Intrinsic Analysis of Radiative and Room-Temperature Nonradiative

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Spectroscopy and Photochemistry; General Theory

Intrinsic Analysis of Radiative and Room-Temperature Nonradiative Processes Based on Triplet State Intramolecular Vibrations of Heavy Atom-Free Conjugated Molecules Toward Efficient Persistent Room-Temperature Phosphorescence Shuzo Hirata J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01711 • Publication Date (Web): 06 Jul 2018 Downloaded from http://pubs.acs.org on July 6, 2018

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The Journal of Physical Chemistry Letters

Intrinsic Analysis of Radiative and RoomTemperature Nonradiative Processes Based on Triplet State Intramolecular Vibrations of Heavy Atom-Free Efficient

Conjugated Persistent

Molecules

Toward

Room-Temperature

Phosphorescence Shuzo Hirata*

Department of Engineering Science and Engineering, The University of ElectroCommunications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan

Corresponding Author * Correspondence and requests for material should be addressed to S. H. (email: [email protected])

TOC GRAPHIC

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The radiative rate (kp) of the lowest triplet excited state (T1) and the nonradiative rate based on intramolecular vibrations at room temperature [knr(RT)] from T1 for heavy atom-free conjugated structures are determined by considering the triplet yield and quenching rate from T1. Donor substitution did not strongly influence knr(RT) but greatly enhanced kp. The knr(RT) values were comparable between donor-substituted molecules and non-substituted molecules, which we explain by similar vibrational spin-orbit coupling (SOC) related to the transition from T1 to the ground state (S0). We attribute the enhancement of kp induced by donor substitution to the appearance of a large SOC between high-order singlet excited states (Sm) and T1 together with the large transition dipole moments of the Sm-S0 transitions. Knowledge of this mechanism is important for developing future efficient persistent room-temperature phosphorescence from doped aromatic materials and aromatic crystals.


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Radiative and nonradiative transitions from the lowest triplet excited state (T1) are an important factor that intrinsically controls a variety of processes via T 1, such as room-temperature phosphorescence (RTP),1 photon upconversion,2 and thermally activated delayed fluorescence.3 In the 1960s, fundamental studies on the efficiency of triplet state formation gave insight into heavy atom effects and provided the El-Sayed rule.4 In 1998, RTP was achieved from the T1 state after its generation with an efficiency of 100%, in heavy metal complexes.5 Highly efficient RTP has contributed to the commercialization of flat panel displays and lighting applications based on organic light emitting diodes. Unlike highly efficient RTP from heavy metal complexes, the T1 states of heavy atom-free conjugated molecules are often deactivated before generation of RTP because the radiative rate from T1 (kp) for heavy atom-free conjugated molecules is very slow and other nonradiative deactivation processes from T1 are much faster than kp.6 However, by suppressing nonradiative processes from T1 states, RTP with lifetimes longer than 1 s, i.e., persistent RTP, have been observed in air from a variety of heavy atom-free conjugated molecules, as reported within the last 5 years.716

Strong and persistent RTP, detected directly after excitation of a material, can be detected

with cost-effective photo detectors.17 There is a broad range of potential applications for these properties in anticounterfeiting,8,10,15 sensors,17,18 and bioimaging applications.19-21 Persistence of RTP has been demonstrated for a variety of heavy atom-free conjugated molecular materials; however, several aspects of nonradiative deactivation processes from the T1 state of heavy atom-free conjugated molecules remain unclear. In the 1980s, the T1 decay rate of benzophenone dopants was increased by increasing local motion in polymeric host matrices.22-24 This result suggested that the motion of the molecular host might induce intramolecular vibrations in the guest, which promoted nonradiative processes. However, recent investigations on highly rigid short conjugated molecular hosts doped with heavy atom-



