Vertical substitution strategy to enable cooperation between spin–orbit coupling and transition dipoles for organic phosphorescence

Domain: biology
Published: 2026-03-17
Editorial outcome: minor_revision

Abstract
The emission from organic molecules can be broadly classified as fluorescence or phosphorescence, and it is used in a wide range of applications from optoelectronics to bioimaging. The common method to enhance the fluorescence from organic chromophores is to introduce horizontal substituents into long conjugated structures. However, this concept does not allow the phosphorescence efficiency in the visible range to be increased to the fluorescence efficiency. Here we introduce a molecular design of conjugated molecules that effectively cooperate spin-orbit and transition dipoles. Increasing the through-space substitution of main-group elements perpendicular to the conjugated plane produces a cooperative effect of the spin–orbit and large transition dipoles of the conjugated plane to enhance the organic phosphorescence. This molecular design, which is different from the fluorescence, will increase the efficiency of the organic phosphorescence to the same level as the fluorescence at all visible wavelengths.

Introduction
The emission from organic dyes is used in a wide range of applications, from bioimaging and other fields of life to lighting and photoelectron devices, such as electroluminescent devices1–10, and it is essential for our lives. The photoluminescence from organic chromophores can be broadly classified as fluorescence without spin conversion of the quantum states or phosphorescence with spin conversion of the quantum states11. The molecular designs for obtaining highly efficient fluorescence include a conjugated π plane in which the donor and acceptor groups are horizontally attached to the rigid π plane, and these designs have been used in the design of laser dyes and two-photon absorption dyes12–14. Heavy metal complexes have been used to implement highly efficient phosphorescence across the entire visible light range in organic light-emitting diodes15–17, and proposals for afterglow emitting imaging using the long lifetime of organic phosphorescence have rapidly increased in the past decade18–22. Although molecules with similar skeletons and substituent characteristics to those that exhibit fluorescence have been reported for organic phosphorescence, the phosphorescence is inefficient, especially in the long-wavelength range23–26. If the fundamental design guidelines that differ between organic fluorescence and phosphorescence could be clarified, it would be greatly assist in reaching 100% yield of the organic phosphorescence in the visible to near-infrared range.

Here we report molecular design concentrating on the organic phosphorescence process. Organic π backbones with horizontally introduced hetero-substituents and organic π backbones with vertically introduced hetero-substituents are synthesized. The introduction of multiple horizontal hetero-substituents induces inefficient phosphorescence, whereas the introduction of multiple vertical hetero-substituents leads to more efficient phosphorescence. Cooperative theoretical and experimental analysis confirms that the multiple vertical hetero-substituents can utilize the large transition dipole along the π plane, which allows for the cooperation of the large transition dipoles and spin–orbit coupling to enhance the phosphorescence radiation. Designed chromophores with enhanced red organic phosphorescence radiation allow high-resolution afterglow imaging using the emission colour and delay time, which contributes to break the limitation of the number of labels functioning in high-resolution and rapid bioimaging.

Results
Molecular design and emission behaviour
The expansion of the π conjugation is a basic strategy to facilitate radiative transition from excited states. One rational design strategy to extend the π conjugation is to introduce multiple hetero-substituents horizontally into an aromatic backbone. Such multiple horizontal hetero-substituents cause a large transition dipole moment (TDM) related to the singlet radiation process, which generally improves the fluorescence yield (Φf). However, the TDM originating from the multiple substituents often cancels the TDM related to the triplet radiation process along the extended conjugation axis (Fig. 1a, left). When the large TDM originating from the extended π system can be used for the triplet radiation process, efficient room-temperature phosphorescence (RTP) can be obtained. Here we report a molecular design that allows a large TDM associated with triplet radiation along the extended conjugation axis and efficient RTP by multiple vertical hetero-substitutions (Fig. 1a, right).

Dibenzo[g,p]chrysene (DBC) (1) derivatives with one or four phenylselane substituent (2 and 3) and one or four naphthalene–phenylselane substituent (4 and 5) were synthesized (Supplementary Figs. 1–14). Computational simulations suggested that the selenium atoms are placed vertically on DBC in 4 and 5 because of the steric hindrance between DBC and the naphthalene unit (Supplementary Fig. 15). Each chromophore was doped into β-estradiol at a concentration of 0.3 wt% to prepare an amorphous film (Supplementary Fig. 16). Soon after ceasing excitation, 2 and 4 showed red afterglow RTP with comparable brightness and RTP yield (Φp) (Fig. 1b, middle). However, 3 showed almost no afterglow capability (Fig. 1b, left). In contrast, chromophore 5 showed the brightest afterglow and highest Φp among chromophores 2–5 (Fig. 1b, right). The opposite behaviour of the RTP between 3 and 5 suggests that each substituent affects the phosphorescence process differently.

Optical properties
To clarify the mechanism, the emission properties of 1–5 and deuterated 5 (5d) in amorphous β-estradiol (Fig. 2a) were investigated. Chromophores 1–5d showed blue fluorescence and red RTP under excitation (Fig. 2b), but they showed only red RTP soon after ceasing excitation (Fig. 2c). Integration sphere measurements showed that the Φf values of 1–5d were 20%, 1.1%, 1.7%, 1.2%, 1.0%, and 0.8%, respectively. The Φp values of 1–5d were 2.9%, 18%, 15%, 18%, 27%, and 35%, respectively (Supplementary Figs. 17–19). These results confirm that increasing the number of horizontal hetero-substituents enhances Φf while reducing Φp, whereas Φp is selectively enhanced with increasing number of vertical hetero-substituents. The RTP decay of 1–5d approached a single exponential nature, and the average RTP lifetimes (τp) of 1–5d were 580, 67, 6.8, 138, 45, and 57 ms, respectively (Fig. 2d). Transient absorption measurements confirmed that the intersystem crossing yields (Φisc) of 1–5d were ≥87% (Supplementary Figs. 20–23 and Supplementary Tables 1 and 2). The comparable Φisc values indicate that the photophysical parameters after formation of the lowest triplet excited state (T1) are responsible for the difference in Φp.

Generally, Φp depends on the rate constant of the radiative transition from T1 (krT) and the rate constant of the nonradiative transition from T1 (knrT). Φp and τp are expressed as Φp = Φisc krT τp and 1/(krT + knrT), respectively. Using the relationship Φp = Φisc krT τp, the krT values of 1–5d in amorphous β-estradiol were determined to be 0.063, 2.8, 23, 1.3, 6.1, and 6.3 s−1, respectively (Supplementary Table 2). By substituting τp and krT into τp = 1/(krT + knrT), the knrT values of 1–5d were determined to be 1.7, 12, 124, 5.9, 16, and 11 s−1, respectively. The selective suppression of knrT from 5 to 5d can be explained by a common isotopic effect. However, the relationship between krT and knrT among 2–5 showed that krT and knrT greatly changed depending on the substituent type (Fig. 2e). From 2 to 3, the slope of krT against knrT was less than one (Fig. 2e, blue arrow), confirming that the magnitude of the krT enhancement was smaller than that of the knrT enhancement. In contrast, from 4 to 5, krT was enhanced by approximately 1.7 times compared with knrT (Fig. 2e, red arrow). Therefore, 5 has a mechanism that enhances krT relative to knrT, causing efficient RTP of 5.

Effect of vertical hetero-substituents for knrT suppression
One reason for the enhancement of krT compared with knrT for vertical hetero-substitutions is that increasing the number of the vertical hetero-substitutions makes knrT less likely to increase compared with common horizontal hetero-substitutions. knrT is generally expressed as22,27
knrT = 2π/ℏ |<T1|HSO|S0>|2 FC, (1)
where <T1|HSO|S0> is the spin–orbit coupling (SOC) between T1 and the ground state (S0), HSO is the spin–orbit Hamiltonian, and FC is the Franck–Condon factor between T1 and S0. FC contains the energy gap law, where knrT increases as the phosphorescence is red-shifted28. Because the phosphorescence energies of 1–5 are comparable (Fig. 2c), the variation of the knrT values among 1–5 is expected to originate from differences in the <T1|HSO|S0>2 values. Indeed, quantum chemical calculations showed a good correlation between the optically determined knrT values and calculated <T1|HSO|S0>2 values for 1–5 (Supplementary Fig. 24a). Therefore, it is reasonable to attribute the difference in the knrT values between 3 and 5 to their respective <T1|HSO|S0>2 values. The first factor that changes <T1|HSO|S0>2 is the overlap of the orbitals. <T1|HSO|S0>2 increases when the overlap of the orbitals involved in the two transitions is large (Fig. 3a(i)). HSO is expressed as6,29,30
HSO = α2 ∑A ∑i (ZA / rAi3) ⃗li 𝐬⃗i, (2)
where α is the fine structure constant, A indicates the nucleus, i indicates the electron, ZA is the atomic number, r is the electron–nucleus distance, ⃗li is the orbital angular momentum, and 𝐬⃗i is the spin angular momentum. The second factor that changes <T1|HSO|S0>2 is the distance between the heavy atoms and the overlap site of the orbitals involved in the T1–S0 transition. The ZA / rAi3 term in Equation (2) means that <T1|HSO|S0>2 increases when the heavy atoms are closer to the overlap site of the orbitals involved in the T1–S0 transition (Fig. 3a(ii)). This is the contribution of the increase in <T1|HSO|S0>2 owing to the introduction of heavier atoms, that is, the heavy atom effect (HAE). The third factor that changes <T1|HSO|S0>2 is the relative orientation of the molecular orbitals. ⃗li 𝐬⃗i in Equation (2) means that <T1|HSO|S0>2 increases when the axes of the two orbitals involved in the overlapping region point in different directions (Fig. 3a(iii)). This enhancement of the SOEC by this term is known as the El-Sayed rule31. When the two orbital axes are in the same direction, no torque is generated to flip the spin because the electron spin and magnetic moment are parallel (left of Fig. 3a(iii), Supplementary Note 5-2, and Supplementary Fig. 25). Conversely, when the axes of the two orbitals are in different directions, a torque that flips the spin is generated because the electron spin and magnetic moment are not parallel (Fig. 3a(iii), right)32. Thus, the three factors of the orbital overlap, HAE, and relative orientation of the molecular orbitals can be individually considered to discuss the difference in <T1|HSO|S0>2 ∝ knrT between 3 and 5.

The suppression of the increase in knrT with increasing number of vertical hetero-substitutions is due to the small overlap of the orbitals involved in the T1–S0 transition. Regarding the orbital overlap, the first factor that changes <T1|HSO|S0>2, the T1–S0 transition is predominantly composed of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for both 3 and 5 (Supplementary Fig. 26). Because the spatial overlap between the HOMO and LUMO on Se of 5 is much smaller than that of 3 (Fig. 3b(i)), the different amounts of orbital overlap contribute to the different <T1|HSO|S0>2 values between 3 and 5. Regarding the HAE, the second factor that changes <T1|HSO|S0>2 for 3 and 5, the Se atom is often considered to be the heavy atom source for the HAE, and it is widely used for organic phosphorescence materials33–35. However, the large difference in the <T1|HSO|S0>2 values between 3 and 5 cannot be well explained by the HAE contribution because the distance between the HOMO and LUMO overlap sites and Se does not significantly differ between 3 and 5 (Fig. 3b(ii)). Regarding the orbital orientation factor, the third factor that changes <T1|HSO|S0>2, the orbital orientation on the Se atoms differs between the HOMO and LUMO of 3 (Fig. 3b(iii), left). Because the HOMO and LUMO on the Se atoms also exhibit different orientations for 5 (Fig. 3b(iii), right), the orbital orientation factor does not well explain the different <T1|HSO|S0>2 values between 3 and 5. Therefore, the spatial overlap between the HOMO and LUMO on Se mainly causes the smaller <T1|HSO|S0>2 of 5 than 3, suppressing the increase of knrT for 5 compared with that for 3.

Effect of vertical hetero-substituents for krT
Another reason for the enhancement of krT relative to knrT by vertical hetero-substitution is that an increase in the number of vertical hetero-substitutions tends to increase krT to a similar level as an increase in the number of horizontal hetero-substitutions. The equation for krT based on first-order perturbation theory is expressed as6,29,30
krT = (ET1−S03 / 3ε0πℏ4c3) |μT1−S0|2, (3)
μT1−S0 = ∑n≥1 (<Sn|HSO|T1> / ESn−T1) μSn−S0 + ∑m≥2 (<Tm|HSO|S0> / ETm−S0) μTm−T1, (4)
where ET1−S0 is the energy gap between T1 and S0, ε0 is the vacuum permittivity, ℏ is the Dirac constant, c is the speed of light, μT1−S0 is the TDM between T1 and S0, <Sn|HSO|T1> is the SOC between the nth-order singlet excited state (Sn, n ≥ 1) and T1, ESn−T1 is the energy gap between Sn and T1, μSn−S0 is the TDM between Sn and S0, <Tm|HSO|S0> is the SOC between the mth-order triplet excited state (Tm, m ≥ 2) and S0, ETm−S0 is the energy gap between Tm and S0, and μTm−T1 is the TDM between Tm and T1. Equation (3) indicates that the enhancement of krT becomes increasingly difficult as the phosphorescence is red-shifted. From Equation (4), however, krT can still be facilitated by the cooperative contributions of <Sn|HSO|T1>2 and μSn−S02, and of <Tm|HSO|S0>2 and μTm−T12 even in the long-wavelength region (Fig. 4a). In terms of SOC elements, Equations (1), (3), and (4) indicate that the selective enhancement of krT relative to knrT tends to occur when <Sn|HSO|T1>2 and <Tm|HSO|S0>2 are larger than <T1|HSO|S0>2. For 1–5, the calculated krT values based on the first-order perturbation showed a good correlation with the optically determined krT values (Supplementary Fig. 24b). For 3, n = 5 and m = 7 mostly contribute to enhance krT, while for 5, n = 2 and m = 9 mainly contribute to krT (Supplementary Figs. 27 and 28). For 3, <S5|HSO|T1>2 for the driving force of krT greatly decreases compared with the large <T1|HSO|S0>2 (Fig. 4b(i)). Thus, while multiple horizontal hetero-substitutions of Se increases <T1|HSO|S0>2, the increase of <Sn|HSO|T1>2 leading to krT enhancement is weak. This characteristic was also confirmed for chromophores with a horizontal phenylseleno substituent at the 3-position of DBC, and Φp of the chromophore was indeed small (Supplementary Figs. 14 and 29–31, and Table 3). In contrast, for 5, <S2|HSO|T1>2 for the driving force of krT is large relative to the small <T1|HSO|S0>2 (Fig. 4b(ii)), and it is comparable with <S5|HSO|T1>2 of 3. Similarly, <T9|HSO|S0>2 of 5 is comparable with <T7|HSO|S0>2 of 3 (Fig. 4b(iii)). Thus, multiple vertical hetero-substitutions suppress the increase in <T1|HSO|S0>2, which causes an increase in knrT, compared with multiple horizontal hetero-substitutions, but they do not stop the increases in <Sn|HSO|T1>2 and <Tm|HSO|S0>2, which leads to an increase in krT based on the relationship from Equations (3) and (4) in Fig. 5a. As a result, <Sn|HSO|T1>2 and <Tm|HSO|S0>2 of 5 increase to levels close to those of 3.

