Switching on/off phosphorescent or non‐radiative channels by aggregation‐induced quantum interference

Pure organic materials with persistent and efficient room‐temperature phosphorescence have recently aroused great research interest due to their vast potential in applications. One crucial design principle for such materials is to suppress as much as possible the non‐radiative decay of the triplet exciton while maintaining a moderate phosphorescent radiative rate. However, molecular engineering often exhibits similar regulation trends for the two processes. Here, we propose that the quantum interference caused by aggregation can be utilized to control the phosphorescent and non‐radiative decay channels. We systematically analyze various constructive and destructive transition pathways in aggregates with different molecular packing types and establish clear relationships between the luminescence characters and the signs of the singlet and triplet excitonic couplings. It is shown that the decay channels can be flexibly switched on or off by regulating the packing type and excitonic couplings. Most importantly, an enhanced phosphorescent decay and a completely suppressed non‐radiative decay can be simultaneously realized in the aggregate packed with inversion symmetry. This work lays the theoretical foundation for future experimental realization of quantum interference effects in phosphorescence.

[23] As for the unfavorable triplet loss channels, methodologies such as crystallization, host-guest complexation, matrix rigidification, H-aggregation, and ionic crystal are generally adopted to enforce molecular rigidification and block oxygen so as to effectively suppress non-radiative decay and minimize quenching processes, which gives rise to the phenomenon of aggregation-induced RTP. [24,25]espite the remarkable progress have been made so far, it is still very challenging to achieve persistent RTP with high efficiency.][28][29][30][31][32][33][34][35][36] The underlying difficulty roots in the fact that it is very hard to reduce the non-radiative decay rate to a negligible level (≪1 s −1 ), so one usually has to simultaneously decelerate the radiative decay to prolong the phosphorescence emission, which nevertheless decreases the efficiency.On the other hand, since both radiative and nonradiative decay involves the spin-forbidden transition, the regulation of the SOC through molecular engineering often has similar influences on the two processes, rendering their independent control very difficult. [25,37]p until now, the aggregation-induced RTP primarily utilizes the rigidity of the solid environment to restrict the intramolecular thermal motion so as to adjust the luminescence character of the single molecule. [36,38]In fact, for fluorescence emission, another well-known effect that may be caused by aggregation is quantum interference.According to the Kasha theory, [39][40][41][42][43] the interference between different fluorescent pathways of the aggregate may lead to aggregation-caused quenching (ACQ) or superradiance, depending on the sign of the singlet excitonic coupling.A similar phenomenon has been analyzed for the singlet fission process, [44] but has rarely been discussed for the phosphorescence.Furthermore, phosphorescence is influenced by the environmental effects on both the individual molecules and the intermolecular electronic interactions, and several experimental results have demonstrated that the arrangement of molecules plays a pivotal role in determining phosphorescent emission. [28,31,32]Therefore, we suspect that aggregation-induced quantum interference may also induce novel fascinating phosphorescent characters and open new avenues for organic RTP materials.
Herein, we theoretically investigate the aggregationinduced quantum interference in phosphorescence and nonradiative channels.We extend the traditional Kasha theory to include both singlet and triplet manifolds as well as the ISC process, and systematically analyze the constructive and destructive pathways in fluorescent decay, ISC, phosphorescent decay, and non-radiative decay processes.It is found that the phosphorescent and non-radiative decay can be independently enhanced or completely suppressed by regulating the signs of the singlet and triplet excitonic couplings.From the analysis of the molecular design principles including the intermolecular CT states, we further find that this novel prediction can be achieved in parallel and inversion packing arrangements, as will be justified by electronic structure theory calculations.