free conjugated molecular guests have indicated that triplet quenching is caused by endothermic energy transfer from a guest to the host. Because this effect increases the rate of nonradiative deactivation from T1 even when the host has a large T1 energy gap,6,7,25 the increase of nonradiative deactivation with temperature is also likely caused by intermolecular energy transfer. These previous results raise questions about whether intramolecular vibrationbased nonradiative deactivation at RT from T1 [knr(RT)] is intrinsically much faster than kp for heavy atom-free conjugated molecules. However, there remains no concrete explanation for the effects of molecular vibrations on heavy atom-free chromophores on knr(RT).26 Thus, there are no intrinsic explanations for the relationship between kp and knr(RT), which has limited research into new molecular persistent luminescent materials. Here, we explain the relationship between kp and knr(RT) for heavy atom-free conjugated molecules, which show efficient persistent RTP. The triplet yield and the quenching rate from T1 to the ground state (S0) of a donor-substituted heavy atom-free aromatic molecule and unsubstituted heavy atom-free aromatic molecules were measured at RT. We used the triplet yield and the quenching rate, to experimentally determine kp and knr(RT) for the molecules. The kp value of the donor-substituted molecule was much greater than that of the unsubstituted molecules; however, their knr(RT) values were comparable. The large kp contributed to the greater RTP yield of the donor-substituted molecules compared with the yields of the unsubstituted molecules. We explained the comparable knr(RT) values of the molecules by their similar vibrational spin orbit coupling (VSOC) in terms of first-order Herzberg–Teller spinorbit coupling (SOC) related to the T1–S0 transition. We attribute the larger kp value of the donor-substituted molecule to a mechanism involving moderate charge transfer (CT) characteristics in high-order singlet excited states (Sm) enabling a large SOC and large transition dipole moment from Sm to S0. Thus, donor substitution of a heavy atom-free


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conjugated structure enhances kp without increasing knr(RT). These findings are useful for rationally designing emitting molecules to obtain higher yields of persistent RTP. Figure 1a shows the chemical structures of dyes 1–3, which we used as heavy atom-free conjugated guests and β-estradiol as a host. Dyes 1 and 2 are representative of non-substituted heavy-atom free conjugated molecules. Dye 3 is a representative heavy-atom free conjugated molecule substituted by secondary amine donors. β-Estradiol is a highly rigid amorphous host that minimizes nonradiative processes from T1, which we used to investigate the kp and knr(RT) behaviors of dyes 1–3.7

Figure 1 Materials and photophysical characteristics. (a) Molecular structures of heavy atomfree conjugated guests (dyes 1–3) and host. (b) RTP spectra of 0.3-wt% guest doped in βestradiol in air. (c) Decay characteristics of persistent RTP of 0.3-wt% guest doped in βestradiol in air (i) and under vacuum (ii). (d) Temperature dependence of the sum of the rate constant of intramolecular vibration based nonradiative deactivation [knr(T)] and quenching rate caused by interactions between the guest and host [kq(T)] under vacuum. Dashed and dashed lines represents fitting curves of knr(T) and kq(T) based on Arrhenius model, respectively. In (b)-(d), lights at 340, 340, and 365 nm were used as excitation for dyes 1, 2, and 3, respectively.



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Figure 1b shows the RTP spectra of dyes 1–3 in β-estradiol soon after stopping the excitation. The dyes 1–3 had comparable T1–S0 energies (E30) and a RTP lifetime [τp(RT)] greater than 1 s under ambient conditions (Fig. 1c, (i)). The τp(RT) values slightly increased after degassing the materials under vacuum (Fig. 1c, (ii)) because the small amount of oxygen contained in βestradiol was removed. We measured the absolute photoluminescence quantum yield using an integrating sphere under excitation light at a power density of 0.3 mWcm −2. The phosphorescence quantum yield at RT [Φp(RT)] of dyes 1, 2, and 3 in β-estradiol were 0.14, 0.61, and 8.6% under ambient conditions, respectively [Supplementary Information (SI), Fig. S1]. Φp(RT) of dyes 1, 2, and 3 in β-estradiol under vacuum were 0.39%, 0.91%, and 10.5%, respectively. The relationships among Φp(RT), τp(RT), kp, and knr(RT) are expressed as:

τp(RT)=1/[kp+knr(RT)+kq(RT)],

(1)

Φp(RT)=Φisc(RT)kp/[kp+knr(RT)+kq(RT)],

(2)

where kq(RT) is the quenching rate from T1 at RT for the conjugated guest, caused by the interactions between the guest and host molecule around the guest, and Φisc(RT) is the quantum yield of intersystem crossing from the lowest singlet excited state (S1) to T1. It has been reported that Φisc(RT) of the target conjugated molecules can be measured by triplet sensitization from a triplet sensitizer to the target heavy atom-free molecule.27-30 Analysis by this method indicated that the Φisc(RT) values of dyes 2 and 3 were 0.84 and 0.61, respectively (SI, Figs. S2-S5, Table S1). For Φisc(RT) of dye 1, a reported value of 0.75 was used.31 By substituting the values of Φisc(RT), τp(RT), and Φp(RT) in vacuum condition for dyes 1–3 into equations 1 and 2, the kp values of dyes 1, 2, and 3 were determined to be 3.7×10−3, 8.0×10−3, and 1.2×10−1 s−1, respectively.


