available NICS indices, NICS(1)_zz is the best for the triplet state. The correlations can be improved from 0.840 to 0.938 when only neutral species are considered, demonstrating the significant effect of the charge on the triplet‐state aromaticity. In addition, calculations suggest that five‐membered cyclic species with “hyperconjugative” aromaticity (and antiaromaticity) in the S₀ state will become antiaromatic (and aromatic) in the T₁ state, indicating an important role of hyperconjugation. Finally, a moderate correlation (r²=0.708) is identified between the NICS(1)_zz values and spin distributions.     

Aromaticity changes along the reaction coordinate connecting the cyclobutadiene dimer to cubane and the benzene dimer to hexaprismane

Aromaticity and reactivity are two deeply connected concepts. Most of the thermally allowed cycloadditions take place through aromatic transition states, while transition states of thermally forbidden reactions are usually less aromatic, if at all. In this work, we perform a numerical experiment to discuss the change of aromaticity that occurs along the reaction paths that connect two antiaromatic units of cyclobutadiene to form cubane and two aromatic rings of benzene to yield hexaprismane. It is found that the aromaticity profile along the reaction coordinate of the [4+4] cycloaddition of two antiaromatic cyclobutadiene molecules goes through an aromatic highest energy point and finishes to an antiaromatic cubane species. Up to our knowledge, this represents the first example of a theoretically and thermally forbidden reaction path that goes through an intermediate aromatic region. In contrast, the aromaticity profile in the [6+6] cycloaddition of two aromatic benzene rings show a slow steady decrease of aromaticity from reactants to the highest energy point and from this to the final hexaprismane molecule a plunge of aromaticity is observed. In both systems, the main change of aromaticity occurs abruptly near the highest energy point, when the distance between the centers of the two rings is about 2.2 Å.     

Peculiar antiaromatic inorganic molecules of tetrapnictogen in Na+Pn4- (Pn = P,As, Sb) and important consequences for hydrocarbons

Although aromaticity has been observed in inorganic and all-metal species, the concept of antiaromaticity has not been extended beyond organic molecules. Here, we present theoretical and experimental evidence that the 6 -electron tetrapnictogen dianions in Na+Pn42- (Pn = P, As, Sb) undergo a transition from being aromatic to antiaromatic upon electron detachment, yielding the first inorganic antiaromatic Na+Pn4- molecules. Two types of antiaromatic structures were characterized, the conventional rectangular species and a new peculiar quasiplanar rhombus species. Aromaticity and antiaromaticity in the tetrapnictogen molecules were derived from molecular orbital analyses and verified by experimental photodetachment spectra of Na+Pn42-. On the basis of our findings for the tetrapnictogen clusters, we predicted computationally that the organic C4H4- anion also possesses two antiaromatic structures: rectangular and rhombus. Moreover, only the rhombus antiaromatic minimum was found for the radical NC3H4, thus extending the peculiar rhombus antiaromatic structure first uncovered in inorganic clusters into organic chemistry.     

Ground- and excited-state aromaticity and antiaromaticity in benzene and cyclobutadiene

The aromaticity and antiaromaticity of the ground state (S 0), lowest triplet state (T 1), and first singlet excited state (S 1) of benzene, and the ground states (S 0), lowest triplet states (T 1), and the first and second singlet excited states (S 1 and S 2) of square and rectangular cyclobutadiene are assessed using various magnetic criteria including nucleus-independent chemical shifts (NICS), proton shieldings, and magnetic susceptibilities calculated using complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). These magnetic criteria strongly suggest that, in contrast to the well-known aromaticity of the S 0 state of benzene, the T 1 and S 1 states of this molecule are antiaromatic. In square cyclobutadiene, which is shown to be considerably more antiaromatic than rectangular cyclobutadiene, the magnetic properties of the T 1 and S 1 states allow these to be classified as aromatic. According to the computed magnetic criteria, the T 1 state of rectangular cyclobutadiene is still aromatic, but the S 1 state is antiaromatic, just as the S 2 state of square cyclobutadiene; the S 2 state of rectangular cyclobutadiene is nonaromatic. The results demonstrate that the well-known "triplet aromaticity" of cyclic conjugated hydrocarbons represents a particular case of a broader concept of excited-state aromaticity and antiaromaticity. It is shown that while electronic excitation may lead to increased nuclear shieldings in certain low-lying electronic states, in general its main effect can be expected to be nuclear deshielding, which can be substantial for heavier nuclei.     

