Excited-State (Anti)Aromaticity Explains Why Azulene Disobeys Kasha’s Rule

Fluorescence exclusively occurs from the lowest excited state of a given multiplicity according to Kasha’s rule. However, this rule is not obeyed by a handful of anti-Kasha fluorophores whose underlying mechanism is still understood merely on a phenomenological basis. This lack of understanding prevents the rational design and property-tuning of anti-Kasha fluorophores. Here, we propose a model explaining the photophysical properties of an archetypal anti-Kasha fluorophore, azulene, based on its ground- and excited-state (anti)aromaticity. We derived our model from a detailed analysis of the electronic structure of the ground singlet, first excited triplet, and quintet states and of the first and second excited singlet states using the perturbational molecular orbital theory and quantum-chemical aromaticity indices. Our model reveals that the anti-Kasha properties of azulene and its derivatives result from (i) the contrasting (anti)aromaticity of its first and second singlet excited states (S1 and S2, respectively) and (ii) an easily accessible antiaromaticity relief pathway of the S1 state. This explanation of the fundamental cause of anti-Kasha behavior may pave the way for new classes of anti-Kasha fluorophores and materials with long-lived, high-energy excited states.


INTRODUCTION
−4 Among them, one fluorophore stands out for exclusively emitting from the second singlet excited state (S 2 ) as the archetype of anti-Kasha fluorophores, azulene. 5zulene's anti-Kasha behavior is particularly robust under structural perturbations.Binsch et al. tried to quell the anti-Kasha properties of azulene through multiple synthetic strategies, including annellation, symmetry lowering, substitution by heavy atoms, and addition of a "loose bolt" substituent (Figure 1A), albeit to no avail. 6All approaches failed to induce the first singlet excited state (S 1 ) emission of the azulene derivatives.
Based on Longuet-Higgins and Beer's hypothesis according to which the anomalous emission of azulene results from its large S 2 −S 1 gap (∼14,000 cm −1 ), 5 Murata et al. followed a more systematic approach to reduce the S 2 −S 1 gap by extensive substitution of the azulene scaffold (Figure 1B). 7hey were able to increase the rate of S 2 −S 1 internal conversion, thereby reducing the quantum yield of the S 2 emission.−15 The anomalous photophysical properties of azulene and its derivatives prompted further research efforts to uncover their underlying mechanism, leading to the following, now wellestablished explanations: (i) the large S 2 −S 1 gap of azulene results in a low rate of IC from S 2 , which in turn leads to a high yield of S 2 emission, 5,7,10 and (ii) the S 1 of azulene rapidly decays by a S 1 −S 0 conical intersection, 18 located near the S 1 minimum energy geometry, thereby accounting for the absence of S 1 emission.Notwithstanding these efforts, no structure− property relationship was provided to explain the anti-Kasha behavior of azulene.In fact, the description of azulene's anti-Kasha behavior has long remained insufficient to guide any attempt at rational molecular design and anti-Kasha property tuning, a shortcoming that we shall overcome herein.
Azulene is a 10π-aromatic fused bicyclic hydrocarbon with no substituents or heteroatoms; therefore, its photophysical phenomena must be a manifestation of its π-electron configuration.−24 Among other characteristics, these descriptors indicate whether their π-electron configuration in a given electronic state is stabilizing or destabilizing, respectively.Accordingly, we hypothesized that the anti-Kasha behavior of azulene could be related to the (anti)aromatic character of S 1 and S 2 .Such a relationship between excited-state (anti)aromaticity and anti-Kasha behavior may explain how the electronic structure of azulene leads to its anti-Kasha behavior, thus providing key mechanistic insights into anti-Kasha fluorophores.

