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Visible-to-ultraviolet (<340 nm) photon upconversion by triplet-triplet annihilation in solvents

In this article, visible-to-ultraviolet photon upconversion (UV-UC) by triplet-triplet annihilation in the emission range shorter than 340 nm, which is previously unexplored, is presented and the relevant physicochemical characteristics are elucidated. Investigations were carried out in several deaerated solvents using acridone and naphthalene derivatives as a sensitizer and emitter, respectively. Both upconversion quantum efficiency and sample photostability under continuous photoirradiation strongly depended on the solvent. The former dependence is governed by the solvent polarity, which affects the triplet energy level matching between the sensitizer and emitter because of the solvatochromism of the sensitizer. To elucidate the latter, first we investigated the photodegradation of samples without the emitter, which revealed that the sensitizer degradation rate is correlated with the difference between the frontier orbital energy levels of the sensitizer and solvent. Inclusion of the emitter effectively suppressed the degradation of the sensitizer, which is ascribed to fast quenching of the triplet sensitizer by the emitter and justifies the use of ketonic sensitizers for UV-UC in solvents. A theoretical model was developed to acquire insight into the observed temporal decays of the upconverted emission intensity under continuous photoirradiation. The theoretical curves generated by this model fitted the experimental decay curves well, which allowed the reaction rate between the emitter and solvent to be obtained. This rate was also correlated with difference between the frontier orbital energy levels of the emitter and solvent. Finally, based on the acquired findings, general design guidelines for developing UV-UC samples were proposed.


Abstract
In this article, visible-to-ultraviolet photon upconversion (UV-UC) by triplet-triplet annihilation in the emission range shorter than 340 nm, which is previously unexplored, is presented and the relevant physicochemical characteristics are elucidated. Investigations were carried out in several deaerated solvents using acridone and naphthalene derivatives as a sensitizer and emitter, respectively. Both upconversion quantum efficiency and sample photostability under continuous photoirradiation strongly depended on the solvent. The former dependence is governed by the solvent polarity, which affects the triplet energy level matching between the sensitizer and emitter because of the solvatochromism of the sensitizer. To elucidate the latter, first we investigated the photodegradation of samples without the emitter, which revealed that the sensitizer degradation rate is correlated with the difference between the frontier orbital energy levels of the sensitizer and solvent. Inclusion of the emitter effectively suppressed the degradation of the sensitizer, which is ascribed to fast quenching of the triplet sensitizer by the emitter and justifies the use of ketonic sensitizers for UV-UC in solvents. A theoretical model was developed to acquire insight into the observed temporal decays of the upconverted emission intensity under continuous photoirradiation.
The theoretical curves generated by this model fitted the experimental decay curves well, which allowed the reaction rate between the emitter and solvent to be obtained. This rate was also correlated with difference between the frontier orbital energy levels of the emitter and solvent.
Finally, based on the acquired findings, general design guidelines for developing UV-UC samples were proposed.

