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INEOS OPEN, 2024, 7 (X), XX–XX  Journal of Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences Download PDF DOI: 10.32931/io2446a

Orange Room-Temperature Phosphorescence in Complexes of Pyrene-d₁₀–β-Cyclodextrin with Bulk Molecules in the Presence of Oxygen

Abstract

The long-lived room temperature phosphorescence (RTP) and fluorescence of a pyrene-d₁₀–β-cyclodextrin (Pd₁₀–CD) complex were studied before and after the removal of O₂ as well as after the addition of bulk molecules (BM), namely, tert-butylbenzene, p-tert-butyltoluene, and adamantane. The biexponential decay of the RTP intensity of the complexes indicates the presence of two types of phosphorescent sites (PSs) in the crystal lattice of 2BM-2CD. The emission and quenching rate constants of Pd₁₀ RTP in all the complexes and the PS structures were calculated by quantum chemistry methods. The assignments and selection rules of vibrational fine structure lines in the emission spectra are discussed.

Key words: room-temperature phosphorescence, pyrene-d₁₀–β-cyclodextrin complex, bulk molecules, phosphorescence emission and quenching constants.

 

Introduction

Figure 3. Fluorescence spectra of Pd₁₀–CD (1) and Pd₁₀–CD–BM (2–4) normalized by the intensity of 0–0 transition (⁰I) with the frequencies of the most intensive vibronic lines.

When passing from the two-component system Pd₁₀@2CD to the three-component complexes, the main difference in the fluorescence spectrum is that for tBB and Ad the ratio I₃/I₁ (in our notation I_III/I_I) decreases to 1.34 and 1.27, respectively, and remains almost unchanged for tBT compared to 1.47 for Pd₁₀@2CD). In addition, the maximum value of the width of line I (0–0 transition) Δν_½ is observed in the Pd₁₀@2CD complex both in fluorescence and RTP. For the series of tBB, tBT, and Ad added molecules, the value of Δν_½ gradually decreases to 197, 176, and 156 cm^–1, respectively, compared to 218 cm^–1 for Pd₁₀@2CD.

The changes in the line widths can be attributed to the fact that in the Pd₁₀@2CD crystal hydrate, pyrene is arranged in a more polar environment (water, vide infra) than in the presence of hydrocarbon BMs. Therefore, the line width of the 0–0 transition in the Pd₁₀@2CD complex is larger than those in the three-component complexes. The minimum value of Δν_½ for Pd₁₀–CD–Ad can be explained by the fact that the RTP spectrum of this system is characterized by a monoexponential decline; therefore, Pd₁₀ inside PS has a uniform environment, since the Ad molecule has a spherical shape.

Thus, different BMs added to the Pd₁₀@2CD complex do not change significantly the structure of the luminescence spectra, and small changes in the parameters of the fluorescence spectra are not enough to judge the changes in the microstructure of this complex on passing to three-component systems. But the addition of BM certainly promotes the appearance of long-lived RTP in the presence of oxygen, and for the Pd₁₀–CD–tBT complex after the removal of oxygen, the value of τ_ph increases to 4.02 s compared to 2.35 s in the case of Pd₁₀@2CD (vide infra).

Lines II and III in the RTP spectra feature shorter wavelengths Δν_II and Δν_III than those in the fluorescence spectra. This implies that the lines of the vibronic structure relate to different vibration frequencies of Pd₁₀. The assignments will be presented below.

2.1.3. Fluorescence and phosphorescence spectra at 77 K, assignments of the vibronic transition lines. In order to obtain higher resolution spectra for more accurate assignment of the vibronic transition lines to the vibrational modes of Pd₁₀, the fluorescence and phosphorescence spectra were recorded at 77 K (Fig. 4).

Figure 4. Fluorescence (a) and phosphorescence (b) spectra Pd₁₀–CD–tBT at 77 K. The vibration transition lines are designated with the Roman numbers. The superscripts 0 and 1 indicate the main and overtone vibrational levels of the Pd₁₀ molecule in the ground state. The values of Δν_½ for line I are presented on both spectra.

The comparison of the data in Table 1 shows that a decrease in the temperature leads to narrowing of line I (0–0 transition) in the fluorescence spectrum of Pd₁₀–CD–tBT more than two times (Δν_½ = 234 and 100 cm^–1 at room temperature and 77 K, respectively), while in the phosphorescence spectrum Δν_½ changes to a lesser extent (from 201 to 133 cm^–1) and the widths of the other lines, including Δν_½ of line III, remain virtually unchanged.