PHOTOPHYSICS IN A SINGLE MOLECULE
We first retrospect the photophysical processes in a single molecule.Figure 1 displays the Jablonski diagram of a single molecule embedded in the aggregate without the consideration of quantum interference.After absorbing light and undergoing rapid internal conversion, the molecule enters the singlet excited state S 1 .Then, the excitation energy can be released through non-radiative decay caused by molecular motion, or through fluorescent decay facilitated by the transition dipole ⃗  S .Alternatively, the energy can be transferred to the T 1 triplet state through ISC accompanied by a further internal conversion.The triplet state then slowly decays to the ground state through phosphorescence emission or non-radiative channels.The reverse ISC process may also occur if the S 1 − T 1 energy gap is small.It is well known that due to the spin-forbidden nature, the non-radiative decay of T 1 should proceed with the aid of the SOC between T 1 and S 0 , denoted as  T 1 S 0 in the following.Similarly, the phosphorescent decay of T 1 is via the SOC-mediated transition dipole ⃗  T , which can be calculated by [45][46][47] ⃗ μ T = Δ⃗ μ 0 where Δ⃗  0 is the permanent dipole difference between T 1 and S 0 , E S n and E T n are the excitation energies of S n and T n with respect to the ground state, ⃗  S n →S 0 and ⃗  T 1 →T n are the transition dipole moments for S n → S 0 and T 1 → T n , respectively, and  T n S m is the SOC strength between T n and S m .The fluorescent decay rate of S 1 is proportional to |⃗  S | 2 , whereas the phosphorescent and non-radiative decay rates of T 1 are proportional to | ⃗  T | 2 and | T 1 S 0 | 2 , respectively.In the following, we will show how aggregation-induced quantum interference can be utilized to solely activate the phosphorescence emission channel while closing both the fluorescence emission and non-radiative channels, thus leading to high-efficiency persistent RTP.