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Next, we measured the temperature dependence of τp(T) to determine individual knr(RT) and kq(RT) values. Arrhenius plots of knr(T)+kq(T) were constructed, as shown in Fig. 1d by substituting the data of kp into τp(T) based on equation 1. The value of knr(RT)+kq(RT) increased with temperature owing to the increase of kq(T), which depends on an endothermic energy transfer from the conjugated guest to the host.7,25 We attribute the linear relationship in the low temperature region of the Arrhenius plot to knr(RT). Therefore, we approximated the knr(RT) and kq(RT) values separately by fitting two straight lines to the different regions of the plot. From the fitting data, we estimated the values of knr(RT) for dyes 1, 2, and 3 in β-estradiol to be 4.3×10−1, 5.7×10−1, and 5.5×10−1 s−1, respectively. Thus, dyes 1–3 had comparable knr(RT) values; however, the kp value of dye 3 was much larger than that of dyes 1 and 2. The experimentally determined values of kp and knr(RT) are summarized in Table 1. In a previous report, we determined Φisc(RT) values by assuming that knr(RT)+kq(RT) becomes zero at 10 K and attributed a large increase of Φp(RT) before and after the donor substitution to the difference of Φisc(RT).7 However, the results of Φisc(RT) in this paper confirmed that this assumption was incorrect. The difference of Φp(RT) was caused by the enhancement of kp but there was no notable increase of knr(RT) after donor substitution.

Table 1. Photophysical parameters of dyes 1–3 doped into β-estradiol. Experimental a

Quantum calculatione 𝑃(𝑅𝑇) ∂ 𝛹

( )

𝐻

𝛹

( )

/𝜕𝑄

Φisc(RT)

Φp(RT)

kp

knr(RT)

τp(RT)

E30b

(%)

(%)

(s-1)

(s-1)

(s)

(nm)

(cm-2)

(a.u.) f

(s-1)

Dye 1

75

0.39 c

3.7×10-3

4.3×10-1

1.4 c

464 c

5.0×10-4

1.4×102

6.9×10-4

Dye 2

84

0.91 c

8.0×10-3

5.7×10-1

1.4 c

510 c

5.7×10-1

1.0×102

3.5×10-3

61

10.5d

1.2×10-1

5.5×10-1

1.5 d

514 d

1.0×102

1.8×10-1

Guest

Dye 3 a

b

𝛹

( )

𝐻

𝛹

( )

1.6×100 c

d

kp

e

Data in vacuum condition. 0-0 transition peak wavelength of RTP spectra. Excitation at 340 nm. Excitation at 365 nm. Conformations of the T1,

including vibrational modes were optimized by density functional theory [Gaussian09/B3LYP/6-31G(d)]. Data of the SOC are treated as a perturbation based on scalar relativistic orbitals. Hybrid-PBE0 and TRZ were used as exchange-correlation functionals and Slater-type all-electron basis, respectively. fArbitary units.



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The comparable knr(RT) values among dyes 1–3 were not be explained by SOC but rather by VSOC. The intramolecular vibration based on nonradiative deactivation at 77 K, i.e., knr(77K), have been discussed based on first order Herzberg–Teller SOC in 1970s. 32,33 In first order perturbation theory, knr(77K) is approximated as,

𝑘 (77𝐾 )~

where 𝛹

( )

𝛹

ℏ

( )

𝐻

𝛹

( )

𝐹𝐶 + 𝑒𝜋 ∑

𝛹

( )

𝐻

𝛹

( )

+ ・・,

𝐹𝐶

is the electronic wavefunction of the v = 0 vibrational level of S0, 𝛹

( )

