Introduction

The TADF mechanism is based on a second-order spin-vibronic coupling between a charge transfer triplet state ( 3 CT) and a local excited triplet ( 3 LE) to mediate the up-conversion reverse intersystem crossing (rISC) of the coupled 3 LE/ 3 CT triplet(s) to the emissive charge transfer singlet ( 1 CT) state [1]. Building on the previous findings [2] and aiming to better understand the connection between analogous D-A and D-A-D molecules, we investigate two isomeric D-A-D TADF emitters comprised of a benzonitrile acceptor and acridine donors attached at the 2,5-or 2,6-positions of the acceptor. Comparison to previously reported D-A materials (facilitated by the self-regulating dihedral angle of DMAC) allows us to compare these systems with minimal additional complexity introduced by the second D unit. Using a combination of experimental and theoretical methods, it was demonstrated that electronic interaction between the donating moieties -modulated by the relative position of each -alters the 3LE energy and thus also ΔE ST and TADF performance.

Computational methodologies, such as DFT, have been developed to bypass time-consuming empirical procedures for the optimization of these formulations.

DFT computations, in particular, offer outstanding levels of accuracy with comparable computation time and are more inexpensive in terms of computational resources than other ab initio approaches currently in use. Additionally, it avoids the many electron wave function in favor of electron density, and has the potential benefit of dealing with only one function of a single spatial coordinate. Moreover, it employs generalized gradient approximations (GGAs), which use the density gradient to generate a more precise function [3].

DFT are a strong and low-cost method for revealing a material's fundamental information, including energy, geometric structure, electrical, and optical characteristics. It offers important theoretical predictions and assistance from the standpoint of material design. It provides crucial information at the levels of atoms, molecules, and unit cells from the perspective of interpreting the results. The influence of element doping on the geometric and electrical characteristics of organic compounds carriers, as well as the interaction between the molecules and the nanocarriers, is considerably aided by DFT calculations [4].

Experimental section 2.1. Related Works

DFT calculation is a primary tool in predicting and investigating excited state configuration, excited state energy, and molecular geometry of TADF molecules [5]. As with the experimental investigation of TADF molecules, most of the research focuses on excited state configurations and energies of relaxed geometry of excited states and explain experimental phenomena with discrete geometries or excited states such as 1 CT, 3 CT, and 3 LE states. Some researches attempted to relate D-A dihedral angle with S 1 and T 1 energies, but they have several limitations; (1) a large discrepancy with experimental energies due to inappropriate selection of functional, (2) lack of explanation to the effect of dihedral angle to excited state configurations or energies of S 1 /T 1 states, or (3) mixed level of theory for S 1 and T 1 leading to inverted S 1 /T 1 energies [6]. These problems arise from difficulties in handling triplet states with TD-DFT due to the so-called triplet instability stemming from the exchange-interaction-sensitive nature of triplet states [7].

Methodology

Quantum chemical calculations of studied derivatives were performed using DFT and TD-DFT implemented in the Gaussian 16 [8] software package. Geometry optimization was provided by means of density functional CAM-B3LYP method and 6-31g(d,p) basis set in the ground S 0 state as well as the lowest excited S 1 state [9].

Results and Discussion

DFT Calculations

To better understand the behaviour of organic compounds we turn to DFT calculations. Figure 1 shows the NTOs and energies calculated for relevant triplet and singlet states in (o,m)ACA and (o,o)ACA. By inspecting the singlet NTOs in (o,m)ACA we first note that the CT singlet associated with the ortho-donor (S 1 ) is lower in energy than that associated with the meta-donor CT state (S 2 ). This is in agreement with expectations and the trends established for oDA and mDA. In (o,o)ACA the S 1 and S 2 states are much closer in energy, and each involves both of the ortho-donor units. These represent symmetric (S 1 ) and antisymmetric (S 2 ) combinations of otherwise degenerate CT states associated with either the left or right donor individually. This is analogous to the formation of symmetric (bonding) and antisymmetric (antibonding) molecular orbitals from combinations of degenerate atomic orbitals (Figure 2a). For the first two triplet states of CT nature similar trends are observed. The first triplet state of LE nature is T 3 , centred on the A unit in both materials and with nearly identical NTOs. This LE triplet state is the one relevant to vibronic coupling and rISC. Interestingly, the calculated T 3 energies of (o,m)ACA and (o,o)ACA are in the opposite order as found experimentally, with about the same difference in triplet energies in both cases (~50 meV). The reason for the experimental (o,m)ACA triplet energy being lower than (o,o)ACA cannot be due to the combination of individual couplings of the A to the two D units. The two materials to either have identical triplet energies (from coupling between the A and the ortho-D in each material), or for (o,m)ACA to have a higher triplet energy than (o,o)ACA (due to coupling between A and meta-D, which is intrinsically higher in energy as in mDA). Any such state-mixing between LE and CT states is also unlikely to be a contributing factor, due to the forbidden nature of mixing these states with different orbital symmetries [10].

