Introduction

Long-persistent luminescence (LPL), due to its ability to emit light for a long time without an external power source, is widely used in many areas, such as night indicators, safety signage, and in vivo bioimaging1,2. Recently, organic LPL (OLPL) materials have attracted widespread interest due to their composition without heavy metal elements, the design flexibility of their chemical structure, and the non-stringent processing conditions3,4,5. The LPL systems that emit visible light are mainly used in scenarios where there is little to no ambient light. The human eye contains different photoreceptor cells that operate under bright and dim lighting conditions, resulting in different spectral sensitivity functions6,7. The sensitivity can be divided into photopic (>0.6 cd/m2), scotopic (<10–3 cd/m2), and mesopic vision in their transition region (Fig. 1a, b)8. Known as the Purkinje phenomenon, the wavelength sensitivity in scotopic vision, which is mainly mediated by rods, is blue-shifted compared to photopic vision, which is mainly mediated by cones9. Therefore, the human eye is more sensitive to materials that emit weak light, such as LPL materials, when the emission spectrum fits the sensitivity function of human scotopic vision.

Fig. 1: CT-to-LE upconversion strategy of OLPL materials.
figure 1

a Luminance and human visual modes. b Human eye sensitivity functions for the scotopic vision regime V′(λ), the photopic vision regime VM(λ), and three mesopic vision regimes based on Formula 1~5 in reference 8; data were taken from reference 49. c Potential energy surface diagram illustrating the different influence of small ΔELE-CT on emission components. 1LE represents the locally excited singlet state on donor (this paper) or acceptor molecules. 1CT represents the intermolecular charge-transfer excited singlet states between donor and acceptor molecules. d Frontier molecular orbital diagram illustrating two types of OLPL systems and the system proposed in this paper. The thickness of the arrows expresses the relative magnitude of the probability of process occurrence.

Full size image

In OLPL systems, energy is stored as charge carriers. Depending on the charge separation mechanism, OLPL can be classified into type I (single-photon charge separation) and type II (two-photon ionization) categories (Fig. 1c). In type I OLPL, charge separation and luminescence occur via the intermolecular charge-transfer (CT) excited states at the donor–acceptor interface, similar to mechanisms found in organic solar cells (OSC). While type I OLPL systems exhibit high charge separation efficiency, they generally emit through intermolecular CT states, leading to broad-spectrum emission that complicates color control3,10. In contrast, type II OLPL relies on stepwise two-photon absorption by the dopant molecules embedded in the host matrix11,12, taking advantage of materials with high photoluminescence quantum yields, such as thermally activated delayed fluorescence (TADF) emitters13. However, type II OLPL requires stronger photoexcitation to achieve two-photon ionization, which poses a significant limitation in charge accumulation. Therefore, achieving color control and high charge separation efficiency simultaneously remains a challenge in OLPL systems.

All previously reported type I OLPL systems3,4,5,10,14,15,16,17,18,19 have shown green to red light with a broad peak that does not match well with scotopic vision. These OLPL systems are mainly based on the luminescence of intermolecular CT excited states, which is more challenging to achieve a blue emission20,21,22,23. Additionally, accurate prediction of the position and width of the intermolecular CT emission peak through quantum chemical calculations is difficult20,24. Although the emission color of the OLPL system can be adjusted by energy transfer from the CT excited state to additional suitable emitters25, blue CT emission is required for the energy transfer to the blue emitters. Therefore, the development of the blue OLPL system that matches the scotopic vision is crucial for achieving OLPL systems with high human visual sensitivity.

In OSC development, materials with minimal energy offsets between the lowest-energy locally excited (LE) and intermolecular CT singlet states (ΔELE-CT = ELE1 – ECT1, Fig. 1d) can reduce nonradiative voltage loss while maintaining high power conversion efficiency26,27,28,29,30,31,32. This leads to enhanced open-circuit voltages, notwithstanding the limited driving force for Frenkel exciton dissociation inherent in a small ΔELE-CT29,33. On this basis, non-fullerene acceptors for OSCs have been designed to have high absorption and emission properties34,35 and utilized for organic light-emitting diodes (OLEDs) with near-infrared luminescence36. Energy offsets may be minimized by selecting materials that either have small differences in their lowest unoccupied molecular orbital (LUMO) energies (ΔELUMO = ELUMO,D – ELUMO,A) or their highest occupied molecular orbital (HOMO) energies (ΔEHOMO = EHOMO,D – EHOMO,A), depending on whether the electron donor or acceptor component has the smallest optical gap in the blend, as

$$\Delta {E}_{{{{\rm{LE}}}}-{{{\rm{CT}}}}}={{{{\rm{IP}}}}}_{{{{\rm{D}}}}}-{{{{\rm{EA}}}}}_{{{{\rm{A}}}}}-{E}_{{{{\rm{S}}}}1}={\Delta E}_{{{{\rm{LUMO}}}}} \, {{{\rm{or}}}} \,{\Delta E}_{{{{\rm{HOMO}}}}}-{E}_{{{{\rm{S}}}}1}^{{{{\rm{b}}}}}$$
(1)

where IPD, EAA, ES1, and \({E}_{{{{\rm{S}}}}1}^{{{{\rm{b}}}}}\) are the electron-donor ionization potential, electron-acceptor electron affinity, lowest singlet excited state energy, and binding energy of the singlet exciton, respectively27,29. Quantum chemical calculation results28 have demonstrated that the CT-to-LE transition is significant when ΔELE-CT is small. However, direct experimental evidence for CT-to-LE upconversion is lacking.

Here, we consider that the upconversion of a CT singlet exciton to an LE singlet state enables emission blueshifting in binary OLPL systems (Fig. 1c), giving the mechanistic similarity of OLPL to the recombination luminescence in OSCs. We prepared a series of OLPL systems having gradient variations in ΔELUMO by selecting a series of donor and acceptor materials having similar structures but gradually varying HOMO or LUMO energy levels (Fig. 2a, b). Comprehensive characterization using steady-state, time-resolved spectroscopy, and wavelength-resolved thermoluminescence (TL) measurements12,37 enabled the analysis of complex emission processes involving charge and energy transfer, including fluorescence, TADF, phosphorescence, and LPL. Further, we confirmed the upconversion from CT to LE singlet state in the small ΔELE-CT systems and achieved blue and cyan OLPL. TL analysis indicates that a thermally activated trap-filling process38,39 and the small ΔELUMO can enhance trap-filling at room temperature. By adding suitable extrinsic electron traps to the system, we achieved strong LPL up to ISO 17398 class A.