<Sn|HSO|T1>2 of the multiple vertical hetero-substituted chromophore approaching that of the multiple horizontal hetero-substituted chromophore can be understood by considering the following three factors, which are the same factors as those explained the SOC regarding knrT in Fig. 3a. First, regarding the overlap of the orbitals before and after the transition that increases <Sn|HSO|T1> in Equation (4), <Sn|HSO|T1> logically increases as the overlap between the orbital overlap density related to the Sn–S0 transition and the orbital overlap density related to the T1–S0 transition increases. For 3, <S5|HSO|T1> significantly contributes to the increase in krT, but the overlap density of the S5–S0 transition [(HOMO-2)×(LUMO)] only slightly overlaps with that of the T1–S0 transition [(HOMO)×(LUMO)] between C and Se (green open circles at the top of Fig. 5b(i) and Supplementary Fig. 32a). Although <S2|HSO|T1> significantly contributes to the increase in krT for 5, similarly, the overlap density of the S2–S0 transition [(HOMO-1)×(LUMO)] only has a small overlap with that of the T1–S0 transition [(HOMO)×(LUMO)] as a through-space interaction between C and Se (green open circle at the bottom of Fig. 5b(i) and Supplementary Fig. 32b). Therefore, the comparable poor orbital overlap hardly changes <Sn|HSO|T1> between 3 and 5. Second, regarding the contribution of the HAE to increasing <Sn|HSO|T1> in Equation (4), the distance between the overlapping site and Se does not significantly change between 3 and 5 (Fig. 5b(ii)). Therefore, the effect of the HAE does not result in a driving force that significantly differentiates between <S5|HSO|T1> of 3 and <S2|HSO|T1> of 5. Third, regarding the contribution of the orbital axis orientation to the change in <Sn|HSO|T1>, for 3, the orbital axes of (HOMO-2)×(LUMO) and (HOMO)×(LUMO) are in different directions (Fig. 5b(iii), top). Similarly, for 5, the orbital axis of the through-space type (HOMO-1)×(LUMO) formed between Se and C is different from that of the (HOMO)×(LUMO) on DBC (Fig. 5b(iii), bottom). Therefore, the orbital axis orientation hardly changes <Sn|HSO|T1> between 3 and 5. Therefore, these similar tendencies regarding the spatial overlap characteristics, HAE, and orbital orientation increases <S2|HSO|T1>2 of 5 to a comparable value to <S5|HSO|T1>2 of 3. When the Se atoms in 5 are replaced with S atoms, the enhancement of <Sn|HSO|T1>2 becomes small owing to the lack of an orbital overlap factor (Supplementary Figs. 13 and 33–35, and Table 4).

The approach of <Tm|HSO|S0> of the multiple vertical hetero-substituted chromophore to that of the multiple horizontal hetero-substituted chromophore can also be understood from the three perspectives of the orbital overlap, HAE effect, and orbital orientation (Fig. 5c). Regarding the orbital overlap (Fig. 5c(i)), the T7–S0 transition in 3 is mainly composed of HOMO-3 and LUMO (Supplementary Fig. 36a), and the T9–T1 transition in 5 is composed of HOMO-2 and LUMO (Supplementary Fig. 36b). The spatial overlap density between HOMO-3 and LUMO on Se in 3 (green open circles at the top of Fig. 5c(i)) is larger than the through-space overlap density between HOMO-2 and LUMO formed between Se and C in 5 (green open circle at the bottom of Fig. 5c(i)). Therefore, the contribution of the orbital overlap term to the enhancement of <T7|HSO|S0> for 3 is larger than that to the enhancement of <T9|HSO|S0> for 5. Regarding the contribution from the HAE, the distance between the HOMO-3 and LUMO overlap sites and Se for 3 is smaller than that for 5 (Fig. 5c(ii)). Therefore, for 3, the HAE plays a role in increasing <Tm|HSO|S0>. Regarding the orbital orientation (Fig. 5c(iii)), the orbital axis directions of the HOMO-3 and LUMO on the Se atoms slightly differ for 3 (Fig. 5c(iii), top). However, for 5, the orbital axis direction of the HOMO-2 of Se significantly differs from that of the LUMO of C on DBC (Fig. 5c(iii), bottom). Therefore, the contribution of the orbital orientation term to the enhancement of <T7|HSO|S0> for 3 is smaller than that to the enhancement of <T9|HSO|S0> for 5. Considering these three factors, the decrease in <T9|HSO|S0> due to the poor orbital overlap and HAE for 5 is compensated for by the increase in <T9|HSO|S0> due to the orbital orientation, which results in <T9|HSO|S0> for 5 being equivalent to <T7|HSO|S0> for 3.

The cooperation between the high-order TDM and the maintained large <Sn|HSO|T1> and <Tm|HSO|S0> contributes an additional factor to the maintenance of the large krT in the suppressed knrT state in the multiple vertical hetero-substituted chromophores. For instance, for 3, μS5−S02 is small because of the symmetry-forbidden nature of (HOMO-2)×(LUMO) as the overlap density of the S5–S0 transition along the extended π-conjugation direction in the x axis (Fig. 6a(i)). As well as the S5–S0 transition, 3 has a symmetry-forbidden nature along the extended π-conjugation in the T7–T1 transition, which prevents a large enhancement of μT7−T12 (Fig. 6a(ii)). The horizontal hetero-substituents therefore lead to cancellation of the large TDMs originating from the π-extended framework, weakening the <Sn|HSO|T1>2 and μSn−S02 cooperation and <Tm|HSO|S0>2 and μTm−T12 cooperation. In contrast, for 5, μS2−S02 and μT9−T12 are large because both the S2–S0 and T9–T1 transitions are constructed from the symmetrically allowed nature along the long π-conjugation direction (Fig. 6b(i) and (ii)). The large TDMs enable strong cooperativities between μS2−S02 and <Sn|HSO|T1>2, and between μT9−T12 and <Tm|HSO|S0>2. As a result of the strong cooperativities and suppressed <T1|HSO|S0>2, selective enhancement of krT compared with knrT is realized for 5. In previous strategies featuring horizontal hetero-substitutions, the extended π-conjugation could not be effectively utilized for the triplet radiation. The vertical hetero-substituent strategy can activate the long π conjugation system for triplet radiation, which serves as a guideline for the design of new organic phosphorescence π-conjugated molecules.

Demonstration of multi-label afterglow imaging
High-resolution multi-label imaging utilizing the colour and afterglow time (Fig. 7a) was demonstrated using 5d with vertically introduced hetero-substituents as a chromophore with bright-red persistent RTP. Four water-dispersible crystalline particles with green RTP and short τp (particle A), green RTP and long τp (particle B), red RTP and short τp (particle C), and red RTP and long τp (particle D) were prepared (Fig. 7b, and Supplementary Note 6-1). The transmittance image confirmed that the existence of cells (Fig. 7c, and Fig 7d, left) and the morphology of the cell membrane remained essentially unchanged for at least 90 min in the presence of the particles (Supplementary Fig. 37). Under irradiation with 360-nm excitation, significant autofluorescence was observed (Fig. 7d, right). However, 20–60 ms after ceasing excitation, only afterglow signals from the particles could be detected with a spatial resolution approaching the diffraction limit (Supplementary Fig. 38). The use of an optical bandpass filter in the green region and a long-pass filter above 685 nm confirmed the existence of green RTP particles (i.e., particles A or B) (Fig. 7e(i)) and red RTP particles (i.e., particles C or D) (Fig. 7e(ii)), respectively. Additionally, by detecting the afterglow at a later time, the green RTP from particle B (Fig. 7e(iii)) and red RTP from particle D (Fig. 7e(iv)) was identified (Supplementary Fig. 39).

Methods
Synthesis and film preparation
Chromophore 1 was commercially available (Tokyo Chemical Industry (TCI), Tokyo, Japan). The synthesis procedures of 2–5d are described in the Supplementary Note 1. To prepare the amorphous film, each chromophore was dissolved in melted β-estradiol (TCI) at a concentration of 0.3 wt%, and the mixture was sandwiched between two quartz substrates at 240 °C. The substrates were quenched to room temperature to produce an amorphous β-estradiol film doped with the chromophore.

Photophysical characteristics
The emission spectrum and RTP decay characteristics were collected using a photonic multichannel analyser (PMA-12, Hamamatsu Photonics, Shizuoka, Japan) and monochromatic light from the excitation unit of a fluorimeter (FP-8300, JASCO, Tokyo, Japan). An absolute quantum yield measurement system (C9920-02G, Hamamatsu Photonics) was used to determine the emission quantum yields. The intersystem crossing yields of the synthesized chromophores were determined based on a transient absorption technique38,39 using a sub-nanosecond transient absorption spectrophotometer (picoTAS, Unisoku, Osaka, Japan) with a 355 nm Q-switched microchip laser (PNV-M02510-1×0, Teem Photonics, Meylan, France).

Theoretical calculations
The optimized geometry of T1 was determined by the Gaussian09 program based on density functional theory (DFT). The optimization was performed using the B3LYP functional and 6-311+G(d,p) basis set. Using the optimized T1 geometry, the SOC elements, μSn−S0, and μTm−T1 were calculated using the Amsterdam Density Functional (ADF) 2025 package with the PBE0 functional and TZP basis set. The molecular orbitals associated with μTm−T1 were estimated by time-dependent DFT (TD-DFT) calculation with the Gaussian09 program using the PBEPBE functional and 6-311G(d,p) basis set. In the TD-DFT calculations, the option iop(3/76=1000002500) was applied to adjust the fraction of the Hartree–Fock exchange to be consistent with the PBE0 functional.

Preparation of the crystalline particles
Water-dispersible afterglow particles A–D were prepared in a similar manner by changing the host and guest molecules. For example, for particle A, (S)-(−)-2,2′-bis(diphenylphosphino)-1,1′-binaphthyl ((S)-BINAP) (Sigma-Aldrich, St Louis, MO, USA) and (S) -(−)-2,2′bis(diphenylphosphino)-5,5′,6,6′,7,7′8,8′-octahydro-1,1′-binaphthyl ((S)-H8-BINAP) (Sigma-Aldrich) were used as the guest and host molecules, respectively (Fig. 4b)40. (S)-BINAP was dissolved in melted (S)-H8-BINAP at a concentration of 1.0 wt% at 240 °C. The mixture was then annealed at 160 °C for 5 min to prepare the 1.0 wt%-(S)-BINAP-doped (S)-H8-BINAP crystalline solid. The crystalline solid (1.0 mg) was added to an aqueous solution of F127 (Sigma-Aldrich) (3.3 g L−1, 1.0 mL), and then the aqueous solution was stirred with an ultrasonic homogenizer (UR-20P, Tomy Seiko Co., Ltd., Tokyo, Japan) for 10 min in an ice bath. The mixture was then filtered through a hydrophilic membrane filter (Millex-AP, glass fibre, 2.0 µm, Merck Millipore Ltd., Tullagreen, Carrigtwohill, Ireland) with a specific pore size. After the filtered solution was centrifuged, the aqueous solution was replaced with pure water to produce particle A dispersed in water. The preparation procedures for particles B–D are described in the Supplementary Note 6-1.

Sample preparation for in vitro imaging
Human embryonic kidney (HEK) 293tSA41 cells were plated on polyethyleneimine-coated glass coverslips and cultured in Dulbecco’s Modified Eagle’s Medium high glucose (Sigma-Aldrich) supplemented with 10% foetal bovine serum, 2 mM glutamine (Gibco) (Thermo Fisher Scientific, Waltham, MA, USA) and 1% penicillin–streptomycin solution (Gibco) (Thermo Fisher Scientific) at 37 °C under 10% CO2 (MCO-19AIC PHCbi, Tokyo, Japan). For the microscopic experiments, each of the aqueous solution (0.5 µL) dispersed crystalline particles A, B, C, and D was injected into the cultured cells.

