Electron delocalization and aromaticity in low-lying excited states of archetypal organic compounds

Aromaticity is a property usually linked to the ground state of stable molecules. Although it is well-known that certain excited states are unquestionably aromatic, the aromaticity of excited states remains rather unexplored. To move one step forward in the comprehension of aromaticity in excited states, in this work we analyze the electron delocalization and aromaticity of a series of low-lying excited states of cyclobutadiene, benzene, and cyclooctatetraene with different multiplicities at the CASSCF level by means of electron delocalization measures. While our results are in agreement with Baird's rule for the aromaticity of the lowest-lying triplet excited state in annulenes having 4nπ-electrons, they do not support Soncini and Fowler's generalization of Baird's rule pointing out that the lowest-lying quintet state of benzene and septet state of cyclooctatetraene are not aromatic.     

Ab initio study of cyclobutadiene in excited states: optimized geometries,electronic transitions and aromaticities

An Ab initio SCF-CI study of planar cyclobutadiene (CB) in ground and excited states has been carried out. The equilibrium geometries of some valence and Rydberg states have been calculated, as well as the energies of the vertical (absorption and emission) and non-vertical transitions. Using the optimized geometries, it is discussed how the aromaticity changes upon excitation of CB to the lowest-lying singlet and triplet states. The following conclusion is made: upon excitation to the fluorescent (S₁) or phosphorscent (T₁), states, the aromaticity of the anti-Hückel system cyclobutadiene increases significantly, whereas that of the Hückel system benzene descreases.     

A DFT study of the ground state multiplicities of linear vs angular polyheteroacenes

Unrestricted density functional calculations in combination with the broken-symmetry approach and spin-projection methods have been employed to study a series of formally 4n pi antiaromatic linear and angular polyheteroacenes. Calculations show that the linear polyheteroacene molecules have either stable singlet zwitterionic 6-9 or singlet diradical 5 ground states because they sacrifice the aromaticity of the central arene to form two independent cyanines. The corresponding angular compounds 10-14 have robust triplet states, since they cannot create independent cyanines to escape their overall antiaromaticity. An analysis based on the SOMO-SOMO energy splittings, their spatial distributions, and the spin density populations for the triplet states is presented to clarify the factors that determine their ground state multiplicities.     

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.     

Proton transfers in aromatic and antiaromatic systems. How aromatic or antiaromatic is the transition state? An ab initio study

An ab initio study of six carbon-to-carbon identity proton transfers is reported. They refer to the benzenium ion/benzene (C6H7(+)/C6H6), the 2,4-cyclopentadiene/cyclopentadienyl anion (C5H6/C5H5(-)), and the cyclobutenyl cation/cyclobutadiene (C4H5(+)/C4H4) systems and their respective noncyclic reference systems, that is, [structure: see text], [structure: see text] and [structure: see text]. For the aromatic C6H7(+)/C6H6 and C5H6/C5H5(-) systems, geometric parameters and aromaticity indices indicate that the transition states are highly aromatic. The proton-transfer barriers in these systems are quite low, which is consistent with a disproportionately high degree of transition-state aromaticity. For the antiaromatic C4H5(+)/C4H4 system, the geometric parameters and aromaticity indices indicate a rather small degree of antiaromaticity of the transition state. However, the proton-transfer barrier is higher than expected for a transition state with a low antiaromaticity. This implies that another factor contributes to the barrier; it is suggested that this factor is angle and torsional strain in the transition state. The question whether charge delocalization at the transition state might correlate with the development of aromaticity was also examined. No such correlation was found, that is, charge delocalization lags behind proton transfer as is commonly observed in nonaromatic systems involving pi-acceptor groups.     

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.

Cibalackrot-type compounds are Hückel instead of Baird aromatic in their first triplet states (T₁). By choice of substituents and additional benzannelation we adjust the T₁ energies, providing a new strategy for singlet fission chromophore design.     

Exploration of the π-electronic structure of singlet, triplet, and quintet states of fulvenes and fulvalenes using the electron localization function

The singlet ground states and lowest triplet states of penta- and heptafulvene, their benzannulated derivatives, as well as the lowest quintet states of pentaheptafulvalenes, either the parent compound or compounds in which the two rings are intercepted by either an alkynyl or a phenyl segment, were investigated at the (U)OLYP/6-311G(d,p) density functional theory level. The influence of (anti)aromaticity was analyzed by the structure-based aromaticity index HOMA, the harmonic oscillator model of aromaticity. The extent of (anti)aromatic character was also evaluated in terms of the π-electron (de)localization as measured by the π component of the electron localization function (ELF(π)). The natural atomic orbital (NAO) occupancies were calculated in order to evaluate the degree of π-electron shift caused by the opposing electron-counting rules for aromaticity in the electronic ground state (S(0); Hückel's rule) and the first ππ* excited triplet state (T(1); Baird's rule). Pentaheptafulvalene (5) shows a shift of 0.5 π electrons from the 5-ring to the 7-ring when going from the S(0) state to the lowest quintet state (Qu(1)). The pentaheptafulvalene 5 and [5.6.7]quinarene 7 were also investigated in their 90° twisted conformations. From our study it is apparent that excitation localization in fulvalenes, but not in fulvenes, to a substantial degree is determined by aromaticity localization to triplet biradical 4n π-electron cycles. Isolated benzene rings in these compounds tend to remain as closed-shell 6π-electron cycles.     