Fig. 2: Molecular structures and their energy levels of materials as well as LPL performance.
figure 2

a Chemical structure of electron donors, acceptors, and a reference dopant. b HOMO, LUMO levels, and optical gaps (OG) of materials; HOMO and LUMO levels of donors and LUMO levels and acceptors were obtained from the electrochemical measurement (Supplementary Figs. 6–9); HOMO of acceptors was calculated from measured LUMO level and OG value (Supplementary Figs. 10–14). c Comparison of the scotopic vision spectrum and LPL spectra. All intensities are normalized to the maximum value (max.) of each dataset. All intensities are normalized to the maximum value (max.) of each dataset. d LPL decay profiles with scotopic luminance as the vertical coordinate unit. Data of (c, d) are measured by spectroradiometer under excitation conditions: 365 nm, 400 µW/cm2, 1 min.

Full size image

Results and discussion

Selection and ΔE LE-CT characterization of donor–acceptor systems

To minimize changes in HOMO and LUMO levels, we selected isomeric or structurally analogous donor–acceptor systems. The carbazole-substituted aromatic amines, DTAPC, AAPC, DAAPC, and the oligoarylamine DDATA, were selected as electron-donating dopants (Fig. 2a, Supplementary Method 1, Supplementary Figs. 1, 2, and Supplementary Table 1). The phosphine oxide-based acceptors, DPEPO, 2-PPT, 2,8-PPT, 4,6-PPT, and 3,7-PPT, were chosen as electron-accepting hosts (Fig. 2a, Supplementary Methods 2, 3, Supplementary Figs. 3–5, and Supplementary Table 2). To mitigate potential chemical impurities, diphenylphosphine-oxide-substituted dibenzothiophene acceptors were prepared using a non-oxidative method, and all materials were purified by sublimation. A TADF molecule, DACT-II40, having a donor structure akin to DTAPC, was selected as a reference compound that will not form the intermolecular CT excited states with all investigated acceptor host molecules.

To precisely probe small variations in HOMO and LUMO levels, we employed differential pulse voltammetry (DPV) and optimized the measurement conditions to enhance the numerical accuracy of the HOMO and LUMO levels (Fig. 2b, Supplementary Method 4, and Supplementary Figs. 6–9). Analysis of the LUMO data revealed deepening LUMO energy levels in order DPEPO (−1.94 eV), 2-PPT (−2.04 eV), 2,8-PPT (−2.20 eV), 4,6-PPT (−2.29 eV), and 3,7-PPT (−2.52 eV). The LUMOs of the carbazole-based donors are slightly higher in energy (ΔELUMO = 0.07–0.65 eV) than those of the corresponding acceptors, while DDATA has a substantially higher LUMO level (ΔELUMO = 0.48–1.06 eV) than those of the acceptors (Table 1). The acceptor HOMO levels are substantially lower than those of the donor (>0.76 eV), precluding hole migration from donor to acceptor molecules after charge separation (Supplementary Figs. 10–14). The donor HOMO levels ascend in the order DTAPC (−4.99 eV), AAPC (−4.92 eV), DAAPC (−4.87 eV), and DDATA (−4.88 eV). The comparison between DAAPC and DDATA serves as an ideal model for studying the effects of ΔELUMO on LPL because the HOMO is almost identical, but the LUMO is different by 0.40 eV. Because the binding energies of the singlet excitons for the four donors are very close to each other (Supplementary Table 3), the main factor that affects ΔELE-CT is ΔELUMO. The ΔELE-CT values for all investigated systems, calculated using Eq. 1, are summarized in Table 1.

Table 1 Relative permittivities (εr) of all host materials, LUMO energy offsets (ΔELUMO), and intermolecular CT singlet states (ΔELE-CT) between donors and acceptors
Full size table

Spectroradiometer evaluation of LPL performance

All mixed films of donor (1 mol%) and acceptor (99 mol%) exhibited LPL upon UV excitation (Fig. 2c, d and Supplementary Figs. 15–21). The LPL spectra of the small ΔELE-CT systems almost entirely fall within the scotopic range (Fig. 2c). Especially, DAAPC/2,8-PPT showed a cyan LPL with the strongest intensity in these materials. Despite the HOMO levels of DDATA a2,8-PPT are close, the DAAPC/2,8-PPT having smaller ΔELE-CT exhibited more than twice LPL intensity as compared to the DDATA/2,8-PPT. In contrast, DDATA/2,8-PPT with a larger ΔELE-CT displayed significant yellow-to-red emission over 550 nm and weaker LPL. Luminescent materials are generally evaluated by luminance based on photopic vision, but materials containing more blue light components are estimated to have a lower luminance value. Because LPL luminance was weak, we analyzed it based on the scotopic vision luminance or unified luminance41 (Fig. 2d and Supplementary Fig. 15c).

Impact of ΔE LE-CT on emission spectra

Although the LPL spectra of the binary OLPL systems are generally based on the intermolecular CT emission, the LPL spectra of the small ΔELE-CT systems are inconsistent with the intermolecular CT emission. Because the HOMO levels of DAAPC and DDATA are equal, identical intermolecular CT singlet emission (1CT) is expected when the materials are doped in 2,8-PPT. However, the LPL spectra of the DAAPC/2,8-PPT and the DDATA/2,8-PPT were different (Fig. 2c and Supplementary Fig. 22). This spectral change is attributed to ΔELE-CT. The 1CT emission is obtained when ΔELE-CT is large (ΔELE-CT = 0.56 eV in DDATA/2,8-PPT), whereas the greater proportion of singlet LE emission of the donor (1LED) was observed when ΔELE-CT is small (ΔELE-CT = 0.23 eV in DAAPC/2,8-PPT).

To exclude the influence of solid-state solvation effects on the spectral properties, we measured the relative permittivity (εr) of all acceptor hosts (Table 1 and Supplementary Figs. 23, 24). Conjugated phosphine oxide-based materials exhibit higher εr values of 6 to 7 than the conventional organic semiconductors (εr of ~4), which could enable the longer-lived LPL in phosphine oxide hosts. The solid-state solvation effects were evaluated by doping DACT-II into host materials because TADF materials are known to exhibit significant solvent effects (Fig. 3a, Supplementary Figs. 25, 26, and Supplementary Tables 4–6). The trend in the spectral redshift of DACT-II in acceptor films was consistent with that in εr (Fig. 3b). Donor materials used in this study, such as AAPC, also exhibit solvation effects owing to their partial intramolecular CT nature (Fig. 3c, d, Supplementary Fig. 27, and Supplementary Table 7). However, in contrast to the DACT-II case, the spectral redshift behavior of donors in acceptor films cannot be correlated with εr, and the redshift is caused by factors other than the solid-state solvent effect (Fig. 3d).