Microscopic measurements
The high-resolution multi-label imaging was performed with an inverted optical microscope (IX73, Olympus, Tokyo, Japan) using an oil immersion objective lens (UPlan FLN×100/1.3 NA, oil, Olympus). A continuous-wave laser emitting at 360 nm (IUV-F-360, CNI, Changchun, China) was used as the excitation source. The two-dimensional images were captured by an electron multiplying charge coupled device (iXon Ultra/life 897, Oxford Instruments, Abingdon, UK). The transmittance image and emission image under excitation were collected through a 405 nm dichroic mirror (Di02-R405, Semrock, NY, USA) and a 405 nm long-pass filter (BLP01-405R, Semrock). A bandpass filter (FF01-520/44-25, Semrock) and a 470 nm dichroic mirror (FF470-Di01, Semrock) were used to detect the green afterglow from particle A and particle B. To detect the red afterglow from particle C and particle D, a long-pass filter (FF01-685/LP-25, Semrock) and a 470 nm dichroic mirror (FF470-Di01, Semrock) were used. The afterglow images of the green channel were captured in the time ranges of 20–60 and 1000–1500 ms after stopping excitation to distinguish the afterglow signals from particle A and particle B, respectively. Similarly, the afterglow images of the red channel were captured in the time range of 20–60 and 120–400 ms after ceasing excitation to distinguish the afterglow signals from particle C and particle D, respectively. In the high-resolution imaging experiments, the excitation intensity was 200 mW cm−2.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript reports a molecular design strategy for enhancing organic room-temperature phosphorescence (RTP) by introducing “vertical” hetero-substituents. The authors demonstrate that cooperative effects between transition dipole moments (TDM) and spin–orbit coupling (SOC) selectively enhance the radiative rate of the T₁ → S₀ transition, leading to efficient RTP. With further discussion on the role of higher triplet states, a more explicit dissection of heavy-atom versus orbital-overlap effects, and a stronger connection to established EHE concepts, the work will have even greater impact. I recommend acceptance after minor revision.\n(1) The discussion mainly focuses on SOC between the lowest triplet state T₁ and higher singlet states (Sₙ). However, the possible contribution of higher triplet states (Tₙ, n > 1) to the radiative transition process has not been addressed. Since multi-state interactions may play a role in modulating T₁ → S₀ phosphorescence, a more systematic consideration of such contributions would strengthen the mechanistic interpretation.\n(2) The manuscript attributes the increase in k_r^T to the cooperative interplay between μ_Sn–S0 and ⟨Sₙ|H_SO|T₁⟩. A critical question remains: is the main driving force the intrinsic heavy-atom effect of Se, or the optimization of orbital overlap and spatial distribution of frontier orbitals? From Fig. 3 it is clear that HOMO–LUMO overlap differs significantly between substituent patterns. I recommend further quantitative comparison, for instance by replacing Se with lighter congeners (S or O) to clarify whether the enhanced k_r^T originates predominantly from heavy-atom SOC or orbital overlap effects.\n(3) The vertical substitution strategy may be conceptually related to the “intramolecular external heavy atom effect” (EHE), where the heavy atom is not directly conjugated with the emissive core but exerts SOC through spatial proximity. It would be valuable for the authors to elaborate on this analogy and position their design within the broader context of heavy-atom effect literature.\n(4) The definition of “cooperative effect” should be more precisely articulated—whether it refers to a simple multiplicative relationship between μ_Sn–S0 and ⟨Sₙ|H_SO|T₁⟩, or if energy matching and symmetry considerations are also involved.\n(5) The discussion would benefit from a clearer comparison with previous “horizontal substitution” strategies, highlighting why they fail to enhance RTP while the vertical substitution succeeds.", "reviewer_2": "In this paper, the author presents that enhanced phosphorescence was achieved by adjusting vertical hetero-substituents into π-conjugated structures. Multiple hetero-substituents vertical to the π plane allow for the effective use of the transition dipole extended to the π plane to cooperate with the spin-orbit coupling to enhance the phosphorescence yield. Considering these thorough results and the potential importance of this research, I believe this work should be published with improved organization and a clear summary.\n1. The phosphorescence radiative rate (kr) and lifetime (τP) are intrinsically governed by the energy gap (ΔEST) between the triplet state (T1) and the ground state (S0), as well as the magnitude of the transition dipole moment for the T1→S0 transition. A larger transition dipole moment and a smaller ΔEST generally favor a higher kr, leading to a shorter τP. This fundamental relationship should be explicitly discussed in the manuscript to provide a more complete photophysical rationale for the observed phosphorescence performance.\n2. The superior performance of compound 5 against compound 3 is likely attributable to a stronger through-space spin-orbit coupling effect based on the heavy atom. This enhancement is probably due to the optimized spatial proximity and orientation of the heavy selenium (Se) atom relative to the central π-core, allowing its potent heavy-atom effect to more effectively perturb the spin densities and facilitate the T1→S0 transition. It seems that explanations regarding this aspect are not mentioned in the article.\n3. The proposed cooperation between strong SOC from high-lying singlets (S5 and S3) and a large transition dipole moment is an intriguing and less common mechanism for enhancing phosphorescence. However, is there any experimental observation evidence to support this hypothesis?\n4. The claim regarding the vertical distribution of substituents relative to the central plane should ideally be corroborated by single-crystal X-ray diffraction data. If such crystal structures are available for the discussed compounds, referencing them would provide direct and unambiguous experimental evidence for this asserted conformation.\n5. The manuscript's language will be thoroughly refined to enhance precision, clarity, and conciseness.", "reviewer_3": "In this work, Hayashi and colleagues present an innovative strategy to enhance organic RTP: cooperative spin–orbit and transition dipoles effect. They point out that the horizontally introduced substituent strategies commonly used in fluorescent materials are not suitable for phosphorescence. By employing a unique Se-containing DBC molecular system, the authors found that multiple vertical hetero-substituents lead to more efficient phosphorescence than horizontal substitution. Theoretical calculations reveal that the reason lies in the larger transition dipole moment along the π plane enabled by vertical substitution, which facilitates the cooperative effect of a large transition dipole moment (TDM) and strong spin-orbit coupling (SOC). They further utilize their molecule in multi-label bioimaging to show its practical application. This work presents an effective and compelling strategy, making it well-suited for publication in Nat Commun. However, some minor revisions, particularly regarding theoretical analysis, should be addressed prior to acceptance.\n1. The author may consider add the term through-space substitution or vertical substitution in the title to emphasize its importance in bringing cooperative spin-orbit and transition dipole and enhancing RTP.\n2. On page 2, line 25, the authors claim that this molecular design can enhance the efficiency of organic phosphorescence to a level comparable to that of fluorescence across the entire visible spectrum. However, there is a lack of discussion regarding fluorescence enhancement in the article. Please clarify this point.\n3. In Figure 2c, comparing RTP intensity through photoluminescence (PL) measurements for solid samples may be challenging due to multiple variables such as film inhomogeneity, doping concentration, and measurement distance. Therefore, it is recommended to supplement the figure with phosphorescence quantum yield values.\n4. Although the authors cite some references in the Supporting Information (Section 5-3), which empirically illustrate that krT is related to TDM(Sn-S0) and SOC(Sn-T1), the structure-property relationship remains unclear. Why the transition dipole moment of Sn and the SOC between Sn and T1 will affect the rate constant of T1? Could the authors provide an explanation from the electronic effect perspective instead of an empirical rule?\n5. In Figure 3b, panels iii and iv show overlap between ΩSn and ΩT1, but only ΩSn (red and blue) is clearly visible, while ΩT1 (orange and blue) is difficult to distinguish. Please clarify this more explicitly and include additional representations of ΩT1 in the Supporting Information. Moreover, for consistency, it is suggested that overlap density be used uniformly in panels i–iv, rather than switching between HOMO/LUMO and ΩSn representations when comparing compounds 3 and 5.\n6. Multi-label imaging is an interesting application. Have the authors conducted cytotoxicity tests to demonstrate the biocompatibility of the material?\n7. An efficient RTP system achieved through similar through-space substitution of main-group elements was recently reported (10.1021/jacs.4c17142), which should be cited. In addition, other recently developed high-performance red RTP systems (e.g., 10.1002/agt2.70124, 10.1038/s41467-025-61714-0) should also be referenced in the Introduction."}, "author_response": "Response letter to reviewers\nResponse to Reviewer 1\n(Overall comments from Reviewer 1):\nThis manuscript reports a molecular design strategy for enhancing organic room-\ntemperature phosphorescence (RTP) by introducing “vertical” hetero-substituents. The\nauthors demonstrate that cooperative effects between transition dipole moments (TDM)\nand spin–orbit coupling (SOC) selectively enhance the radiative rate of the T₁ → S₀\ntransition, leading to efficient RTP. With further discussion on the role of higher triplet\nstates, a more explicit dissection of heavy-atom versus orbital-overlap effects, and a\nstronger connection to established EHE concepts, the work will have even greater impact.\nI recommend acceptance after minor revision.\n(Response)\nWe sincerely appreciate your constructive comments. We have addressed your comments,\nas outlined in the following responses. Below, our response to the comments from\nReviewer 1 is in blue, and the specific text and supporting information that we revised\nare in red.\n(Comment 1 from Reviewer 1)\nThe discussion mainly focuses on SOC between the lowest triplet state T₁ and higher\nsinglet states (Sₙ). However, the possible contribution of higher triplet states (Tₙ, n > 1)\nto the radiative transition process has not been addressed. Since multi-state interactions\nmay play a role in modulating T₁ → S₀ phosphorescence, a more systematic consideration\nof such contributions would strengthen the mechanistic interpretation.\n(Response)\nThank you for your important comment. As Reviewer 1 pointed out, the rate constant of\nthe radiation transition from T (kT) is enhanced by contribution of higher triplet states\n1 r\n(T , m ≥ 2). The kT based on the first order perturbation is expressed as (Chem. Rev. 66,\nm r\n199–241 (1966); J. Phys. Chem. A 111, 10490–10499 (2007); Chem. Rev. 117, 6500–6537\n(2017)),\n𝑘T =\n𝐸T1−S0 3\n|𝜇 |\n2\n, (R1-1)\nr 3𝜀0𝜋ℏ4𝑐3 T1−S0\n𝜇 = ∑\n⟨S 𝑛|𝑯 SO|T 1⟩\n𝜇 + ∑\n⟨T 𝑚|𝑯 SO|S 0⟩\n𝜇 , (R1-2)\nT1−S0 𝑛 ≥ 1\n𝐸S𝑛−T1\nS𝑛−S0 𝑚 ≥ 2\n𝐸T𝑚−S0\nT𝑚−T1\nwhere E is the energy gap between T and S , ε is the vacuum permittivity, ℏ is the\nT1-S0 1 0 0\nDirac constant, c is the speed of light, μ is the transition dipole moment (TDM)\nT1-S0\nbetween T and S , <S |H |T > is the spin-orbit coupling (SOC) between the nth-order\n1 0 n SO 1\nsinglet excited state (S , n ≥ 1) and T , E is the energy gap between S and T , μ\nn 1 Sn-T1 n 1 Sn-S0\nis the TDM between S and S , <T |H |S > is the SOC between T and S , E is the\nn 0 m SO 0 m 0 Tm-S0\nenergy gap between T and S , μ is the TDM between T and T . These parameters\nm 0 Tm-T1 m 1\nare visualized in Fig. R1a. Equation (R1-2) shows that the <T |H |S > and μ\nm SO 0 Tm-T1\ncontribute to kT as well as <S |H |T > and μ . In original manuscript, the Amsterdam\nr n SO 1 Sn-S0\nDensity Function (ADF) 2018 package was used to calculate kT values. However, the\nr\ncalculation version could not evaluate the contribution of T , and the obtained kT\nm r\nreflected only first term of equation (R1-2). Therefore, we performed quantum chemical\ncalculations with considerations of second term of equation (R1-2) using the ADF 2025\npackage. Because the calculation methods are changed from original manuscript, the\nparameters for SOC elements, TDM values, and calculated kT values are also changed.\nr\nThe calculated kT values still have good positive correlation with the optically measured\nr\nkT values (Fig. R1b(i)). Furthermore, the calculated <T |H |S >2, which proportional to\nr 1 SO 0\nthe rate constant of the nonradiative transition from T (k T), was consistent with optically\n1 nr\ndetermined k T (Fig. R1b(ii)). Therefore, we could discuss the changes in kT and k T\nnr r nr\nbased on ADF 2025 calculation. In particular, the magnitude of kT of 5 was approximately\nr\nmaintained up to that of 3 when compared with the difference in the k T between 3 and 5\nnr\n(arrows in Fig. R1b(i) and (ii)). Due to the maintenance of kT relative to the suppressed\nr\nk T, 5 has efficient RTP capability than 3.\nnr\nFig. R1 a, Schematic energy diagram illustrating the key factors contributing to kT.\nr\nb, Relationship\nr\n(i) between optically measured and calculated kT and (ii) between optically measured k T and\nr nr\ncalculated <T |H |S >2. The quantum chemical calculations were performed using ADF 2025\npackage with considerations of <T |H |S >, E , and μ contributions in addition to the\nm SO 0 Tm-S0 Tm-T1\n<S |H |T >, E , and μ contributions.\nn SO 1 Sn-T1 Sn-S0\nThe maintenance of kT of 5 relative to its suppressed k T involves contribution\nr nr\nfrom <T |H |S >2 as well as from <S |H |T >2. In terms of SOC elements, equations\nm SO 0 n SO 1\n(R1-1) and (R1-2) indicate that the relative enhancement of kT to k T tends to occur when\nr nr\n<S |H |T >2 and <T |H |S >2 are larger than <T |H |S >2. For 3, n = 5 and m = 7\nn SO 1 m SO 0 1 SO 0\nmostly contribute to enhance kT, while for 5, n = 2 and m = 9 mainly contribute to kT.