(3)

is the

is the spin-orbit

electronic wavefunction of the v = 0 vibrational level of T1, 𝐻

Hamiltonian, 𝑄 is the mass weighted normal coordinates, FC is the Franck–Condon factor, and

is the slope of FC. In equation 3, it has been reported that the total of the first and

second terms is much greater than the contributions from other terms for simple aromatic hydrocarbons at 77 K.32 Hence, here we considered only the first and second terms. Equation 3 indicates that knr(77K) is approximated by the SOC term ( 𝛹 term (∂ 𝛹

( )

𝐻

𝛹

( )

( )

𝐻

𝛹

( )

) and VSOC

/𝜕𝑄 ). For simple planer aromatic polycyclic carbons, it has been

concluded that the VSOC term becomes much larger than the SOC term and that the VSOC terms mainly determines the magnitude of knr(77K).32,33 However, no relationships have been reported between experimentally observed knr(RT) and theoretical knr(RT) values because the large kq(RT) often precludes accurate experimentally observation of knr(RT).26 Discussions relating to knr(77K) in the 1970s did not consider an increase of vibration with temperature; however, high-energy vibrations might be activated at RT and these activated vibrations are potentially related to knr(RT). The temperature dependence of intramolecular vibrations is


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typically considered as a vibrational factor in the theoretical analysis of internal conversion process using the following equation,34,35:

(

(

. )

𝑃 (𝑇) = ∑ (𝑣 + 0.5)𝑒

. )

) ,

(∑ 𝑒

(4)

where ωp is the wavenumber of the pth vibrational mode, v denotes the vibrational state, k is the Boltzman constant, and T is the temperature. Therefore, knr(T) could be approximately considered to be:

𝑘 (𝑇)~

𝛹

ℏ

( )

𝐻

𝛹

( )

𝐹𝐶 + 𝑒𝜋 ∑ 𝑃 (𝑇) ∂ 𝛹

( )

𝐻

𝛹

( )

/𝜕𝑄

𝐹𝐶

. (5)

The first term of equation 5 is independent of temperature. We consider that FC does not so change among dyes 1–3 in equation 5 because the T1-S0 transition has locally excited (LE) transition characteristics, as shown by the molecular orbital overlap of T1 and S0, described later in this paper. Furthermore, we consider that

relating to the low energy gap in

equation 5 also does not change among dyes 1–3 because E30 is comparable for the dyes (Fig. 1b and Table 1). Therefore, knr(RT) among dyes 1–3 can be discussed in terms of the magnitude of

𝛹

( )

𝐻

The parameter

𝛹

( )

𝛹

( )

and ∑ 𝑃(𝑇) ∂ 𝛹 𝐻

𝛹

( )

( )

𝐻

𝛹

( )

/𝜕𝑄

according to equation 5.

of dyes 1–3 was treated as a perturbation based on the

scalar relativistic (SR) orbitals after the conformation was optimized at T1 by density functional theory (DFT) using Gaussian09 program with B3LYP functional and 6-31G(d) basis sets. Hybrid-PBE0 and TRZ were used as exchange-correlation functionals with a Slater-type allelectron basis to calculate the perturbative SOC, respectively. As shown in Table 1,



𝛹

( )

𝐻

𝛹

( )

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of dye 1 (5.0×10−4 cm−2) was much smaller than those of dye 2 and 3

(~100 cm−2). This result largely differs from our expectations based on the similar knr(RT) values of dyes 1–3. We attribute this difference to

𝛹

( )

𝐻

( )

𝛹

typically being

calculated from the conformation at T ≈ 0 K; however, real molecules feature conformational changes, which depend on their vibrations. Therefore, the first term in equation 5 is not suitable for comparison with the experimentally observed knr(RT). However, the SOC depends on the molecular vibrations and is considered as VSOC in the second term of equation 5. To determine the second term, we calculated the relationship between 𝛹

( )

( )

𝛹

𝐻

and Qp for dyes

1–3. Figure 2a shows the vibration with ωp = 103.42 cm−1 of dye 1. When a magnitude of Qp changes from −1.0 [arbitrary unit (a.u.)] to +1.0 (a.u.) where the conformation with Qp = 0 (a.u.) is ascribed to the conformation of triplet state at T ≈ 0 K, 𝛹

( )

𝛹

𝐻

( )

changed from ( )