Fig. 3: Influence of ΔELE-CT on components of the emission spectra.
figure 3

a, b Solvatochromic shift analysis (a) and PL spectra (b) of DACT-II doped in different hosts. c,d, Solvatochromic shift analysis of solutions (b) and doped films (c) of AAPC. Details are provided in Supplementary Figs. 25, 26 and Supplementary Tables 4–6. THF tetrahydrofuran, EA ethyl acetate, MTBE t-butyl methyl ether. e, f PL spectra of DAAPC (e) and DDATA (f) in different hosts. The red dashed line emphasizes the two emission peaks at the same wavelength position. All spectra transformed from the original spectra through Jacobian conversion64. g, h Emission decay profiles of DAAPC-doped materials from 100 ps to 10 ms (g) and from 1 ms to 104 s (h). The blue dashed arrows indicate the relative contribution of the corresponding luminescence components, which decrease progressively following the order of the listed host materials from top to bottom. Relative time-resolved spectra: see Supplementary Fig. 31a–f. Spectra and decay profiles of 0.1 ns–10 ms were measured by streak camera with an exaction of the 343 nm femtosecond laser (Pulse energy = 2 μJ, width = 165 fs, repetition rate = 25 Hz) except DAAPC/3,7-PPT (400 nm). Decay profiles of >10 ms were measured using a multipixel photon counter (MPPC). Excitation conditions: 340 nm, 400 µW, 1 min. i, j The Jablonski diagram of DDATA/2,8-PPT (i large ΔELE–CT) and DAAPC/2,8-PPT ( j small ΔELE–CT) systems. The 1LED, 1LEA and 1LEA,neat film energy is from Supplementary Figs. 13, 14, 37. The 1,3CT and 3LED energy is from Supplementary Fig. 38a, b. Because the CT state energies of DDATA/2,8-PPT and DAAPC/2,8-PPT are identical (Supplementary Fig. 38d), the 1,3CT energy values from DDATA/2,8-PPT were used in the schematic of DAAPC/2,8-PPT as well. ΔELE-CT values calculated from spectra data were slightly different from the results shown in Table 1. kLE1, kCT1 is calculated from Supplementary Fig. 36e, f. The doping concentration of all doped film samples in this figure is 1 mol%.

Full size image

The spectral change owing to the 1LED contribution was confirmed from the host dependence of different donor materials. When hosts cannot form an intermolecular CT state with a guest such as ZEONOR4 or polymethyl methacrylate (PMMA), the intrinsic 1LED emission can be obtained (Fig. 3b, e–h, Supplementary Fig. 28). Because DTAPC (HOMO = −4.99 eV, LUMO = −1.87 eV) and AAPC (HOMO = −4.92 eV, LUMO = −1.78 eV) have identical optical gaps, their spectral peaks in ZEONOR and PMMA are consistent (Table 1 and Supplementary Fig. 28). Similarly, because the HOMO energies are almost equal, DAAPC/3,7-PPT and DDATA/3,7-PPT exhibit identical broad PL spectra corresponding to their 1CT (Fig. 3e, f). Further, the donor PLs in DPEPO and 2-PPT closely resembled those in PMMA, suggesting that their emissions are primarily from 1LED with the redshift induced by solid-state solvation. A comparative analysis with other investigated systems (Supplementary Fig. 22) revealed that the emissions are predominantly from 1CT when ΔELUMO is larger than 0.6 eV, and predominantly from 1LED when the ΔELUMO is smaller than 0.3 eV. A noticeable mixture of 1LED and 1CT emissions was observed when ΔELUMO = 0.3–0.6 eV. In systems where the spectral components are exclusively either 1LED or 1CT, the PL and LPL spectra are almost identical. However, in the 1LED and 1CT coexisting systems, the LPL spectra show a significant redshift and broadening compared with the PL spectra attributed to the higher proportion of CT emission in the LPL spectra. This is because LPL emissions are dominated by geminate charge recombination, whereas PL primarily evolves from the initial excited states. The broadening of the electroluminescence spectrum relative to the PL spectrum further supports this hypothesis (Supplementary Figs. 29, 30).

Transient spectroscopy further differentiates among fluorescence, TADF, and LPL in different material systems (Fig. 3g, h and Supplementary Figs. 31–35). The fluorescence process occurs within 1 μs, while LPL dominates after 1 s. Between 1 μs and 1 s, the primary process is TADF, though some systems (e.g., DAAPC/3,7-PPT) also show significant LPL in this time range. Since the carbazole-based donor molecules have a partial intramolecular CT nature (Supplementary Fig. 27 and Supplementary Table 7), they exhibited weak intramolecular TADF with long lifetime, e.g., DAAPC/PMMA (Supplementary Fig. 36a, b). PL of carbazole-based donors also showed higher quantum yields than DDATA (Supplementary Table 8). To avoid confusion with the TADF of the intermolecular CT (3CT or 3LED to 1CT), TADF arising from intramolecular CT within the donor molecule as a transition from the lowest-energy triplet LE state (3LED) to the relative singlet LE state (1LED). The intramolecular TADF (3LED to 1LED) and intermolecular TADF (3CT or 3LED to 1CT) processes can be distinguished by the excitation time dependence of emission intensities (Supplementary Fig. 31j, k). The intramolecular TADF intensity remains constant with excitation time under fixed power, while LPL grows progressively, creating a clear demarcation in time-resolved profiles. This boundary disappears in intermolecular systems due to their shared donor cation/acceptor anion radical structures. In such cases, the distributed charge-separated states of LPL with varied lifetimes (some comparable to CT states) form a continuous transition between components (Supplementary Fig. 31k).