The LE T 3 states in both (o,m)ACA and (o,o)ACA interact with higher-lying LE states delocalised across both donor units (D-D states). A representative state diagram is presented in Figure 2b, showing how these unoccupied electronic states would form.

The proposed D-D states are formed by linear combinations of the individual donor LE states (Figure 2b), and so one of these D-D states (the symmetric combination) is expected to be the lowest-

Energy / [eV]

energy LE singlet state in each molecular system. These D-D states are also unoccupied, which explains why the DFT calculations are unable to accurately predict the order of (o,m)ACA and (o,o)ACA T 3 energies compared to experiment. Accurately accounting for such interactions with unoccupied states would instead require more advanced multireference or complete active space abinitio methods, which are impractical for molecules of this size.

Applying molecular orbital theory in the symmetric and asymmetric D-A-D systems, we can infer several properties of the D-D states and how they would differ. Due to different conjugation strengths across the linker unit for (o,m)ACA (pD-D state) than for (o,o)ACA (mD-D state), the pD-D state to be lower in energy and have larger electron density on the central bridge region (Figure 2b). This would subsequently lead to a larger overlap between the pD-D state and the 3 LE state associated with the A unit (3LE A ) in (o,m)ACA as compared to mD-D in (o,o)ACA. The resulting state mixing between D-D and 3LE A states lowers the observed phosphorescence energies in both materials compared to calculations, which cannot account for interactions with unoccupied orbitals. Due to increased orbital overlap the state mixing with the 3LE A is more extensive for pD-D than for mD-D, leading to a yet lower triplet energy in (o,m)ACA and the observed ordering of experimental phosphorescence energies (Figure 2c). While other higher-energy LE states would also be influenced by interactions with the D-D states, none of these higher LE states are measured or expected to influence the TADF properties. Due to differences in orbital symmetry the CT states are not expected to interact with the D-D states, and so are totally unaffected both in calculations and experiment. The lower triplet energy in (o,m)ACA is therefore identified as an emergent property of the pair of donors. This lowering of triplet energy is irrelevant to the analogous oDA or mDA materials, and is impossible to predict by considering these fragments in isolation.

Although based on well-established principles of molecular orbital theory, much of the previous explanation is speculative. Nonetheless some evidence for the existence of the proposed D-D states can be found in the experimental absorption spectra (Figure 3). the mD-D state is expected to exist at higher energies, and therefore remains subsumed by the main donor DMAC absorption band. Furthermore, the absorbance spectra also show the same weak direct CT absorption bands in both (o,o)ACA and (o,m)ACA at ~375 nm. In each material this band corresponds to two closely spaced CT state absorptions, consistent with the DFT calculations and prior understanding of the oDA or mDA materials. In both cases this indicates that formation of the CT state involves only a single donor, and is unimpacted by the presence of the other (consistent with both materials sharing the same PL spectrum). Because (o,m)ACA and (o,o)ACA introduce minimum additional complexity compared to oDA or mDA, there are few other explanations aside from D-D interactions that can potentially explain the trends seen here. While an intuitively satisfying example of basic physical chemistry principles in action, these results also demonstrate a new method of control in TADF materials. In contrast to external host-tuning of CT singlet states to minimise ΔE ST , multi-donor interactions may in future be used as a tool to selectively tune triplet states. These results also firmly demonstrate that 'bottom-up' approaches to understanding TADF materials are overly simplistic, and that understanding the properties of D-A-D materials purely in terms of their D-A subunits may not be a generally achievable goal.

Conclusion

Two D-A-D TADF materials were compared with analogous D-A compounds. Despite displaying near-identical singlet energies and PLQYs, the triplet energies -and subsequent TADF performances -were markedly different and showed opposite trends as the D-A materials. Molecular orbital interactions with higher energy multi-donor LE states are responsible for these unexpected changes in triplet energy, with interaction strength modulated by the linkage patterns of the two donor subunits. The identification of these emergent multi-donor effects -not complicated here by any additional impacts of steric environment changes -demonstrates that bottom-up approaches to understanding TADF behaviour are unlikely to succeed. Due to different conjugation strengths across the linker unit for (o,m)ACA (pD-D state) than for (o,o)ACA (mD-D state), the pD-D state to be lower in energy and have larger electron density on the central bridge region. This would subsequently lead to a larger overlap between the pD-D state and the 3 LE state associated with the A unit (3LEA) in (o,m)ACA as compared to mD-D in (o,o)ACA. The absorbance spectra showed the weak direct CT absorption bands in both (o,o)ACA and (o,m)ACA at ~375 nm. In each material this band corresponded to two closely spaced CT state absorptions, consistent with the DFT calculations and prior understanding of the oDA or mDA materials. In both cases this indicated that formation of the CT state involves only a single donor, and is unimpacted by the presence of the other.