EXTENDED KASHA THEORY INCLUDING TRIPLET STATES AND INTERSYSTEM CROSSING
The conventional Kasha theory establishes a connection between the molecular packing arrangements and the characteristics of the absorption and emission spectra in the aggregate.These properties can be easily understood by aggregation-induced quantum interference (for a detailed discussion, see Section S1).Taking a parallel-packed dimer as an example, the singlet adiabatic excited states can be expressed as where |S 1 S 0 ⟩ and |S 0 S 1 ⟩ represent the locally-excited states.
The energies of |S ± ⟩ are E S ± J S , with E S being the excitation energy of |S 1 S 0 ⟩ and |S 0 S 1 ⟩, and J S being the excitonic coupling between them.Due to the stacking geometry, the transition dipole moments of the two monomers are parallel and have the same direction.As a result, |S + ⟩ inherits all of the oscillator strengths of the monomers, and its transition dipole moment is √ 2 ⃗  S , enlarged by a factor √ 2 relative to the monomer.On the contrary, the exact cancellation of the transition dipole moments makes |S − ⟩ it optically dark and non-fluorescent.That is, where μ = μ1 + μ2 , and μi is the dipole operator of the i-th monomer.Under the point-dipole approximation, "head-to-tail" (J-aggregate) and "side-by-side" (H-aggregate) packing arrangements lead to J S < 0 and J S > 0, respectively.As such, J-and H-type aggregation give rise to red-shift and blue-shift of the absorption peak and also lead to the well-known phenomena of superradiance and ACQ, respectively. [48]It is also worth mentioning that there is another well-known theory called aggregation-induced emission (AIE) that explains why certain molecules do not emit light in good solvents but form aggregates and exhibit enhanced luminescence in poor solvents.The key mechanism behind this phenomenon is the confinement of intramolecular motion caused by aggregation. [58]s the triplet states are incorporated, one has to consider additional ISC and phosphorescence emission channels.Similar to the singlet case, we can express triplet adiabatic states of the dimer as the linear combinations of two locally-excited triplet states and the energies of |T ± ⟩ are E ± T = E T ± J T , where E T is the energy of locally-excited states and J T is the excitonic coupling between them.There are two kinds of ISC channels, one is between |S ± ⟩ and |T ± ⟩, which determines the energy exchange between the singlet excited states and triplet states, and the other is from |T ± ⟩ to the ground state |S 0 S 0 ⟩, which dominantly controls the non-radiative decay.
At first glance, the number of ISC channels between |S ± ⟩ and |T ± ⟩ increases from two to four upon dimerization, and the ISC efficiency should be promoted.However, aggregation-induced interference leads to the forbidden transfer in two of the channels.To demonstrate it, we explicitly write out the relevant SOC operator (5) From Equation ( 1)-( 5), we can obtain the following SOC strength between the delocalized states It manifests that only the ISC transitions between states with the same symmetry are allowed, and the corresponding SOC strengths are identical to that in the monomer.In Figure 2, we display the symmetry-allowed and symmetry-forbidden ISC between S ± and T ± with solid and dashed arrows, respectively.As such, one cannot use aggregation-induced interference to control the effective SOC strengths between singlet excited states and triplet states.Nevertheless, the energy splitting caused by excitonic couplings may significantly lower the singlet-triplet energy gaps and therefore facilitate the ISC.Such a protocol has been proposed to enhance the phosphorescence efficiency. [49,50]s for non-radiative decay, the SOC strengths between the delocalized triplet states and the ground state determine the decay rates.The associated SOC operator is very similar to Equation ( 5), but with  T 1 S 1 and the states |S 1 S 0 ⟩ and |S 0 S 1 ⟩ being replaced by  T 1 S 0 and |S 0 S 0 ⟩, respectively.Accordingly, it is straightforward to find that Therefore, the quantum interference effects in the nonradiative emission are very similar to those in the fluorescence decay, that is, the symmetry-allowed non-radiative decay rate can be enhanced twice.
The situation of the phosphorescence emission is much more complicated because the associated transition dipole moments originate from various SOC-mediated channels as has been discussed in Equation (1).As the monomers aggregate, intermolecular CT may also participate in the phosphorescence process.For a general situation, the effective transition dipole moments of |T 1 S 0 ⟩ and |S 0 T 1 ⟩ in a parallel-packed dimer are given by ⃗ T , where ⃗  inter T and ⃗  CT T correspond to the intermolecular excitation and intermolecular CT contributions, respectively, and their concrete expressions are shown in Equations (S13) and (S14) in SI.Using Equation (4), we further obtain where μeff represents the effective dipole moment operator that includes SOC as a perturbation in the primitive dipole moment operator.In general, the magnitudes of ⃗  inter T and ⃗  CT T are quite small as compared with that of ⃗  T , and ⃗  eff T ≈ ⃗  T is a good approximation.Equation ( 8) clearly manifests that the phosphorescence emission in the dimer follows the same behavior as the non-radiative decay given by Equation (7).Therefore, aggregation-induced interference seems to enhance or suppress phosphorescence emission and non-radiative decay simultaneously.
In Figure 2, we summarize the four possible situations of the photophysical processes in a parallel-packed dimer as categorized by the signs of the singlet and triplet

SWITCHING ON/OFF RADIATIVE PHOSPHORESCENCE OR NON-RADIATIVE CHANNELS INDIVIDUALLY
From the above analysis, it appears contradictory to simultaneously activate the phosphorescent channels and suppress the non-radiative channels through aggregation-induced interference.Nevertheless, this observation relies on the presumption that the transition dipole moment and SOC (to the ground state) of |T 1 S 0 ⟩ are identical to those of |S 0 T 1 ⟩, which is only true for a parallel-packed dimer.In fact, neither of the two quantities is rotation-invariant, and their interference behaviors will change as the relative orientation of the two monomers varies.It is noted that the fluorescence emission in non-parallel dimers has already been thoroughly discussed in the literature. [48]After careful analysis (see Sec. S3 in SI for details), we find that the inversion symmetry operation on the monomer can reverse the direction of its transition dipole moments while keeping the SOC unchanged.As a result, for an inversion-packed dimer, Equation (3) and Equation ( 8) become and respectively, whereas Equations ( 6) and (7) remain unchanged.
The possible photophysical channels in the inversionpacked dimer are shown in Figure 3, from which it is clearly seen that fluorescent, phosphorescent, and nonradiative decay channels can all be individually controlled.Specifically, Figure 3C shows that with J S < 0 and J T > 0, the fluorescent and non-radiative channels are completely suppressed and the phosphorescence emission is the only allowed channel.This is a promising scenario to utilize the quantum interference effect to overcome the current bottleneck for achieving highly efficient and persistent RTP.