The magnitude of ΔELE−CT significantly influences the composition and lifetime of fluorescence and TADF. In negative ΔELE−CT systems (non-exciplex) where the LE state is S1, e.g., DAAPC/DPEPO, only 1LED fluorescence and 3LED-to-1LED TADF are observed. The exciplex systems with a large ΔELE-CT, e.g. DAAPC/3,7-PPT and DDATA/2,8-PPT, exhibit 1CT fluorescence and 3CT-to-1CT TADF (Fig. 3g). However, exciplex systems with a small ΔELE−CT, e.g., DAAPC/2,8-PPT, shows a mixture of 1LED and 1CT fluorescence, as well as 3LED-to-1CT TADF (1–100 μs). In the DAAPC/2-PPT system with a very small ΔELE−CT, 1CT fluorescence and 3LED-to-1CT TADF were barely detectable (Supplementary Fig. 31c). The 3LED-to-1LED intramolecular TADF of DAAPC/2-PPT was stronger than that of DAAPC/PMMA, suggesting an enhancement in intersystem crossing and reverse intersystem crossing facilitated by the intermolecular CT excited state10,42. Starting from tens of microseconds, a transition from 1CT to 1LED was observed in the TADF spectrum (Supplementary Fig. 31). This transition can be explained by the mechanism of 1CT-to-1LED upconversion following 3LED-to-1CT reverse intersystem crossing. This explanation aligns with the longer lifetime of the 1CT exciton compared to the 1LED exciton, allowing an equilibrium to form between these two states (Figs. 1d, 3i, j and Supplementary Table 3). Since the radiative process of 1LED is faster than that of 1CT, the equilibrium shifts toward 1LED as ΔELE−CT decreases. This interconversion equilibrium is influenced by the magnitude of ΔELE−CT (Supplementary Table 3). When ΔELE−CT is large, the LE-to-CT rate (kLE-CT) dominates, leading to preferential 1CT emission (Fig. 3i and Supplementary Fig. 37, 38). As ΔELE−CT decreases, the 1CT-to-1LED rate (kCT-LE) becomes comparable, gradually shifting the equilibrium toward 1LED (Fig. 3j). In systems with very small ΔELE−CT values (<0.1 eV), such as DAAPC/2-PPT, the equilibrium is rapidly achieved (kCT-LE ≈ kLE-CT) and the 1LED is predominantly observed due to faster radiative process, namely 1CT takes the radiative pathway of 1LED to emit light 30,31.

Experimental and theoretical evidence for 1CT-to-1LE upconversion

To ascertain the 1LED-to-1CT upconversion in the small ΔELE−CT systems, we performed wavelength-resolved TL measurements (Fig. 4 and Supplementary Figs. 39–41). TL and LPL are intrinsically linked, reflecting the charge recombination luminescence induced by the thermally stimulated detrapping of carriers (Fig. 4a) and do not include the initial singlet and triplet excitons generated directly by photoexcitation43,44. Unlike transient PL spectra, TL and LPL do not contain initial 1LED fluorescence generated during photoluminescence. The recombination of detrapped charges directly produces excitons in the lowest excited state without the involvement of higher-energy excited states. Compared to variable-temperature electroluminescence, the TL process does not introduce an external electric field. To more clearly illustrate the change in spectral components with temperature, we fitted the TL spectra at different temperatures with the spectra of 1LED, 3LED, and 1CT (3CT is very close to 1CT) to obtain the relative proportions of the three spectral components (Fig. 4b and Supplementary Note 1). In the DAAPC/DPEPO system where 1LED serves as S1 (Fig. 4c, d), only LE emission is observed and 1LED fluorescence component exists even at low temperatures (<100 K). For systems with a large ΔELE-CT (DDATA/2,8-PPT a2,8-PPT/3,7-PPT, Fig. 4e, f and Supplementary Fig. 39) only exhibited emission components across all temperatures. However, in the DAAPC/2,8-PPT system with small ΔELE−CT (Fig. 4g, h), 1LED emission components were not contained in the TL spectra at low temperatures, but at high temperature (>100 K). This result demonstrates that in small ΔELE−CT systems, 1LED excitons are converted from 1CT excitons, as the TL recombination process simultaneously produces singlet excitons in the lowest excited state. Above 200 K, the proportion of 1LED and CT components increases with temperature, supporting the equilibrium shift between LE and CT states. In the DAAPC/2-PPT system with a very small ΔELE−CT (0.07 eV), 1LED emission is still observed even at low temperatures (Supplementary Fig. 39), which further confirms that 1LED is generated by upconversion from 1CT, rather than through the reverse intersystem crossing of a triplet state.

Fig. 4: Evidence of 1CT to 1LE upconversion.
figure 4

a A simplified schematic of the TL process of small ΔELE–CT material. ET electron trap state. b Spectral component fraction of 1LED, 3LED, and 1,3CT in TL spectra of DAAPC/2,8-PPT. c–e TL maps for materials with different ΔELE–CT. The red dashed line represents spectral onset. Text annotations indicate the major origin of the TL spectra at high (≥300 K) and low (50 K) temperatures. Excitation conditions: 365 nm, 1 min, 16.96 mW/cm2 (DAAPC/DPEPO), 6.90 mW/cm2 (DAAPC/2,8-PPT), 21.7 mW/cm2 (DDATA/2,8-PPT). f–h The corresponding sliced spectra. All intensities are normalized to the maximum value (max.) of each dataset. Red and purple text annotations illustrate the origin of the components of the LPL and TL spectra at 300 and 50 K, respectively. For the complete material comparison, see Supplementary Note 1. The 10 K data were obtained from the time-resolved spectra measured at 10 K.

Full size image

The excited state calculations show that the calculated average ΔELE-CT of DAAPC/2-PPT (68 meV) is much smaller than that of DAAPC/2.8-PPT (255 meV) and DDATA/2.8-PPT (492 meV) (Fig. 5a–c and Supplementary Table 9). This is consistent with the experimental evidence that DAAPC/2,8-PPT has a small ΔELUMO. The natural transition orbitals of all systems show that the lowest singlet excited state (S1) can be identified predominantly as the 1CT in DDATA/2,8-PPT a2,8-PPT/2,8-PPT, whereas the S1 state of DAAPC/2-PPT corresponds to 1LED on the DDATA moiety or 1LED-1CT hybrid excitation. Next, we estimated the coefficients of electronic hybridization between the LE (fLE) and the CT (fCT) states in the framework of first-order perturbation theory (\({f}_{{LE}}={\left[\frac{{V}_{{LE}-{CT}}}{{\Delta E}_{{LE}-{CT}}}\right]}^{2}\); fLE + fCT = 1) from the electronic coupling (VLE−CT) and ΔELE−CT estimated by density functional theory (Fig. 5c and Supplementary Table 9). The average fLE of DAAPC/2-PPT exceeds 0.2, which is larger than those of DDATA/2,8-PPT a2,8-PPT/2,8-PPT, owing to hybridization between CT and LE states in the S1 states. The small ΔELE-CT will increase the radiative ability of the CT state by hybridizing the CT and LE, known as the intensity-borrowing mechanism30,45,46. Crucially, the small ΔELE-CT enables the upconversion from the 1CT to the highly emissive 1LE. This opens an additional radiative relaxation pathway from the CT state through the highly emissive LE state. Because of the very small ΔELE‑CT in the DAAPC/2-PPT system, thermal activation is not required for the upconversion from 1CT to 1LE. This is reflected in the TL map, where distinct 1LE emissions are observed even below 100 K and with almost no visible CT state emission.