Introduction
Photon upconversion (UC) is a technology to convert presently wasted sub-bandgap photons into those with higher energies (i.e., light of shorter wavelength), which are useful in many fields including photovoltaics and photocatalysis. To date, UC using triplet-triplet annihilation (TTA) between organic molecules has been widely explored because of its applicability to low-intensity and non-coherent light. 15 Most of the previous studies focused on visible-to-visible UC. 140 If TTA-UC technology can be reliably extended to the ultraviolet (UV) region (<400 nm), it will become suitable for a broader range of applications, such as for hydrogen generation by water splitting using anatase titanium dioxide (a-TiO2), which has a band gap of 3.2 eV (gap ~385 nm). 41 Since the pioneering studies by Castellano and co-workers 42,43 and Merkel and Dinnocenzo, 44 there have been multiple reports 4552 exploring UC of visible light to UV light (UV-UC). Here, the principle of TTA-UC is briefly described (Fig. 1a). First, a sensitizer molecule absorbs a lowenergy photon (visible photon in this context) and transforms to the excited singlet (S1) state, which immediately converts to the triplet (T1) state with a certain quantum yield through intersystem crossing. If the energy of the T1 state of the emitter is similar to or lower than that of the sensitizer, the T1 energy of the sensitizer can be transferred to the emitter (triplet energy transfer; TET), creating a T1 emitter (Fig. 1b). When two T1 emitters interact and undergo TTA, an S1 emitter can be generated from which an upconverted photon (UV photon in this context) is emitted as delayed fluorescence.
Most previous UV-UC studies were carried out using pyrene or a derivative, whose UC emission maxima range between ca. 375 and 425 nm, 42,45,50 or 2,5-diphenyloxazole (PPO), whose UC emission maxima range between 350 and 400 nm, 43,44,46,48,49,51 as the emitter. For PPO, 2,3-butanedione (biacetyl) has often been used as the sensitizer. 43,46,49 As far as we surveyed, except for our previous technical documents 53 on which this study is based, the shortest emission peak wavelength reported for UV-UC by TTA is 343344 nm using terphenyl as the emitter. 47,50 Therefore, UV-UC with emission maxima shorter than 340 nm has not been well explored thus far.
Shortening emission wavelengths further is meaningful for the following reasons. First, although gap of a-TiO2 is ca. 385 nm, which was determined by tangentially extrapolating its absorbance or reflectance spectrum to the horizontal axis, 54 a general characteristic of semiconductors is that their absorption coefficient is low near gap. 55 For example, sufficient absorption is attained only below ca. 350 nm in the case of a-TiO2 nanoparticles. 54,56 Second, the quantum efficiency of water-splitting photocatalysts increases with the energy of incident photons. 57 This present article investigates UV-UC with emission maxima shorter than 340 nm and elucidates the relevant physicochemical characteristics.
However, we have noticed that such UV-UC, whether the samples used in this article or other samples such as those made using biacetyl and/or PPO, is accompanied by non-trivial or sometimes remarkable photodegradation, although such characteristics were not explicitly presented and discussed previously. Only recently, Lee et al. 50 showed fast photodegradation caused by continuous photoirradiation at 455 nm in deaerated tetrahydrofuran (THF) when PPO and terphenyl were used as emitters. They showed that, among the emitters tested, only pyrene exhibited satisfactory photostability in deaerated THF. 50 Previously, we reported visible-to-visible UC in systems using an ionic liquid as the solvent. 16,2123,28 These samples, when properly sealed, exhibited excellent photostability and their lifetime exceeded several years (Fig. S1, ESI † ). However, when the same ionic liquid was combined with the sensitizer and emitter used in the present study for UV-UC (Fig. 1c), such photostability was not observed (Fig. S1, ESI † and also below). We also found that the combination of biacetyl and PPO in deaerated dimethylformamide (DMF), which were used previously, 46,49 showed poor stability under continuous photoirradiation (Fig. S2, ESI † ).
Based on these observations, we consider that UV-UC at wavelengths shorter than ca. 370 nm tends to suffer from low photostability, presumably because the use of high-energy triplet states may induce photochemical reactions, such as hydrogen abstraction from the solvent. This is an unaddressed issue that should be investigated before UV-UC technology is used in applications.
Therefore, it is important to obtain understanding of the governing factors and/or mechanism of such photodegradation in UV-UC.
In this study, based on our previous technological findings regarding UV-UC, 53 we develop UV-UC samples that exhibit photoemission peaks in the 320340 nm range. We find that both the UC quantum efficiency (UC) and photostability of these samples depend on the solvent. To understand this phenomenon, we conduct a systematic investigation by performing both experiments and theoretical analysis. The aim of this article is to elucidate the factors governing such solvent dependence and obtain general guidelines for designing UV-UC systems with high UC efficiency and photostability.

Experimental
We used 10-butyl-2-chloro-9(10H)-acridinone (1) and 2,6-di-tert-butylnaphthalene (2) as the sensitizer and emitter, respectively (Fig. 1c). Both 1 and 2 (purity: >98%) were purchased from TCI; 1 was recrystallized before use and 2 was used as received. We chose 1, in which the photoexcitation is the n* transition, because the small overlap between the n and * orbitals around its carbonyl group leads to a small S1T1 energy gap and the n,* state has a high quantum yield of S1-to-T1 intersystem crossing (T,sen), 58 both of which are desirable for sensitizers for TTA-UC. After testing several acridones, we found that 1 was preferable over the other candidates because of its visible absorption in the 400425 nm range (Fig. S3, ESI † ) and ability to undergo TET with naphthalenes. We chose 2 because of its relatively high fluorescence quantum yield and suitable fluorescence spectrum for the purpose of this study.
Samples were prepared using the solvents listed in Table 1. Details of the solvents are given in Table S1 in the ESI † . We included D-limonene because it has been reported to prevent degradation of solutes in visible-to-visible UC by functioning as a strong antioxidant that quickly scavenges residual oxygen. 59 Additionally, in the former half of this study, we included the ionic liquid [C4dmim][NTf2] as a reference solvent because it enables highly stable red-to-blue UC 16  of the capillary was immediately closed with a low-melting-point solder as previously described. 16,2123 The seals were checked by placing the capillary under vacuum for a long period (hours or days); an effective seal was confirmed by the sample volume remaining constant. This sealing method works for at least several years (e.g., the sample in Fig In reference experiments, photodegradation was controllably induced in a sample using a setup where the excitation laser beam was expanded to irradiate almost the entire volume of a sample liquid (ca. 2 mL) in a hermetically sealed glass vial from below (see Fig. S4 in the ESI † for details).
In these experiments, the photoirradiation was continued until each molecule of 1 in the sample turned to the T1 state 85 times on average. The duration of photoirradiation was set by assuming that the initial absorbance of 1 at 405 nm did not change during the course of the irradiation. All photoemission spectra in this report were corrected by the wavelength-dependent sensitivities of the grating in a monochromator and CCD array detector as described in our previous reports. 16,2123 All quantum-chemical simulations were carried out using Gaussian 16 ® at the B3LYP/6-31G++(d,p) level.