2.3×10−2 cm−1 to 1.1×100 cm−1. Figure 2b shows the relationship between 𝛹 and Qp for representative vibration modes of dye 1. Because ∂ 𝛹 corresponds to the slope of each symbols Fig. 2b and proportional to Qp, ∂ 𝛹 difference between 𝛹

( )

( )

𝐻

𝛹

𝐻

𝛹

( )

( )

( )

𝐻

𝐻

𝛹

𝛹

( )

𝛹 ( )

( )

/𝜕𝑄

is almost

/𝜕𝑄 of each vibration mode was approximated as the at Qp = +1.0 (a.u.) and 𝛹

(a.u.). Figure 2c is the relationship between 𝑃 (𝑅𝑇) ∂ 𝛹 From Fig. 2c, the values of

𝛹

( )

𝐻

∑ 𝑃 (𝑇) ∂ 𝛹

( )

𝐻

𝛹

( )

( )

/𝜕𝑄

𝐻

( )

𝐻

𝛹

( )

𝛹

( )

/𝜕𝑄

at Qp = 0 and ωp.

of dyes 1, 2, and 3 were

1.4×102 (a.u.), 1.0×102 (a.u.), and 1.0×102 (a.u.), respectively. The comparable values of ∑ 𝑃 (𝑇) ∂ 𝛹

( )

𝐻

𝛹

( )

/𝜕𝑄

reflect the comparable knr(RT) for dyes 1–3. In addition,


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∑ 𝑃 (𝑇) ∂ 𝛹

( )

𝛹

𝐻

( )

of benzophenone [4.7×104 (a.u.)] was 3–5×102 times

/𝜕𝑄

larger than those of dyes 1–3 (SI, Fig. S6). This results also explains the experimentally observed knr(RT) of benzophenone (2×102 s−1)22-24 in non-conjugated solid hosts being 2–4×102 times larger than that of dyes 1–3. Therefore, knr(RT) is likely strongly dependent on VSOC between T1 and S0. In dyes 1–3, in-plane C-C and C-H vibrations have small ∂𝛹

( )

𝐻

𝛹

( )

values because the vibrations hardly change 𝛹

/𝜕𝑄

( )

𝐻

𝛹

( )

[(i) of Fig. 2d and SI, Figs. S7-S9]. However, out-of-plane C-C and C-H vibrations considerably 𝛹

( )

𝐻

𝛹

increase ( )

∂𝛹

( )

𝛹

𝐻

( )

because

/𝜕𝑄

the

vibrations

change

with the conformation changes depending on the vibrations [(ii) of Fig. 2d

and SI, Figs. S7-S9]. For dye 3, the out-of-plane C-C and C-H vibrations at the fluorene moiety considerably increased ∂ 𝛹

( )

𝛹

𝐻

( )

/𝜕𝑄

[(ii) and (iii) in Fig. 2d]; however, the in

plane vibrations had little effect on this parameter [(iv) in Fig. 2d]. Vibrations in other aromatic parts [(v) in Fig. 2d] do not greatly increase ∂ 𝛹

( )

𝐻

𝛹

( )

/𝜕𝑄

either. This result

might be because of the overlapping density of molecular orbitals relating to the T1-S0 transition being mainly located at the fluorene moiety [(vi) in Fig. 2d]. As the temperature increased, higher frequency modes of small ωp make a slight contribution to 𝑃 (𝑇) ∂ 𝛹

( )

𝐻

∑ 𝑃 (77𝐾) ∂ 𝛹

𝛹 ( )

( )

𝐻

/𝜕𝑄 𝛹

( )

(SI, Fig. S10). However, the relative increases from /𝜕𝑄

to

∑ 𝑃 (𝑅𝑇) ∂ 𝛹

( )

𝐻

𝛹

( )

/𝜕𝑄

for

dyes 1, 2, and 3, were 1.18, 1.11, and 1.07 times, respectively. These increases are comparable to the magnitude of the small increase from knr(77K) to knr(RT) (SI, Table S2). This finding also indicates that the experimentally determined value of knr(RT) is related to spin orbit



Page 12 of 24

triggered intramolecular vibrations, i.e., the VSOC mechanism. Because intramolecular vibrations hardly changed the T1-S0 energy in aromatic polycyclic carbons,

Figure 2. Analysis of knr(RT) depending on the VSOC of dyes 1–3. (a) Relationship between 𝛹

( )

𝐻

𝛹

( )

and out-of plane vibration at ωp = 103.42 cm−1 of dye 1. (i) Qp = −1 (a.u.).