Fig. 5: Quantum chemical calculations of OLPL systems.
figure 5

a Donor/acceptor cluster model consisting of a donor molecule (DDATA or DAAPC) and 10 acceptor molecules (2,8-PPT or 2-PPT) optimized using the semiempirical quantum-chemistry approach PM7. b Box plots of the calculated ΔELE-CT. c Box plots of the calculated coefficients fLE, which represent the possibility of electronic hybridization between the CT and the LE states. Data points above 1 were neglected.

Full size image

Although the dielectric constant and molecular conformation change with temperature, the spectra change cannot be fully explained without consideration of CT-to-LE upconversion. For example, CT emission is nearly identical for different donor molecules with the same HOMO and similar structures when paired with the same acceptor (DAAPC/3,7-PPT and DDATA/3,7-PPT, Fig. 3e, f and Supplementary Fig. 22). However, significant differences in overall emission are observed in the isomers 2,8-PPT and 4,6-PPT, which have nearly identical dielectric constants, with the DAAPC-doped systems showing clear 1LE emission components (transient spectra, Supplementary Fig. 31). This phenomenon cannot be explained solely by molecular conformational changes.

Impact of ΔE LE-CT on LPL intensity and trap-filling dynamics

To understand the influence of a small ΔELE‑CT on LPL, we compared the TL and relative temperature-dependent LPL profiles of 2,8-PPT, DDATA/2,8-PPT, a2,8-PPT/2,8-PPT at various initial temperatures (Fig. 6 and Supplementary Fig. 40). The area under the TL curve represents the distribution of deeper traps at a given excitation temperature (Fig. 6a–c), whereas the area under the LPL curve primarily represents the distribution of shallower traps (Fig. 6d–f). The change in corresponding PL with temperature reflects the contributions of thermal quenching and TADF (3LED to 1CT) (Supplementary Fig. 40). As shown in Fig. 5g–i, the PL intensity decreased with increasing temperature in all systems, confirming thermal quenching. Only DAAPC/2,8-PPT demonstrated a subtle effect of TADF on PL. In contrast, the LPL and TL intensity of DAAPC/2,8-PPT and DDATA/2,8-PPT become stronger over 150 K, indicating more efficient trap filling at higher temperatures38. Since such thermally activated trap filling is absent in 2,8-PPT alone but occurs in the type I OLPL system, this suggests that more deep traps are filled in the type I OLPL system at room temperature, leading to stronger LPL. Given that DAAPC/2,8-PPT and DDATA/2,8-PPT have nearly identical activation energies for trap filling (74.6 ± 5.9 meV and 68.8 ± 2.9 meV, respectively; Supplementary Note 2) a2,8-PPT has a higher quantum yield, the stronger LPL in DAAPC/2,8-PPT at room temperature should be primarily due to lower nonradiative energy loss of 1LE emission in DAAPC, benefiting from a smaller ΔELE-CT31.

Fig. 6: The effect of ΔELE-CT on the trap filling.
figure 6

a–c TL curves of 2,8-PPT (a), DDATA/2,8-PPT (b), and DAAPC/2,8-PPT (c) at different excitation temperatures, respectively. d–f Relative LPL curves of 2,8-PPT (d), DDATA/2,8-PPT (e), and DAAPC/2,8-PPT (f) for TL curves at different excitation temperatures, respectively. Data points in the graph that deviated from the curve were caused by switching the neutral density filter. g–i Excitation temperature dependence of the integrated TL intensity (g), integrated LPL intensity (e), and mean PL intensity in TL measurement (i). Integration range: excitation temperature to 400 K (TL); 35–9920 s (LPL). The solid curve is the peak fitting curve of relative data. The integrated TL shows a marked decrease after 225 K, because more than one-third of the TL curve above 225 K was not measured at the set termination temperature. The low glass transition temperature of 2,8-PPT necessitates that higher temperatures cannot be set to ensure the repeatability of TL tests. Excitation conditions and sample thicknesses: 2,8-PPT: 280 nm, 10 µW/cm2, 1 min, 0.050 ± 0.014 mm; DDATA/2,8-PPT: 340 nm, 0.4 µW/cm2, 1 min, 0.050 ± 0.009 mm; DAAPC/2,8-PPT: 340 nm, 1 µW/cm2, 1 min, 0.021 ± 0.006 mm.

Full size image

ΔELE−CT is not the only factor affecting the intensity and duration of LPL. DAAPC/2-PPT has a very small ΔELUMO, but the LPL is also influenced by the thermal stability of the host phase19, and 2-PPT, which has a lower glass transition temperature, exhibited a much weaker LPL than the DAAPC/2,8-PPT (Fig. 3h). Because of the larger overlap between the absorption of the charge-separated states and the LPL spectra, the 4,6-PPT and 3,7-PPT systems exhibited shorter LPL durations (Supplementary Figs. 41, 42).

Enhancing LPL via extrinsic electron traps and practical evaluation

To enhance the LPL of DAAPC/2,8-PPT, we incorporated two more compounds, m-BTB and PPTDO, as extrinsic electron traps (Fig. 7). The introduction of external electron trapping material facilitates charge retention due to the larger detrapping energy15,19,25. The optimized concentration of the trapped molecule was around 1% (Supplementary Fig. 43). Their LUMO levels are 0.54 and 0.79 eV deeper than that of 2,8-PPT, respectively. Given that the optical gaps of these traps significantly exceed the CT gap of DAAPC/2,8-PPT, the PL and LPL spectra of the final doped systems remain largely consistent with those of DAAPC/2,8-PPT, and the minor variations can be attributed to respective radical ion absorption (Supplementary Fig. 41).