Results and discussion
The fluorescence and absorption spectra of sensitizer 1 exhibited large solvatochromic shifts whereas those of emitter 2 did not (see Fig. 2a for the fluorescence spectra and Fig. S3 in the ESI † for the optical absorption spectra). This behavior is ascribed to the large (negligible) permanent dipole moment of 1 (2) (Fig. S5, ESI † ). Figure 2b shows photoemission spectra of samples prepared using hexane, ethyl acetate, and toluene upon excitation at 405 nm. The UC emission spectra were structured with the emission maximum at 322 nm and other peaks in the range of 320340 nm, which are at shorter wavelengths than the spectra of previous UV-UC systems. 4252 The photoemission spectra also contained peaks originating from fluorescence from the S1 state of 1 in the 400500 nm range. The intensity of this fluorescence relative to that of the UC emission varied considerably between samples, which is partially attributed to the difference of F,sen in these solvents (F,sen = 0.006, 0.274, and 0.191 in hexane, ethyl acetate, and toluene, respectively; cf. Table 1).
The dependence of UC of the samples with hexane and ethyl acetate on excitation intensity was determined (Fig. 2c). For UC in this article, we customarily describe efficiency in percent and thus the maximum is 100%, which is twice the maximum UC quantum yield of 0.5. The emission intensity between 310 and 380 nm was used to calculate UC; i.e., the emission between 380 and 405 nm was not used to exclude the tail of the fluorescence and thermally induced UC emission.
The procedure used to determine UC is described in Section 7 of the ESI † . As shown in Fig. 2c, the samples with hexane and ethyl acetate attained high UC of 8.2% and 4.9%, respectively, at an excitation intensity of ca. 1.75 W/cm 2 . The data points in Fig. 2c were acquired while first increasing the excitation intensity and then while decreasing the excitation intensity to confirm the reproducibility of the UC values. Although UC measured while decreasing the excitation intensity were slightly lower than those obtained with increasing excitation intensity for both samples, the differences were smaller than the related error bars and thus UC values were considered reproducible.
We found that UC and photostability strongly depended on the solvent. To systematically compare UC and the rates of photoinduced changes of the samples prepared using different solvents, in the following experiments we set the laser power irradiated onto the sample sealed in a glass capillary (see the Experimental section for details) such that the irradiation generated the UC is correlated with the solvent polarity and decreases as the polarity increases.
As mentioned above, 1 has a large dipole moment (Fig. S5, ESI † ) and thus exhibits a large bathochromic shift as the solvent polarity increases, whereas 2 does not (Fig. 2a). Therefore, as the solvent polarity increases, the T1 level of 1 is considered to be lowered relative to that of 2, making TET thermodynamically unfavorable (i.e., Case B in Fig. 1b). The solvent dependence of UC of our samples is mainly attributed to this mechanism. In addition, the solvent dependences of T,sen and F,emi (Table 1) should also affect UC.
The stability of the samples under continuous photoirradiation strongly depended on the solvent ( Fig. 2e). For example, UC emission in toluene decayed rapidly whereas that in hexane lasted much longer; the reason for this behavior is investigated below. It is noted that no UC emission was observed when D-limonene and methanol were used (Table 1). While the lack of UC emission in methanol can be explained by the above discussion regarding Fig. 2d, the reason for the absence of UC emission in D-limonene is unclear. It may be caused by the high reactivity of D-limonene, which has a reactive unsaturated C=C bond, with high-energy triplet states of 1 and 2.
Here, we note the following three points. First, although the use of solvents with different certified purities resulted in a minor but recognizable effect on the intensity of UC emission, this difference did not alter the qualitative profile of the temporal UC emission intensity change ( Fig.   S6, ESI † ). Second, the temporal decays of the UC emission intensity observed in Fig. 2e were not considered to be governed by residual oxygen in the solvents, which was the case in previous visible-to-visible UC studies. 6266 This is partly because the use of D-limonene, which scavenged residual oxygen efficiently and helped to attain stable visible-to-visible UC, 59 completely suppressed the UC emission in the present study. That the UC emission decays observed in Fig.   2e were not caused by residual oxygen was also supported by the thorough FPT treatment and tightly sealed samples used here. Third, the decay rate of the UC emission in hexane in the present study is much slower than that of a previously reported biacetyl/PPO/DMF system 46,49 when compared using the similar triplet generation rate on 1 (Fig. S2, ESI † ).
In the following investigations, we excluded the sample with methanol because it did not realize UC and the sample with [C4dmim][NT2] because its UC efficiency was low and the photochemical reaction with a molten salt is complex.
To understand the solvent-dependent photostability of our samples, first, we investigated samples containing only 1. When each sample in a glass capillary was excited at a triplet generation rate of 1.9×10 3 M/s, the decay rate of the fluorescence intensity of 1 depended on the type of solvent ( Fig. 3a and Fig. S7 in the ESI † for the fluorescence intensities and spectra, respectively).
We confirmed that the photoirradiation induced a decrease of the absorbance of 1 (Fig. 3b and Fig. Here we use the frontier orbital theory to discuss the observed photoinduced degradation of 1 in the solvents. Generally, excited states of ketones such as the T1 state of 1 have n,* electronic configuration where n and * are singly occupied molecular orbitals (SOMOs) and can serve as electron-accepting and -donating orbitals, respectively. 58 Generally, such SOMOs interact with the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of an adjacent molecule and create new orbitals into which electrons from both molecules are partially or fully transferred; such a charge transfer generally allows energetic stabilization and may lead to formation of an excited-state complex. 58 For the n,* state of ketones, such intermolecular interaction with a ground-state molecule such as a solvent molecule may cause hydrogen abstraction from the latter because of the half-filled orbital on the oxygen atom of the ketone.