RESULTS AND DISCUSSION
To understand how the electronic structure of azulene leads to its anti-Kasha behavior, we analyzed its ground-and excitedstate (anti)aromaticity in increasing order of complexity.The ground singlet state (S 0 ) and first-excited triplet state (T 1 ) of small conjugated cyclic hydrocarbons typically show contrasting aromaticity/antiaromaticity, as per Huckel's and Baird's rules. 20Moreover, the aromaticity of the first excited quintet state (Qu 1 ) of azulene has been previously reported. 25,26ence, we computationally investigated the S 0 , T 1 , and Qu 1 to model the (anti)aromatic character of azulene in the lowest states of each multiplicity.Subsequently, we compared their electronic structures and various aromaticity indices (Section S5) with those of S 1 and S 2 , which account for the anti-Kasha behavior of azulene.This approach enabled us to establish the relationship between the anti-Kasha behavior of azulene and its excited-state (anti)aromaticity.
Ground state azulene is a Huckel 10π-aromatic molecule, as shown by all calculated aromaticity indices (Figure 2 and Chapter S5.1).Yet, only when comparing the calculated aromaticity indices of all possible delocalization circuits within its molecular geometry (Figure S6) do we find that the aromaticity of azulene originates from the delocalization along its perimeter.The calculated delocalization indices [aromatic fluctuation (FLU), multicenter delocalization (MCI), and electron density of delocalized bonds (EDDB)] indicate (Table S1) that most of the delocalized 10π-electron density is situated along the perimeter of azulene (cyclodecapentaenyl circuit).Conversely, delocalization circuits involving the transannular bond (cyclopentadienyl and cycloheptatrienyl) exhibit poor π-electron delocalization (Figure 2 and Table S1).By calculating EDDB P electron counts (Table S2), we quantified the electron delocalization within the transannular bond of azulene (ΔC 10 ).This bond exhibited only a negligible contribution, 0.02 electrons, to the global delocalized electron density of azulene (Figure 2).The virtual absence of ground-   state transannular delocalization in azulene corresponds to its unusually long transannular bond of approximately 1.5 Å. 27 The 10π-aromaticity of azulene was predicted in previous studies. 26,28However, the relevance of this finding has been largely overlooked.For example, the permanent dipole moment of azulene is usually explained by resonance structures that invoke delocalization through the transannular bond, 29 but these resonance structures do not significantly contribute to the net electronic structure of azulene (Figure 2a), as evidenced by the negligible ΔC 10 value.As a case in point, we found that homoazulene, 30 the homoannelated counterpart of azulene without a conjugated transannular bond, has a similar permanent dipole moment (Chapter S13.1).Furthermore, in contrast to many other polycyclic aromatic hydrocarbons (PAH), such as the isoelectronic naphthalene (Chapter S13.2), which is known to favor the formation of multiple, 6π-aromatic rings, 31,32 azulene's S 0 electronic structure resembles a single 10π-aromatic ring.Therefore, in the ground state, the bicyclic molecular geometry of azulene should be treated as a single 10π-aromatic hydrocarbon rather than a PAH.
In the first triplet excited state, azulene follows Baird's rules 19 and is antiaromatic (Figure 3).This antiaromaticity is partly alleviated by transannular bond contraction.As a result, the delocalization decreases in the perimeter but increases in the cyclopentadienyl and cycloheptatrienyl circuits of azulene, as shown by our calculations (Table S5), and these circuits adopt the electronic structures of their corresponding cyclic radicals, as demonstrated by the EDDB (Chapter S12).The consequences of this enhanced geometric relaxation and the associated changes in the electronic structure of azulene can also be observed in the calculated isomerization stabilization energies (ISE) (Table S30), which are close to zero, or negative, for methylated isomers of T 1 azulene.Despite the extensive reorganization and significant loss of antiaromaticity, T 1 azulene remains, nevertheless, moderately antiaromatic.
The Qu 1 of azulene has never been observed experimentally.However, previous theoretical studies have indicated that Qu 1 azulene is aromatic. 25,26Furthermore, our results showed that the aromaticity of Qu 1 originates primarily from the delocalization along its perimeter (Figure 3 and Table S9).The contrasting preferred electronic structures of T 1 and Qu 1 azulene are supported by both the perturbational molecular orbital (PMO) theory 28 (Chapter S3.1.1)and Mandado's rules 33 (Chapter S3.1.2).