Fig. 7: Photoluminescence properties of ternary OLPL systems.
figure 7

a Chemical structures of electron trap dopants. b HOMO and LUMO levels, and OG of materials in ternary OLPL systems. c Spectra of PL and LPL luminescence of reference binary system (1 mol% DAAPC-doped 2,8-PPT), and m-BTB or PPTDO doped ternary systems (1 mol% of traps, 1 mol% of D in 98 mol% of A). All intensities are normalized to the maximum value (max.) of each dataset. d LPL decay profiles of ternary OLPL systems with luminance as the vertical coordinate based on the measurement condition from ISO 17398. Class A, B, C, and D are luminescence classes of afterglow performance under the Xenon light excitation (1000 lx, 5 min) from ISO 17398.

Full size image

Currently, LPL lacks intrinsic evaluation parameters, and its brightness and duration depend on the excitation conditions and samples, resulting in a lack of comparability across publications3,4,5,10,13,14,15,16,17,18,19,25,47,48. Therefore, as a practical benchmark, we used the ISO standard conditions for safety signs of LPL materials (ISO 17398) (Supplementary Fig. 44). Although our sample is only 0.5-mm thick, m-BTB/DAAPC/2,8-PPT achieved Class A under ISO 17398, which is the entry-level for safety sign application, making it arguably the brightest OLPL material to date (Supplementary Discussion). However, the LPL of PPTDO/DAAPC/2,8-PPT was weaker than that of DAAPC/2,8-PPT on short time scales, likely because of the absorption peak of the PPTDO radical anions in the 400–700 nm range (Supplementary Fig. 41c). Because the luminance used in ISO 17398 is based on photopic vision, the scotopic luminance of these two materials should be stronger.

In conclusion, the strategy of the upconversion from CT to LE using a small ΔELUMO, meaning a small ΔELE-CT system, enabled a blue to cyan LPL matching the mesopic and scotopic vision49. Steady-state, transient, and TL spectroscopy measurements were utilized for multiple donor–acceptor combinations with different energy levels to elucidate the complex emission mechanism including fluorescence, TADF, phosphorescence, and LPL. Wavelength-resolved TL measurements provide direct experimental evidence for the upconversion from 1CT to 1LED. The incorporation of extrinsic traps enhanced the LPL and achieved Class A under ISO 17398 testing conditions. This result demonstrates that OLPL materials have the potential to achieve afterglow performance comparable to that of commercial inorganic LPL materials. The validation of this upconversion will not only facilitate the development of future OLPL systems and OSCs but also provide a potential direction for the development of blue OLEDs.

Methods

Materials

DACT-II was purchased from Xi’an Polymer Light Technology Corp. Bis[2-(diphenylphosphino)phenyl]ether oxide (DPEPO), 3,3′-bis(4,6-diphenyl-1,3,5-triazin-2-yl)-1,1′-biphenyl (m-BTB) and 2,8-Bis(diphenylphosphoryl)dibenzothiophene Sulfone (PPTDO) were prepared based on references50,51,52 (Supplementary Method 3). ZEONOR 1060 R and PMMA were purchased from ZEON Japan and Sigma-Aldrich (St. Louis, USA), respectively. All dopant and host materials were purified by high-vacuum, gradient temperature sublimation before use and stored in a glovebox. Tetrabutylammonium hexafluorophosphate (TBAPF6) and ferrocene (Fc) were purchased from TCI Chemicals (Tokyo, Japan). TBAPF6 was purified by recrystallization before use. Bis(trifluoromethane)sulfonimide lithium salt (LiTFSI) with 99.95% purity and trace metals basis was purchased from Sigma-Aldrich (St. Louis, USA). N,N-dimethylformamide (DMF) for spectrochemical analysis and the anhydrous DMF for DPV measurements were purchased from Wako Pure Chemical Industries (Osaka, Japan). All other materials and solvents were purchased from TCI Chemicals (Tokyo, Japan), Sigma-Aldrich (St. Louis, USA), and Wako Pure Chemical Industries (Osaka, Japan).

Basic characterization

1H-nuclear magnetic resonance (NMR) spectra were recorded using a Bruker AVANCE III 400 or 500 MHz spectrometer with chloroform-d, dichloromethane-d2 or benzene-d6 as the solvent and tetramethylsilane (TMS) as the internal standard at room temperature. Thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) were performed with a SHIMADZU DTG-60AH and NETZSCH DSC 204 instrument, respectively, under nitrogen at a heating rate of 10 °C/min. Thermal decomposition temperatures (Td) were determined at 5% weight loss. The cyclic voltammetry (CV) and differential pulse voltammetry (DPV) measurements were carried out using an electrochemical analyzer (Model 608D + DPV, BAS).

Film fabrication

Thick films of all materials for optical measurement were fabricated on the glass substrates with a groove (10 × 10 × 0.5 mm) by the melt-casting method at the temperature higher 10 °C than the melting point of used host with a quick cooling. Thin films for the UV-vis absorption and thermoluminescence (TL) measurements were fabricated by sandwiching the melted sample between two quartz substrates at a temperature 10 °C higher than the melting point of host materials. The thickness of the thin film for the TL measurement were measured in three different positions on each film using a micrometer screw gauge and averaged.