Due to the temperature narrowing, it can be seen that the fluorescence spectra of the Pd₁₀ molecule consist of two vibrational progressions corresponding to the transition to the ground (designated with the superscript 0) and the first overtone (designated with the superscript 1) levels with a difference in the progressions of the ground and excited vibrational states of Δν = 1399 cm^–1. The line at 25583 cm^–1 (Fig. 4) is the beginning of the overtone vibrational progression and, therefore, has two designations ⁰V and ¹I. The difference in the progression is consistent with an analogous value in the absorption spectra of the double complex P@2CD: 1431 cm^–1 [13b]. An interesting feature of the low-temperature fluorescence spectrum is that the ratio I₃/I₁ drastically changes compared to the spectrum at room temperature (0.93 and 1.34, respectively). This indicates that the empirical rule that the value of I₃/I₁ is a measure of the polarity of the environment of the P molecule in solutions [21] or complexes [13] is valid only for the spectra measured at room temperature.

For the phosphorescence spectrum (Fig. 4b), the lines of the vibrational progression II–V of the ground vibrational state are also reliably determined, although the temperature narrowing of the lines is smaller compared to that observed in the fluorescence spectrum.

The general comparison shows that the values of differences Δν_i in both emission spectra are consistent with each other. Visually, it may seem that the same vibrational levels are populated in the radiative transitions S₁→S₀ and T₁→S₀, respectively. Thus, in the fluorescence spectra, lines II, III, IV, and V correspond to the fully symmetric A_g-type vibrational transitions ν₁₃, ν₁₁, ν₉, and ν₆ of the Pd₁₀ molecule [13b]. However, from the average values of Δν_i, it is obvious that when going from the fluorescence spectrum to the RTP spectrum for all the Pd₁₀–CD–BM explored, the frequencies of lines II and III differ. This fact calls into question the assignment of lines II and III in the phosphorescence spectra to ν₁₃ and ν₁₁ transitions by analogy with the fluorescence spectra. Since the assignments  based on Ref. [23] show that the vibrational fine structure of the emission spectra involves vibrations of even symmetry, in particular, A_g, then the closest even vibration to ν₁₁ and ν₁₃ are ν₂₃ (735 cm^–1) and ν₂₅ (457 cm^–1) of B_3g symmetry. Thus, we assumed that lines II, III, IV, and V in the RTP spectra belong to ν₂₅, ν₂₃, ν₉, and ν₆ vibrational transitions of the ground S₀ state of Pd₁₀, and, consequently, the difference in the selection rules for vibrational transitions in fluorescence and phosphorescence spectra is that lines II and III in the former belong to the A_g-type vibrations, while in the latter they belong to B_3g-type vibrations.

Table 2 shows that the vibration frequencies ν_i of the Pd₁₀ molecule calculated by the DFT/PBE method are in satisfactory agreement with the average values of ν_i in both emission spectra.

Table 2. Values of E_total (a.u.) and ν_0–0 transitions (cm^–1) in the fluorescence and RTP spectra calculated by the DFT/B3LYP/D3 and TDDFT/B3LYP/D3 methods with full geometry optimization for Pd₁₀·2BM@CD complexes

Complex, type	Etotal S0 (DE)	Etotal S1	ν0–0 (F)	ν0–0 (RTP)
P×@2CD, I	–1226.29655	–1226.30369	27911 26861a	17586 17004a
P×2tBT@2CD, I	–1473.13976	–1473.00576	26967 26840	17194 17011
P×2tBT@2CD, II	–1473.13674 (1.9)b	–1473.00213 (2.3)	28957	18664
P×2tBB@2CD, I	–1394.52193	–1394.38973	26721 26840	16466 17013
P×2tBB@2CD, II	–1394.52899 (–4.4)	–1394.39379 (–2.5)	28740	18417
P×2Ad@2CD, I	–2597.76634	–2597.63136	28016 26875	17784 17018
P×2Ad@2CD, II	–2597.78203 (–9.8)	–2597.64670 (–9.6)	27890	17738

a experiment; b DE, energy difference between structures I and II, kcal/mol.