Hydrogen abstraction by ketones has been widely studied. 6769 Two factors are known to govern this intermolecular reaction: (i) the energetic proximity of the frontier orbitals of the two interacting molecules and (ii) the constructive spatial overlap of these orbitals. 58 To study factor (i), we calculated the HOMO and LUMO levels of 1, 2, and the solvents, as depicted in Fig. 3c. In this figure, SOMO levels of the T1 states of 1 and 2 are also shown. From the relation between ksen,degr and the energetic separations of the HOMOs and LUMOs between 1 and the solvents (denoted as |HOMO| and |LUMO|, respectively), we found a clear correlation of ksen,degr with |HOMO|, whereas no obvious correlation was found between ksen,degr and |LUMO| (Fig. 3d). The same tendency was also observed when the difference between the ionization energies of 1 and the solvents (which physically corresponds to |HOMO|) and that between their electron affinities (which corresponds to |LUMO|) were plotted (Fig. S9, ESI † ).
These results reveal that the electron transfer from the solvent to 1 is the rate-limiting step of this photodegradation, which can be interpreted as an electron transfer-initiated hydrogen abstraction process. 69,70 We also estimated the quantum efficiency of the degradation of the T1 state of 1 in each solvent (sen,rxn) from the decease of the absorbance of 1 induced by the controlled photoirradiation (cf. Fig. S4, ESI † ). The procedure followed to calculate sen,rxn is described in Section 13 of the ESI † . Although the scatter of the data points is larger than that in the case of ksen,degr, a similar correlation with |HOMO| was also found for sen,rxn (Fig. 3e).
Next, we investigated photoinduced changes of samples containing both 1 and 2. For the sample with hexane, photodegradation of 1 was suppressed by the presence of 2×10 3 M of 2, as recognized from the invariance of the optical absorption spectrum of 1 during photoirradiation ( Fig. 4a). This suppression is ascribed to prompt TET from 1 to 2 in hexane, which drastically shortens the lifetime of the T1 state of 1, meaning that 2 strongly suppresses the probability of 1 reacting with the solvent. A similar tendency was also found for the samples with other solvents ( Fig. S8 and S10 in the ESI † ). However, for the sample with DMF, the decrease in the absorbance of 1 was not well suppressed (Fig. S10, ESI † ); this could be because of inefficient TET from 1 to 2 caused by the relatively high polarity of DMF (cf. Fig. 2d and 1b). The suppressed photodegradation of 1 in hexane induced by addition of 2 was also evidenced by the invariance of the fluorescence emission intensity of 1 even after 80 min of photoirradiation (Fig. 4b); the similar tendency was also seen for the samples with other solvents (see Fig. S7 and S11 in the ESI † ).
Our results reveal that by adding an energy-accepting emitter at sufficient concentration (of the order of 10 3 M), preferable aspects of ketones as the sensitizer (cf. first paragraph of the Experimental section) can be harnessed for UV-UC while effectively suppressing the drawback of using triplet ketones; i.e., the relatively high reactivity of their T1 state. Considering the viscosities of the solvents employed in this study (ca. 0.30.6 mPas at room temperature), the diffusioncontrolled rate constant kdiff was estimated to be 12×10 10 M 1 s 1 using the following equation 16,58 (1) where R, T, and  are the gas constant, temperature, and solvent viscosity, respectively. From the concentration of the energy acceptor 2 (2×10 3 M) and assuming Case A in Fig. 1b, the lifetime of the T1 state of 1 was estimated to be only 2550 ns, which supports the results in Fig. 4a and 4b.
The rate of the reaction between the T1 state of 1 and ground state of 2 was considered to be negligible, even though their ground-state HOMO levels are close (Fig. 3c), for the following reasons. First, a bimolecular reaction rate is proportional to the product of the concentrations of the two species involved. In our samples, the concentration of 2 (2×10 3 M) was much lower than that of the solvents (720 M). Second, the interaction time between the T1 state of 1 and ground state of 2 should be very short because such an encounter immediately causes an exothermic TET, 11 unlike the interaction between the T1 state of 1 and the solvent, which can last much longer.
We have reached the point to discuss the temporal decay curves of the UC emission intensity under continuous photoirradiation in Fig. 2e. To analyze these decay curves, we developed the theoretical model described below. First, we postulate that the triplet emitter (E*) becomes a new species () by reacting with a surrounding solvent molecule (sol) at a rate of kemi,rxn [s 1 ]. This  is assumed to quench both E* and the triplet sensitizer (S*) at the kdiff given by eqn (1). Therefore, Here, E and S are the ground states of the emitter and sensitizer, respectively, and * is the excited state of . In this model, E >> E* and S >> S* are assumed and the reaction between S* and solvent is neglected based on the considerations mentioned above. Photoirradiation of the sample was confirmed to shorten the triplet lifetime of 2 (T) (Section 16 of the ESI † ). Furthermore, it is assumed that * converts into an inactive species (inactive) at a quantum yield of ,rxn, presumably by reacting with the solvent as follows.
In addition, we consider initial impurity species in the solvent, Q, which quenches both E* and S*.
Similar to the case of , we introduce the kinetic relations of We further assume that the second-order rate constant between E* molecules for the TTA process (k2) is close to kdiff (i.e., k2  kdiff), which was found to be a quantitatively good approximation. 36 Although the degradation phenomenon considered here is transient, the timescales of the abovedescribed kinetics are much shorter than those of the change of the UC emission intensity.
Therefore, at each instantaneous moment during continuous photoirradiation, the quasi-steadystate approximation is considered to hold well for E*, * ≅ 0.
Combining all these relations, the proposed model describing the temporal change of UC emission intensity under continuous photoirradiation is obtained as Here, kT is the first-order decay rate of E* (= T 1 ), which was determined by time-resolved photoemission measurements using light pulses (cf. Experimental section).  is the generation rate of the T1 state of the sensitizer, which was 1.9×10 3 M/s. Eqn (10)   In Fig. 4d, the values of kemi,rxn obtained from the fitting are plotted against |HOMO| and |LUMO|; a correlation was found only for |LUMO| and kemi,rxn. The same tendency was also observed when the difference between the ionization energies of 2 and the solvents and that between the electron affinities of 2 and the solvents were plotted (Fig. S13, ESI  † ). These results suggest that the process described by eqn (2) is limited by electron transfer from 2 to the solvent; i.e., electron transfer in the opposite direction to that in the reaction between 1 and the solvent discussed above. We did not carry out further detailed investigation of the reaction mechanism because it is beyond the scope of the present study. Nevertheless, the findings acquired from our experimental and theoretical investigations revealed that the photostability of this UV-UC system is controlled by the energetic difference between the relevant frontier orbital levels of the solute (1 or 2) and solvent, and that these photodegradation reactions are rate-limited by the electron transfer between molecules.