THE AGGREGATION PACKING TYPE VERSUS THE SIGNS OF EXCITONIC COUPLINGS
The remaining design strategy for realizing such a scenario is how to tune the signs and magnitudes of excitonic couplings J S and J T to flexibly enhance or suppress the radiative and non-radiative decay channels.
It is well known that J S comes from both the longrange Coulomb interaction and short-range Dexter exchange interaction whereas the J T is only from the latter one.To make the interference robust, one has to arrange the two monomers close enough to enlarge the excitonic coupling strengths.[53][54] Both the shortrange exchange and superexchange interactions make the relationship between the relative molecular orientation and the signs of couplings ambiguous.One thus cannot use conventional H-and J-aggregate to predict the signs of excitonic couplings.It is noted that the H-aggregation concept has been adopted to explain the stability of the triplet exciton and the ultralong RTP achieved in carbazole derivatives, which has aroused certain controversies. [26,55]ere, we take a fluorescent molecule acridine (ACR) as an example to reveal the relationship between the packing geometry and the excitonic couplings by electronic structure calculations.ACR has a good π-conjugated plane and shows a slight degree of curvature in a crystal environment.A heteroatom N is contained in the molecular skeleton to increase SOC based on the El-Sayed rule, [16] which can also be conveniently used to distinguish the molecular orientation.Figure 4 displays the structures of both the ACR monomer and the dimer with a face-to-face inversion packing mode.In the numerical calculations, the time-dependent density functional theory (TDDFT) is used to obtain the properties of singlet and triplet adiabatic states, including excitation energies, transition dipole moments, and SOC.Subsequently, the fragment particle-hole density (FPHD) method is adopted (C and D) highlight the regions of RTP (J S < 0, J T > 0, red) and ACQ (J S < 0, J T < 0, gray), respectively.
to construct the quasi-diabatic states and acquire the excitonic couplings. [56]All the calculation details are described in Section S4.
To illustrate the correlation between packing geometry and excitonic couplings, we establish the x-and y-axes as the short and long axis directions of the monomer, respectively (see Figure 4), with the z-axis passing through the center of the hexagonal ring and intersecting the x-and yaxes at the origin of the coordinate system.We then vary the position of one of the monomers along the x-and yaxes while keeping the z-coordinate constant at a value of 3.5 Å.
Figure 5A,B exhibits the contour plots of J S and J T in the x-y plane, respectively.It is seen that the variation trends of J S and J T at different positions differ due to their distinct primary sources.Two important regimes are identified from these plots.Figure 5C shows the regime with J S < 0 and J T > 0, which is associated with high-efficiency RTP.On the other hand, Figure 5D corresponds to the regime with J S < 0 and J T < 0, which is associated with ACQ.
To demonstrate the interference behavior and validate the theoretical predictions, we further calculate the essential parameters associated with RTP at the geometry P shown in Figure 5C.The coordinates of geometry P are x = 0.90 Å and y = 1.05 Å, with the excitonic couplings J S = −42.6 meV and J T = 11.85 meV.Table 1 compares the results of the monomer and the dimer at this geometry.It can be seen that these numerical results are well in line with our previous analysis as illustrated in Figure 3C.Concretely speaking, | ⃗  S 1 | and  T 1 S 0 in the dimer become vanishingly small as compared with those in the monomer, indicating that the fluorescent decay channel of S 1 and the non-radiative decay channel of T 1 are completely suppressed by the quantum interference.On the other hand, |⃗  T 1 | is approximately enlarged by √ 2, suggesting an enhanced phosphorescence emission.As such, the dimer with the P geometry has the potential to achieve both high efficiency and long-lifetime phosphorescence.It is worth noting that the S 1 → T 1 ISC process is also suppressed in the dimer due to the symmetry mismatching of T 1 .Nevertheless, the S 1 → T 2 process is symmetry-allowed with Δ E S 1 T 2 = 1.809 eV and  S 1 T 2 = 0.155 cm −1 .The smaller TA B L E 1 Electronic structure parameters of the acridine (ACR) monomer and dimer (at geometry P) relevant to various photophysical processes.

