Introduction

The ultimate challenge in manipulating conjugated molecules1,2 for optoelectronic applications is to develop universal approaches capable of controlling excited states for efficient electron-light conversions, affording not only conventional fluorescence3 and phosphorescence4, but also many other photophysical phenomena including triplet-triplet annihilation (TTA)5, singlet fission (SF)6 and thermally activated delayed fluorescence (TADF)7. The rich photophysical properties of organic molecules have led to many revolutionary developments in organic electronics8. Notably, the TTA compounds, which can harvest one singlet exciton from two low-lying triplet excitons, can benefit OLEDs with improved external quantum efficiency (EQE) theoretically up to 12.5% by harvesting the 75% electronically generated triplet excitons to produce singlet excitons for fluorescence9; the SF process, which transforms a singlet exciton into two triplet excitons on neighboring molecules with EQE up to 200%, is especially attractive for solar cells in providing doubled photocurrent from high-energy photons10; the recently developed TADF materials by harvesting 100% triplet excitons via reversed intersystem crossing have achieved EQEs of 20.6% in blue and 30.0% in green TADF OLED devices11,12, which are comparable to the heavy metal-based phosphorescent emitters13,14.

To control the triplet/singlet excited states in a designed manner for a desired optoelectronic property, the rational adjustment of the singlet-triplet energy gap (ΔEST) between the first singlet (S1) and triplet (T1) excited states is the key. Typically in Fig. 1, when ΔEST normally laid between 0.5 and 1.0 eV7 in conventional compounds is reduced (ΔEST ≤ 0.37 eV)15, TADF could be resulted via activated endothermic RISC process from T1 to S1 by the thermal motions of the molecule atoms for the E-type delayed fluorescence16. Meanwhile, when the ΔEST is increased and the energy of two triplet excitons are close to, or larger than, one singlet exciton (ET1/ES1 ≳ 0.5), TTA could happen between triplet exciton interaction pair following the spin statistics rule17. SF process, either isoergic or slightly exoergic in producing two triplet excitons with a net spin of zero, is spin-allowed and favorable for fast generation of doubled triplet excitons from high-lying singlet excitons, when S1 excitation energy is comparable with twice the energy of T1 excitation (ET1/ES1 < 0.5)18.

Figure 1
figure 1

Energy level diagrams depicting diversified photophysical processes determined by singlet-triplet splitting (ΔEST) between energies of the lowest singlet (ES1) and triplet (ET1) excited states.

Noted that F, P, DF, TADF, TTA, SF represent fluorescence, phosphorescence, delayed fluorescence, thermally activated delayed fluorescence, triplet-triplet annihilation and singlet fission, respectively. The weak emissions and transitions are in dotted line.

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Extensive efforts have been so far devoted to reducing ΔEST via separated the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) strategy to construct efficient TADF molecules8. In contrast, TTA and SF molecules were designed by enhancing HOMO-LUMO overlap to the maximum possible degree with enlarged ΔEST18,19. Consequently, efficient TADF compounds were generally found in donor-acceptor (D-A) molecules20, while TTA and SF compounds were mostly observed in alternant hydrocarbons with an even number of carbons in conjugated close-shell S0 systems18. Considering the four-electron picture transformation of SF process, the involvement of charge transfer (CT) character through either inter- or intra-molecular D-A interactions is also crucial for the ultrafast fission21,22. However, despite these advances to date, it remains a challenge to rationally manipulate ΔEST in a large scale via subtle molecular structure adjustments to produce energy levels applicable not only for TADF but also for TTA and SF processes.