Homobenzene: homoaromaticity and homoantiaromaticity in cycloheptatrienes

Cycloheptatriene (C(s)) is firmly established to be a neutral homoaromatic molecule based on detailed analyses of geometric, energetic, and magnetic criteria. Substituents at the 7 (methylene) position, ranging from the electropositive BH2 to the electronegative F, favor the equatorial conformation but influence the aromaticity only to a small extent. By the same criteria, the planar transition state (C(2v)) for cycloheptatriene ring inversion is clearly antiaromatic. This is attributed to the involvement of the pseudo-2pi-electrons of the CH2 group with the 6pi-electrons of the ring to give an 8pi-electron system. Similarly, the participation of the CH2 groups into C(2v) cyclopentadiene and cyclononatetraene lead to significant 4n + 2 pi electron aromaticity. The cyclization of cycloheptatriene to norcaradiene proceeds via a highly aromatic transition structure, but norcaradiene itself is less aromatic than cycloheptatriene. An annelated cyclopropane ring does not function as effectively as a double bond in promoting cyclic electron delocalization.     

The critical re-evaluation of the aromatic/antiaromatic nature of Ti3(CO)3: a missed opportunity?

The nature of bonding and aromaticity of Ti(3)(CO)(3), a mill-shaped metal-carbonyl complex, is studied carefully. A unique bonding mechanism between metal and carbonyl groups is found in this species. Ti(3)(CO)(3) is an example of a metal-carbonyl complex with prominent metal to carbonyl donation. Moreover, it is proven that not only is Ti(3)(CO)(3) not an antiaromatic complex but also it is the first synthesized example of d-block, σ+π aromatic species. A quick survey among the first row of transition metals in the periodic table shows that other local minima with similar structures and aromaticity are present and Ti(3)(CO)(3) is the first synthesized species of an unknown family.     

Interatomic magnetizability: a QTAIM-based approach toward deciphering magnetic aromaticity

Interatomic magnetizability provides insight into the extent of electronic current density between two adjacent atomic basins. By studying a number of well-known aromatic, nonaromatic, and antiaromatic molecules, it is demonstrated that interatomic magnetizability (bond magnetizability) not only is able to verify the exact nature of aromaticity/antiaromaticity among different molecules, but also can distinguish the correct aromaticity order among sets of aromatic/antiaromatic molecules. The interatomic magnetizability is a direct measure of the current flux between two adjacent atomic basins and is the first QTAIM-derived index that evaluates aromaticity based on a response property, that is, magnetizability. Bond magnetizability is easy to compute, straightforward to interpret, and can be employed to evaluate the pure π- or σ-orbital contributions to magnetic aromaticity.     

Dianion and dication of tetrabenzo[5.7]fulvalene. Greater antiaromaticity than aromaticity in comparable systems

The dianion, 5(2-), and dication, 5(2+), of tetrabenzo[5.7]fulvalene represent an aromaticity/antiaromaticity continuum in which the fluorenyl system changes from aromatic in 5(2-) to antiaromatic in 5(2+). Conversely, the antiaromatic dibenzotropylium system of 5(2-) becomes an aromatic system in 5(2+), allowing an examination of aromaticity/antiaromaticity within the same carbon framework. Dianion 5(2-) was prepared and characterized by (1)H NMR spectroscopy. The fluorenyl system of 5(2-) showed the downfield shifts expected for an aromatic system, while the dibenzotropylium system showed the paratropic shifts expected for an antiaromatic system. The conclusions from (1)H NMR spectroscopy were supported by NICS(1) zz calculations for each system. Comparison of the (1)H NMR spectrum and NICS(1) zz of 5(2-) with those of 5(2+) supported the assignments of aromaticity/antiaromaticity for each system. Aromaticity/antiaromaticity were further examined through comparison of the degree of bond length alternation, which showed that the bond length alternation was slightly greater for the antiaromatic ring systems than for the aromatic systems. However, when structures of 5(2-) and 5(2+) with no bond length alternation were examined, there was a dramatic increase in the degree of antiaromaticity for the antiaromatic ring systems as evaluated through NICS. This result suggests that a decrease in bond length alternation results in an increase in antiaromaticity as well as an increase in aromaticity. The magnitude of the antiaromaticity of the fluorenyl system in 5(2+) was greater than the magnitude of the aromaticity in the fluorenyl system of 5(2-), with similar effects shown by the analogous tropylium systems. This is consistent with the behavior of the antiaromatic dication of tetrabenzo[5.5]fulvalene, compared to that of its aromatic dianion, and also with the behavior of the cyclopentadienyl cation/anion and tropylium cation/anion.     