(ii) Qp=0 (a.u.). (iii) Qp = +1 (a.u.). (b) 𝛹

( )

𝐻

𝛹

( )

−Qp relationship at representative

vibration modes of dye 1. (c) Relationship between 𝑃 (𝑅𝑇) ∂ 𝛹 ωp for dyes 1 (i), 2 (ii), and 3(iii). (d) 𝑃 (𝑅𝑇) ∂ 𝛹

( )

𝐻

𝛹

( )

( )

𝐻 /𝜕𝑄

𝛹

( )

/𝜕𝑄

and

in representative

vibration modes for dyes 1–3 (i-v) and electron density overlap of molecular orbitals relating to the T1–S0 transition of dye 3 (vi).


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knr(RT) is determined not from FC but rather from the VSOC term in equation 1. Although dyes 2 and 3 have different aromatic cores, knr(RT) of unsubstituted fluorene could not be determined because the absorption spectrum of unsubstituted fluorene was completely obscured by that of β-estradiol. Therefore, knr(RT) of unsubstituted fluorene was determined in ZEONEX®, which is a rigid cyclo-olefin non-conjugated polymeric host, under vacuum conditions. The determined value was similar to knr(RT) of dye 3 in β-estradiol (SI, Table S2, Figs. S11-S13). Furthermore, we examined the similar behavior of the dibenzo[g,p]chrysene core before and after donor substitution (SI, Figs. S14 and S15, and Table S3). Therefore, donor substitution by groups such as secondary amines does not increase knr(RT) because VSOC is largely unaffected by substitution. We note that the intramolecular-vibration-based nonradiative rate at RT is not fast compared with kp based on VSOC. knr(RT) may become much faster than small kp when the intermolecular vibrations induced at RT in the heavy atomfree aromatic structures allow the conformation to change the conical intersection between the T1 and S0 potential surfaces; however, many heavy atom-free molecules might not have the considerable effect and accurately calculating the T1 potential surface remains challenging. Therefore, the intramolecular vibration based on the nonradiative rate at RT is not as fast as kp for many heavy atom-free aromatic structures. Therefore, long-lived triplet excitons are possible at RT for a variety of heavy atom-free conjugated structures under appropriate conditions that minimize kq(RT). Restricting out-of-plane C-C and C-H vibrations in the conjugated structures is a key factor for minimizing knr(RT). Unlike the comparable knr(RT) values for dyes 1–3, we found a distinctly larger kp value for dye 3 compared with those of dyes 1 and 2. We attribute this larger value to the substitution of the secondary amine enabling a greater SOC between T1 and Sm and a larger transition dipole moment from Sm to S0. In the framework of first order perturbation theory, kp can be formulated as36:



→

|2,

=∑ 𝜆 ×𝜇

→

𝑘 = 𝜈̅ 𝜇̅

→

𝜆 = 𝜆 ʹ= where 𝜇̅

→

|𝜇̅

( )

𝛹 𝛹

( )

𝐻

𝛹

𝐻

𝛹

Page 14 of 24

(6) +∑ 𝜆 ′×𝜇

→

,

(7)

( )

,

(8)

,

(9)

( )

is the transition dipole moment for phosphorescence; 𝜇

→

is the transition

dipole moment for fluorescence that occurs from Sm to S0; Ψm1(0) is the electronic wavefunction of the v = 0 vibrational level of Sm; λm and λmʹ are prohibition factors with respect to the SOC of the T1−S0 transition; 3E1−1Em is the energy difference between Sm and T1; and 3Em−1E0 is the energy difference between the m-order triplet excited state (Tm) and S0. The value of 𝜆 ʹ is often very small compared with λm and because 3Em−1E0 is large compared with 3E1−1Em, the perturbative SOC approximately considers λm and 𝜇

→

to predict kp, based on the following

relationship, 𝑘 ∝ (∑ 𝜆 𝜇

→

) .