The lack of quantitative means in descripting HOMO-LUMO overlap and separation extents should be a main obstacle in establishing accurate relations between ΔEST and molecular structures. Here, we demonstrate a convenient approach in quantifying the frontier orbital overlap and separation with a set of new parameters in both S1 and T1 states. With the aid of these quantitative parameters, we proposed a molecular symmetry controlling strategy to fine tune the excited state energy levels for accommodation of excitons with diversified spin states and for the support of their varied excited state transfer processes following corresponding photophysical mechanisms of TADF, TTA and SF. In a typical example demonstrated in 1,3,5-triazine-based molecules, we designed a series of symmetric and asymmetric triazines and successfully realized a widely varied ΔEST in a range from ultralow (0.0003 eV) for TADF and extra-large (1.47 eV) for SF according to time-dependent density functional theory (TD-DFT) calculations and experimental measurements of selectively synthesized molecules. The widely-tuned ΔEST via a subtle symmetric control in a uniform molecular architecture is attractive not only for providing a practical guide for material design of TADF, TTA and SF processes, but also for developing a better understanding of the factors that influence the energy levels and spin states of the excited states of organic optoelectronic molecules.

Results

Theoretical considerations

The lowest singlet-triplet splitting (ΔEST) between the molecular energies at the lowest singlet (ES1) and triplet (ET1) excited states were equal to twice of the electron exchange energy (J) as illustrated in equation (1) and (2), where J is determined by the spatial separation and overlap extents of HOMO (φH) and LUMO (φL)23. From equation (3), the ΔEST is closely related to the frontier orbital overlap extent and separation distance at S0 state; higher overlap of HOMO and LUMO and smaller spatial separation (r1 – r2) lead to higher J and ΔEST.

The orbital overlap extent (IH/L) between HOMO (H) and LUMO (L) can be calculated using the overlap integral function of Multiwfn (eq. (4))24. Mean separation distance (<rH/L>) of HOMO and LUMO can be obtained from the barycenter (rtot) of the absolute value of the corresponding molecular orbitals (equation (5, 6, 7, 8))25. Similarly, the overlap extent and mean separation distance between the highest occupied natural transition orbitals (HONTOs) and the lowest unoccupied natural transition orbitals (LUNTOs) at both S1 (IS and <rS>) and T1 (IT and <rT>) states were also calculated to give a full-picture analysis of the factors that influence ΔEST. The detailed definitions and calculations of ΔEST, IH/L, IS, IT, <rH/L>, <rS> and <rT> were presented in Supplementary Information.

Molecular design

Triazine, which possesses high electron affinity and good thermal stability, is chosen as a basic building block to demonstrate our ΔEST tuning strategy for achieving varied photophysical behaviors of TADF, TTA and SF in a uniform molecular architecture with symmetry control. The symmetric or asymmetric substitution of various donors or acceptors on three reactive sites of 1,3,5-triazine have resulted in a large number of triazine-based molecules with varied optoelectronic properties26. The competition and coordination effects between the substituents, triazine core and the D-A molecular architecture significantly tuned the molecular energy structures for the singlet and triplet excitons transitions when excited either optically or electronically and thus leading to rich and/or exceptional optoelectronic properties27. Here, we designed a series of triazine-based molecules bearing various donors and acceptors substituted asymmetrically (labeled as A1, etc.) and symmetrically (labeled as S7, etc.) at three substitution sites of the triazine core (Fig. 2, S1 and S2). Triazines of A2, A3 and A4, were experimentally investigated in the literature27,28, while S9 and A15 were synthesized in this study (Scheme S1) and their properties were measured to verify the computational results.

Figure 2
figure 2

Molecular structures and ΔEST of asymmetric (A1–A6) and symmetric (S7–S10) triazines.

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Singlet-triplet splitting (ΔEST)

As a key parameter in determining the exciton migration and population on excited states, ΔEST is of the most importance8. To choose an optimal calculation approach to evaluate ΔEST, TD-DFT methods including B3LYP, PBE0, BMK, M062X, M06HF and long-range correction functionals (ωB97XD and CAM-B3LYP) at 6–31G(d) basis set level were tested. Compared to the experimental ΔEST values (Fig. S3 and Table 1), it is clear that B3LYP gives the best prediction of ΔEST not only for molecules with small ΔEST but also those with large ΔEST. In the following investigations, B3LYP/6-31G(d) was selected to predict ΔEST of the designed compounds that lack experimental explorations. The calculated ΔEST demonstrate that the asymmetric triazines have small ΔEST ranging from 0.001 to 0.46 eV, while the symmetric triazines show high ΔEST up to 1.47 eV. Thus, a wide controlling range of ΔEST from almost zero to 1.47 eV has been successfully realized in a uniform molecular system by adopting the conventional symmetry control of triazine substituents (Scheme S2).