System
The structure of the monoazabiphenylene (MON) monomer and the main transition configurations of T1 and S1.
singlet-triplet energy gap in the dimer is beneficial for the ISC process.
To briefly summarize, we have observed that J S exhibits alternating positive and negative oscillations when the two molecules slide relative to each other.This phenomenon is primarily due to the combined effect of the long-range Coulombic interaction and the CT-mediated superexchange coupling.The former one changes sign at a half-molecular length scale as the molecules move, whereas the latter one changes sign at the C-C bond length scale.In contrast to J S J T is mainly determined by the degree of orbital overlap between the two molecules and is of the same origin as the CT-mediated superexchange coupling.Its variation trend is consistent with the CT-mediated superexchange coupling, showing rapid oscillation decay and alternating signs as the two molecules slide relative to each other.By altering the relative positions of the phosphorescence molecules, different combinations of J S and J T can be achieved, thereby modifying their emission properties.However, because the CT-mediated superexchange coupling and J T have the same origin, simultaneously achieving opposite signs and large magnitudes for J S and J T is highly challenging.

MOLECULAR AGGREGATES EXHIBITING HIGH-EFFICIENCY AND PERSISTENT PHOSPHORESCENCE
Now we demonstrate how to achieve high-efficiency and long-lifetime phosphorescence via aggregation-induced quantum interference.We choose the monoazabiphenylene (MON) aggregate with an inversion packing mode as one of the potential candidates.The MON monomer is featured by very weak fluorescence.As such, the conditions J S < 0 and J T > 0 can be relaxed to J T > 0 since it is no longer necessary to require a negative J S for suppressing fluorescence.
Figure 6 shows the structure of the MON monomer as well as the isosurfaces of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).Since both HOMO and LUMO are approximately centrally symmetric under inversion, the HOMO-to-LUMO transition is not optically favorable due to the parityforbidden selection rule.As a result, the S 1 state is only weakly fluorescent with a very small transition dipole moment of |⃗  S 1 | = 0.16 a.u.
Figure 7A,B illustrates the energy-level alignments and photophysical channels in the MON monomer and the inversion-packed dimer, respectively, where the concrete numerical data are listed in Table S1.For the singlet states, the dimer naturally inhibits the fluorescence emission because of the small transition dipole moment ⃗  S 1 in the monomer.By forming an inversion-packed dimer, the non-radiative decay channel of T 1 is effectively closed ( T 1 S 0 = 0.052 and 0.000 cm −1 for the monomer and dimer, respectively), and the radiative decay channel is significantly boosted (| ⃗  T | = 4.12 × 10 −5 and 7.24 × 10 −5 a.u.for the monomer and dimer, respectively), resulting in an efficient and long-lifetime phosphorescence character.Due to small intermolecular distance, the intermolecular CT significantly contribute to both J S and J T , and their values are as large as 184 and 105 meV, respectively.It is noted that intermolecular CT states not only contribute to the excitonic couplings but also modify the SOC strength of ISC channels due to the resonant mixing of singlet CT states with singlet locally-excited states.The | S 1 T 1 | for the dimer is 0.02 cm −1 , enlarged by four times as compared with 0.005 cm −1 for the monomer, which makes ISC easier to proceed.