2.1.4. Lifetimes and decay kinetics of RTP of the three-component systems. The RTP decay curve of Pd₁₀@2CD shows (Fig. 5a) that the RTP decay is the sum of two exponentials with long-lived (2.4 s) and short-lived (0.17 s) lifetimes. It can be assumed that the presence of the biexponential decay indicates that RTP is generated by the Pd₁₀ molecules in two PSs of different structures, introduced as microimpurities into the CD crystal lattice and characterized by different rate constants of nonradiative deactivation k_nr of Pd₁₀ phosphorescence (vide infra).

Figure 5. Experimental RTP decay curve in the absence of oxygen for Pd₁₀@2CD complex (a). An inset presents the results of decomposing the curve into a sum of two exponents with times of 2.4 and 0.17 s (R-factor = 0.997). Experimental RTP decay curve in the presence of oxygen for Pd₁₀–CD–tBT complex 1 and its presentation as a sum of calculated exponents 2 and 3 (b). An inset presents the RTP decay curves for Pd₁₀–CD–tBt in the absence of oxygen.

The RTP decay for Pd₁₀–CD–tBT and Pd₁₀–CD–tBB is also biexponential. Figure 5b shows as examples the decay curves only for Pd₁₀–CD–tBT, since for Pd₁₀–CD–tBB the analogous curves were obtained. In all cases, the RTP decay curve in these complexes represented the sum of two exponentials I = I₁ exp(–t/τ₁) + I₂ exp(–t/τ₂) (Fig. 5b), which indicates the presence of two different PS structures. At the same time, for Pd₁₀–CD–Ad, the RTP decay turned out to be monoexponential (R-factor = 0.997) with a lifetime of 2 s. Table 3 presents the results of calculating the kinetic characteristics of RTP for all the Pd₁₀ complexes explored based on the formula given above and the formulas for calculating the constants in Section 2.3 (vide infra).

From Table 3 it follows that k_nr for the Pd₁₀@CD complex is higher than the corresponding values for the Pd₁₀–CD–BM complexes. This is not surprising, since k_nr characterizes the degree of quenching effect of the Pd₁₀ microenvironment on its RTP in PS, preferably having structure I (vide infra), where the luminophore is surrounded only by highly mobile water molecules.

Table 3. Lifetimes τ₁ and τ₂ and normalized amplitudes (I₁) and (I₂) of the RTP decay curves for Pd₁₀ in Pd₁₀–CD–BM complexes in the presence (+O₂) and absence (–O₂) of oxygen; k_q and k_nr are rate constants of quenching with oxygen and non-radiative process for the short-lived (a) and long-lived (b) components of RTP of Pd₁₀

System	τ1, s (I1) +О2	τ2, s (I2) +О2	τ1, s (I1) –О2	τ2, s (I2) –О2	kq×[O2], s–1		knr, s–1
					a	b	a	b
Pd10@2CD	–	–	0.175	2.35	–	–	5.72	0.262
Pd10–CD–tBB	0.39 (0.77)	1.88 (0.23)	1.41 (0.35)	2.56 (0.65)	1.64	0.12	0.55	0.227
Pd10–CD–tBT	1.09 (0.75)	2.27 (0.25)	1.81 (0.6)	4.02 (0.4)	0.33	0.17	0.39	0.086
Pd10–CD–Ad		2.2		2.9		0.1		0.182

The maximum values of RTP τ_ph equal to 1.81 and 4.02 s for the Pd₁₀–CD–tBT system in the absence of oxygen correspond to the minimum values of the quenching constants k_nr compared to k_nr in the complexes with tBB and Ad. This indicates that the use of tBT as a BM forms such a microenvironment of Pd₁₀ in the complex that most effectively isolates the luminophore from RTP quenching due to nonradiative processes. At the same time, the Pd₁₀–CD–Ad system in the studied series of BMs is characterized by the minimum value of k_q[O₂]. This indicates that the Pd₁₀ microenvironment in it prevents phosphorescence quenching by oxygen more effectively than in other systems.

2.2. Proposed structures of the phosphorescent sites

2.2.1. Two-component system Pd₁₀@2CD. Since pyrene in the presence of CD forms an inclusion complex P@2CD in an aqueous solution [12], the long-lived RTP with a lifetime of τ_ph = 2.4 s observed by us belongs to the Pd₁₀ molecule in the Pd₁₀@2CD complex included in the CD crystal hydrate. The assumption about the presence of two types of PS for two-component Pd₁₀@2CD complexes is consistent with the result of previously performed molecular dynamics calculations [13b, 24], according to which inclined I and transverse II orientations of P relative to the vertical axis of the CD dimer, from which the crystal is built, are possible (Fig. 6).