\nr r\nFor 3, <S |H |T >2 for the driving force of kT greatly decreases compared with the large\n<T |H |S >2 (Fig. R2(i)). In contrast, for 5, <S |H |T >2 for the driving force of kT is\nlarge relative to the small <T |H |S >2 (Fig. R2(ii)), and it is maintained up to the\n<S |H |T >2 of 3. Similarly, <T |H |S >2 of 5 is comparable with <T |H |S >2 of 3\n(Fig. R2(iii)). Thus, the 5 suppresses the increase in <T |H |S >2, which leads to an\nincrease in k T, but it does not stop the increases in <T |H |S >2 as well as <S |H |T >2\nnr m SO 0 n SO 1\nto enhance kT.\nr\nFig. R2 Histograms of <T |H |S >2, <S |H |T >2, and <T |H |S >2 values for 3 (left) and\n<T |H |S >2, <S |H |T >2, and <T |H |S >2 values for 5 (right).\nFurthermore, high-order TDMs collaborating with the maintained SOC in T\nm\ncontribution as well as S contribution serve as an additional factor that sustains the large\nn\nkT relative to suppressed k in 5. For instance, for 3, μ 2 is small because of the\nr nr S5-S0\nsymmetry-forbidden nature of the overlap density between HOMO-2 and LUMO for the\nS –S transition along the extended π-conjugation direction in the x axis (Fig. R3a(i)). As\n5 0\nwell as the S –S transition, 3 has a symmetry forbidden nature along the extended π-\n5 0\nconjugation in the T –T transition, which prevents a large enhancement of μ 2 (Fig.\n7 1 T7-T1\nR3a(ii)). The horizontal hetero-substituents therefore lead to cancellation of the large\nTDMs originating from the π-extended framework, weakening the <S |H |T >2 and μ\n2 cooperation and <T |H |S >2 and μ 2 cooperation. In contrast, for 5, μ 2 and\nS0 7 SO 0 T7-T1 S2-S0\nμ 2 are large because both the S –S and T –T transitions are constructed from the\nT9-T1 2 0 9 1\nsymmetrically allowed nature along the long π-conjugation direction (Fig. R3b(i) and (ii)).\nThe large TDMs enable strong cooperativities between μ 2 and <S |H |T >2, and\nS2-S0 2 SO 1\nbetween μ 2 and <T |H |S >2. As a result of the strong cooperativities and suppressed\nT9-T1 9 SO 0\n<T |H |S >2, selective enhancement of kT relative to k T is realized for 5. Thus, the\ncooperative effect of TDM and SOC is confirmed not only in the S contribution but also\nn\nin the T contribution in vertically hetero-substituents, leading to enhanced organic\nm\nphosphorescence process.\nFig. R3 a, Molecular orbitals and energy diagram relating (i) μ 2 and (ii) μ 2 for 3. b, Molecular\nS5-S0 T7-T1\norbitals and energy diagram relating (i) μ 2 and (ii) μ 2 for 5. In a and b, μ 2, <S |H |T >2,\nS2-S0 T9-T1 Sn-S0 n SO 1\nμ 2, and <T |H |S >2 in energy diagram values calculated with the Amsterdam Density Functional\nTm-T1 m SO 0\n(ADF) 2025 package using the PBE0 functional and TZP basis set. The molecular orbitals shown in\npanel (ii) were calculated with Gaussian09 program using the PBEPBE functional and 6-311G(d,p)\nbasis set. The isovalue of 0.00016 is used for the overlap density between HOMO-2 and LUMO\n[(HOMO-2)×(LUMO)] in 3 and the overlap density between HOMO-1 and LUMO [(HOMO-\n1)×(LUMO)] in 5. β-HOMO-2 and β-LUMO of 3 and β-HOMO-1 and β-LUMO of 5 are shown with\nan isovalue of 0.01.\nFrom the above, we changed the display items and sentences due to the addition of\nthe T contribution. Although the sentences related to discussion on <T |H |S >,\nm 1 SO 0\n<S |H |T >, and <T |H |S > was also changed in revised manuscript, the discussion on\nn SO 1 m SO 0\nthe SOC will describe in the next response.\nFirst of all, we revised the illustration in Fig. 1a to revise the diagram to simply\nshow the use of π-plane transition dipoles for triplet radiation as follow.\nBefore revision: Fig. 1a in original manuscript\nCaption of Figure 1a, Illustration of the concept and energy diagrams of chromophores with\nhorizontal hetero-substitution (left) and vertical hetero-substitution (right).”\nAfter revision: Fig. 1a in revised manuscript\nCaption of Figure 1a, Illustration of the concept and energy diagrams of chromophores with\nhorizontal hetero-substitution (left) and vertical hetero-substitution (right).”\nIn addition, we revised the following sentences due to the modification of Fig. 1.\nBefore revision: Lines 8–17 in p. 4 in original manuscript\n“The multiple horizontal hetero-substituents cause a large transition dipole moment\n(TDM) relating the singlet radiation process (TDM-S) along the conjugated plane, which\ngenerally improves the fluorescence yield (Φ) (Fig. 1a, blue arrow in the left figure).\nf\nHowever, the multiple substituents often induce a TDM relating the triplet radiation\nprocess (TDM-T) in a direction orthogonal to the aromatic backbone (Fig. 1a, red arrow\nin the left figure). When the TDM-T direction can be aligned with the long-conjugation\nplane, efficient room-temperature phosphorescence (RTP) can be obtained. Here we\nreport a molecular design that allows large TDM-T along the long-conjugation plane and\nefficient RTP by multiple vertical hetero-substitution (Fig. 1a, right).”\nAfter revision: Lines 8–17 in p. 4 in revised manuscript\n“Such multiple horizontal hetero-substituents cause a large transition dipole moment\n(TDM) related to the singlet radiation process, which generally improves the fluorescence\nyield (Φ). However, the TDM originating from the multiple substituents often cancels\nf\nthe TDM related to the triplet radiation process along the extended conjugation axis (Fig.\n1a, left). When the large TDM originating from the extended π system can be used for the\ntriplet radiation process, efficient room-temperature phosphorescence (RTP) can be\nobtained. Here we report a molecular design that allows a large TDM associated with\ntriplet radiation along the extended conjugation axis and efficient RTP by multiple vertical\nhetero-substitutions (Fig. 1a, right).”\nNext, we changed Fig. 3a of original manuscript to Fig. 4 of revised manuscript to\nillustrate the T contribution to kT.\nm r\nBefore revision: Fig. 3a in original manuscript\nCaption of Figure 3a, Schematic energy diagram illustrating (i) <T |H |S >, (ii) <S |H |T >, and\n(iii) μ .”\nSn-S0\nAfter revision: Fig. 4 in revised manuscript\nFig. 4 Selectivity of the spin–orbit coupling (SOC) enhancement among <T |H |S >2,\n<S |H |T >2, and <T |H |S >2. a, Schematic energy diagram illustrating μ 2, <S |H |T >2, μ\nn SO 1 m SO 0 Sn-S0 n SO 1 Tm-\n2, and <T |H |S >2. b, Histograms of the <T |H |S >2, <S |H |T >2, and <T |H |S >2 values for\nT1 m SO 0 1 SO 0 5 SO 1 7 SO 0\n3 (left) and <T |H |S >2, <S |H |T >2, and <T |H |S >2 values for 5 (right).”\nFurthermore, we changed the sentences regarding factors that associate with kT\nr\nbecause of addition of the T contribution.\nm\nBefore revision: Lines 12–16 in p. 6 in original manuscript\n“kT is approximated by kT ∝ [Σ (μ <S |H |T >)]2 (n ≥ 1), where <S |H |T > is the\nr r n Sn-S0 n SO 1 n SO 1\nSOC between the nth-order singlet excited state (S ) and T (Fig. 3a(ii)), and μ is the\nn 1 Sn-S0\nTDM in the S –S transition (Fig. 3a(iii))6,26. Therefore, selective enhancement of kT\nn 0 r\ncompared with k T requires the strong cooperation of <S |H |T >2 and μ 2 without a\nnr n SO 1 Sn-S0\nsignificant increase in <T |H |S >2.”\nAfter revision: From line 7 in p. 9 to line 1 in p. 10 in revised manuscript\n“Another reason for the enhancement of kT relative to k T by vertical hetero-substitution\nr nr\nis that an increase in the number of vertical hetero-substitutions tends to increase kT to a\nr\nsimilar level as an increase in the number of horizontal hetero-substitutions. The equation\nfor kT based on first-order perturbation theory is expressed as6,29,30\nr\n𝑘T =\n𝐸T1−S0 3\n|𝜇 |\n2\n, (3)\nr 3𝜀0𝜋ℏ4𝑐3 T1−S0\n𝜇 = ∑\n⟨S 𝑛|𝑯 SO|T 1⟩\n𝜇 + ∑\n⟨T 𝑚|𝑯 SO|S 0⟩\n𝜇 , (4)\nT1−S0 𝑛 ≥ 1\n𝐸S𝑛−T1\nS𝑛−S0 𝑚 ≥ 2\n𝐸T𝑚−S0\nT𝑚−T1\nwhere E is the energy gap between T and S , ε is the vacuum permittivity, ℏ is the\nT1-S0 1 0 0\nDirac constant, c is the speed of light, μ is the TDM between T and S , <S |H |T >\nT1-S0 1 0 n SO 1\nis the SOC between the nth-order singlet excited state (S , n ≥ 1) and T , E is the\nn 1 Sn-T1\nenergy gap between S and T , μ is the TDM between S and S , <T |H |S > is the\nn 1 Sn-S0 n 0 m SO 0\nSOC between the mth-order triplet excited state (T , m ≥ 2) and S , E is the energy\nm 0 Tm-S0\ngap between T and S , and μ is the TDM between T and T . Equation (3) indicates\nm 0 Tm-T1 m 1\nthat the enhancement of kT becomes increasingly difficult as the phosphorescence is red-\nr\nshifted. From equation (4), however, kT can still be facilitated by the cooperative\nr\ncontributions of <S |H |T >2 and μ 2, and of <T |H |S >2 and μ 2 even in the\nn SO 1 Sn-S0 m SO 0 Tm-T1\nlong-wavelength region (Fig. 4a).”\nIn addition, we added the sentences regarding comparison of <T |H |S >2,\n<S |H |T >2, and <T |H |S >2 values between 3 and 5.\nn SO 1 m SO 0\nAfter revision: Lines 1–20 in p. 10 in revised manuscript\n“In terms of SOC elements, equations (1), (3), and (4) indicate that the selective\nenhancement of kT relative to k T tends to occur when <S |H |T >2 and <T |H |S >2\nr nr n SO 1 m SO 0\nare larger than <T |H |S >2. For 1–5, the calculated kT values based on the first-order\nperturbation showed a good correlation with the optically determined kT values\nr\n(supplementary Fig. S24b). For 3, n = 5 and m = 7 mostly contribute to enhance kT, while\nr\nfor 5, n = 2 and m = 9 mainly contribute to kT (supplementary Figs. S27 and S28). For 3,\nr\n<S |H |T >2 for the driving force of kT greatly decreases compared with the large\n<T |H |S >2 (Fig. 4b(i)). Thus, while multiple horizontal hetero-substitutions of Se\nincreases <T |H |S >2, the increase of <S |H |T >2 leading to kT enhancement is weak.\nThis characteristic was also confirmed for chromophores with a horizontal phenylseleno\nsubstituent at the 3-position of DBC, and Φ of the chromophore was indeed small\np\n(supplementary Figs. S14 and S29–S31, and Table S3). In contrast, for 5, <S |H |T >2\nfor the driving force of kT is large relative to the small <T |H |S >2 (Fig. 4b(ii)), and it\nr 1 SO 0\nis comparable with <S |H |T >2 of 3. Similarly, <T |H |S >2 of 5 is comparable with\n<T |H |S >2 of 3 (Fig. 4b(iii)). Thus, multiple vertical hetero-substitutions suppress the\nincrease in <T |H |S >2, which causes an increase in k T, compared with multiple\nhorizontal hetero-substitutions, but they do not stop the increases in <S |H |T >2 and\nn SO 1\n<T |H |S >2, which leads to an increase in kT based on the relationship from equations\nm SO 0 r\n(3) and (4) in Fig. 5a. As a result, <S |H |T >2 and <T |H |S >2 of 5 increase to levels\nn SO 1 m SO 0\nclose to those of 3.”\nNext, we changed Fig. 3b(v) and (vi) of original manuscript to Fig. 6 of revised\nmanuscript due to addition of the μ 2 contribution.\nTm-T1\nBefore revision: Fig. 3b(v) and (vi) in original manuscript\nCaption of Figure 3b, Molecular orbitals and their calculated values relating (i) and (ii) <T |H |S >2,\n(iii) and (iv) <S |H |T >2, and (v) and (vi) μ 2. In (i) and (ii), the red-blue orbitals and orange-light\nn SO 1 Sn-S0\nblue orbitals are the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular\norbital (LUMO), respectively. In (iii) and (iv), the red-blue orbitals are Ω or Ω and the orange-light\nS3 S5\nblue orbitals are Ω . In (i)–(iv), the white arrows represent the orbital angular momentum (OAM)\nT1\nvectors. The isovalues of the HOMO of 3, LUMO of 3, and HOMO of 5 are 0.02. The isovalue of\n0.0085 is used for the LUMO of 5. The isovalues of Ω , Ω , and Ω are 0.00016.”\nS3 S5 T1\nAfter revision: Fig. 6 in revised manuscript\nFig. 6 Cooperativity between the transition dipole moment and SOC in the triplet radiation\nprocess. a, Molecular orbitals and energy diagram relating (i) μ 2 and (ii) μ 2 for 3. b, Molecular\nS5-S0 T7-T1\norbitals and energy diagram relating (i) μ 2 and (ii) μ 2 for 5. In a and b, μ 2, <S |H |T >2,\nS2-S0 T9-T1 Sn-S0 n SO 1\nμ 2, and <T |H |S >2 in the energy diagram are values calculated with the Amsterdam Density\nTm-T1 m SO 0\nFunctional 2025 package using the PBE0 functional and TZP basis set. The molecular orbitals shown\nin panel (ii) were calculated with the Gaussian09 program using the PBEPBE functional and 6-\n311G(d,p) basis set. The isovalue of 0.00016 is used for the overlap density of (HOMO-2)×(LUMO)\nin 3 and the overlap density of (HOMO-1)×(LUMO) in 5. β-HOMO-2 and β-LUMO of 3 and β-\nHOMO-1 and β-LUMO of 5 are shown with an isovalue of 0.01.”\nFurthermore, we changed the sentences in revised manuscript regarding the TDM\ncontribution to kT because of the addition of the μ 2 contribution.\nr Tm-T1\nBefore revision: From lines 19 in p. 7 to line 9 in p. 8 in original manuscript\n“Finally, most importantly, the vertically introduced hetero-substituents have the\ncharacteristics of μ 2 collaborating with the maintained large <S |H |T >2 for the\nSn-S0 n SO 1\nenhanced phosphorescence (Fig. 3b, C). For instance, in 3, μ mostly contributing to\nS5-S0\nkT is small along the z axis because of the symmetry-forbidden nature of the overlap\nr\ndensity for the S –S transition (Ω ) in the x axis direction (Fig. 3b(v)). Owing to the\n5 0 S5\nsmall μ , the cooperativity between <S |H |T >2 and μ 2 becomes weak. In\nS5-S0 5 SO 1 S5-S0\ncontrast, μ 2 mostly contributing to kT of 5 is large because Ω has a symmetrically\nS3-S0 r S3\nallowed transition nature along the long-conjugated direction in the x axis (Fig. 3b(vi)).\nThe large μ 2 leads to strong μ 2 and <S |H |T >2 cooperation. As a result of the\nS3-S0 S3-S0 3 SO 1\nsmall <T |H |S >2 and strong cooperation between <S |H |T >2 and μ 2, selective\nenhancement of kT compared with k T is realized in 5. Previous horizontal substitution\nr nr\nin the π plane direction was unable to contribute to the TDM of the conjugated plane to\ntriplet radiation. The vertically introduced hetero-substituents have the characteristics to\neffectively utilize the conjugated plane for triplet radiation, which serves as a guideline\nfor the design of new organic phosphorescence π-conjugated molecules.”