Table 1 Calculated ΔEST (eV) and frontier orbital overlap extents (IH/L, IS and IT (%)) using various functionals at 6–31G(d) basis set level in comparison with experimental data of ΔEST (eV).
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The origin of the different effects of symmetric and asymmetric substituents on triazines was investigated via frontier orbital analysis. Theoretically, the HOMO is dominated by donor moiety while the LUMO is by acceptor moiety29. As a result, the strong donors of tricarbazole and indolocarbazole substituents generally lead to high-lying HOMOs; the strong acceptors of benzonitrile, benzothiazole and pyrrolo[3,2-b]pyrrole lead to low-lying LUMOs30; the LUMOs and HOMOs of the symmetric triazines are degenerated due to their symmetric molecular structures. The electron density distributions of the triazines also support the above analysis, where the HOMOs are delocalized on the donor moieties and the LUMOs are on the acceptor moieties (Fig. S4 and S5). The asymmetric triazines tend to produce asymmetric distributions of electron density, leading to clearly separated HOMOs and LUMOs. This distinct difference of the frontier orbital distributions between symmetric and asymmetric triazines should be the main reason for their distinct difference in ΔEST.

HOMO-LUMO overlap extent

To give a quantitative investigation of HOMO-LUMO overlap, their overlap extent (IH/L) was calculated using Multiwfn24. As illustrated in Fig. 3a, ΔEST gradually increases from A1 to S10, when molecular symmetry changes from asymmetric to symmetric with increasing IH/L. However, in the cases of compounds A5 and A6, despite their obvious HOMO-LUMO separation with low IH/L and comparable average HOMO-LUMO separation distance (<rH/L>) to that of A1 which has an ultralow ΔEST, they exhibit quite large ΔEST. This is apparent contrary to the general understandings expressed in equation (1, 2, 3, 4, 5, 6, 7, 8), suggesting that there are also other undiscovered factors that influence ΔEST significantly.

Figure 3
figure 3

The influence of the frontier orbital overlap on ΔEST.

(a) The relations between the calculated ΔEST, IH/L, IS and IT of triazines. Insets: HONTO and LUNTO for S1 and T1 of A1, A6 and S10 from left to right, respectively; (b) The types of triazines with different HONTO-LUNTO overlap patterns at S1 and T1 states.

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The inconsistence between IH/L and ΔEST can be also observed in TADF molecules (compound 2 in Table S1) experimentally investigated by Adachi et al.11 recently. Notably, this inconsistence may not be the calculations errors of B3LYP; other methods also well reproduced the mismatch between IH/L and ΔEST (Table S2). One main reason for this mismatch is possibly that it is not accurate to use only one transition mode of HOMO → LUMO to describe the transition nature of S1 or T1 states. The TD-DFT calculations usually describe excited states in terms of various combinations of transitions between canonical molecular orbitals and S1 and T1 are described by a set of transitions, e.g., HOMO → LUMO, HOMO → LUMO + 1, etc31. Thus, a simple consideration of HOMO → LUMO transition may overlook intrinsic photophysical essence, leading to false estimations of optoelectronic properties and ΔEST, especially when the content of HOMO → LUMO transition is low or symmetrically forbidden. From Tables S1 and S3, the HOMO → LUMO transition was absent in the compositions of T1 of compounds 2, A5 and A6, leading to obviously mismatched IH/L and ΔEST.