Optical measurements

The absorption spectra were recorded on a UV-vis-NIR spectrophotometer (Shimadzu UV-3600i Plus). The absorption spectra of the radical species were obtained under electrical redox (WaveNow Wireless Potentiostat, Pine Research Instrumentation) in a solution containing 0.1 M TBAPF6 by a UV-VIS-NIR spectrometer (ULS2048CL-EVO, Avantes) and NIR spectrometer (AvaSpec-NIR256-2.5-HSC-EVO, Avantes) or UV-vis-NIR spectrophotometer (Shimadzu UV-3600i Plus). The steady-state fluorescence and phosphorescence (77 K) spectra of solution at room temperature and phosphorescence spectra at 77 K were recorded on a photonic multichannel analyzer (PMA-12, C14631-01, Hamamatsu Photonics) excited using 280-nm and 340-nm LED (M280L6, M340L5, Thorlabs) with a bandpass filter (280 ± 5 nm and 340 ± 5 nm). Absolute fluorescence quantum yields (PLQY) were measured on an integrating sphere with a photoluminescence measurement unit (Quantaurus-QY, C11347-01, Hamamatsu Photonics). Fluorescence lifetime of solution and time-resolved spectra and decay profiles in 0.1 ps-10 ms at room temperature and 10 K were recorded on a streak camera system (C14832-110, Hamamatsu Photonics) equipped with a 300 mm triple grating imaging spectrograph (SpectraPro, HRS-300-SS, Princeton Instruments). The excitation was provided by a Yb:KGW femtosecond laser (PHAROS, Light Conversion). The temperature controller is a cryostat (PS-HT-200, Nagase techno-engineering). At room temperature, spectra and decay profiles of 0.1 ns–10 ms were measured by streak camera with an exaction of the 343 nm femtosecond laser (Pulse energy = 2 μJ, width = 165 fs, repetition rate = 25 Hz) except DAAPC/3,7-PPT (400 nm). Decay profiles of >10 ms were measured using a multipixel photon counter (MPPC). Excitation conditions: 340 nm, 400 µW, 1 min, 300 K. LPL photographs of thick films were recorded on a Sony α7sII digital camera with the encapsulated sample excited using a 365-nm UV lamp at room temperature.

LPL measurements

The LPL spectra and decay profiles were obtained by a custom-built experimental setup (Supplementary Fig. 44a, b) based on a spectroradiometer (SR-5A, Topcon) or a laboratory-constructed measurement setup19 based on a silicon photomultiplier (MPPC module, C13366-1350GA, Hamamatsu Photonics) without wavelength sensitivity calibration and a multichannel photodetector (PMA-12, C14631-01, Hamamatsu Photonics). The fabricated film samples were encapsulated and placed in the dark box for room temperature measurements or in a cryostat (PS-HT-200, Nagase Techno-Engineering) for variable-temperature measurements. Samples were excited by various wavelengths of LEDs (M280L6, M340L5, M365LP1, M405L4, M455L4, M505L4, MINTL5, M595L4, Thorlabs) with plano-convex lenses (ASL2520-UV, Thorlabs) and bandpass filters (280 ± 5 nm, 340 ± 5 nm, 365 ± 5 nm, 400 ± 5 nm, 450 nm ± 5 nm, 500 ± 5 nm, 550 nm ± 5 nm, 590 ± 5 nm, Edmund Optics) with a specific excitation intensity and duration. LED excitation intensity was measured with a power meter (S120VC, Thorlabs). The LPL decay measured under the condition based on the brand ISO 17398 are excited by a 150 W Xe lamp (L14972, Hamamatsu). The scotopic and unified luminescence are calculated by the following functions8,41:

$$P={\int }_{380{{{\rm{nm}}}}}^{780{{{\rm{nm}}}}}I\left(\lambda \right){V}_{M}\left(\lambda \right)d\lambda$$
(2)
$$S={\int }_{380{{{\rm{nm}}}}}^{780{{{\rm{nm}}}}}I\left(\lambda \right)V^{\prime} \left(\lambda \right)d\lambda$$
(3)
$$L=\frac{\frac{X}{683}P+\frac{1-X}{1700}S}{\frac{X}{683}+\frac{1-X}{1700}}$$
(4)
$$X=\frac{L-0.001}{0.599}$$
(5)

where P, S, and L are the photopic, scotopic, and unified luminance, respectively. I(λ) is the spectral radiance distribution of the light source. VM(λ) is the CIE 1988 modified 20 spectral luminous efficiency function for photopic vision. V′(λ) is the CIE scotopic spectral luminous efficiency function. X is a parameter. Below 0.001 cd/m2, X = 0; above 0.6 cd/m2, X = 1.

Sample permittivity evaluation

The relative permittivities of electron acceptors (\({\varepsilon }_{{{{\rm{r}}}}}\)) were evaluated using displacement current measurement (DCM)53,54,55,56. In DCM, a triangular wave voltage (\(V\)) is applied to a sample, such as metal-insulator-(organic) semiconductor (MIS) devices, and the current response (\(I\)) is measured (Supplementary Fig. 23a). The current is expressed as

$$I=\frac{{dQ}}{{dt}}=C\frac{{dV}}{{dt}}+V\frac{{dC}}{{dt}}$$
(6)

where \(Q\) and \(C\) represent the charge amount and capacitance of the device, respectively. In the case where \(C\) does not depend on time, \(I\) is given by

$$I=C\frac{{dV}}{{dt}}$$
(7)

Because a ramp rate (\({dV}/{dt}\)) is constant with a positive value during the forward scan (\({dV}/{dt} \, > \, 0\)) and negative during the backward scan (\({dV}/{dt} \, < \, 0\)), a constant current, which is proportional to \(C\), flows during DCM (Supplementary Fig. 23b).

In organic MIS devices, the capacitance measured by DCM (\({C}_{{{{\rm{m}}}}}\)) is governed by a series combination of capacitances of the organic semiconductor (\({C}_{{{{\rm{o}}}}}\)) and the insulator (\({C}_{{{{\rm{i}}}}}\)) when charges are not injected. \({C}_{{{{\rm{m}}}}}\) can be expressed as

$${C}_{{{{\rm{m}}}}}=\frac{{C}_{{{{\rm{o}}}}}{C}_{{{{\rm{i}}}}}}{{C}_{{{{\rm{o}}}}}+{C}_{{{{\rm{i}}}}}}$$
(8)

Since \({C}_{{{{\rm{i}}}}}\) can be estimated if a dielectric material with a known relative permittivity is used, \({C}_{{{{\rm{o}}}}}\) is determied by DCM. Note that \({C}_{{{{\rm{o}}}}}\) is given by

$${C}_{{{{\rm{o}}}}}={{\varepsilon }_{{{{\rm{r}}}}}\varepsilon }_{{{{\rm{o}}}}}\frac{S}{d}$$
(9)

where \({\varepsilon }_{0}\), \(S\), and \(d\) indicate the dielectric constant of the vacuum, the device area, and the thickness of the organic layer. By using this equation, \({\varepsilon }_{{{{\rm{r}}}}}\) can be determied because \({\varepsilon }_{0}\) is constant, both \(S\) and \(d\) are design values of the device.