Consistent aromaticity evaluations of methylenecyclopropene analogues

Quantitative evaluations of the aromaticity (antiaromaticity) of neutral exocyclic substituted cyclopropenes (HC)(2)C=X (X = BH to InH (group 13), CH(2) to SnH(2) (group 14), NH to SbH (group 15), O to Te (group 16)) by their computed extra cyclic resonance energies (ECRE, via the block-localized wave function method) and by their aromatic stabilization energies (ASEs, via energy decomposition analyses) correlate satisfactorily (R(2) = 0.974). Electronegative X-based substituents increase the aromaticity of the cyclopropene rings, whereas electropositive substituents have the opposite effect. For example, (HC)(2)C=O is the most aromatic (ECRE = 10.3 kcal/mol), and (HC)(2)C=InH is the most antiaromatic (ECRE = -15.0 kcal/mol). The most refined dissected nucleus-independent chemical shift magnetic aromaticity index, NICS(0)(πzz), also agrees with both energetic indexes (R(2) = 0.968, for ECRE; R(2) = 0.974, for ASE), as do anisotropy of the induced current density plots.     

Predicting an Antiaromatic Benzene Ring in the Ground State Caused by Hyperconjugation

Benzene, the prototype of aromatics, has six equivalent C?C bonds (1.397 Å), which are intermediate between a C?C double bond and a C?C single bond. For over 80 years, chemists have spent much effort on freezing a localized structure to obtain a distorted bond‐length alternating benzene ring in the ground state, leading to various localized trisannelated benzene rings. However, most of the central benzene rings are still aromatic or nonaromatic. Here we report an antiaromatic benzene ring caused by hyperconjugation. Specifically, symmetric annulation of 5,5‐difluorocyclopentadiene results in an antiaromatic benzene ring, which is supported by various aromaticity indices, including nucleus‐independent chemical shift, anisotropy of the induced current density, π‐separated electron‐localization function and heat of hydrogenation. Our findings highlight a strong power of hyperconjugation, a “weak” interaction in organic chemistry, paving the way for designing and realizing more novel (anti)aromatics.     

Influence of the H/F replacement on the homoaromaticity of homotropylium ion: a GIAO/DFT theoretical study

The problem of homoaromaticity in mono-, di- and polyfluorinated- homotropylium cations is addressed by the B3LYP/6-311++G** DFT method. The energetic, structural and magnetic criteria are used for this purpose. They convincingly show that the ground state equilibrium species are aromatic, or in other words that the homoaromaticity is preserved by the (poly)fluorination. In contrast, a considerable decrease in the aromatic stabilization is observed in the transition structures (TS). According to the NICS(0) index, they vary form strongly antiaromatic, via weakly and non-aromatic to slightly aromatic transition states. However, the hierarchy of the aromaticity in fluorinated homotropylium ions predicted by NICS(0) is completely unrelated to that obtained by using the energy criterion assuming a kinetic definition of aromaticity. On the other hand the latter is closely related to geometric parameters of the equilibrium and transition structures.     

Unique Role of Heterole-Fused Structures in Aromaticity and Physicochemical Properties of 7,8-Dehydropurpurins

Porphyrins with a fused five-membered ring, such as 7,8-dehydropurpurins, have appeared as an emerging class of unique porphyrinoids. Their altered absorption spectra, relatively short lifetimes of excited states, and small HOMO–LUMO gaps arise from the harmony of the antiaromatic 20π-circuit and the aromatic 18π-circuit. In this regard, the electronic properties of 7,8-dehydropurpurins are expected to be controlled by modulating the contribution of the antiaromatic π-circuit to the whole aromaticity. Here the comparison of pyrrole- and phosphole-fused 7,8-dehydropurpurins is reported in terms of their aromaticity and physicochemical properties. The spectroscopic investigation revealed the larger contribution of the antiaromatic 24π-circuit in pyrrole-fused 7,8-dehyrdopurpurins than in phosphole-fused 7,8-dehydropurpurins. The DFT calculations also supported the feasibility of tuning the aromaticity of 7,8-dehydropurpurins by heterole-fused structures. Thus, the introduction of heterole-fused structures into porphyrinoids is a universal strategy to get new insight into aromaticity and their intrinsic properties in cyclic π-conjugated molecules.     