\nAfter revision: Lines 1–20 in p. 13 in revised manuscript\n“The cooperation between the high-order TDM and the maintained large <S |H |T > and\nn SO 1\n<T |H |S > contributes an additional factor to the maintenance of the large kT in the\nm SO 0 r\nsuppressed k T state in the multiple vertical hetero-substituted chromophores. For\nnr\ninstance, for 3, μ 2 is small because of the symmetry-forbidden nature of (HOMO-\nS5-S0\n2)×(LUMO) as the overlap density of the S –S transition along the extended π-\n5 0\nconjugation direction in the x axis (Fig. 6a(i)). As well as the S –S transition, 3 has a\n5 0\nsymmetry-forbidden nature along the extended π-conjugation in the T –T transition,\n7 1\nwhich prevents a large enhancement of μ 2 (Fig. 6a(ii)). The horizontal hetero-\nT7-T1\nsubstituents therefore lead to cancellation of the large TDMs originating from the π-\nextended framework, weakening the <S |H |T >2 and μ 2 cooperation and\n<T |H |S >2 and μ 2 cooperation. In contrast, for 5, μ 2 and μ 2 are large\nbecause both the S –S and T –T transitions are constructed from the symmetrically\n2 0 9 1\nallowed nature along the long π-conjugation direction (Fig. 6b(i) and (ii)). The large\nTDMs enable strong cooperativities between μ 2 and <S |H |T >2, and between μ\nS2-S0 2 SO 1 T9-\n2 and <T |H |S >2. As a result of the strong cooperativities and suppressed\nT1 9 SO 0\n<T |H |S >2, selective enhancement of kT compared with k T is realized for 5. In\nprevious strategies featuring horizontal hetero-substitutions, the extended π-conjugation\ncould not be effectively utilized for the triplet radiation. The vertical hetero-substituent\nstrategy can activate the long π conjugation system for triplet radiation, which serves as\na guideline for the design of new organic phosphorescence π-conjugated molecules.”\nNext, we changed the calculation procedure in Methods section because of the\nchange in the calculation methods.\nBefore revision: Lines 5–7 in p. 12 in original manuscript\n“Using the optimized T geometry, the SOC elements and μ were calculated using the\nAmsterdam Density Functional (ADF) 2018 package with the PBE0 functional and TZP\nbasis set (see the Supplementary Information).”\nAfter revision: Lines 5–11 in p. 19 in revised manuscript\n“Using the optimized T geometry, the SOC elements, μ , and μ were calculated\nusing the Amsterdam Density Functional (ADF) 2025 package with the PBE0 functional\nand TZP basis set. The molecular orbitals associated with μ were estimated by time-\nTm-T1\ndependent DFT (TD-DFT) calculation with the Gaussian09 program using the PBEPBE\nfunctional and 6-311G(d,p) basis set. In the TD-DFT calculations, the option\niop(3/76=1000002500) was applied to adjust the fraction of the Hartree–Fock exchange\nto be consistent with the PBE0 functional.”\nIn addition, we changed the calculation result regarding T optimized geometry in\n1\nsupplementary information because of the change in the calculation methods.\nBefore revision: Section 2 in original supplementary information\n“2. T optimized geometry of chromophores estimated by theoretical calculation\n1\ndetermined by Gaussian09 program based on the density functional theory (DFT) using\nT optfreq mode. In the calculation, B3LYP and 6-311G+(d,p) were used as a functional\n1\nand a basis set, respectively. In T optimized structure of 2 and 3, Se atom is horizontally\n1\nattached to DBC moiety. In 4 and 5, where naphthalene is introduced as a spacer unit, Se\natom is vertically placed on DBC because DBC and naphthalene unit are twisted by the\nsteric hindrance.\nFig. S13. T optimized structures of 1–5.”\n“2. T optimized geometry of chromophores estimated by theoretical calculation\n1\n(Figure S15)\nThe optimized structures of the lowest triplet excited state (T ) of 1–5 (Fig. S15) were\n1\ndetermined by Gaussian09 program based on the density functional theory (DFT).\nIn the\ncalculation, B3LYP and 6-311G+(d,p) were used as a functional and a basis set,\nrespectively. In T optimized structure of 2 and 3, Se atom is horizontally attached to\n1\ndibenzo[g,p]chrysene (DBC) moiety. In 4 and 5, where naphthalene is introduced as a\nspacer unit, Se atom is vertically placed on DBC because DBC and naphthalene unit are\ntwisted by the steric hindrance\nFig. S15. T optimized structures of 1–5.”\nregarding the correlation between the measured and calculated kT as well as the measured\nr\nk T and calculated <T |H |S >2 because of the change in the calculation methods.\nnr 1 SO 0\nBefore revision: Section 5-1 in original supplementary information\n“5-1. Calculated values of k T and <T |H |S >2\nr 1 SO 0\nCalculation procedure of T optimized structure for 1–5 were described in supplementary\n1\nsection 2. Using the T optimized structure (Fig. S13), single-point calculations were\n1\nperformed using the time-dependent (TD) DFT with the Amsterdam Density Functional\n(ADF) 2018 package to calculate kT and the spin–orbit coupling (SOC) between T and\nr 1\nS (<T |H |S >). The parameter <S |H |T > was treated as a perturbation based on\n0 1 SO 0 n SO 1\nscalar relativistic orbitals using the PBE0 as a functional and TZP as a basis sets. The\nscalar relativistic-time-dependent DFT calculations included 10 singlet and 10 triplet\nexcitations, which were used as the basis for the perturbative expansions in the\ncalculations.\nFrom the above calculations, the good correlation between calculated kT and\nr\nmeasured kT (Fig. S21a) and between calculated <T |H |S >2 and measured k T (Fig.\nr 1 SO 0 nr\nS21b) were observed. From 2 to 3, the magnitude of calculated kT enhancement (Fig.\nr\nS21a, blue arrow) was smaller than that of <T |H |S >2 enhancement (Fig. S21b, blue\narrow). In contrast, from 4 to 5, calculated kT was more enhanced compared with\nr\n<T |H |S >2 (Figs. S21a and S21b, red arrows). Thus, the more selective enhancement\nof kT compared with k T of 5 was observed from theoretical calculations as well as optical\nr nr\nmeasurements. Therefore, the discussion on the differences in measured kT and k T based\nr nr\non the quantum chemical calculation was reasonable.\nFig. S21. Relationship between measured and calculated parameters relating phosphorescence process.\na, Correlation between measured and calculated kT. b, Correlation between measured k T and\nr nr\ncalculated <T |H |S >2.”\nAfter revision: Section 5-1 in revised supplementary information\n“5-1. Calculated values of k T and <T |H |S >2 (Figure S24)\nr 1 SO 0\nCalculation procedure of T optimized structure for 1–5 were described in supplementary\n1\nperformed using the time-dependent (TD) DFT with the Amsterdam Density Functional\n(ADF) 2025 package to calculate kT and the spin–orbit coupling (SOC) between T and\nr 1\nS (<T |H |S >). The parameter <S |H |T > and <T |H |S > were treated as a\n0 1 SO 0 n SO 1 m SO 0\nperturbation based on scalar relativistic orbitals using the PBE0 as a functional and TZP\nas a basis sets. The scalar relativistic-time-dependent DFT calculations included 10\nsinglet and 10 triplet excitations, which were used as the basis for the perturbative\nexpansions in the calculations.\nFrom the above calculations, the good correlation between calculated <T |H |S >2\nand measured k T (Fig. S24a) and between calculated kT and measured kT (Fig. S24b)\nnr r r\nwere observed among synthesized chromophores. From 2 to 3, the magnitude of\ncalculated kT enhancement (Fig. S24b, blue arrow) was smaller than that of <T |H |S >2\nr 1 SO 0\nenhancement (Fig. S24a, blue arrow). In contrast, from 4 to 5, calculated kT was more\nr\nenhanced compared with <T |H |S >2 (Figs. S24a and S24b, red arrows). Thus, the more\nselective enhancement of kT relative to k T of 5 was observed from theoretical\nr nr\ncalculations as well as optical measurements. Therefore, the discussion on the differences\nin measured kT and k T based on the quantum chemical calculation is reasonable.\nr nr\nFig. S24. Relationship between measured and calculated parameters relating phosphorescence process.\na, Correlation between measured k T and calculated <T |H |S >2. b, Correlation between measured\nnr 1 SO 0\nand calculated kT.”\nr\nAdditionally, we changed the calculated parameters in revised supplementary\ninformation relating to the kT due to the change of calculation methods and addition of\nr\nthe T contribution.\nm\nBefore revision: Section 5-3 in original supplementary information\n“5-3. Calculated parameters relating to k T\nr\nThe formula for kT can be expressed approximately as the following equations6,7.\nr\nkT ≈ Σ (μ <S |H |T >)2, (S5)\nr n Sn-S0 n SO 1\nλ = <S |H |T >/E , (S6)\nn n SO 1 Sn-T1\nwhere μ is the transition dipole moment between nth order singlet excited states (S )\nSn-S0 n\nand S , <S |H |T > is the SOC between S and T , E is the energy difference between\n0 n SO 1 n 1 Sn-T1\nS and T . Based on the equations (S5) and (S6), good correlation between calculated and\nn 1\nmeasured kT was reported in many π-conjugated molecules[1,3,5,7–13]. Therefore, the\nr\ncontributions of μ 2 and <S |H |T >2 to kT were discussed to explain the selective kT\nSn-S0 n SO 1 r r\nenhancement of 5 in main text.\nThe calculated values of μ 2λ 2 (Figs. S23a–S23d, top) indicate that n = 6, n = 5, n\nSn-S0 n\n= 9, n = 3 are mainly contributing to the kT for 2, 3, 4, and 5, respectively. In 2 with a\nr\nhorizontal selenium substitution, μ 2λ 2 is small due to the small <S |H |T >2 (Fig.\nS6-S0 6 6 SO 1\nS23a). In 3 with the multiple introductions of horizontal substituents, <S |H |T >2 for\nn SO 1\neach n were increased overall compared with that of 2 (Fig. S23b). Additionally, the μ\nSn-\n2 for n = 1, 4, 6 are large compared with that of 2 due to expansion of π-conjugation\nS0\nhorizontally. However, the cooperativity of μ 2 and <S |H |T >2 at n = 5 where\nSn-S0 n SO 1\nmainly contributes to kT is weak because of the small μ 2. For multiple vertical\nr S5-S0\nsubstituents, <S |H |T >2 of 5 is still large and not drastic decreased compared with\n<S |H |T >2 of 3 (Fig. S23d). Meanwhile, μ 2 of 5 is larger than μ 2 of 3. Thus,\nquantum chemical calculations confirm the strong cooperation between μ 2 and\nSn–S0\n<S |H |T >2 in 5.\nn SO 1\nFig. S23. Histograms of μ 2λ 2 (top), <S |H |T >2 (middle), and μ 2 (bottom) for each n = 1 to\nSn-S0 n n SO 1 Sn-S0\n10. a, Chromophore 2. b, Chromophore 3. c, Chromophore 4, d, Chromophore 5.”\nAfter revision: Section 5-4 in revised supplementary information\n“5-4. Calculated parameters relating to k T (Figure S27)\nr\nThe calculated values of <S |H |T >2E –2μ 2 are the largest at n = 6, n = 5, n = 7,\nn SO 1 Sn–T1 Sn-S0\nand n = 2 for 2, 3, 4, and 5, respectively (Fig. S27a). Accordingly, these n mostly\ncontribute to the first term of equation (4) for chromophores 2–5, respectively. For the\nsecond term of equation (4), the largest value of <T |H |S >2E –2μ 2 indicate that\nm SO 0 Tm–S0 Tm-T1\nm = 9, m = 7, m = 5, and m = 9 dominantly contribute to kT for 2, 3, 4, and 5, respectively\nr\n(Fig. S27b).\nFig. S27. Histograms of calculated parameters relating to kT. a, Histograms of <S |H |T >2E –\nr n SO 1 Sn–T1\n2μ 2 (top), <S |H |T >2 (middle), and μ 2 (bottom) for 2–5. b, Histograms of <T |H |S >2E\nSn-S0 n SO 1 Sn-S0 m SO 0 Tm–\n–2μ 2 (top), <T |H |S >2 (middle), and μ 2 (bottom) for 2–5.”\nS0 Tm-T1 m SO 0 Tm-T1\n(Comment 2 from Reviewer 1)\nThe manuscript attributes the increase in k_r^T to the cooperative interplay between\nμ_Sn–S0 and ⟨Sₙ|H_SO|T₁⟩. A critical question remains: is the main driving force the\nintrinsic heavy-atom effect of Se, or the optimization of orbital overlap and spatial\ndistribution of frontier orbitals? From Fig. 3 it is clear that HOMO–LUMO overlap differs\nsignificantly between substituent patterns. I recommend further quantitative comparison,\nfor instance by replacing Se with lighter congeners (S or O) to clarify whether the\nenhanced k_r^T originates predominantly from heavy-atom SOC or orbital overlap\neffects.\n(Response)\nThank you for your critical comments. We consider that the heavy atom effect (HAE) is\nnot the driving force behind the different RTP properties between substituent patterns.\nThe formula for spin-orbit coupling itself expresses the HAE and other effects separately.\nHowever, it may be often intended for mathematicians and physicists, and does not\ninclude diagrams or other explanations to make it easy to understand for people in a wide\nrange of fields. Therefore, we first revised it to explain the effects of increasing SOC from\nthree different perspectives: the orbital overlap term, the HAE term, and the orbital\norientation term related to the orbital angular momentum vector.\nFirst, we would like to introduce the factors governing magnitude of SOC, using\nk T as an example. The k T is generally expressed as (Chem. Phys. Lett. 16, 353–358\nnr nr\n(1972)),\n𝑘T = 2𝜋 ⟨T |𝑯 |S ⟩2𝐹𝐶, (R1-3)\nnr 1 SO 0\nℏ\nwhere, FC is the Franck-Condon factor between T and S . The first factor that changes\n1 0\n<T |H |S >2 is the overlap of the orbitals. <T |H |S >2 increases when the overlap of\nthe orbitals involved in the two transition is large (Fig. R4(i)). H is expressed as (Chem.\nSO\nRev. 66, 199–241 (1966); J. Phys. Chem. A 111, 10490–10499 (2007); Chem. Rev. 117,\n6500–6537 (2017)),\n𝑯 = 𝛼2∑ ∑ 𝑍𝐴 𝑙⃗ 𝑠⃑ , (R1-4)\nSO 𝐴 𝑖 𝑟𝐴𝑖 3 𝐴𝑖 𝑖\nwhere α is the fine structure constant, A indicates the nucleus, i indicates the electron, Z\nis the atomic number, r is the electron–nucleus distance, 𝑙⃗ is the orbital angular\nmomentum, and 𝑠⃗ is the spin angular momentum. The second factor that changes\n<T |H |S >2 is the distance between the heavy atoms and the overlap site of the orbitals\ninvolved in the T –S transition. The\n𝑍𝐴\nterm in equation (R1-4) means that\n1 0\n𝑟𝐴𝑖 3\n<T |H |S >2 increases when the heavy atoms are closer to the overlap site of the orbitals\ninvolved in the T –S transition (Fig. R4(ii)). This is the contribution of the increase in\n1 0\n<T |H |S >2 owing to the introduction of heavier atoms, that is, HAE. The third factor\nthat changes <T |H |S >2 is the relative orientation of the molecular orbitals. 𝑙⃗ 𝑠⃑ in\nequation (R1-4) means that <T |H |S >2 increases when the axes of the two orbitals\ninvolved in the overlapping region point in different directions (Fig. R4(iii)). This\nenhancement of the SOC by this term is known as the El-Sayed rule (J. Chem. Phys. 38,\n2384–2938 (1963)). Thus, the three factors of the orbital overlap, HAE, and the orbital\norientation characteristics govern the magnitude of <T |H |S >2.\nFig. R4 Schematic illustration of the parameters affecting <T |H |S >2: the (i) orbital overlap,\n(ii) heavy atom effect (HAE), and (iii) orbital orientation.