(10)

Because experimentally observed kp values of heavy atom complexes are well predicted by the perturbative self-consistent SOC-time dependent DFT,37 we used the same method to calculate kp. The calculated values of kp were comparable to the magnitude of the experimentally observed ones (Table 1). Therefore, the contribution of λm and 𝜇

→

to the difference of kp of dyes 1–

3 was investigated. Figure 3a shows the relationship between 𝛹 Figure 3b shows the relationship between 𝜇

→

( )

𝐻

𝛹

( )

and m.

and m. For unsubstituted conjugated


Page 15 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


( )

molecules, such as dye 2, 𝛹

𝐻

10 [(i) of Fig. 3a]. Conversely, 𝜇

𝛹 →

( )

has a moderate influence when m is 4, 6, 9, and

is very small for m = 4, 6, 9, and 10 [(ii) of Fig. 3b].

Consequently, m = 5 makes the largest contribution to kp; however, the value of 𝜆 × 𝜇

→

is not large [(i) of Fig. 3c]. These effects result in a small kp value for dye 2. A similar tendency leading to a small kp was observed for dye 1. Unlike the behavior of dyes 1 and 2, in dye 3 𝛹

( )

𝐻

𝛹

( )

as well as 𝜇

resulting in a large ∑ 𝜆 × 𝜇

→

→

are large for m = 5 and 6 [(ii) of Fig. 3a and 3b], in dye 3 [(ii) of Fig. 3c]. This effect is the main factor

contributing to the large kp value based on equation 10. The large contributions of 𝛹

( )

𝐻

𝛹

( )

and 𝜇

, owing to the secondary amine substitution, were also

→

observed for the dibenzo[g.p.]chrysene aromatic cores (SI, Fig. S16 and Table S3). Furthermore the large increase of kp induced by the secondary amino substitution was also observed for fluorene cores in ZEONEX® experimentally and theoretically (SI, Table S2, Figs. S11-S13). An increase of 𝜇

→

after crystallization from isolated molecules has been

reported to increase kp.38 However, the large contribution of 𝜆

and 𝜇

→

from high-order

singlet excited states to increasing kp has yet to be clarified in persistent RTP materials. We note that Φp(RT) of dye 3 based on this mechanism for the high-order singlet state remained at a high level for persistent RTP materials with a lifetime greater than 1 s.



Page 16 of 24

Figure 3 Calculated SOC and transition dipole moments relating to kp for dyes 2 (i) and 3 (ii). (a) Relationship between 𝛹

( )

𝐻

𝛹

( )

(c) Relationship between normalized 𝜆 × 𝜇

and m. (b) Relationship between 𝜇 →

and m.

→

and m, where the value of 𝜆 × 𝜇

→

of

dye 3 was normalized to 1. After the conformation was optimized at T1 with DFT [Gaussian09/B3LYP/6-31G(d)], the ADF program (Hybrid-PBE0/TZP) was used to calculate 𝛹

( )

𝐻

𝛹

( )

and 𝜇

→

. Scalar relativistic (SR)-time dependent DFT calculations

included 10 singlet + 10 triplet excitations, which are used as the basis for the perturbative expansions in the calculations. Perturbative SOC corrections were also applied to the ground state.

The combination of a large 𝜆

and 𝜇

→

in dye 3 can be understood by considering

the relevant molecular orbitals. In dye 2, the S5–S0 transition has a large 𝜇

→

and LE

characteristics [(i) of Fig. 4a]. Because the T1–S0 transition also has LE characteristics [(ii) of Fig. 4a], 𝛹

( )

𝐻

𝛹

( )

becomes small, based on the El-Sayed rule. Consequently, it is

not possible to obtain both a large 𝛹

( )

𝐻

𝛹

( )

and 𝜇

→

, which prevents a large kp.

In dye 3, electrons are delocalized over the whole the molecule in S0 but localized over the two diphenyl amine groups in S5 and S6 [(i) and (ii) of Fig. 4b]. Therefore, 𝛹

( )

and 𝛹

( )

have

moderate CT characteristics. However, electrons are delocalized over the molecule before and


Page 17 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


after the T1–S0 transitions [(iii) of Fig. 4b], indicating that 𝛹 Therefore, 𝛹

( )

𝐻

𝛹

( )

and 𝛹

( )

𝐻

𝛹

( )

( )

has strong LE characteristics.

become large, based on the El-Sayed

rule. In addition, the moderate CT transition characteristics, based on delocalized molecular orbitals, do not greatly decrease the transition dipole moment for the singlet-singlet transition,35,39 Therefore, the S5–S0 and S6–S0 transitions remain large 𝜇 values of 𝛹