Antiaromaticity in fluorenylidene dications. Experimental and theoretical evidence for the relationship between the HOMO/LUMO gap and antiaromaticity

The relationship between the calculated energy of the HOMO-LUMO gap, where (epsilonLUMO - epsilonHOMO)/2 is defined as DeltaHL, and of the longest wavelength transition in the UV-visible spectrum, DeltaE, was examined for a series of aromatic and antiaromatic cations and dications. TD-DFT calculations accurately modeled the energies of a series of dications including fluorenylidene dications whose UV-visible spectra are reported, as well as the energies of a series of aromatic and antiaromatic monocations whose spectra were previously reported. There is a linear correlation of the energy of the longest wavelength transition, DeltaEcalc, with DeltaHL. There is no linear relationship between DeltaEcalc and the sum of the NICS values, but there is a linear relationship between DeltaEcalc multiplied by the number of atoms in the conjugated system, DeltaEcalcT, and the sum of the NICS values. There is also an approximate linear relationship between the average 1H NMR shift and the sum of the NICS values. These relationships give further support to the suggestion that the magnetic and energetic criteria of aromaticity and antiaromaticity are related. Furthermore, the data suggest that species that have DeltaEcalcT < 20 are antiaromatic whereas those with DeltaEcalcT > 30 are aromatic.     

Neural networks as a tool to classify compounds according to aromaticity criteria

Aromaticity is a fundamental concept in chemistry, with many theoretical and practical implications. Although most organic compounds can be categorized as aromatic, non-aromatic, or antiaromatic, it is often difficult to classify borderline compounds as well as to quantify this property. Many aromaticity criteria have been proposed, although none of them gives an entirely satisfactory solution. The inability to fully arrange organic compounds according to a single criterion arises from the fact that aromaticity is a multidimensional phenomenon. Neural networks are computational techniques that allow one to treat a large amount of data, thereby reducing the dimensionality of the input set to a bidimensional output. We present the successful applications of Kohonen's self-organizing maps to classify organic compounds according to aromaticity criteria, showing a good correlation between the aromaticity of a compound and its placement in a particular neuron. Although the input data for the training of the network were different aromaticity criteria (stabilization energy, diamagnetic susceptibility, NICS, NICS(1), and HOMA) for five-membered heterocycles, the method can be extended to other organic compounds. Some useful features of this method are: 1) it is very fast, requiring less than one minute of computational time to place a new compound in the map; 2) the placement of the different compounds in the map is conveniently visualized; 3) the position of a compound in the map depends on its aromatic character, thus allowing us to establish a quantitative scale of aromaticity, based on Euclidean distances between neurons, 4) it has predictive power. Overall, the results reported herein constitute a significant contribution to the longstanding debate on the quantitative treatment of aromaticity.     

An energetic measure of aromaticity and antiaromaticity based on the Pauling-Wheland resonance energies

Various criteria based on geometric, energetic, magnetic, and electronic properties are employed to delineate aromatic and antiaromatic systems. The recently proposed block-localized wave function (BLW) method evaluates the original Pauling-Wheland adiabatic resonance energy (ARE), defined as the energy difference between the real conjugated system and the corresponding virtual most stable resonance structure. The BLW-derived ARE of benzene is 57.5 kcal mol(-1) with the 6-311+G** basis set. Kistiakowsky's historical experimental evaluation of the stabilization energy of benzene (36 kcal mol(-1)), based on heats of hydrogenation, seriously underestimates this quantity due to the neglect of the partially counterbalancing hyperconjugative stabilization of cyclohexene, employed as the reference olefin (three times) in Kistiakowsky's evaluation. Based instead on the bond-separation-energy reaction involving ethene, which has no hyperconjugation, as well as methane and ethane, the experimental resonance energy of benzene is found to be 65.0 kcal mol(-1). We derived the "extra cyclic resonance energy" (ECRE) to characterize and measure the extra stabilization (aromaticity) of conjugated rings. ECRE is the difference between the AREs of a fully cyclically conjugated compound and an appropriate model with corresponding, but interrupted (acyclic) conjugation. Based on 1,3,5-hexatriene, which also has three double bonds, the ECRE of benzene is 36.7 kcal mol(-1), whereas based on 1,3,5,7-octatetraene, which has three diene conjugations, the ECRE of benzene is 25.7 kcal mol(-1). Computations on a series of aromatic, nonaromatic, and antiaromatic five-membered rings validate the BLW-computed resonance energies (ARE). ECRE data on the five-membered rings (derived from comparisons with acyclic models) correlate well with nucleus-independent chemical shift (NICS) and other quantitative aromaticity criteria. The ARE of cyclobutadiene is almost the same as butadiene but is 10.5 kcal mol(-1) less than 1,3,5-hexatriene, which also has two diene conjugations. The instability and high reactivity of cyclobutadiene thus mainly result from the sigma-frame strain and the pi-pi Pauli repulsion.     