\nAlthough we mentioned that the orbital orientation feature is an important factor\nfor the SOC strength, the following points should be clarified to avoid potential\nmisinterpretation. Transitions between singlet and triplet states necessarily involve a\nchange in 𝑠⃗ . According to the conservation of total angular momentum, such a spin\nconversion must be accompanied by the change in 𝑙⃗ (ΔL). The resulting ΔL exserts a\ntorque on the electron, thereby promoting spin flipping. The magnitude of ΔL depends on\nthe vector cross product of the respective 𝑙⃗ (Acc. Chem. Res. 55, 1573–1585 (2022)).\nTherefore, understanding the direction of the 𝑙⃗ is essential when discussing the\nelectronic transitions that require spin flipping.\nThe orbital orientation axis is directly related to orientation of 𝑙⃗ . In case of p\nz\norbital, 𝑙⃗ exhibits an effective component within the xy-plane (Fig. R5a(i)). When the\nprojection component is considered, 𝑙⃗ is oriented perpendicular to the orbital orientation\naxis (Fig. R5a(ii)). When two orbitals are oriented along the same axis, their\ncorresponding 𝑙⃗ are aligned in the same direction (Fig. R5b(i)). In this case, ΔL becomes\nnegligible, and no torque is generated to induce spin flip (Fig. R5b(ii)). Conversely, ΔL\nincreases when the two orbitals are oriented in different directions and reaches a\nmaximum when their orbital orientation axes are perpendicular (Fig. R5b(iii)). Under\nthese conditions, the electron experiences a large torque, which strongly promotes the\nspin-flip process (Fig. R5b(iv)). Therefore, discussing changes in orbital orientation axis\nis effectively equivalent to discussing the orientation and magnitude of ΔL, providing\nan intuitive approach for visualizing the magnitude of SOC.\nFig. R5 a, Relationship between (i) atomic orbital and effective component of 𝑙⃗ and (ii) orbital\norientation axis and projected component of 𝑙⃗. b, Schematic illustrations of (i) two orbitals have the\nsame orientation axis, (ii) the absence of torque generation for spin flipping, (iii) two orbitals oriented\nalong different axes, and (iv) the electron experiencing a large torque that promotes spin flipping. In\npanels (ii) and (iv), B and μ represent the effective magnetic field generated by 𝑙⃗ and the electron\neff S\nspin magnetic momentum, respectively.\nThe use of the three factors of the orbital overlap, HAE, and the orbital orientation,\nhelps us understand the reason for the significantly suppressed k T of 5 compared with\nnr\nthat of 3 (energy diagrams in Fig. R6, left). First, in terms of the orbital overlap, different\nFig. R6 a, Molecular orbitals and schematic illustrations related to the (i) orbital overlap, (ii) HAE,\nand (iii) orbital orientation to explain the smaller k T of 5 than 3. In (iii), white arrows represent the\nnr\norbital orientation axes. The isovalues of the HOMO of 3, LUMO of 3, and HOMO of 5 are 0.018.\nThe isovalue of 0.0072 is used for the LUMO of 5. Because the probability of the existence of the\nLUMO near Se in 5 is extremely small, the isovalue is set small to express the very small existence.\namounts of orbital overlap are confirmed between 3 and 5. In both 3 and 5, HOMO and\nLUMO mainly contribute to the T –S transition. In 3, HOMO and LUMO largely overlap\n1 0\naround Se atom (Fig. R6(i), top). Meanwhile, the much smaller overlap between HOMO\nand LUMO was confirmed in 5 (Fig. R6(i), bottom). Therefore, the contribution of orbital\noverlap factor to <T |H |S >2 is suppressed in 5 compared with 3. Second, regarding\nHAE factor, the Se atom is often considered to be the heavy atom source for the HAE and\nit is widely used for organic phosphorescence materials. However, the difference in the\n<T |H |S >2 values between 3 and 5 cannot be well explained by the HAE contribution\nbecause both the distance between Se atom and HOMO-LUMO overlap sites does not\nsignificantly differ between 3 and 5 (Fig. R6(ii)). Third, regarding the orbital orientation\nfactor that changes <T |H |S >, the orbital orientation on the Se atoms differs between\nthe HOMO and LUMO of 3 (Fig. R6(iii), top). Because the HOMO and LUMO on the\nSe atoms also exhibit different orientations for 5 (Fig. R6(iii), bottom), the orbital\norientation factor does not well explain the different <T |H |S >2 values between 3 and\n5. Therefore, the spatial overlap between the HOMO and LUMO on Se mainly causes the\nsmaller <T |H |S >2 of 5 than 3, suppressing the increase k T for 5 compared with that\nfor 3. Thus, consideration of the orbital overlap, HAE, and orbital orientation factors\nprovide us with an understanding of the different characteristics of <T |H |S >2.\nThe argument for dividing SOC into three parts, orbital overlap, HAE, and orbital\norientation, also worked for the <S |H |T > related to kT as explained below. First,\nn SO 1 r\nregarding the orbital overlap factor, magnitude of <S |H |T > logically increases as the\nn SO 1\noverlap between the orbital overlap density related to the S –S transition and the orbital\nn 0\noverlap density related to the T –S transition increases. For 3, <S |H |T > significantly\n1 0 5 SO 1\ncontributes to the increase in kT, but the overlap density of the S –S transition [(HOMO-\nr 5 0\n2)×(LUMO)] only slightly overlaps with that of the T –S transition [(HOMO)×(LUMO)]\n1 0\nbetween C and Se (green open circle at the top of Fig. R7(i)). Although <S |H |T >\nsignificantly contributes to the increase in kT for 5, similarly, the overlap density of the\nr\nS –S transition [(HOMO-1)×(LUMO)] only has a small overlap with that of the T –S\n2 0 1 0\ntransition [(HOMO)×(LUMO)] as a through-space interaction between C and Se (green\nopen circle at the bottom of Fig. R7(i)). Therefore, the comparable poor orbital overlap\nhardly changes <S |H |T > between 3 and 5. Second, regarding the contribution of the\nn SO 1\nHAE to increasing <S |H |T >, the distance between the overlapping site and Se does\nn SO 1\nnot significantly change between 3 and 5 (Fig. R7(ii)). Therefore, the effect of the HAE\ndoes not result in a driving force that significantly differentiates between <S |H |T > of\n3 and <S |H |T > of 5. Third, regarding the contribution of the orbital axis orientation\nto the change in <S |H |T >, for 3, the orbital axes of the (HOMO-2)×(LUMO) and\nn SO 1\n(HOMO)×(LUMO) are in different directions (Fig. R7(iii), top). Similarly, for 5, the\norbital axis of the through-space type (HOMO-1)×(LUMO) formed between Se and C is\ndifferent from that of the (HOMO)×(LUMO) on DBC (Fig. R7(iii), bottom). Therefore,\nthe orbital axis orientation hardly changes <S |H |T > between 3 and 5. Therefore, these\nn SO 1\nsimilar tendencies regarding the spatial overlap characteristics, HAE, and orbital\norientation increases <S |H |T >2 of 5 to a comparable value to <S |H |T >2 of 3.\nFig. R7 Molecular orbitals and schematic illustrations showing that <S |H |T >2 of 3 (top) and\n<S |H |T >2 of 5 (bottom) have comparable magnitudes. Panels (i), (ii), and (iii) represent the orbital\noverlap, HAE, and orbital orientation effect, respectively. The white arrows in (iii) represent the orbital\naxis orientations. The isovalues of the overlap density regarding (HOMO-2)×(LUMO) and\n(HOMO)×(LUMO) for 3 and (HOMO-1)×(LUMO) and (HOMO)×(LUMO) for 5 are 0.00011.\nIn addition, the argument for dividing SOC into three parts, orbital overlap, HAE,\nand orbital orientation, also worked for the <T |H |S > related to kT as following\nm SO 0 r\nexplanation. First, the orbital overlapping feature, the T –S transition in 3 is mainly\n7 0\ncomposed of HOMO-3 and LUMO, and the T\n9\n–T\n1\ntransition in 5 is composed of HOMO-\n2 and LUMO. The spatial overlap between HOMO-3 and LUMO on Se in 3 (green open\ncircles at the top of Fig. R8a(i)) is larger than the through-space overlap density between\nHOMO-2 and LUMO formed between Se and C in 5 (green open circle at the bottom of\nFig. R8(i)). Therefore, the contribution of the orbital overlap term to the enhancement of\n<T |H |S > for 3 is larger than that to the enhancement of <T |H |S > for 5. Second, in\nterms of HAE contribution, the distance between the HOMO-3 and LUMO overlap sites\nand Se for 3 is smaller than that between HOMO-2 and LUMO overlap site and Se for 5\n(Fig. R8(ii)). Therefore, for 3, the HAE plays a role in increasing <T |H |S >.\nm SO 0\nThird, in\nrespect to orbital orientation, the orbital axis directions of the HOMO-3 and LUMO on\nthe Se atoms slightly differ for 3 (Fig. R8(iii), top). However, for 5, the orbital axis\ndirection of the HOMO-2 of Se significantly differs from that of the LUMO of C on DBC\n(Fig. R8(iii), bottom). Therefore, the contribution of the orbital orientation term to the\nenhancement of <T |H |S > for 3 is smaller than that to the enhancement of <T |H |S >\nin 5. Considering these three factors, the decrease in <T |H |S > due to the poor orbital\noverlap and HAE for 5 is compensated for by the increase in <T |H |S > due to the\norbital orientation, which results in <T |H |S >2 for 5 being equivalent to <T |H |S >2\nfor 3.\nFig. R8 Molecular orbitals and schematic illustrations explaining the comparable magnitudes of\n<T |H |S >2 for 3 (top) and <T |H |S >2 for 5 (bottom). Panels (i), (ii), and (iii) represent the orbital\noverlap, HAE, and orbital orientation effect, respectively. The white arrows in (iii) represent the orbital\naxis orientations. The isovalue of 0.013 is used for HOMO-3 and LUMO of 3 and HOMO-2 and\nLUMO of 5.\nAs explained in our response on pages 23 to 25, the factors that change the SOC\nrelated to k T can be considered separately as HAE and other two terms. The SOC related\nnr\nto kT can also be considered separately as HAE and other two terms. In vertical hetero-\nr\nsubstitutions such as 5, the overlap of orbitals with two different orientations related to\nthe T 1–S\n0\ntransition cannot occur near the heteroatom, making it difficult to enhance\n<T |H |S >2 ∝ k T. On the other hand, in vertical hetero-substitution, orbitals with two\ndifferent orientation axes related to <S |H |T >2 and <T |H |S >2 overlap as through-\nn SO 1 m SO 0\nspace states near the heteroatom, resulting in a more selective enhancement of\n<S |H |T >2 and <T |H |S >2 over <T |H |S >2. Thus, because the overlap of orbitals\nn SO 1 m SO 0 1 SO 0\nand the orientation of the orbitals that make up the overlap cause the difference in the\nincrease in kT and k T, the HAE effect does not directly contribute significantly to the\nr nr\nincrease in kT relative to k T.\nr nr\nHowever, as Reviewer 1 pointed out, the comparison between Se and S is crucial\nfor evaluating the HAE contribution. Following your suggestion, we synthesized R1 as a\nreference chromophore with replacement of Se atoms of 5 with S atoms (Fig. R9, right).\nThe Φ of R1 was 10.4%, which is lower than that of 5 (= 27%). The kT and k T of R1\np r nr\nwere determined to be 0.28 s–1 and 2.1 s–1, respectively. Since kT and k T of 5 are 6.1 s–1\nr nr\nand 16 s–1, respectively, kT largely decreases compared with k T depending on the change\nr nr\nfrom 5 to R1 (Fig. R9).\nFig. R9 Chemical structures and optically determined values of kT and k T for 5 (left) and R1 (right).\nr nr\nThe decrease in kT relative to k T of R1 compared with 5 could be confirmed from\nr nr\nthe differences in the balance between <T |H |S >2 and <S |H |T >2. Quantum\nchemical calculation revealed that <S |H |T >2 mainly contributes to kT of R1. In R1,\nthe <S |H |T >2 is slightly smaller than <T |H |S >2 (arrow in Fig. R10a), while in 5,\n<S |H |T >2 is much larger than <T |H |S >2 (arrow in Fig. R10b). This calculation\nresults regarding balance of <T |H |S >2 and <S |H |T >2 indicate that some factors are\npreventing <S |H |T >2 from increasing in R1.\nThe perspective of the orbital overlap, HAE, orbital orientation factor provided a\nreason for the small <S |H |T >2 of R1. First, regarding orbital overlap as a factor that\nchanging <S |H |T >, for R1, the overlap density of the S –S transition\nn SO 1 3 0\n[(HOMO)×(LUMO+1)] hardy overlaps with that of the T –S transition\n1 0\n[(HOMO)×(LUMO)] at through-space region between S and DBC (green open circle at\nthe top of Fig. R10c(i)). On the other hand, for 5, the overlap density of the S –S\n2 0\ntransition [(HOMO-1)×(LUMO)] well overlaps with that of the T –S transition\n1 0\n[(HOMO)×(LUMO)] at through-space site between Se and DBC (green open circle at the\nbottom of Fig. R10c(i)). Therefore, the contribution of the orbital overlapping term to\nenhancement of <S |H |T > for R1 is significantly smaller than that to enhancement of\n<S H |T > for 5. Second, the contribution from HAE, the distance between the overlap\nsite and Se does not significantly change between R1 and 5 (Fig. R10c(ii)). However, the\neffect of the HAE on 5 is larger than that on R1 due to the heavier atoms. Third, regarding\norbital orientation factor, for R1, the orbital axes of (HOMO)×(LUMO+1) and\n(HOMO)×(LUMO) are in different directions at through-space site (Fig. R10c(iii), top).\nSimilarly, for 5, the orbital axis of the through-space type (HOMO-1)×(LUMO) is\ndifferent from that of the (HOMO)×(LUMO) on DBC (Fig. R10c(iii), bottom). Therefore,\nthe orbital axis orientation hardly changes <S |H |T > between R1 and 5. When\nn SO 1\nconsidering these three factors, in 5, a through-space orbital overlap forms to selectively\nincreases <S |H |T >. Therefore, kT increases relative to k T, acting as the driving force\nn SO 1 r nr\nfor the enhancement of the phosphorescence yield. On the other hand, in R1, the orbital\noverlap effect to selectively enhance <S |H |T > is not fully achieved. Therefore, a large\nn SO 1\n<S |H |T > is not obtained, and kT does not increase significantly relative to k T.\nTherefore, the phosphorescence yield does not improve significantly. Thus, the\nexperimental and computational results regarding the replacement of Se with S indicates\nthat the orbital overlap term is a key to maintenance of large <S |H |T >.\nn SO 1\nFig. R10 a, Histogram of <T |H |S >2 and <S |H |T >2 for R1. b, Histogram of <T |H |S >2 and\n<S |H |T >2 for 5. c, Molecular orbitals and schematic illustrations related to (i) orbital overlap, (ii)\nHAE, and (iii) orbital orientation to explain the smaller <S |H |T >2 of R1 (top) compared with <S |H |T >2\nof 5 (bottom). The white arrows in (iii) represent the orbital axes orientations. The isovalues of the\noverlap density regarding (HOMO)×(LUMO+1) and (HOMO)×(LUMO) for R1 is 0.000055. The\nisovalue of 0.0001 is used for the overlap density regarding (HOMO-1)×(LUMO) and\n(HOMO)×(LUMO) for 5. When isovalue = 0.0001 is used for the overlap density regarding\n(HOMO)×(LUMO+1) and (HOMO)×(LUMO) for R1, no overlap region appears between Se and C.