( )

𝐻

𝛹

( )

and 𝜇

→

→

. The large

contribute to the high kp. The Φp(RT) value of

many un-substituted aromatic structures is low but can be improved for many donor-substituted aromatic structures through doping of the molecules into a highly rigid host with a high triplet energy (SI, Table S4 and Fig. S17).7 The compatibility of the large 𝛹 large 𝜇

→

( )

𝐻

𝛹

( )

and

allowed by the moderate CT at Sm is likely independent of VSOC, which

increases knr(RT). These investigations indicate that the substitution of the aromatic core with a secondary amine raises kp without increasing knr(RT), which is intrinsically small. However, the donor substitution of some aromatic cores may sometimes decrease Φisc(RT). In addition, the donor substitution of an aromatic core with small T1 energy further decreases the T1 energy, triggering acceleration of knr(RT) caused by the increase of FC based on the energy gap law. These two reasons induce the decrease of Φp(RT). Secondary amino substitution often results in large Φp(RT) with large τp(RT) (SI, Table S4); therefore, it is still unclear whether the physics regarding the large Φp(RT) upon donor substitution is universally applicable to every aromatic



core. However, the ability to raise kp without increasing knr(RT) using donor substitution is a new physical insight. Cooperative consideration of this new physical insight relating the RT ISC transition from T1 to S0 observed in this report with the science regarding the ISC transition from S1 to T1 summarized in the 1960s4 will be important to realize highly efficient persistent RTP.

Figure 4 Explanation of the mechanism of enhancement of kp with a Jablonsky diagram and molecular orbitals for (a) Dye 2 and (b) dye 3. Figures next to the gray arrows represent the weight factor for the transitions.


Page 18 of 24

Page 19 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The values of kp and knr(RT) for donor-substituted heavy atom-free conjugated molecules and unsubstituted atom-free conjugated molecules were determined by taking Φisc(RT) and kq(RT) into consideration. Analysis based on VSOC in the first order Herzberg–Teller SOC suggested that the experimentally measured knr(RT) was caused by out-of-plane vibrations at the overlap density of the molecular orbitals relating to the T1–S0 transition. Because donor substitution does not greatly affect VSOC relating to the T1–S0 transition, knr(RT) was not increased by substitution. Conversely, substitution considerably increased kp. This increase can be explained by the CT characteristics of Sm enabling a large SOC between Sm and T1 together with the large transition dipole moment of the Sm–S0 transitions. Thus, the concept of raising kp without increasing knr(RT) was clarified for heavy atom-free conjugated structures. Owing to the enhancement of kp, a persistent RTP with Φp(RT) approaching 10% was obtained for a donor-substituted heavy atom-free conjugated structure dispersed in a rigid short conjugated host in ambient condition. Although the intrinsic behavior of knr(RT) for heavy atom-free conjugated structures has been unclear for a long time, our analysis from experimental and theoretical viewpoints clarifies that knr(RT) for many heavy atom-free conjugated molecules is intrinsically small and approaches kp. Furthermore, this report indicates that persistent RTP characteristics can be obtained from a variety of conjugated structures under appropriate conditions that minimize quenching from T1. Minimization of the quenching factor is important for obtaining efficient persistent RTP. This insight may be important for considering future efficient persistent RTP not only from doped aromatics materials but also from aromatic crystals. Unlike heavy metal complexes, kp⋙knr(RT) has not been obtained for heavy atomfree conjugated molecules. Prediction of kp and knr(RT) by calculating the transition dipole moment, SOC, and VSOC from T1 might also be useful for finding heavy atom-free molecular structures leading to highly efficient persistent RTP.



ASSOCIATED CONTENT

Supporting Information.

Sample preparation, details of photophysical measurements, and theoretical calculations. This material is available free of charge online at http://pubs.acs.org.

CONFLICT OF INTEREST DISCLOSURE

The authors declare no competing financial interests.

ACKNOWLEDGMENTS This work was supported by a program of Leading Initiative for Excellent Young Researchers (LEADER) from the Japan Society for the Promotion of Science (JSPS), and JSPS KAKENHI Grant Numbers JP18H02046, JP18H04507, 26107014, JP17K19152.

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Intrinsic Analysis of Radiative and Room-Temperature Nonradiative

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