The HONTO-LUNTO overlap extent

To consider a whole picture of electron transitions in excited states, natural transition orbital (NTO) analysis, obtained via the singular value decomposition of the 1-particle transition density matrix (T), was performed to offer a compact orbital representation for the electronic transition density matrix31,32. All one electron properties associated with the transition can be interpreted in a transparent way as a sum over the occupied natural transition orbitals, each orbital being paired with a single unoccupied orbital, weighted with the appropriate eigenvalue, providing a convenient description of an excited state with fewer orbital pairs than the ones given on the basis of frontier molecular orbitals. The overlap extents between HONTO and LUNTO at S1 (IS) and T1 (IT) states, which take full considerations of electron transition components at the corresponding excited states, were also calculated using Multiwfn24. From Fig. 3a, symmetric triazines generally have high IS and IT, but high IT can be also observed in asymmetric molecules, leading to relatively large ΔEST of those compounds33. Typically, in compounds of A5 and A6 that were misunderstood by low IH/L, their IS are very low (<5%), but the IT are around 80%, suggesting that there are severe overlaps at T1 and the high IT should be very likely the main reason for their relatively large ΔEST (~0.45 eV).

Take a close look at the HONTO and LUNTO distributions at S1 and T1. When ΔEST is extremely low (0.0011 eV) as in A1, both HONTO and LUNTO are separated with low IS and IT (~5%); when ΔEST is relatively high (0.46 eV) as in A6, HONTO and LUNTO are separated at S1 with low IS (<5%) but they are overlapped at T1 with high IT (~80%); when HONTO and LUNTO are overlapped at both S1 and T1 with high IS and IT (~50% and 80% respectively) as in S10, very high ΔEST (1.47 eV) can be resulted. To this end, three types of molecules can be distinguished according to HONTO and LUNTO overlap pattern (Fig. 3b). In Type A, ultralow ΔEST is resulted from the separated HONTO and LUNTO at both S1 and T1 (small IS and small IT) states. In Type B, moderately low ΔEST can be observed with separated HONTO and LUNTO at S1 state but overlapped HONTO and LUNTO at T1 (small IS but large IT) state. Type C has large ΔEST due to overlapped HONTO and LUNTO at both S1 and T1 states (large IS and large IT). The newly revealed relation between ΔEST and overlap extents of IS and IT highlights the importance of full consideration of molecular orbital participations at related spin states, when studying the exciton transfer processes between these excited states. Notably, these finds are independent of TD-DFT computational functionals; as presented in Table 1, same relations can be also concluded from other computational methods.

The frontier orbital separation distance

The success in dividing molecules into Types A, B and C according to IS and IT qualitatively cannot be achieved when analyzing their individual difference quantitatively. For example, S7 has higher IS and similar IT in comparison with S8, but its ΔEST is quite lower than that of S8. The same inconsistence can be also found between A4 and A5. From equation (3), ΔEST was determined not only by the molecular orbital overlap but also by their separation distance34. Larger separation distance leads to lower ΔEST35. Hence, we need to further quantitatively investigate the effects of mean separation distances between HOMO and LUMO (<rH/L>) and between HONTO and LUNTO at S1 (<rS>) and T1 (<rT>).

From A1 to S10 whose ΔEST increases gradually, the expected gradually decreased <rH/L> was broken obviously by A5 and A6; A5 has the largest <rH/L> (Fig. 4a). This abnormal is in line with their unexpectedly low IH/L in Fig. 3a, indicating again the inaccuracy of IH/L and <rH/L> in assessing ΔEST. Benefited from NTO analysis on the whole picture of the electron transitions for the excited states, the low <rT> of A5 and A6 should be a main reason for their high ΔEST, although their <rS> are also quite high. Notably, symmetric triazines generally have lower <rH/L>, <rS> and <rT> than asymmetric triazines, resulting in the high ΔEST according to equation (3).

Figure 4
figure 4

The influence of the frontier orbital separation distance on ΔEST.

(a) The <rH/L>, <rS> and <rT>. (b) The values of ΔEST/(IH/L2/<rH/L>) and ΔEST/(IS2/<rS> + IT2/<rT>).