The concepts developed based on the S 0 , T 1 , and Qu 1 azulene enabled us to evaluate the aromaticity of azulene in S 1 and S 2 (Figure 4).The complete active space self-consistent field (CASSCF) aromaticity indices (Table S13) indicated that the S 1 azulene is antiaromatic, whereas its S 2 is aromatic.
We investigated the (anti)aromaticity of S 1 and S 2 azulene further by calculating the magnetically induced current density (MICD) at the CASSCF(10,10) level. 34,35We found that azulene in S 2 , similarly to S 0 , exhibited a diatropic ring current along its perimeter.Conversely, azulene in S 1 exhibited a paratropic ring current, localized primarily within the cyclopentadienyl and cycloheptatrienyl circuits (Figure 4B).The polarity of the MICD confirmed the antiaromaticity of azulene in S 1 and the aromaticity in S 2 .
The S 1 antiaromaticity of azulene followed Baird's rules.Although Baird's rules were originally formulated only for molecules in T 1 , 19 in many molecules, the rules can be applied to S 1 as well. 20The similarity between the S 1 and T 1 azulene is indicated by the calculated energies, minimum energy molecular geometries, aromaticity indices, and EDDB values (Figure 4 and Chapter S5.4).
Our findings also explain the aromaticity of S 2 azulene.The root-optimized CASSCF(10,10) wave function of S 2 azulene has a significant multireference character (Figure 4 and Tables S18 and S19).The wave function attributed near-degenerate occupancy by unpaired electrons to HOMO − 1 and LUMO and to HOMO and LUMO + 1.This factor plays a key role in the S 2 aromaticity of azulene.The multireference character of S 2 azulene mimics the Qu 1 state by adopting a similar normalized π-orbital occupancy, in a relationship not unlike S 1 −T 1 .Consequently, the S 2 and Qu 1 states of azulene share a similar aromatic character.
In summary, S 1 azulene is antiaromatic, and its geometry relaxes significantly to alleviate its antiaromaticity, whereas S 2 azulene is aromatic, and its geometry does not relax significantly, thus preserving the energy gained upon excitation.Moreover, in antiaromatic S 1 , azulene adopts a biradical electronic structure.The biradical electronic structure of S 1 azulene leads to spatial segregation of its two unpaired electrons into π and π* orbitals.Thus, in S 1 , azulene's unpaired electrons exhibit low interelectron repulsion, which contributes to its low S 1 energy (previously also described by Michl and Thulstrup). 36In the aromatic S 2 , conversely, the two unpaired electrons are delocalized within the azulene's perimeter circuit.Accordingly, in S 2 azulene, the unpaired electrons share a higher orbital overlap, resulting in higher interelectron repulsion.This contrast between the extent of geometric relaxation of azulene in S 1 and S 2 and the resulting difference in interelectron repulsion explains the large S 2 −S 1 energy separation and, consequently, leads to a low rate of S 2 −S 1 internal conversion (IC).
At this point, the absence of S 1 emission caused by the depletion of S 1 states via a S 1 −S 0 conical intersection 18 remained unaddressed though.To account for this key feature of the anti-Kasha behavior of azulene, we optimized the S 1 −S 0 conical intersection geometry and calculated the CASSCF aromaticity indices (Section S5.5), as previously performed for S 1 and S 2 .In the optimized conical intersection geometry, S 1  (10,10) wave functions of the S 0 , S 1 , S 2 , T 1 , and Qu 1 of azulene, grouped by their shared aromaticity (S 1 ∼ T 1 , S 2 ∼ Qu 1 ), including their (from top): relative energies in reference to the S 0 (E rel. ) which in case of S 1 (318 nm) and S 2 (647 nm) directly relate to the UV−vis absorption bands of azulene (see Figure 6B), bond lengths (C 2V symmetry), assigned aromatic character, canonicalized active-space natural MOs [reduced to (4,4) for clarity], their normalized occupancy (in brackets), and scheme of the dominant configuration(s).(B) CASSCF(10,10) MICD plot of azulene in S 0 , S 1 , and S 2 , constructed 1 au above the molecular plane (for full resolution plots, see Figures S38−S40), and the numerically integrated ring current susceptibilities of the cyclopentadienyl (χ C5 ) and cycloheptatrienyl (χ C7 ) rings (for integration planes, see Figure S7).azulene adopts the electronic structure of two acyclic radicals separated by a double bond (Figure 5), in turn increasing the overall energy.This increase is offset by subsequent nonradiative transition to the aromatic ground state (Table S1).As suggested by canonicalized active-space natural MO's (Figure 5c), at the CI geometry, azulene exhibits low HOMO−LUMO separation.This low separation favors the pairing of its two unpaired electrons (in S 1 ), thus providing a nonradiative pathway to S 0 .Therefore, the conical intersection enables S 1 antiaromaticity relief.