I	II

Figure 6. P×(H₂O)₈@2CD (I) and P×(H₂O)₁₂@2CD (II) images of instant structures from molecular dynamic trajectories (here, carbon atoms are marked in blue, oxygen atoms are marked in red, and hydrogen atoms are marked in grey) [13b].

Configuration I is more stable than configuration II and exists for 72% of the total simulation time. The more favorable configuration I contains four water molecules in each of the cavities. In structure II, six water molecules are placed in each of the cavities, since the free volume of the cavity in II is larger than that in I. Water molecules filling the free volume in the cavity actually act as BM, but at the same time they are carriers of oxygen, the main quencher of phosphorescence. Therefore, to observe RTP of the Pd₁₀@2CD complex, it was necessary to remove O₂. It can be assumed that in the crystalline precipitate of Pd₁₀@2CD, structures I and II play the role of PS, which correspond to two exponents in the RTP attenuation of Pd₁₀. The reality of structure II is confirmed by the presence of two crystal structures with the codes ABUTEY, PUKPIU and PUKPOA in the Cambridge Crystallographic Data Bank CCDC [25].

2.2. Structures, formation energies, and spectral characteristics of the phosphorescent sites. The concentration ratio of the reagents (CD and BM ~10^–2, Pd₁₀ ~10^–6 M) used for the preparation of the samples shows that Pd₁₀ is actually a microimpurity in the 2BM@2CD crystal. This resembles the previously studied phenanthrene–tBB–CD system [24a], which, as was shown by the MD calculations [24b], is included in a crystal whose lattice consists of 2tBB@2CD dimers packed into columns (Fig. 7).

Figure 7. Arrangement of 2CD in the crystalline lattice.

Phenanthrene molecules are embedded inside some of them. Such three-component complexes play the role of PSs. The calculations showed that the crystal lattice built from CD dimers retains stability, weakly depending on the structure of the embedded BM, provided that its molecule fits into the cavity of the dimer. Therefore, we assumed that our system is constructed in a similar way, and PSs represent three-component complexes Pd₁₀·2BM@2CD, embedded in the crystal lattice of 2BM@2CD dimers. The most probable structures of the three-component complexes were calculated using quantum chemistry methods.

Comparing the structures of tBB and tBT with structures I and II in Fig. 6, it can be seen that in structure II, according to the MFCV principle, the P plane should contact with the tert-butyl group of tBB or tBT, whereas for structure I, in the case of tBB, P should contact with the benzene ring, and in the case of tBT, the contact should be realized with the methylphenyl group (Fig. 8).

Figure 8. Structure of the P·2tBT@CD complex calculated by the DFT/B3LYP/D3 method.

The criterion for assessing the correctness of the choice among the calculated structures of the complexes that could be selected as the PS model, calculated by quantum chemistry methods, were the values of relative energies of the P·2BM@2CD complexes of types I and II, as well as the values of ν_0–0 in the fluorescence and phosphorescence spectra (within the TDDFT method, the vibrational structure of the spectra is not calculated). These criteria are fully satisfied by the structure presented in Fig. 8. The results of the calculations of the energy and spectral characteristics of the complexes are given in Table 2.

The calculated data suggests that among all the P·2BM@2CD complexes, structure I is advantageous only for P·2tBT@2CD, since it is characterized by a more negative value of E_total compared to that of structure II and, the value of ΔE is positive in both S₀ and S₁ states. The calculated values of ν_0–0 for P·2tBT@2CD I are closest to the experimental values of 26840 and 17013 cm^–1 (Table 2).

For the Pd₁₀–CD–tBB system, only the calculated value of ν_0–0 is comparable with the experimental value of 17013 cm^–1, whereas for Pd₁₀–CD–Ad, the agreement between the calculation and experiment is worse than for the other systems.

Figure 8 shows that the structure of P·2tBT@2CD is characterized by the minimum free volume (i.e., it best corresponds to the MFCV principle). The geometric and spectral advantage of the P·2tBT@2CD structure is consistent with the fact that the use of tBT as a BM leads to the longest RTP and, consequently, to the minimum nonradiative constant k_nr, 0.086 s^–1, which indicates the densest microenvironment of Pd₁₀ in PS. For the complexes with tBB and Ad, on the contrary, structure II is energetically more favorable. At the same time, the agreement between the calculated and experimental frequencies of ν_0–0 for P·2tBB@2CD and P·2Ad@2CD is significantly worse than that for P·2tBT@2CD.