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To elucidate quantitative relations between ΔEST and factors of IH/L and <rH/L>, we simplified equation (3) to get equation (9) (see Supplementary Information).

where ΔEST is in eV and <rH/L> is in Å. From the 35 compounds except for A5 and A6, the average ΔEST/(IH/L2/<rH/L>) is 25.7 (Fig. S6)36, which is very close to the 28.8 in equation (9). The very high values observed in A5 and A6 (Fig. 4b) suggest again the unfitness of the normal HOMO-LUMO transition analysis, since there are very low HOMO → LUMO transition components for their T1 states. Therefore, it is necessarily to address not only the conventional HOMO → LUMO transition but also the other frontier orbital transition components.

With the aid of NTO analysis to contain all the possible transitions, new parameters of IS, IT, <rS> and <rT> were obtained and found to be useful in investigating the influence factors of ΔEST. The quantitative relations were supposed to be a linear combination of S1 and T1 components in equation (10):

where CS and CT are combination constants of S1 and T1 states, respectively. From all the compounds studied (A1 ~ S37) including A5 and A6, the nonlinear least square fitted CS and CT are found to be 0.23 and 0.39 respectively with R-square of 0.9685. If CS is set to be equal to CT, they were changed to 0.385 with R-square of 0.9912. The higher CT than CS in the first fit with slight decrease in the second fit, suggests that the T1 component plays a dominate role in determining ΔEST. For all the 37 studied compounds, ΔEST/(IS2/<rS> + IT2/<rT>) varies in a relatively narrow range from 0.15 to 11.16 (Fig. 4b and S6), indicating that the simplified equation (10) presents a good correlation between ΔEST and parameters of IS, IT, <rS> and <rT> derived from NTO analysis. Thus, it is advisable to consider the whole picture of frontier orbital transitions (HONTO and LUNTO) at both S1 and T1 states to accurately understand ΔEST tuning.

Design of ideal TADF molecules with ultralow ΔEST

In light of the sophisticated tuning of ΔEST via symmetric control on IS and IT and distance control on <rS> and <rT>, we first use the above developed molecular design strategy to construct high-performance TADF molecules with ultralow ΔEST; the development of novel TADF molecules is one of the hottest topics in current research of organic electronics8. To test the validity of the above studies on the relations between ΔEST and these new parameters of IH/L, IS, IT, <rH/L>, <rS> and <rT>, four efficient TADF molecules recently reported by Adachi and co-workers11 was investigated. Indeed, the smaller IH/L cannot lead to lower ΔEST; the larger ΔEST can be explained by the larger IT of these molecules (Table S1); the higher IS with higher frontier orbital overlap at S1 state may lead to higher luminescent efficiency of the D-A molecules when the low IT can still maintain a small ΔEST. Still, these finds are independent of calculation methods (Table S2). Our approach gave a good prediction on the reported experimental results, indicating the high reliability of these new parameters for ΔEST describing.