Conclusions
Using sensitizer 1 and emitter 2, UV-UC to a shorter wavelength than 340 nm (maximum intensity at 322 nm) was achieved in various solvents. Both UC and the photostability of 1 under continuous photoirradiation depended on the solvent. The use of hexane yielded the highest UC of 8.2%, which is close to that of 10.2% reported for UV-UC in the 350400 nm range achieved using a nanocrystal sensitizer and PPO, 51 and also the highest photostability among the tested solvents.
We found that UC was mainly governed by solvent polarity, which varied the relative T1 energylevel matching between 1 and 2 because of the solvatochromic shift imposed on 1. The solvent dependence of T,sen and F,emi should also affect UC.
When the samples were prepared without 2, ksen,degr was large in most of the tested solvents and found to be correlated with |HOMO| between 1 and the solvent. This correlation indicated that the photodegradation of 1 was rate-limited by electron transfer from the solvent to 1 and likely to be an electron transfer-initiated hydrogen abstraction process. However, when the energy acceptor 2, which quenches the T1 state of 1, was added to the samples, the degradation of 1 was effectively suppressed. This finding justifies the use of a ketonic sensitizer for UV-UC as long as the emitter concentration is higher than the order of 10 3 M in non-viscous solvents.
We developed a theoretical model and the curves generated by this model fitted the experimentally acquired temporal decay curves of the UC emission intensity well. This fitting provided several insights into the characteristics of the present UV-UC system. For example, the initial rapid rise of the UC emission intensity for the sample with hexane (cf. Fig. 4c) was ascribed to the presence of a trace amount of impurities (Q ~1.9×10 7 M). Furthermore, kemi,rxn obtained from the fitting was correlated with |LUMO|, which revealed that the photodegradation of 2 was rate-limited by electron transfer to the solvent. These findings indicate that the energetic difference between the frontier orbitals of the solute and solvent is the primary factor determining the photostability. Besides this viewpoint, the frontier orbital theory also addresses the importance of spatial overlap between two frontier orbitals involved in a reaction. Decreasing such overlap by addition of bulky groups to solutes may enhance their photostability.
Overall, this experimental and theoretical study has provided several fundamental insights regarding UV-UC in solvents. As general design guidelines for sample development, one should optimize solvent polarity to maximize UC and use a combination of solvent and solute whose frontier energy levels are as far apart as possible to enhance solute photostability. These guidelines have not previously been explicitly proposed for UV-UC or visible-to-visible UC. The physicochemical insights obtained from this study will help to establish stable and efficient UV-UC systems in the future.