2.2.3. RTP lifetimes of arenes in the complexes with β-cyclodextrin. Table 4 compares the lifetimes of the arene RTP in the complexes with β-cyclodextrin with added identical BMs.

Table 4. RTP lifetimes of three-component A–CD–BM complexes in the presence and absence of O₂

A	BM	τph +O2	τph –O2
Naphthalene-d8	tBB tBT Ad	14 [19] 4.8 [19] 10 [11a]	16.4 [19] 6.6 [19] 15 [11a]
Phenanthrene	tBB Ad	2.4 [19, 20] 2.2 [11b]	2.7 [19, 20] 4.1 [11b]
Pyrene-d10a	tBB tBT Ad	1.88 2.27 2.2	2.56 4.02 2.9

a for the data on pyrene-d10, see Table 2.

It is obvious that among simple arenes, the naphthalene-d₈ complexes give the longest phosphorescence. However, each arene phosphoresces in its own spectral range. The advantages of pyrene are as follows. Since it is widely used in analytical practice, the discovery of new properties can expand its application scope. First of all, this relates to the long-lived RTP, which has not been studied before. We demonstrated that it can be observed relatively easily even without removing oxygen and with the naked eye as a bright orange emission.

3. Experiment and calculations

3.1. Experimental section

3.1.1. Sample preparation. Double-distilled water, Pd₁₀ (Aldrich), CD (Acros Organics), reagent grade tBB, tBT, and Ad were purchased from commercial sources and used in the complex preparation without purification. Pd₁₀@CD complex was prepared by adding 2 mL of an aqueous solution of CD with a concentration of 10^–2 M to a quartz cuvette, on the walls of which, after evaporation from a hexane solution, Pd₁₀ was present in the form of a thin layer in such an amount that its concentration in the solution was several μM. After heating the cuvette in a thermostat at 50 °C with simultaneous ultrasonic irradiation for 1 h, an aqueous solution of Pd₁₀@CD complex was formed.

When an aqueous solution of CD with a concentration of 6·10^–2 M was added to a cuvette with Pd₁₀, a microcrystalline precipitate formed on the walls of the resulting complex solution, in which Pd₁₀ exhibited long-lived RTP after the addition of sodium sulfite used to remove oxygen.

To obtain the three-component complexes, several μL of tBB or tBT were added to a cuvette with an aqueous solution of Pd₁₀@CD. The complexes with Ad were obtained in a similar manner by adding an aqueous solution of CD to a cuvette where Ad was applied to the walls in addition to Pd₁₀. The cuvettes were then subjected to heating in a thermostat as described above. The resulting samples represented aqueous suspensions of microcrystals of the three-component complexes, the sedimentation time of which always exceeded the measured RTP lifetimes by orders of magnitude. The concentrations of CD, tBB, tBT, and Ad in the samples were 10^–2 M. Therefore, it could be expected that with such a ratio of the reagents, all Pd₁₀ would be bound into Pd₁₀–CD–BM complexes. The measurements were performed both in the presence of oxygen and in its absence after the addition of Na₂SO₃.

3.1.2. Measurements. The lifetime of Pd₁₀ RTP in the complexes was measured using a modernized experimental unit [18]. The maximum value of τ_ph for Pd₁₀ in Pd₁₀–CD–tBT complex at 77 K (τ₇₇), which we measured for the first time, composed 6.13 s and was used to calculate the rate constants of nonradiative deactivation k_nr of a triplet state of Pd₁₀. The steady-state fluorescence and phosphorescence spectra of Pd₁₀ in the complexes were measured on a modernized Elumin-2M spectrofluorometer with excitation by a UVTOP335 LED (Sensor Electronic Technology) with an emission maximum at 335 nm. All the main measurements were performed at 21 °C. The fluorescence and phosphorescence spectra of the Pd₁₀ complexes were measured at a spectral slit width of the monochromator of 1 and 2 cm^–1, respectively.