CONCLUSIONS
In conclusion, the (anti)aromaticity of the lowest three singlet states of azulene (S 0 , S 1 , and S 2 ) explains its anti-Kasha behavior.Azulene is aromatic in its ground state, antiaromatic in its S 1 , and aromatic in the S 2 .The (anti)aromaticity of each state matches its lifetime, as experimentally determined by transient absorption spectroscopy (Figure 6 and Chapter S11).Moreover, the S 1 azulene's geometry relaxes significantly to alleviate its antiaromaticity.Consequently, the S 1 minimumenergy geometry of azulene is found near a conical intersection.
In the antiaromatic, S 1 minimum-energy geometry, azulene readily undergoes a favorable, nonradiative transition to its aromatic ground state through a conical intersection (Figure 6A).The depletion of S 1 through the conical intersection provides unimolecular antiaromaticity relief.By contrast, the aromatic S 2 is stabilized, does not undergo significant geometric relaxation, and maintains at high energy, which  causes a low rate of S 2 −S 1 IC.For this reason, the S 2 state of azulene is long-lived and emitting, breaking Kasha's rule.

METHODS
Both PMO analysis 28 and Mandado's rules, 33 wherein π-electrons are separated by their spin (m), were extensively used in this study and supported by quantum chemical calculations of delocalization and aromaticity indices.We calculated HOMA, 37,38 MCI, 39 and FLU 40 and I ring 41 indices for the C 5 , C 7 , and C 10 circuits (Figure S6); in both "net" and "spin-separated" formulations, for all above states.We used the EDDB scheme, which represents electron delocalization that cannot be assigned to atoms or bonds due to its (multicenter) delocalized nature, to integrate the number of globally (EDDB G and EDDB H ) and locally (EDDB F , EDDB E , and EDDB P ) delocalized πelectrons 42,43 and, in particular, the density of delocalized π-electrons in the transannular bond of azulene (ΔC 10 ).Note that the spinseparated values of each index can be interpreted in line with Mandado's rules in open-shell systems.We also calculated the NICS 44 at the centroid of C 5 and C 7 fragments and constructed ACID 45 plots of S 0 , T 1 , and Qu 1 azulene and MRSCF MICD at CASSCF(10,10) level for S 0 , S 1 , and S 2 . 34,35ISE of methylated derivatives of S 0 and T 1 azulene were also calculated. 46Full details on the computational methods and theoretical approach and the measured stationary absorption and emission and transient absorption spectra are provided in the Supporting Information.
PMO theory and Mandado's rules, computational methods, ground and excited state aromaticity calculations, S

Figure 1 .
Figure 1.Examples of anti-Kasha azulene derivatives: (A) substituent effects explored by Binsch et al., 6 (B) derivatives (numbered as in the original publication) explored by Murata et al. (left) and a plot of fluorescence quantum yields as a function of S 1 −S 2 gap (right).7

7
Figure 1.Examples of anti-Kasha azulene derivatives: (A) substituent effects explored by Binsch et al., 6 (B) derivatives (numbered as in the original publication) explored by Murata et al. (left) and a plot of fluorescence quantum yields as a function of S 1 −S 2 gap (right).7

Figure 5 .
Figure 5. Summary of properties of the S 1 CASSCF(10,10) wave functions of the S 1 −S 0 conical intersection of azulene, calculated in the S 1 state; (a) scheme of the proposed electronic structure and the bond lengths of CI azulene, (b) EDDB H plot, (c) canonicalized active-space natural MOs [reduced to(4,4) for clarity], their normalized occupancy (in brackets), and scheme of the dominant configuration.