Conflicts of interest
There are no conflicts to declare.

Photostability of visible-to-visible UC in an ionic liquid
We have reported several examples of visible-to-visible photon upconversion (UC) by triplettriplet annihilation (TTA) using ionic liquids as the solvent. S1S4 To underpin the motivation of the present study, this supplementary section considers the photostability of such visible-to-visible UC and then the contrasting low photostability of visible-to-ultraviolet UC (UV-UC).
The inset of Fig. S1b shows a photograph of the sample used here, which was prepared and sealed in a quartz tube with a 2×2 mm square cross section on October 30, 2012, according to the procedure described prevously. S1S4 This sample was prepared using meso-

Photostability of UV-UC using biacetyl and PPO in DMF
To date, several examples of UV-UC using 2,5-diphenyloxazole (PPO), which generates UV emission around 350400 nm, as the emitter have been reported. S5S10 The most representative sensitizer combined with PPO is 2,3-butanedione (biacetyl), as used in the pioneering work by Singh-Rachford and Castellano. S5  were the same as those used in Fig. 3b and 4a of the main text. After this photoirradiation, the absorbance of biacetyl had disappeared (Fig. S2a). We also measured the temporal changes of the fluorescence spectrum and intensity ( Fig. S2b and S2c, respectively) for this sample sealed in a 1×1-mm glass capillary exposed to an excitation power at 405 nm that induced a triplet generation rate of biacetyl of ca. 1.65×10 3 M/s (i.e., slightly weaker excitation conditions than those used for

Information about the solvents used in this study
Information about the solvents used in this report is summarized in Table S1. The refractive index values were used to calculate UC in Section 7 of this Supplementary Information.

Calculated dipole moments of the sensitizer and emitter
Dipole moments of the sensitizer 1 and emitter 2 were calculated using Gaussian 16  at the B3LYP/6-31G++(d,p) level, as summarized in Table S2. The corresponding graphics are shown in Fig. S5, where the blue arrows represent dipole moment vectors.