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.     

Can Anti‐Aufbau DFT Calculations Estimate Singlet Excited State Aromaticity? Correspondence on “Dibenzoarsepins: Planarization of 8π‐Electron System in the Lowest Singlet Excited State”

The simple anti‐aufbau DFT approach for estimating singlet excited state aromaticity suggested in a recent Communication published in this journal is shown to produce incorrect results because it targets a linear combination of the singlet and triplet configurations involving the HOMO and LUMO rather than the first singlet excited state. If the S₁ state of a molecule is dominated by the HOMO→LUMO excitation, a comparably simple but theoretically consistent and qualitatively correct approximation to the S₁ wavefunction can be achieved by performing a small “two electrons in two orbitals” CASSCF(2,2) calculation which can be followed by the evaluation of magnetic aromaticity criteria such as NICS.     

Can Anti-Aufbau DFT Calculations Estimate Singlet Excited State Aromaticity? Correspondence on “Dibenzoarsepins: Planarization of 8π-Electron System in the Lowest Singlet Excited State”

The simple anti-aufbau DFT approach for estimating singlet excited state aromaticity suggested in a recent Communication published in this journal is shown to produce incorrect results because it targets a linear combination of the singlet and triplet configurations involving the HOMO and LUMO rather than the first singlet excited state. If the S₁ state of a molecule is dominated by the HOMO→LUMO excitation, a comparably simple but theoretically consistent and qualitatively correct approximation to the S₁ wavefunction can be achieved by performing a small “two electrons in two orbitals” CASSCF(2,2) calculation which can be followed by the evaluation of magnetic aromaticity criteria such as NICS.     

Fulvenes, fulvalenes, and azulene: are they aromatic chameleons?

On the basis of the theory of Baird on reversal of Hückel's rule for aromaticity and antiaromaticity of annulenes when going from the electronic ground state (S0) to the lowest pipi* triplet state (T1) (J. Am. Chem. Soc. 1972, 94, 4941), we argue that fulvenes, fulvalenes, and azulene are "aromatic chameleons". The dipole moments of fulvenes in T1 should be of comparable magnitude to those of S0, but due to the reversal of Hückel's aromaticity rule in T1, their dipole should be in the opposite direction. Thereby, they are capable of adopting some aromaticity in both the T1 and S0 states as they adapt their dipolar resonance structures. The same applies to fulvalenes and azulene in their lowest quintet states (Q1) when compared to S0. Our hypothesis on chameleon behavior is supported by quantum chemical OLYP, CASSCF, and CASPT2 calculations of dipole moments, pi-orbital populations, and energies.     

Ring-current aromaticity in open-shell systems

The ab initio ipsocentric approach to calculation and mapping of induced orbital current density is extended to open-shell π systems. ROHF/6-31G^** calculations document the (magnetic) aromaticity of planar 4nπ triplet states of 4π/8π annulenes and isobenzofulvene, and quintet excited-state azulene. An orbital model for currents rationalises the generalised form of Baird’s rules, by which 4n + 2 annulenes are aromatic (antiaromatic) in states of even (odd) total spin (vice versa for 4nπ annulenes). In contrast to geometric criteria, ring-currents predict antiaromaticity for the doublet naphthalene radical anion.     

Effect on ring current of the Kekulé vibration in aromatic and antiaromatic rings

Derivative current-density maps are used to follow the changes in ring-current (and hence, on the magnetic criterion, the changes in aromaticity) with the Kekulé vibrations of the prototypical aromatic, antiaromatic, and nonaromatic systems of benzene, cyclooctatetraene (COT), and borazine. Maps are computed at the ipsocentric CHF/6-31G**//RHF/6-31G** level. The first-derivative map for benzene shows a growing-in of localized bond currents, and the second-derivative map shows a pure, paratropic "antiring-current", leading to the conclusion that vibrational motion along the Kekulé mode will reduce the net aromaticity of benzene, on average. For planar-constrained D(4h) COT, the Kekulé mode (positive for reduction of bond-length alternation) increases paratropicity at both first and second order, indicating an average increase in antiaromaticity with zero-point motion along this mode. On the ring-current criterion, breathing expansions of benzene and D(4h) COT reduce aromaticity and increase antiaromaticity, respectively.     