Diazulenorubicene as a Non-benzenoid Isomer of peri-Tetracene with Two Sets of 5/7/5 Membered Rings Showing Good Semiconducting Properties

Non-benzenoid polycyclic aromatic hydrocarbons (PAHs) have received a lot of attention because of their unique optical, electronic, and magnetic properties, but their synthesis remains challenging. Herein, we report a non-benzenoid isomer of peri-tetracene, diazulenorubicene (DAR), with two sets of 5/7/5 membered rings synthesized by a (3+2) annulation reaction. Compared with the precursor containing only 5/7 membered rings, the newly formed five membered rings switch the aromaticity of the original heptagon/pentagon from antiaromatic/aromatic to non-aromatic/antiaromatic respectively, modify the intermolecular packing modes, and lower the LUMO levels. Notably, compound 2 b (DAR-TMS) shows p-type semiconducting properties with a hole mobility up to 1.27 cm² V⁻¹ s⁻¹. Moreover, further extension to larger non-benzenoid PAHs with 19 rings was achieved through on-surface chemistry from the DAR derivative with one alkynyl group.     

Interplay among aromaticity, magnetism, and nonlinear optical response in all-metal aromatic systems

All-metal aromatic molecules are the latest inclusion in the family of aromatic systems. Two different classes of all-metal aromatic clusters are primarily identified: one is aromatic only in the low spin state, and the other shows aromaticity even in high-spin situations. This observation prompts us to investigate the effect of spin multiplicity on aromaticity, taking Al(4)(2-), Te(2)As(2)(2-), and their copper complexes as reference systems. Among these clusters, it has been found that the molecules that are aromatic only in their singlet state manifest antiaromaticity in their triplet state. The aromaticity in the singlet state is characterized by the diatropic ring current circulated through the bonds, which are cleaved to generate excess spin density on the atoms in the antiaromatic triplet state. Hence, in such systems, an antagonistic relationship between aromaticity and high-spin situations emerges. On the other hand, in the case of triplet aromatic molecules, the magnetic orbitals and the orbitals maintaining aromaticity are different; hence, aromaticity is not depleted in the high-spin state. The nonlinear optical (NLO) behavior of the same set of clusters in different spin states has also been addressed. We correlate the second hyperpolarizability and spin density in order to judge the effect of spin multiplicity on third-order NLO response. This correlation reveals a high degree of NLO behavior in systems with excess spin density. The variance of aromaticity and NLO response with spin multiplicity is found to stem from a single aspect, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), and eventually the interplay among aromaticity, magnetism, and NLO response in such materials is established. Hence, the HOMO-LUMO energy gap becomes the cornerstone for tuning the interplay. This correlation among the said properties is not system-specific and thus can be envisaged even beyond the periphery of all-metal aromatic clusters. Such interplay is of crucial importance in tailoring novel paradigm of multifunctional materials.     

Stabilization of an all-metal antiaromatic molecule (Al4Li4) using BH and C as caps

It has been reported by Pati et al. ( J. Am. Chem. Soc. 2005, 127, 3496) that coordination with a transition metal can stabilize the "antiaromatic", all-metal compound Al4Li4. Here, we report that it can also be stabilized by capping with a main group element like C and its isoelectronic species BH. Our calculations of binding energy, nuclear independent chemical shift, energy decomposition analysis, and molecular orbital analysis support the capping-induced stability, reduction of bond length alternation, and increase of aromaticity of these BH/C-capped Al4Li4 systems. The interaction between px and py orbitals of BH/C and the HOMO and LUMO of Al4Li4 is responsible for the stabilization. Our calculations suggest that capping can introduce fluxionality at room temperature.