\nFrom the above, first of all, we added following Fig. 3a in revised manuscript to\nillustrate the three factors governing SOC.\nAfter revision: Fig. 3a in revised manuscript\nCaption of Figure 3a, Schematic illustration of the parameters affecting <T |H |S >2: the (i) orbital\noverlap, (ii) heavy atom effect (HAE), and (iii) orbital orientation.”\nFurthermore, we added the sentences in revised manuscript to explain the three\nfactors governing SOC.\nAfter revision: From line 15 in p. 6 to line 8 in p. 8 in revised manuscript\n“One reason for the enhancement of kT compared with k T for vertical hetero-\nr nr\nsubstitutions is that increasing the number of the vertical hetero-substitutions makes k T\nnr\nless likely to increase compared with common horizontal hetero-substitutions. k T is\nnr\ngenerally expressed as22,27\n𝑘T = 2𝜋 ⟨T |𝑯 |S ⟩2𝐹𝐶, (1)\nnr 1 SO 0\nℏ\nwhere <T |H |S > is the spin–orbit coupling (SOC) between T and the ground state (S ),\nH is the spin–orbit Hamiltonian, and FC is the Franck–Condon factor between T and\nSO 1\nS . FC contains the energy gap law, where k T increases as the phosphorescence is red-\n0 nr\nshifted28. Because the phosphorescence energies of 1–5 are comparable (Fig. 2c), the\nvariation of the k T values among 1–5 is expected to originate from differences in the\nnr\n<T |H |S >2 values. Indeed, quantum chemical calculations showed a good correlation\nbetween the optically determined k T values and calculated <T |H |S >2 values for 1–5\nnr 1 SO 0\n(supplementary Fig. S24a). Therefore, it is reasonable to attribute the difference in the\nk T values between 3 and 5 to their respective <T |H |S >2 values. The first factor that\nnr 1 SO 0\nchanges <T |H |S >2 is the overlap of the orbitals. <T |H |S >2 increases when the\noverlap of the orbitals involved in the two transitions is large (Fig. 3a(i)). H is expressed\nSO\nas6,29,30\n𝑯 = 𝛼2∑ ∑ 𝑍𝐴 𝑙⃗ 𝑠⃑ , (2)\nSO 𝐴 𝑖 𝑟𝐴𝑖 3 𝐴𝑖 𝑖\nwhere α is the fine structure constant, A indicates the nucleus, i indicates the electron, Z\nis the atomic number, r is the electron–nucleus distance, 𝑙⃗ is the orbital angular\nmomentum, and 𝑠⃗ is the spin angular momentum. The second factor that changes\n<T |H |S >2 is the distance between the heavy atoms and the overlap site of the orbitals\ninvolved in the T –S transition. The 𝑍𝐴 term in equation (2) means that <T |H |S >2\n1 0 1 SO 0\n𝑟𝐴𝑖 3\nincreases when the heavy atoms are closer to the overlap site of the orbitals involved in\nthe T –S transition (Fig. 3a(ii)). This is the contribution of the increase in <T |H |S >2\n1 0 1 SO 0\nowing to the introduction of heavier atoms, that is, the heavy atom effect (HAE). The\nthird factor that changes <T |H |S >2 is the relative orientation of the molecular orbitals.\n𝑙⃗ 𝑠⃑ in equation (2) means that <T |H |S >2 increases when the axes of the two orbitals\n𝐴𝑖 𝑖 1 SO 0\ninvolved in the overlapping region point in different directions (Fig. 3a(iii)). This\nenhancement of the SOC by this term is known as the El-Sayed rule31. When the two\norbital axes are in the same direction, no torque is generated to flip the spin because the\nelectron spin and magnetic moment are parallel (left of Fig. 3a(iii), supplementary Section\n5-2, and supplementary Fig. S25). Conversely, when the axes of the two orbitals are in\ndifferent directions, a torque that flips the spin is generated because the electron spin and\nmagnetic moment are not parallel (Fig. 3a(iii), right)32. Thus, the three factors of the\norbital overlap, HAE, and relative orientation of the molecular orbitals can be individually\nconsidered to discuss the difference in <T |H |S >2 ∝ k T between 3 and 5.”\nAdditionally, we added the relationship between orbital orientation and 𝑙⃗ in\nSection 5-2 in revised Supplementary information.\nAfter revision: Section 5-2 in revised supplementary information\n“5-2. Relationship between orbital orientation characteristics and spin flip (Figure\nS25)\nTransitions between singlet and triplet states necessarily involve a change in the spin\nangular momentum (𝑠⃗). According to the conservation of total angular momentum, such\na spin conversion must be accompanied by the change (ΔL) in the orbital angular\nmomentum (𝑙⃗). The resulting ΔL exserts a torque on the electron, thereby promoting spin\nflipping. The magnitude of ΔL depends on the vector cross product of the respective 𝑙⃗7.\nTherefore, understanding the direction of the 𝑙⃗ is essential when discussing the\nelectronic transitions that require spin flipping.\nThe orbital orientation axis is directly related to orientation of 𝑙⃗. In case of p orbital, 𝑙⃗\nz\nexhibits an effective component within the xy-plane (Fig. S25a(i)). When the projection\ncomponent is considered, 𝑙⃗ is oriented perpendicular to the orbital orientation axis (Fig.\nS25a(ii)). When two orbitals are oriented along the same axis, their corresponding 𝑙⃗ are\naligned in the same direction (Fig. S25b(i)). In this case, ΔL becomes negligible, and no\ntorque is generated to induce spin flip (Fig. S25b(ii)). Conversely, ΔL increases when the\ntwo orbitals are oriented in different directions and reaches a maximum when their orbital\norientation axes are perpendicular (Fig. S25b(iii)). Under these conditions, the electron\nexperiences a large torque, which strongly promotes the spin-flip process (Fig. S25b(iv)).\nTherefore, discussing changes in orbital orientation axis is effectively equivalent to\ndiscussing the orientation and magnitude of ΔL, providing an intuitive approach for\nvisualizing the magnitude of SOC.\nFig. S25. Relationship between orbital orientation characteristics and spin flip. a, Relationship\nbetween (i) atomic orbital and effective component of 𝑙⃗ and (ii) orbital orientation axis and projected\ncomponent of 𝑙⃗. b, Schematic illustrations of (i) two orbitals having the same orientation axis, (ii) the\nabsence of torque generation for spin flipping, (iii) two orbitals oriented along different axes, and (iv)\nthe electron experiencing a large torque that promotes spin flipping. In panels (ii) and (iv) of b, B\neff\nand μ represent the effective magnetic field generated by 𝑙⃗ and the electron spin magnetic\nS\nmomentum, respectively.”\nNext, we changed Fig. 3b(i) in original manuscript into following Fig. 3b in revised\nmanuscript to explain the differences in <T |H |S >2 between 3 and 5 using the orbital\noverlap, HAE, and the orbital orientation factors.\nBefore revision: Fig. 3b(i) and (ii) in original manuscript\nCaption of Figure 3b, Molecular orbitals and their calculated values relating (i) and (ii) <T |H |S >2,\n(iii) and (iv) <S |H |T >2, and (v) and (vi) μ 2. In (i) and (ii), the red-blue orbitals and orange-light\nn SO 1 Sn-S0\nblue orbitals are the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular\norbital (LUMO), respectively. In (iii) and (iv), the red-blue orbitals are Ω or Ω and the orange-light\nS3 S5\nblue orbitals are Ω . In (i)–(iv), the white arrows represent the orbital angular momentum (OAM)\nT1\nvectors. The isovalues of the HOMO of 3, LUMO of 3, and HOMO of 5 are 0.02. The isovalue of\n0.0085 is used for the LUMO of 5. The isovalues of Ω , Ω , and Ω are 0.00016.”\nS3 S5 T1\nAfter revision: Fig. 3b in revised manuscript\nCaption of Figure 3b, Molecular orbitals and schematic illustrations related to the (i) orbital overlap,\n(ii) HAE, and (ii) orbital orientation to explain the smaller k T of 5 than 3. In (iii) of a and b, the white\nnr\narrows represent the orbital orientation axes. The isovalues of the highest occupied molecular orbital\n(HOMO) of 3, lowest unoccupied molecular orbital (LUMO) of 3, and HOMO of 5 are 0.018. The\nisovalue of 0.0072 is used for the LUMO of 5. Because the probability of the existence of the LUMO\nnear Se in 5 is extremely small, the isovalue is set small to express the very small existence.”\nAdditionally, we changed the sentences in revised manuscript to discuss why\n<T |H |S >2 of 3 is significantly smaller than that of 5 using the three factors governing\nSOC.\nBefore revision: From line 20 in p. 6 to line 7 in p. 7 in original manuscript\n“First, compared with the horizontal hetero-substituents, the vertically introduced hetero-\nsubstituents suppress <T |H |S >2 (Fig. 3b, A). In 3, the highest occupied molecular\norbital (HOMO) and lowest unoccupied molecular orbital (LUMO) greatly overlap on\nthe Se atom and have different directions of the orbital angular momentum (OAM)\nvectors on Se (Fig. 3b(i)). Because the spin–orbit Hamiltonian involves the OAM\noperator that rotates the vector by 90°26, <T |H |S >2 increases when the HOMO and\nLUMO have large overlap and different directions of the OAM vectors. Therefore, 3 has\nlarge <T |H |S >2 owing to such molecular orbitals on Se. In 5, however, the spatial\noverlap of the HOMO and LUMO on Se is small, although the HOMO and LUMO have\ndifferent directions of the OAM vectors on Se (Fig. 3b(ii) and supplementary Fig. S22).\nOwing to the small overlap on Se, <T |H |S >2 of 5 is significantly smaller than that of\n3.”\nAfter revision: From line 9 in p. 8 to line 4 in p. 9 in revised manuscript\n“The suppression of the increase in k T with increasing number of vertical hetero-\nnr\nsubstitutions is due to the small overlap of the orbitals involved in the T –S transition.\n1 0\nRegarding the orbital overlap, the first factor that changes <T |H |S >2, the T –S\ntransition is predominantly composed of the highest occupied molecular orbital (HOMO)\nand lowest unoccupied molecular orbital (LUMO) for both 3 and 5 (supplementary Fig.\nS26). Because the spatial overlap between the HOMO and LUMO on Se of 5 is much\nsmaller than that of 3 (Fig. 3b(i)), the different amounts of orbital overlap contribute to\nthe different <T |H |S >2 values between 3 and 5. Regarding the HAE, the second factor\nthat changes <T |H |S >2 for 3 and 5, the Se atom is often considered to be the heavy\natom source for the HAE, and it is widely used for organic phosphorescence materials33–\n35. However, the large difference in the <T |H |S >2 values between 3 and 5 cannot be\nwell explained by the HAE contribution because the distance between the HOMO and\nLUMO overlap sites and Se does not significantly differ between 3 and 5 (Fig. 3b(ii)).\nRegarding the orbital orientation factor, the third factor that changes <T |H |S >2, the\norbital orientation on the Se atoms differs between the HOMO and LUMO of 3 (Fig.\n3b(iii), left). Because the HOMO and LUMO on the Se atoms also exhibit different\norientations for 5 (Fig. 3b(iii), right), the orbital orientation factor does not well explain\nthe different <T |H |S >2 values between 3 and 5. Therefore, the spatial overlap between\nthe HOMO and LUMO on Se mainly causes the smaller <T |H |S >2 of 5 than 3,\nsuppressing the increase of k T for 5 compared with that for 3.”\nnr\nIn addition, we changed the calculation result in revised supplementary information\nregarding the molecular orbitals relating to <T |H |S >2 because of the changes in the\ncalculation methods.\nBefore revision: Section 5-2 in original supplementary information\n“5-2. Molecular orbitals relating to <T |H |S >2\nThe T –S transition of 3 and 5 are mainly constructed from HOMO and LUMO (Figs.\n1 0\nS22a and S22b). Because 3 and 5 have similar nature in both HOMO and LUMO at DBC\nunit, the orbital’s nature around a Se atom were focused to explain the large difference in\n<T |H |S >2 between 3 and 5. In 3, HOMO and LUMO delocalize to Se atom (Fig. S22c).\nSimilarly, HOMO of 5 is delocalized on Se atoms. In LUMO of 5, however, a significantly\nsmall electron density at Se atom was observed and could not be confirmed using isovalue\nof more than 0.01 (Fig. S22d). Therefore, the spatial overlap between HOMO and LUMO\nof 5 is significantly small. Although the direction of the orbital angular momentum\n(OAM) vectors of HOMO and LUMO are comparable in both 3 and 5, the <T |H |S >2\nof 5 becomes smaller than that of 3 due to the small overlap between HOMO and LUMO\nas shown in (i) and (ii) of Fig. 3b in the main text.\nFig. S22. Differences in molecular orbitals relating to <T |H |S >2. a, HOMO and LUMO of 3. b,\nHOMO and LUMO of 5. c, HOMO (left) and LUMO (right) around a Se atom of 3. d, HOMO (left)\nand LUMO (right) around a Se atom of 5. In a) and b), isovalue of 0.02 is used for HOMO and LUMO.”\nAfter revision: Section 5-3 in revised supplementary information\n“5-3. Molecular orbitals relating to <T |H |S >2 (Figure S26)\nThe T –S transition of 3 and 5 are mainly constructed from HOMO and LUMO (Fig.\n1 0\nS26a, top and S26b, top). Because 3 and 5 have similar nature in both the HOMO and\nLUMO at DBC unit, the orbital’s nature around the Se atom were focused to explain the\nlarge difference in <T |H |S >2 between 3 and 5. For 3, HOMO and LUMO delocalize\nto Se atom (Fig. S26a, bottom). Similarly, HOMO of 5 is delocalized on Se atom.\nHowever, in LUMO of 5, a significantly small electron density at Se atom was observed\nand could not be confirmed using isovalue of more than 0.008 (Fig. S26b, bottom).\nFig. S26. Molecular orbitals relating to <T |H |S >2 for 3 and 5. a, HOMO and LUMO of 3. b,\nHOMO and LUMO of 5.”\nNext, we changed Fig. 3b(iii) and (iv) in original manuscript into Fig. 5 in revised\nmanuscript to add the T contribution and to discuss the <S |H |T >2 and <T |H |S >2\nm n SO 1 m SO 0\nusing the orbital overlap, HAE, and the orbital orientation factors. Because Reviewer 1\nrequested some considerations related to kT in higher triplet states, we have included that\nr\ninformation in Figure 5c in revised manuscript.\nBefore revision: Fig. 3b(iii) and (iv) in original manuscript\nCaption of Figure 3b, Molecular orbitals and their calculated values relating (i) and (ii) <T |H |S >2,\n(iii) and (iv) <S |H |T >2, and (v) and (vi) μ 2. In (i) and (ii), the red-blue orbitals and orange-light\nn SO 1 Sn-S0\nblue orbitals are the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular\norbital (LUMO), respectively. In (iii) and (iv), the red-blue orbitals are Ω or Ω and the orange-light\nS3 S5\nblue orbitals are Ω . In (i)–(iv), the white arrows represent the orbital angular momentum (OAM)\nT1\nvectors. The isovalues of the HOMO of 3, LUMO of 3, and HOMO of 5 are 0.02. The isovalue of\n0.0085 is used for the LUMO of 5. The isovalues of Ω , Ω , and Ω are 0.00016.”