Determination of UC
The upconversion quantum efficiency UC (with a defined maximum of 100%) in this article was determined using the following standard relationship. S12 Φ 2Φ (S1) Here, R, A, I Em , I Ex , h, and n represent the fluorescence quantum yield of a reference sample, absorbance, photoemission intensity, excitation light intensity, photon energy at the excitation wavelength, and the refractive index of the solvent, respectively. The subscripts "UC" and "R" represent an UC sample and reference, respectively. For the second term on the right-hand side, we used 110 A , which is absorptance, instead of its mathematically approximated form of A (see ref. S12 for further details).
We used a toluene solution of 9,10-diphenylanthracene (concentration: 4×10 4 M) deaerated by FPT cycles as the reference sample, which was determined to have R of 0.940 at the excitation wavelength of 405 nm using our absolute quantum yield spectrometer (Quantaurus-QY, Hamamatsu). The values of n were taken from Table S1. The emission intensity between 310 and 380 nm was used to calculate UC; i.e., the emission between 380 and 405 nm was not used to exclude the tail of the fluorescence and thermally induced UC emission. All photoemission spectra in this report, including those used to determine UC, were corrected by the wavelength-dependent sensitivities of the grating in our monochromator and CCD array detector as reported previously. S1S4 Figure S6 compares temporal decay profiles of UC acquired from three samples prepared under the same conditions using hexane of different purity grades (cf. Table S1). The black curve is the same as that shown in Fig. 2e of the main text. The results reveal that the solvent purity affected the magnitude of UC, especially when low-purity hexane ( 95%, in green) was used, but it did not change the qualitative character of the temporal decay profile. Error bars: 10 % of ver cal axis values Figure S6. Effect of solvent purity on the decay profiles of  UC measured for three samples prepared using hexane with different purity grades (cf. Table S1). The black curve is the data presented in Fig

Procedure to calculate k sen,degr
Here we describe the procedure used to calculate the photodegradation rate of sensitizer 1 during irradiation with 405-nm laser light from the fluorescence intensity decay curves shown in Fig. 3a of the main text. As mentioned in the main text, these curves were acquired under the same excitation condition; that is, the triplet state of 1 was generated at a rate of ca. 1.9×10 3 M/s. Our aim here is to estimate the consumption rate of the sensitizer molecules under this excitation To estimate ksen,degr, we fitted the normalized experimental fluorescence intensity decay curves shown in Fig. 3a of the main text with the following double-exponential function Although the real photophysics should be described by more complex kinetic equations, as discussed in the main text, the present procedure is sufficient to obtain values of ksen,deg. As illustrated by the fitting curves in Fig. 3a of the main text, eqn (S1) fitted the experimental fluorescence decay curves well in all cases. In eqn (S1), the relation y0 + A1 + A2 = 1 holds by definition and the initial condition I(0) = 1 corresponds to the initial sensitizer concentration of Then, we employed two reasonable assumptions that (i) the intensity of the fluorescence, which arose from the S1 state, was proportional to the concentration of intact 1 in the solution, and thus that (ii) both constants k1 and k2, although phenomenological, provide quantitative information about the consumption rate of intact 1. Based on these assumptions, the degradation rate of 1 at t = 0 (i.e., when the sensitizer concentration was 2×10 4 M), ksen,degr, was calculated from the relation Here, C0 is the initial sensitizer concentration of 2×10 4 M. Table S3 summarizes the fitting results and calculated values of ksen,degr for 1 in different solvents.

Plots of k sen,degr against ionization energy and electron affinity
The results in Fig. 3d of the main text were presented based on HOMO and LUMO levels.
Although the representation using HOMOs and LUMOs is easy to understand intuitively, in general, the quantitative reliability of orbital energy levels is affected by the choice of the basis set and level of theory used in the calculation. (In this report, all quantum-chemical calculations were performed using Gaussian 16  at the B3LYP/6-31G++(d,p) level.) To alleviate this concern, use of the ionization energy (IE) and electron affinity (EA), which physically correspond to HOMO and LUMO energies, respectively, can enhance the quantitative reliability of analysis. This is because both IE and EA are calculated based on the total energy of the molecule considered, which means they are less affected by the choice of the basis set and calculation level than calculated HOMO and LUMO energies. Specifically, IE can be calculated by subtracting the energy of the neutral ground-state species from that of the radical cation species, and EA can be calculated by subtracting the energy of the radial anion species from that of the neutral ground-state species. Here, energies of the radial cation and radical anion were calculated using the molecular structure of the neutral ground-state species (i.e., vertical assumption). Figure S9 shows plots of ksen,degr against the difference between the IEs (left, corresponding to |HOMO|) of 1 and the solvents and that between the EAs (right, corresponding to |LUMO|) of 1 and the solvents. We observed that ksen,degr was correlated with the difference of IEs, whereas no correlation of ksen,degr with the difference of EAs was found, supporting the results in Fig. 3d of the main text.