3.2. Calculations

3.2.1. Calculation of the constants of nonradiative deactivation and quenching of RTP. The lifetime of phosphorescence of A is determined by the formula

,

where k_ph, k_nr, and k_q are the rate constants of the radiative transition, nonradiative processes, and oxygen quenching, respectively. The formulas for calculating the constants k_q and k_nr were publihsed elswhere [19]:

 

where τ_+O2 and τ_–O2 are the phosphorescence lifetimes in the presence and absence of oxygen, respectively, and [O₂] = 2.65·10^–4 M is the oxygen concentration in the aqueous suspension of the complex at room temperature [26].

3.2.2. Quantum chemical calculations. To determine the preferred arrangement of PS in the CD dimer, the equilibrium geometry of isolated P·2BM@2CD complexes in the ground S₀ and excited S₁ states was calculated using the ORCA-5.0.3 software package [27] by the RI/DFT/B3LYP/D3BJ and RI/TDDFT-TDA/B3LYP/D3BJ methods (where D3BJ is the procedure allowing for consideration of the dispersion correction), respectively, in the three-exponential def2-TZVP basis. The number of calculated excited states was 5 for each state. The calculations were carried out using the ONIOM procedure, in which 2CD dimer was calculated using the semiempirical PM3 method (QM1), while the embedded complex P·2BM was calculated using the DFT/D3BJ and TDDFT/D3BJ (QM2) methods in the same def2-TZVP basis. Simultaneously, the frequency of 0–0 transitions of the vibronic fluorescence and phosphorescence spectra (ν_0–0) was calculated. The vibration frequencies and displacement vectors of the atoms in the Pd₁₀ molecule were calculated using the DFT method with the PBE functional in the three-exponential 3ζ basis using Priroda-04 program [28].

Conclusions

The long-lived room-temperature phosphorescence of Pd₁₀ was detected for the first time in the crystalline precipitate of Pd₁₀@2CD complex after oxygen removal (τ_ph =2.4 s), as well as in the crystalline precipitates formed after the addition of BM (tBB, tBT, and Ad) to a solution of Pd₁₀@2CD. In these crystalline precipitates, Pd₁₀ plays the role of a phosphorescent probe. Due to the densest packing of PS, provided by the addition of tBT, Pd₁₀–CD–tBT system demonstrates maximum τ_ph of 1.8 and 4.02 s in the presence and absence of oxygen, respectively. The biexponential character of the RTP decay observed for Pd₁₀–CD–tBT and Pd₁₀–CD–tBB is likely to be associated with two types of PS packing in the CD dimer, calculated earlier by the molecular dynamics method.

The rate constants of RTP emission and quenching, determined based on the experimental data, containing information on the packing density of Pd₁₀ in PS, correlate with the PS structure, which was calculated by quantum chemistry methods. According to the results obtained, the PSs are nanosized three-component complexes Pd₁₀·2BM@2CD, incorporated as microimpurities into the crystal lattice of 2BM@2CD dimers.

An important feature of the supramolecular systems explored is that the excited molecule of Pd₁₀ has two levels of protection from oxygen. It is isolated from the environment, being firmly clamped between two BM molecules in the three-component complex P·2BM@2CD. The latter is additionally stabilized by inclusion in the crystal lattice built from binary complexes 2BM@2CD. Earlier the mechanism of RTP quenching in A·2BM@2CD systems under the action of oxygen was discussed using the example of naphthalene and phenanthrene complexes with CD [19, 20].

The phosphorescence and fluorescence spectra of Pd₁₀–CD–BM at room temperature and 77 K revealed a fine vibronic structure, which belongs to two progressions of transitions to the ground and first overtone vibrational level of the S₀ state. The assignment carried out based on the calculations of the vibrational spectra of Pd₁₀ shows that even symmetry A_g vibrational transitions ν₁₃, ν₁₁, ν₉, ν₆ and ν₂₅, ν₂₃ (B_3g), ν₉, ν₆ (A_g) in the fluorescence and phosphorescence spectra of Pd₁₀, respectively, are active in radiative transitions from the excited levels S₁ and T₁.

Acknowledgements

This work was performed with financial support from the Ministry of Science and Higher Education of the Russian Federation within the framework of the State Assignments of the NRC "Kurchatov Institute" in the part of "Quantum-chemical calculations" and the Federal Research Center for Chemical Physics and Medicinal Chemistry of the Russian Academy of Sciences in the part of "Photonics of molecular and nanoscale systems" (124013000686-3).

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