\nS3 S5 T1\nAfter revision: Fig. 5 in revised manuscript\nFig. 5 Difference in the factors governing <S |H |T >2 and <T |H |S >2 between horizontal\nn SO 1 m SO 0\nand vertical hetero-substituents. a, Simplified expression of the kT equation. b, Molecular orbitals\nr\nand schematic illustrations showing that <S |H |T >2 of 3 (top) and <S |H |T >2 of 5 (bottom) have\ncomparable magnitudes. The isovalues of the overlap density regarding (HOMO-2)×(LUMO) and\n(HOMO)×(LUMO) for 3 and (HOMO-1)×(LUMO) and (HOMO)×(LUMO) for 5 are 0.00011. c,\nMolecular orbitals and schematic illustrations explaining the comparable magnitudes of <T |H |S >2\nfor 3 (top) and <T |H |S >2 for 5 (bottom). The isovalue of 0.013 is used for HOMO-3 and LUMO\nof 3 and HOMO-2 and LUMO of 5. In b and c, panels (i), (ii), and (iii) represent the orbital overlap,\nHAE, and orbital orientation effect, respectively. The white arrows in (iii) represent the orbital axis\norientations.”\nAdditionally, we changed the sentences in revised manuscript to discuss why\n<S |H |T >2 of 3 were maintained up to that of 5 using the three factors governing SOC.\nn SO 1\nBefore revision: Lines 8–18 in p. 7 in original manuscript\n“Next, multiple vertically introduced hetero-substituents maintain <S |H |T >2,\nn SO 1\nenhancing kT to a comparable magnitude to <T |H |S >2 (Fig. 3b, B). In 3 and 5, n = 5\nr 1 SO 0\nand n = 3 mainly enhance kT, respectively (supplementary Fig. S23). In 3, <S |H |T >2\nr 5 SO 1\nfor the driving force of kT greatly decreases compared with the large <T |H |S >2 (Fig.\nr 1 SO 0\n3b(iii)). In contrast, <S |H |T >2 for the driving force of kT increases compared with the\nsmall <T |H |S >2 in 5. In 5, the overlap density for the S –S transition (Ω ) composed\nof HOMO-1 and LUMO forms a through-space interaction between Se and C of DBC\n(Fig. 3b(iv), green open circle, and supplementary Fig. S24b). Because this partially\noverlaps with the overlap density for the T –S transition (Ω ) of C on DBC, the spatial\n1 0 T1\noverlap with different OAM directions for Ω and Ω between the Se and C atoms\nS3 T1\nresults in the sufficient <S |H |T >2 in 5 (Fig. 3b(iv)).”\nAfter revision: From line 21 in p. 10 to line 2 in p. 12 in revised manuscript\n“<S |H |T >2 of the multiple vertical hetero-substituted chromophore approaching that\nn SO 1\nof the multiple horizontal hetero-substituted chromophore can be understood by\nconsidering the following three factors, which are the same factors as those explained the\nSOC regarding k T in Fig. 3a. First, regarding the overlap of the orbitals before and after\nnr\nthe transition that increases <S |H |T > in equation (4), <S |H |T > logically increases\nn SO 1 n SO 1\nas the overlap between the orbital overlap density related to the S –S transition and the\nn 0\norbital overlap density related to the T –S transition increases. For 3, <S |H |T >\n1 0 5 SO 1\nsignificantly contributes to the increase in kT, but the overlap density of the S –S\nr 5 0\ntransition [(HOMO-2)×(LUMO)] only slightly overlaps with that of the T –S transition\n1 0\n[(HOMO)×(LUMO)] between C and Se (green open circles at the top of Fig. 5b(i) and\nsupplementary Fig. S32a). Although <S |H |T > significantly contributes to the increase\nin kT for 5, similarly, the overlap density of the S –S transition [(HOMO-1)×(LUMO)]\nr 2 0\nonly has a small overlap with that of the T –S transition [(HOMO)×(LUMO)] as a\n1 0\nthrough-space interaction between C and Se (green open circle at the bottom of Fig. 5b(i)\nand supplementary Fig. S32b). Therefore, the comparable poor orbital overlap hardly\nchanges <S |H |T > between 3 and 5. Second, regarding the contribution of the HAE to\nn SO 1\nincreasing <S |H |T > in equation (4), the distance between the overlapping site and Se\nn SO 1\ndoes not significantly change between 3 and 5 (Fig. 5b(ii)). Therefore, the effect of the\nHAE does not result in a driving force that significantly differentiates between\n<S |H |T > of 3 and <S |H |T > of 5. Third, regarding the contribution of the orbital\naxis orientation to the change in <S |H |T >, for 3, the orbital axes of (HOMO-\nn SO 1\n2)×(LUMO) and (HOMO)×(LUMO) are in different directions (Fig. 5b(iii), top).\nSimilarly, for 5, the orbital axis of the through-space type (HOMO-1)×(LUMO) formed\nbetween Se and C is different from that of the (HOMO)×(LUMO) on DBC (Fig. 5b(iii),\nbottom). Therefore, the orbital axis orientation hardly changes <S |H |T > between 3\nn SO 1\nand 5. Therefore, these similar tendencies regarding the spatial overlap characteristics,\nHAE, and orbital orientation increases <S |H |T >2 of 5 to a comparable value to\n<S |H |T >2 of 3. When the Se atoms in 5 are replaced with S atoms, the enhancement\nof <S |H |T >2 becomes small owing to the lack of an orbital overlap factor\nn SO 1\n(supplementary Figs. S13 and S33–S35, and Table S4).”\nNext, we added the following sentence regarding properties of R2 in revised\nmanuscript.\nAfter revision: Lines 10–12 in p. 10 in revised manuscript\n“This characteristic was also confirmed for chromophores with a horizontal phenylseleno\nsubstituent at the 3-position of DBC, and Φ of the chromophore was indeed small\np\n(supplementary Figs. S14 and S29–S31, and Table S3).”\nAdditionally, we added the synthesis procedure and characterization data of R2 in\nSection 1 in revised supplementary information.\nAfter revision: Section 1 in revised supplementary information\n“Dibenzo[g,p]chrysene-3-yl(phenyl)selane (R2):\n9-Fluorenone (1.35 g, 7.50 mmol), 2-bromo-9-fluorenone (648 mg, 2.50 mmol), zinc\n(4.21 g, 64.4 mmol), and zinc chloride (2.73 g, 20.0 mmol) in tetrahydrofuran (25 ml)\nand pure water (25 ml) was stirred at room temperature for 4 h. After completion of the\nreaction, dichloromethane was added to the reaction solution and filtrated to remove the\nundissolved solid. Pure water was added to the solution and extracted with\ndichloromethane. The organic layer was dried over anhydrous Na SO and evaporated\n2 4\nunder reduced pressure to give a white powder (2.09 g). The powder (2.09 g) in acetic\nacid (35.5 ml) and sulfuric acid (1.8 ml) was heated at 85 °C for 4 h. After cooling to\nroom temperature, dichloromethane was added to the reaction mixture and washed with\npure water and extracted with dichloromethane. The organic layer was dried over\nanhydrous Na SO and concentrated under reduced pressure. The residue was purified by\n2 4\ncolumn chromatography (silica gel; dichloromethane: hexane = 3: 7) to give C H BrO\n26 16\n(430 mg) as a white powder. Although the products of C H BrO had potentially three\n26 16\nkinds of isomers, the products were directly used for the next reaction without further\npurification. C H BrO (430 mg, 1.02 mmol), sodium borohydride (67.3 mg, 1.78 mmol)\n26 16\nin anhydrous tetrahydrofuran (15 ml) and methanol (15 ml) was stirred at 60 °C for 3 h\nunder a nitrogen atmosphere. After completion of the rection, dichloromethane was added\nto the solution and washed with pure water. The organic layer was dried over anhydrous\nNa SO and concentrated under reduced pressure to give a white powder (391 mg). The\n2 4\npowder (391 mg) in acetic acid (28 ml) and sulfuric acid (0.70 ml) was heated at 85 °C\nfor 4 h. After cooling to room temperature, pure water was added to the reaction solution\nand extracted with dichloromethane. The extracted organic layer was dried over\nanhydrous Na SO and evaporated under reduced pressure. The residue was purified by\n2 4\ncolumn chromatography (silica gel; dichloromethane: hexane = 1: 9) to yield 3-\nbromodibenzo[g,p]chrysene (212 mg) as a white powder. The reaction yield of 3-\nbromodibenzo[g,p]chrysene from 2-bromo-9-fluorenone was 20.8%. 3-\nBromodibenzo[g,p]chrysene (142 mg, 0.349 mmol), diphenyl diselenide (172 mg. 0.552\nmmol), [1,1'-bis(diphenylphosphino)ferrocene]palladium(II) dichloride (40.4 mg, 0.0552\nmmol), and zinc (72.2 mg, 1.10 mmol) in anhydrous tetrahydrofuran (11 ml) was stirred\nat reflux tem,perature for 16 h under a nitrogen atmosphere. After completion of the\nreaction, chloroform was added to the reaction solution. The organic phase was washed\nwith pure water three times, dried over anhydrous Na SO , and concentrated under the\n2 4\nreduced pressure to give a crude product. The crude product was purified by column\nchromatography (silica gel; dichloromethane: hexane = 12: 88) to give R2 as a pale-\nyellow powder (73.7 mg, 43.7%). Chromophore R2 was purified further by sublimation.\n1H NMR (CDCl , 500 MHz): δ = 8.71 (sd, J= 1.5 Hz, 1H), 8.68–8.63 (m, 5H), 8.58 (d, J\n3\n= 8.5 Hz, 1H), 8.36 (dd, J = 8.0, 1.0 Hz, 1H), 7.75 (dd, J = 8.5, 1.5 Hz, 1H), 7.69−7.57\n(m, 7H), 7.45 (ddd, J = 7.5, 6.9, 1.4 Hz, 1H), 7.33−7.29 (m, 3H) (Fig. S14a). 13C NMR\n(CDCl , 125 MHz): δ = 133.70, 132.69, 131.01, 130.97, 130.78, 130.54, 130.36, 130.15,\n3\n129.99, 129.78, 129.51, 129.22, 129.06, 128.98, 128.91, 128.89, 128.47, 128.06, 127.65,\n126.76, 126.75, 126.71, 126.69, 126.58, 126.56. 124.38, 123.61, 123.52, 123.45 (Fig.\nS14b). HRMS-MALDI (m/Z): [M]+ calcd. for C H Se, 484.0730; found 484.0729 (Fig.\n32 20\nS14c). Anal. Caled. for C H Se: C, 79.50; H, 4.17; Se, 16.33. Found C, 79.62; H, 4.26.\n32 20\nFig. S14. Characterization data of R2. a, 1H NMR spectrum in CDCl . b, 13C NMR spectrum in\nin revised supplementary information.\nAfter revision: Section 5-6 in revised supplementary information\n“5-6. Calculation results and photophysical properties of chromophore R2 (Figures\nS29–S31 and Table S3)\nTo clearly clarify the contribution of the intramolecular external heavy atom effect (HAE)\nderived from spatial proximity between heavy atom and central π-core, chromophore R2\nin which a phenylseleno substituent is horizontally introduced at the 3-position of the\nDBC core was synthesized (Fig. S29a). In R2, Se atom is not directly conjugated with\nemissive core because of no electron density at 3-position of DBC. Therefore, R2 has a\npotential characteristic of the intramolecular external HAE. Additionally, the distance\nbetween Se and the 3-position of DBC is 1.94 Å in T optimized geometry (Fig. S29b).\nseparated spatially, the intramolecular external HAE may play significantly in R2.\nThe R2 was doped in the amorphous β-estradiol at a concentration with 0.3 wt%.\nThe amorphous film of R2-doped β-estradiol showed blue fluorescence under excitation\nand red RTP after ceasing excitation (Fig. S29c and Fig. S29d). The Φ of R2 was\np\nmeasured to be 11.5%, which is lower than that of 4 (= 17.6%) and 5 (= 27.0%). The τ\np\nof R2 was determined to be 92.9 ms from RTP decay characteristics (Fig. S29e). From\nthe equations Φ = Φ kTτ , τ = 1/(kT + k T), and Φ = 1 – Φ, the values of kT and k T\np isc r p p r nr isc f r nr\nof R2 were determined to be 1.2 s–1 and 9.5 s–1, respectively (Table S3). Compared with\n4 and 5, the small enhancement of kT relative to k T was observed in R2 from 1 (green\nr nr\narrow in Fig. S29f). The small enhancement of kT relative to k T indicates that the\nr nr\ncontribution of spatial proximity between Se and DBC core to kT enhancement is weak.\nr\nFig. S29. Photophysical characteristics of R2. a, Chemical structure of R2. b, Distance between Se\natom and C atom at 3-position of DBC. c, Emission spectrum of R2 in amorphous β-estradiol under\nexcitation. d, RTP spectrum of R2 in amorphous β-estradiol soon after ceasing excitation. e, RTP decay\ncharacteristics of R2 in amorphous β-estradiol. e, Relationship between optically determined kT and\nr\nk T among 1, 4, 5, and R2.\nnr\nTable S3. Photophysical parameters of R2.\nChromophoresa) Φ Φ b) Φ τ kT k T\nf isc p p r nr\n[%] [%] [%] [ms] [s–1] [s–1]\nR2 0.66 99.3 11.5 92.9 1.2 9.5\na)The concentration of chromophores was 0.3 wt% in amorphous β-estradiol. b) Values determined\nfrom 1 – Φ.\nf\nThe relatively small enhancement of kT compared with k T in R2 could be\nr nr\nconfirmed from the different contributions of SOC to kT and k T. Quantum chemical\nr nr\ncalculation confirmed that n = 6 is mostly contribute to kT of R2 (Fig. S30a). In R2, the\nr\n<S |H |T >2 that enhances kT is smaller than <T |H |S >2 ∝ k T (arrow in Fig. S30b).\nFig. S30. Calculated parameters relating to kT in R2. a, Histograms of calculated parameters of\nr\n<S |H |T >2E –2μ 2 (top), <S |H |T >2 (middle), and μ 2 (bottom) for R2. b, Histogram of\nn SO 1 Sn–T1 Sn-S0 n SO 1 Sn-S0\nthe <T |H |S >2 and <S |H |T >2 values for R2.\nThe perspective of the orbital overlap factor that changes SOC strength provided a\nrational reason for the small enhancement of <S |H |T > of R2. The S –S transition of\nn SO 1 6 0\nR2 consists primarily of two components with 28.4% and 28.3% contributions,\nrespectively. The former is composed of HOMO-2 and LUMO. The latter is composed of\nHOMO and LUMO+2. The overlap density between HOMO-2 and LUMO for S\n6\n–S\n0\ntransition [(HOMO-2)×(LUMO)] hardy overlaps with that between HOMO and LUMO\nfor T – S transition [(HOMO)×(LUMO)] (Fig. S31, left). Similarly, no spatial overlap\n1 0\nwas observed between the overlap density of HOMO and LUMO+2 for S –S transition\n6 0\n[(HOMO)×(LUMO+2)] and the (HOMO)×(LUMO) for T –S transition (Fig. S31, right).\n1 0\nThese lack of spatial overlap does not allow enhancement of <S |H |T > in R2. Indeed,\n<S |H |T >2 of R2 is 6.97 cm–2, which is much lower than <S |H |T >2 of 4 (14.1 cm–\n2), and <S |H |T >2 of 5 (361 cm–2). Therefore, simply placing the heavy atom in close\nproximity to the central π-core is insufficient. The orbital overlap selectively working on\n<S |H |T >, which is realized for 5, is a key molecular design strategy for achieving a\nn SO 1\nlarge kT.\nr\nFig. S31. Molecular orbitals and schematic illustrations related to orbital overlap to explain small\n<S |H |T >2 of R2. The isovalues of the overlap density regarding (HOMO-2)×(LUMO),\n(HOMO)×(LUMO), and (HOMO)×(LUMO+2) are 0.00016.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "All the issues have been well solved, the manuscript can be published as it is.", "reviewer_2": "The manuscript has been greatly improved in response to the reviewers' comments. It is recommended to be accepted.", "reviewer_3": "The authors have adequately revised their manuscript according to my previous comments and suggestions. The quality of the manuscript has been improved after the revision. The revised manuscript is recommended for publication in its present form."}, "author_response": ""}]

Decision letter