Procedure to calculate  sen,rxn
The experiments in Fig. S8 above were carried out by the method described in Section 5 of this Supplementary Information. As written therein, the photoirradiation time for each experiment was chosen assuming that the absorbance of 1 at 405 nm did not change during photoirradiation. To First, we introduce the molar quantity of the intact sensitizer in the test vial of Fig. S4, denoted as z, which is a function of time t and thus z(t). The initial value z(0) is (2×10 4 mol/L)×(2×10 3 L) = 4×10 7 mol. We also introduce the absorbance of the sample liquid with an optical path length of 10 mm (cf. Fig. S4) at a wavelength of 405 nm, denoted as A, which is also a function of time and thus A(t). The initial value A(0) was calculated from A405nm in Table 1 of the main text. Using these parameters, z(t) and sen,rxn were related with each other by Here, NA is the Avogadro constant, Gph is the number of photons at 405 nm incident to the sample per unit time, and T,sen is the triplet quantum yield of 1 listed in Table 1 of the main text.
Furthermore, there is a relationship of where  is a proportionality constant with a unit of mol 1 .  depends on the solvent and was in the range of ca. 1.66×10 6 mol 1 in the present study. By substituting eqn (S4) into eqn (S3), we obtain On the right-hand side of eqn (S6), all parameters except sen,rxn are known. Thus, the parameter  in eqn (S5) is an undetermined constant that is the function of only sen,rxn.
From the experimental results in Fig. S8

Effect of photoirradiation on the triplet lifetime of the emitter
Here, to confirm the postulation of our theoretical model described in the main text, the photoirradiation-induced generation of quenching species is investigated. To do this, we used the experimental setup and photoirradiation conditions described in Section 5 of this Supplementary Information to controllably induce photodegradation of samples before measuring triplet lifetimes.
We measured and compared the triplet lifetimes (T) of the emitter 2 in three samples prepared by different methods described below. All these samples used hexane, which is the representative solvent in this report. T was obtained by doubling the single-exponential decay time constant of the UC emission (UC) acquired with a weak pulsed excitation where TTA is not a dominant process of triplet depopulation; i.e., T  2UC. S2 The measurements were carried out using nanosecond light pulses as described in the Experimental section of the main text.
The first sample was a normal (fresh) sample without prior photoirradiation, deaerated by FPT cycles and sealed in a glass capillary. The UC emission decay curve of this samples is indicated by black dots in Fig. S12 and its T was found to be 114 s. The second sample (control sample #1) was prepared by the following procedure. A solution containing only the sensitizer was deaerated by FPT cycles and then photoirradiated using the setup in Fig. S4. The fresh emitter was dissolved in the solution and then it was deaerated again by FPT cycles before being sealed in a glass capillary. The decay curve for control sample #1 is shown by blue dots in Fig. S12, exhibiting T of 12.5 s. The third sample (control sample #2) was prepared by photoirradiation of the normal deaerated sample containing both the sensitizer and emitter first, and then deaerated again by FPT cycles before being sealed into a glass capillary. The emission decay curve for control sample #2 is indicated by green dots in Fig. S12, showing T of 63.8 s. These results reveal that photoirradiation shortened T of the emitter, which supports our postulation in the proposed model that photoirradiation generates species that quench the triplet species in the sample.

Calculation details of our theoretical model
Here we describe in detail the method used to calculate the temporal UC emission curves, examples of which are shown in Fig. 4c of the main text, from the results of our kinetic model Figure S12. UC emission decay curves acquired for three samples prepared by different methods, which are the normal deaerated sample with fresh sensitizer and emitter (black dots), the sample prepared using the photoirradiated sensitizer solution to which fresh emitter was added and deaerated again (blue dots), and the sample first photoirradiated in the presence of both sensitizer and emitter and then deaerated again (green dots). These intensity decay curves were acquired using weak pulsed excitation at 410 nm and monitored at 335 nm. All these curves were fitted well by single-exponential decay functions, as shown by the orange lines. Determined values of  UC and  T are shown near each curve.

UC Emission Intensity (Normalized)
These integral equations can readily be computed by iterating numerical loops in which an infinitesimal time step t is taken in each loop to calculate the temporal evolution for t  t + t.
In the actual computation, we introduced an additional variable [disappear], which is the cumulative amount of species  deactivated by the process described by eqn (4) in the main text. Overall, the set of numerical relations used for the computation is: the main text were obtained from this fitting procedure. As mentioned in the main text, the fittings yielded Q0 of 5×10 4 M or lower in this study, which is equivalent to a molar fraction of 0.005% or lower. This is a trace amount and thus does not contradict the certified purities of the solvents (cf. Table S1).

Plots of k emi,rxn against ionization energy and electron affinity
Similar to Section 12 of this Supplementary Information, in Fig. S13 below, we plotted kemi,rxn against the difference between the IEs of 2 and the solvents (left) and that between the EAs of 2 and the solvents (right). As seen, kemi,rxn is correlated with the difference of EAs, whereas no correlation of kemi,rxn with the difference of IEs is found, supporting the results in Fig. 4d of the main text.