Based on triazine architecture, we adopt an asymmetric molecular structure to minimize ΔEST by fine-tuning the substitution positions and varied types of donor and acceptor substituents37. Started from the asymmetric triazine molecule of A3, which is an efficient host material for phosphorescent OLED with experimental ΔEST of 0.34 eV27, we enhanced the electron donating ability of the carbazolyl substituent by introducing additional donors of carbazole at 2,7- or 3,6- position; on the other hand, we enhanced the electron accepting ability of the two phenyl substituents by attaching the strong acceptor of cyano group (CN) at the para (p), meta (m), or ortho (o) positions (Fig. 5a). According to the TD-DFT calculations, this strategy is succeed in producing ultralow (almost zero) ΔEST especially in A1, A13 and A14, when the additional donors are connected through 2,7-positions of the carbazolyl substituent and the CN is introduced either at p, m, or o position. The 3,6- connection results in slight HOMO distribution on triazine core, which will overlap with LUMO distribution, leading to slightly higher ΔEST of A11 (Table S4 and Fig. S5a). Besides carbazolyl substituents, other electron donating groups such as alkyl, phenyl, diamine, alkoxyl, etc. as in A16 ~ A21, are also effective in reducing ΔEST (Fig. S5b). But, without the additional donors to increase the HOMO, ΔEST will be apparently increased as found in A15. Also, without the additional acceptors on the phenyl substituents to reduce the LUMO, ΔEST will be large as in A22. Still, other kinds of accepting groups of trifluoromethyl, diphenylphosphoryl, nitryl, diphenylboronyl and 2-methylenemalononitrile in A24 ~ A28, work well too, producing ultralow ΔEST (low to 0.0003 eV in A28) (Fig. S5c). However, fluoro and benzothiazolyl substitution cannot lead to low ΔEST due to their failure in avoiding overlap at both S1 and T1; the large IT and small <rT> of A5 and A23 clearly indicates the large overlap at T1 states (Fig. 5a,b). Compared to the experimentally investigated TADF molecule of A2, which has exhibit an external quantum efficiency (EQE) of 14% ± 1% with the experimental ΔEST of 0.02 eV and calculated one of 0.09 eV based on B3LYP/6-31G(d) (Table 1)28, these newly designed TADF molecules are expected to have improved device performance, considering their well separated S1 and T1 with low IS and IT and long <rS> and <rT> simultaneously.

Figure 5
figure 5

The ΔEST of the designed asymmetric triazines TADF molecules.

(a) The overlap extents of IH/L, IS and IT and (b) the average frontier orbital separation distances of <rH/L>, <rS> and <rT>. Insets: HONTO and LUNTO for S1 and T1 of A5 (left) and A28 (right).

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Design of TTA and SF molecules with large ΔEST

Contrary to the asymmetric triazine-based TADF molecules showing very low ΔEST, symmetric triazines can lead to large ΔEST which is required for TTA and SF molecules. According to equation (9) and (10), large ΔEST needs large IH/L, IS and IT as well as short <rH/L>, <rS> and <rT>. In other words, large transition orbital overlap with localized excitation will result in large ΔEST34. Here, two approaches were adopted to design symmetric triazine-based TTA and SF molecules. The first one is to use electron-withdrawing substituents to make the S1 and T1 locally excited. The other one is by introducing polycyclic aromatic fragments, which have been widely used in many TTA and SF molecules due to their large conjugation beneficial for electron localization at excited states.

In Fig. 6a, the molecules are arranged in an increasing order of ΔEST from 0.92 to 1.47 eV. When ET1/ES1 is close but higher than 0.5, TTA process is supposed potentially to be applicable; when ET1/ES1 is lower than 0.5, SF process is possible18,19. According to these criterions, S10, S34 and S35 are SF molecules, while S29 ~ S33, S36 and S37 are TTA molecules. From Fig. S7, the electron acceptor of triazine core participates the formation of LUMO to a large content for all the symmetric compounds, while it shows only apparent effects on HOMOs of S36 and S37 whose substituents are acceptors, because HOMO is dominated by the donor unit in D-A molecules. Delocalized HONTO and LUNTO at both S1 and T1 of S36 was also observed, which is in contradictory to the D-A molecule of S35 (Fig. S8a and b). The more localized and overlapped HONTO and LUNTO of S35 makes it a good SF molecule with lower ET1 and ET1/ES1. Notably, the increase of ΔEST will not certainly leads to SF molecules; the T1 energy of S36 and S37 are comparably too high (Table S5), resulting in ET1/ES1 > 0.5, although their ΔEST are among the largest ones. The high-lying T1 may have close relations with the triazine core38. The large participation of the triazine core at T1 of S36 was further confirmed by its delocalized spin density distribution (Fig. S8c). Since the triazine core has high T1, its large participation may enable the compound to inherit the high T1 of triazine, resulting in high ET1/ES1 of S36 and S37.

Figure 6
figure 6

The designed symmetric triazines for TTA and SF.