The phosphorescence properties of the MON monomer and dimer can be further evaluated based on the phosphorescence lifetime  P and the phosphorescence quantum efficiency Φ P .According to the Jablonski diagram displayed in Figure 7,  P and Φ P can be calculated by (11)   and respectively, where k P and k nr are the phosphorescent and non-radiative decay rates of T 1 , respectively, is the ISC efficiency, and k F and k ISC are the fluorescent decay rate and ISC rate of S 1 , respectively.From Equations ( 11) and ( 12), the first necessary requirement for achieving efficient and prolonged RTP is that the ISC is highly efficient, and the second one is that the phosphorescent decay is slow but still fast enough to surpass non-radiative decay (k P ≫ k nr ).As such, extremely inhibiting the nonradiative decay while maintaining a moderate phosphorescent decay rate becomes one of the central issues in designing pure organic materials with highly efficient persistent RTP.Table 2 lists the calculated rate constants and quantum efficiencies of various photophysical processes in the MON monomer and dimer (see Section S4 for the computational details).It is seen that the fluorescence emission rate in the dimer reduces to 3.58 × 10 3 s −1 although it is already quite small with a value of 7.22 × 10 5 s −1 in the monomer as compared with conventional fluorescence molecules.The phosphorescence emission rate is enhanced twice and the non-radiative rate from T 1 to S 0 vanishes.The ISC rate from S 1 to T 1 in the dimer is enlarged by nearly two orders of magnitude, which mainly comes from the reduced singlettriplet energy gap.Obviously, the phosphorescence lifetime and efficiency in the dimer ( P = 66.9 s, Φ P = 0.8) have been significantly improved as compared with the monomer ( P = 0.003 s, Φ P ≈ 0).It is of interest and significance to extend the dimer mechanism to multimers.To ensure inversion symmetry between two nearest-neighboring molecules, we construct the aggregates using an alternating arrangement.Figure 8 presents a schematic diagram of the aggregates constructed from different numbers of monomers, along with the corresponding energetic levels and photophysical channels.Table 3 and Table S2 list various photophysical parameters from MON monomer to hexamer.As can be seen from Table 3, the excitation energies of S 1 and T 1 decrease as the number of monomers increases, a result of the excitonic couplings and polarization effect. [48,57]In all aggregates, the transition dipole moment of S 1 (| ⃗  S 1 | in Table 3) is smaller than that in the monomer, indicating that the fluorescence is suppressed  3) increases with an increasing number of monomers, enhancing the phosphorescence radiation by aggregation.Interestingly, the SOC strengths for the nonradiative channel are zero for the aggregates with an even number of monomers, whereas they are nonzero (but still very small) for an odd number of monomers.Therefore, aggregates containing an even number of monomers are preferred for high-efficiency and long-lifetime phosphorescence.
The quantum interference in multimers can be understood by the superposition of different locally-excited states.Let us consider the triplet states of aggregates as an example (the same argument can be applied to singlet states in a similar way).Label the wave vector of a locallyexcited triplet state with the n-th monomer being excited as |n; T 1 ⟩, and assume that the excitonic couplings between the nearest-neighboring monomers are identical and denoted as J T .Then, it is easy to derive the following delocalized eigenstates of an N-monomer chain with an open boundary condition where k = 1, … , N, and the corresponding energies are E k = E T 1 + 2J T cos( ßk N+1 ) (see Section S5 for derivation details).For J T > 0, the eigenstates with k = N and k = 1 correspond to the lowest-and highest-lying states, respectively.For a large N, all of the eigenstates form a band with a width of about 4J T .
To a good approximation, we can write the effective transition dipole moment operator (incorporating SOC effects as perturbation) in the triplet manifold as where |G⟩ represents the singlet ground state, ⃗  T is the transition dipole moment of T 1 of the monomer, and the phase factor (−1) n+1 accounts for the alternating molecular inversion arrangement.Invoking Equation (13), it is straightforward to obtain the triplet transition dipole moment for the radiative