In this work, we prepared organic MIS devices with a structure of p+-Si/SiO2 (100 nm)/Electron accepter (\(d\) nm)/Al (100 nm). \(d\) of 3,7-PPT is 57 nm, while the other materials are 100 nm. \(S\) is 3.14 mm2 for all devices. In DCM, \(V\) was swept from –2 to 2 V, \({dV}/{dt}\) was set to be 100 V/s. DCM results are summarized in Supplementary Fig. 24.

Refractive index measurements

All samples of organic films for the VASE measurement were prepared using vacuum deposition on cleaned fused silica substrates in a vacuum of <10−4 Pa at an evaporation rate of <0.2 nm/s. The VASE measurement was performed using a fast spectroscopic ellipsometer (FLS-300, J. A. Woollam Co. Inc.). Measurements were taken at seven multiple angles of incident light from 45° to 75° in steps of 5°. At each angle, experimental ellipsometric parameters Ψ and Δ were simultaneously obtained in steps of 0.8 nm throughout the spectral region from 245 to 1000 nm. An analysis of the data was performed using the software WVASE32 (J. A. Woollam Co., Inc), which can perform a batch analysis of all data at all different incident angles and wavelengths, including the transmission spectra.

Analysis of the solvation effects

The solvatochromic effect follows Ooshika-Lippert-Mataga (OLM) equation57:

$${\bar{\nu }}_{{{{\rm{a}}}}}-{\bar{\nu }}_{{{{\rm{f}}}}}=-\frac{2}{{hc}}{\left({\mu }_{{{{\rm{e}}}}}-{\mu }_{{{{\rm{g}}}}}\right)}^{2}{a}^{-3}\Delta f+{{{\rm{const}}}}.$$
(10)

where \({\bar{\nu }}_{{{{\rm{a}}}}}\), \({\bar{\nu }}_{{{{\rm{f}}}}}\) are the average shifts in the frequencies of 0-0 absorption and fluorescence transitions in solution due to polar interactions. \({\bar{\nu }}_{{{{\rm{a}}}}}-{\bar{\nu }}_{{{{\rm{f}}}}}\) represents the Stokes shift. \({\mu }_{{{{\rm{e}}}}}-{\mu }_{{{{\rm{g}}}}}\) is the absolute magnitude of the charge-transfer dipole moment. The orientation polarizability (Δf) is defined as

$$\Delta f=\frac{\varepsilon -1}{2\varepsilon+1}-\frac{{n}^{2}-1}{2{n}^{2}+1}$$
(11)

where ε and n are the macroscopic relative permittivity and refractive index.

\({\bar{\nu }}_{{{{\rm{a}}}}}\), \({\bar{\nu }}_{{{{\rm{f}}}}}\) can be replaced with the peak positions of absorption and fluorescence, and if expressed in electron volts, Eq. (10) can be rewritten as

$${E}_{{{{\rm{a}}}}}-{E}_{{{{\rm{f}}}}}=-2{\left({\mu }_{{{{\rm{e}}}}}-{\mu }_{{{{\rm{g}}}}}\right)}^{2}{a}^{-3}\Delta f+{{{\rm{const}}}}.$$
(12)

When the emissive state is a charge-transfer state that is not attainable by direct excitation (absorption spectrum missing), based on Weller’s theory for exciplexes, Eq. (10) can be rewritten as

$${E}_{f}=2{\mu }_{e}^{2}{a}^{-3}\varDelta {f}^{{\prime} }+{{{\rm{const}}}}.$$
(13)

where \(\Delta f^{\prime}=\frac{\varepsilon -1}{2\varepsilon+1}-\frac{{n}^{2}-1}{4{n}^{2}+2}.\)

If the shift of fluorescence spectra in different polarity environments is solely due to the solvatochromic effect, then Ef as a function of Δf ′ should be a linear function, indicating a linear dependence in Lippert’s plot57.

Thermoluminescence (TL) measurements

The TL curves and spectra were obtained by a laboratory-constructed measurement system (Supplementary Fig. 44c) based on a photomultiplier tube (H11890, Hamamatsu Photonics) without wavelength sensitivity calibration and a multichannel photodetector (PMA-12, C14631-01, Hamamatsu Photonics). The excitation light source is 280 or 340 nm LED (M280L6, M340L5, 365 ± 5 nm, Thorlabs) with plano-convex lenses (ASL2520-UV, Thorlabs) and bandpass filters (280 ± 5 nm, 340 ± 5 nm, 365 ± 5 nm, Edmund Optics). The dwell time (t0) for TL spectrum maps and curves were set as 1 h and 9940 s, respectively (Supplementary Fig. 44d). For TL spectrum maps, film thicknesses are about 0.5 mm. For TL curves measurement, film thicknesses are 50 ± 14 μm (2,8-PPT), 50 ± 9 μm (1 mol% DDATA/2,8-PPT), 21 ± 6 μm (1 mol% DAAPC/2,8-PPT).

Quantum-chemistry calculations

Evaluation of intramolecular CT and LE components in donor molecules: The ground-state geometries of the ground states of all isolated donor molecules were optimized at the B3LYP/6-31 G(d) level. TD-DFT calculations were then performed on these donor molecules at the ωB97XD/6-31 G(d) level. The DFT levels were performed with Gaussian 1658. Multiwfn v3.859 was used to perform hole-electron analysis.

Simulation of DAAPC/2,8-PPT, DDATA/2,8-PPT, a2,8-PPT/2-PPT

For the isolated DDATA, DAAPC, 2,8-PPT, and 2-PPT molecules, the ground-state geometries were optimized at the B3LYP/6-31 G(d) level. The doping configuration and spatial molecular packing of guest molecules in the host matrix were first generated by using the Molclus program60, and then, the geometrical structures of the D/A clusters consisting of a donor molecule (DDATA or DAAPC) and 10 acceptor molecules (2,8-PPT or 2-PPT) were optimized by semiempirical quantum-chemistry approach PM7 with a dispersion correction.

With the above optimized clusters by PM7, the D/A molecular pairs were extracted, and their excited-state transition energies and oscillator strengths were calculated by time-dependent DFT calculations based on the Tamm–Dancoff approximation61. Here, the PCM solvation model was used for all the calculations to imitate the dielectric environment in solids. TD-DFT calculations were then performed on these extracted D/A molecular pairs at the ωB97XD62 level with the non-empirical tuned ω set of 0.0020–0.0051. The tuning ω was carried out using xwtune program63. Geometry optimizations of the ground states at the PM7 and the DFT levels were performed with Gaussian 1658. Multiwfn v3.859 was used to perform hole-electron analysis.