(a) ΔEST and ET1/ES1; (b) IH/L, IS, IT, <rH/L>, <rS> and <rT>.

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From Fig. 6b, significantly higher IH/L and shorter <rH/L> of the symmetric triazines in comparison with that of asymmetric triazines were observed, demonstrating the success in modifying the molecular orbital overlap and separation distance via symmetry control in designing molecules with large ΔEST for TTA or SF processes. As further revealed by IS and IT, heavier overlap seems to happen at T1 with much shorter <rT> than <rS>, highlighting the dominative role of T1 in the enlargement of ΔEST. For the construction of triazine-based TTA and TADF molecules, they can be facilely designed by symmetrically introducing TTA molecules of perylene, pyrene and anthracene or SF molecules of naphthacene and pentacene correspondingly. Typically, the S1 energy of S10 with the largest ΔEST of 1.47 eV is more than twice higher than its T1 energy, affording S10 to be a good candidate for SF process18.

Discussion

We have succeed in manipulating excited state electronic structures for accommodation of various organic excitons via symmetry control of ΔEST in a wide range from ultralow (0.0003 eV) for TADF and extra-large (1.47 eV) for SF all in a triazine-based molecular architecture based on a combined quantum chemistry modeling and experimental exploring. The HOMO-LUMO overlap (IH/L) and separation distance (<rH/L>) were quantified successfully. It was found that asymmetry triazines possess separated HOMO-LUMO with low IH/L and long <rH/L>, leading to low ΔEST; while symmetry triazines contain highly overlapped HOMO-LUMO with high IH/L and short <rH/L>, resulting in large ΔEST. However, it is difficult for IH/L and <rH/L> to well describe ΔEST. Consequently, we further developed a set of new parameters of IS, IT, <rS> and <rT> benefitted from NTO analysis to consider whole pictures of the electron transitions at both S1 and T1 states. According to these firstly proposed parameters, three types of molecules can be classified. Type A has ultralow ΔEST due to both separated S1 and T1 with low IS (long <rS>) and IT (long <rT>); Type B has small ΔEST due to separated S1 but overlapped T1 with low IS (long <rS>) and high IT (short <rT>); Type C shows large ΔEST due to overlapped S1 and T1 with high IS (short <rS>) and IT (short <rT>). A quantitative relation between ΔEST and IS, IT, <rS> and <rT> was established and the T1 component was found to play a dominate role in determining ΔEST. These findings are important in providing quantitative approaches for fundamental understandings on the intrinsic factors influencing ΔEST tuning, representing a major step towards technological advances in expanding the scope of excited state manipulation.

Methods

The molecular geometries in the ground state (S0) were optimized via spin-restricted DFT calculations at the B3LYP/6-31G(d) level of theory using Gaussian 09 package39. The spin-unrestricted formalism was used in geometry optimization of the lowest triplet excited state (T1). Vibrational frequency calculations were subsequently carried out to confirm that all the optimized structures are corresponding to the minima on the potential energy surfaces. The excited singlet (Sn) and triplet (Tn) states were investigated by the time-dependent DFT (TD-DFT) formalism with the same functional and basis set of B3LYP/6-31G(d) on the optimized ground-state geometries40. TD-DFT calculations based on the standard B3LYP functional offer a reasonable description for singlet and triplet states of medium-sized molecules, which has been widely used in the theoretical studies of TADF, TTA and SF molecules11,41. To obtain a precise picture of the excited states, we further performed natural transition orbitals (NTOs) analysis, which can offer a compact orbital representation for the electronic transition density matrix36.

To get a solid support of the computational study, the experimental measurements of the synthesized triazines were analyzed and compared. The detailed synthesis, structure characterizations and photophysical property measurements of these triazines can be found in Supplementary Information.

Additional Information

How to cite this article: Chen, T. et al. Understanding the Control of Singlet-Triplet Splitting for Organic Exciton Manipulating: A Combined Theoretical and Experimental Approach. Sci. Rep. 5, 10923; doi: 10.1038/srep10923 (2015).