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.     

Theoretical study on the photolysis mechanism of 2,3-diazabicyclo[2.2.2]oct-2-ene

A CASPT2/CASSCF study has been carried out to investigate the mechanism of the photolysis of 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) under direct and triplet-sensitized irradiation. By exploring the detailed potential energy surfaces including intermediates, transition states, conical intersections, and singlet/triplet crossing points, for the first excited singlet (S(1)) and the low-lying triplet states (T(1), T(2), and T(3)), we provide satisfactory explanations of many experimental findings associated with the photophysical and photochemical processes of DBO. A key finding of this work is the existence of a significantly twisted S(1) minimum, which can satisfactorily explain the envelope of the broad emission band of DBO. It is demonstrated that the S(1) (n-pi*) intermediate can decay to the T(1) (n-pi*) state by undergoing intersystem crossing (rather inefficient) to the T(2) (pi-pi*) state followed by internal conversion to the T(1) state. The high fluorescence yield and the extraordinarily long lifetime of the singlet excited DBO are due to the presence of relatively high barriers, both for intersystem crossing and for C-N cleavage. The short lifetime of the triplet DBO is caused by fast radiationless decay to the ground state.     

Aromaticity Reversal in the Lowest Excited Triplet State of Archetypical Möbius Heteroannulenic Systems

The aromaticity reversal in the lowest triplet state (T₁) of a comparable set of Hückel/Möbius aromatic metalated expanded porphyrins was explored by optical spectroscopy and quantum calculations. In the absorption spectra, the T₁ states of the Möbius aromatic species showed broad, weak, and ill‐defined spectral features with small extinction coefficients, which is in line with typical antiaromatic expanded porphyrins. In combination with quantum calculations, these results indicate that the Möbius aromatic nature of the S₀ state is reversed to Möbius antiaromaticity in the T₁ state. This is the first experimental observation of aromaticity reversal in the T₁ state of Möbius aromatic molecules.     

Symmetry restrictions as starting point for the determination of geometric representations and the dynamics of cyclic π systems

A quasiclassical‐state approach was developed for probing π bonding and delocalization energies focused on benzene. A more general picture is now given for neutral n π‐conjugated cyclic systems with a geometry distortion from D_nh into D_1/2nh (n=4,6,8,…,16), which results in a new aromaticity‐antiaromaticity criterion. For n=6 and 8 the corresponding divalent charged systems were studied in relation to zero‐field splittings of the triplet ground state and geometry, respectively. Attention is also given to antiaromatic π‐conjugated systems focused on the cyclopropenyl anion, the cyclopentadienyl cation, and the cycloheptatrienyl anion and their relaxed states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 641–650, 2000     

Does the concept of Clar's aromatic sextet work for dicationic forms of polycyclic aromatic hydrocarbons?--testing the model against charged systems in singlet and triplet states

The concept of Clar's π-electron aromatic sextet was tested against a set of polycyclic aromatic hydrocarbons in neutral and doubly charged forms. Systems containing different types of rings (in the context of Clar's concept) were chosen, including benzene, naphthalene, anthracene, phenanthrene and triphenylene. In the case of dicationic structures both singlet and triplet states were considered. It was found that for singlet state dicationic structures the concept of aromatic sextet could be applied and the local aromaticity could be discussed in the context of that model, whereas in the case of triplet state dicationic structures Clar's model rather failed. Different aromaticity indices based on various properties of molecular systems were applied for the purpose of the studies. The discussion about the interdependence between the values of different aromaticity indices applied to neutral and charged systems in singlet and triplet states is also included.     

Achieving Adaptive Aromaticity in Cyclo[10]carbon by Screening Cyclo[n]carbon (n=8−24)

Discovery of species with adaptive aromaticity (being aromatic in both the lowest singlet and triplet states) is particularly challenging as cyclic species are generally aromatic either in the ground state or in the excited state only, according to Hückel's and Baird's rules. Inspired by the recent realization of cyclo[18]carbon, here we demonstrate that cyclo[10]carbon possesses adaptive aromaticity by screening cyclo[n]carbon (n=8?24), which is supported by nucleus‐independent chemical shift (NICS), anisotropy of the current‐induced density (ACID), π contribution of electron localization function (ELF_π) and electron density of delocalized bonds (EDDB) analyses. Further study reveals that the lowest triplet state of cyclo[10]carbon is formed by in‐plane ππ* excitation. Thus, the major contribution to the aromaticity from out‐of‐plane π molecular orbitals does not change significantly in the lowest singlet state. Our findings highlight a crucial role of out‐of‐plane π orbitals in maintaining aromaticity for both the lowest singlet and triplet states as well as the aromaticity dependence on the number of the carbon in cyclo[n]carbon.