𝜋
) sin 1 ⟩ with the lowest energy.For odd N, the triplet states with higher energies are also permitted for emission.In Figure 8, we have displayed the triplet states permitted for emission with yellow.
Likewise, the SOC operator shown in Equation ( 5) for the dimer can be adapted to Compared with Equation ( 14), there is no phase factor in Equation ( 16) since the inversion operation does not change the SOC.Following a similar procedure, the SOC between |T k 1 ⟩ and the ground state is given by ) .(17)   It is seen that the selection rule for the non-radiative decay is completely opposite to the phosphorescent decay.Concretely, the lowest-lying state |T N 1 ⟩ is symmetry-forbidden for non-radiative decay, whereas the highest-lying state |T 1 1 ⟩ is symmetry-allowed with a SOC strength enhanced by √ N. The state |T N 1 ⟩ is strictly forbidden for even N, whereas it is partially allowed for odd N. Therefore, in the inversionpacked aggregates with J T > 0 and an even number of monomers, the phosphorescence emission is enhanced by N times, very similar to the superradiance phenomenon for fluorescence emission, whereas the non-radiative decay is completely suppressed.For those aggregates with J T < 0, the opposite situation occurs.

CONCLUSION
In summary, we have extended the conventional Kasha theory to include the triplet manifold and ISC channels.The new theory suggests that aggregation-induced quantum interference, in conjunction with varying molecular packing modes, can be utilized to flexibly switch on/off the fluorescence, phosphorescence, and ISC channels.Especially, we have theoretically designed an aggregate arranged with the inversion symmetry of monomers to simultaneously enhance the phosphorescence emission channel and close the non-radiative decay channel, mapping out the optimal conditions for achieving RTP.The present work may raise a new strategy for designing highly efficient and persistent RTP.However, it is important to note that these findings, while promising, are largely theoretical and the practical realization of these designs would require further extensive experimental verification.

2
The symmetry-allowed and symmetry-forbidden channels of various photophysical processes in a parallel-packed dimer, caused by aggregation-induced interference.Φ F and Φ P are the quantum efficiencies of fluorescence and phosphorescence, respectively.excitonic couplings.It is found that the interference can selectively open the fluorescence emission channel Figure2Cor the phosphorescence channel Figure2B.It can also close both fluorescence and phosphorescence emission channels Figure2A, known as the ACQ phenomenon.If the ISC process is fast enough to compete against fluorescence emission, the aggregate may be featured by dual emission, as depicted in Figure2D.However, the phosphorescent and nonradiative channels for the triplet states cannot be separately controlled, as mentioned above.

) 3
The symmetry-allowed and symmetry-forbidden channels of photophysical processes in an inversion-packed dimer, caused by aggregationinduced interference.Φ F and Φ P are the quantum efficiencies of fluorescence and phosphorescence, respectively.

F I G U R E 4
Structures of the acridine (ACR) monomer and the faceto-face inversion-packed dimer.
U R E 5 (A and B) are the contour plots of J S and J T , respectively, at different packing geometries of an acridine (ACR) inversion-packed dimer.
Yi Kong acknowledges Dr. Zheng Pei for insightful discussions about the spin-orbit coupling operator and triplet transition dipole moment calculations.This work is supported by the National Science Foundation of China (Grant Nos.22033006, 21833006, 22173074, and 22203068) and the China Postdoctoral Science Foundation (Grant No. 2021M702734).C O N F L I C T O F I N T E R E S T S TAT E M E N TThe authors declare no conflict of interest.D ATA AVA I L A B I L I T Y S TAT E M E N T NoneO R C I DYu-Chen Wang https://orcid.org/0009-0003-2264-1247WanZhen Liang https://orcid.org/0000-0002-5931-2901Yi Zhao https://orcid.org/0000-0003-1711-4250RE F E R E N C E S Parameters related to the photophysical processes from monoazabiphenylene (MON) monomer to multimer.
|μ eff |G⟩ ≈ 0. For the aggregates with less than 10 monomers (N < 10), the ⟨T k 1 |μ eff |G⟩ is sensitive to the parity of the monomer number N. For even N, phosphorescence is dominantly emitted from |T N