=Paper=
{{Paper
|id=Vol-3885/paper16
|storemode=property
|title=Density Functional Theory Calculations in Designing Symmetric and Asymmetric TADF Emitters
|pdfUrl=https://ceur-ws.org/Vol-3885/paper16.pdf
|volume=Vol-3885
|authors=Dalius Gudeika
|dblpUrl=https://dblp.org/rec/conf/ivus/Gudeika24
}}
==Density Functional Theory Calculations in Designing Symmetric and Asymmetric TADF Emitters==
https://ceur-ws.org/Vol-3885/paper16.pdf
Density Functional Theory Calculations in Designing
Symmetric and Asymmetric TADF Emitters*
Dalius Gudeika1,∗,†
1
Vilnius University, Akademijos Str. 4, 08412, Vilnius, Lithuania
Abstract
A pair of thermally activated delayed fluorescence (TADF) emitters with symmetric and
asymmetric D-A-D structure are investigated. The introduction of density functional theory
(DFT) has tremendously aided the application of computational material science in the
design and development of organic materials. The use of DFT and other computational
approaches avoids time-consuming empirical processes. Therefore, this review explored
how the DFT computation may be utilized to explain some of the features of organic
systems. First, we went through the key aspects of DFT and provided some context. Then
we looked at the essential characteristics of an organic system that DFT simulations could
predict. Gaussian software had been employed with the B3LYP functional and 6-31G(d, p)
basic sets for organic systems.
Keywords
DFT, TADF emitters, B3LYP, 6-31G(d, p) basic sets
1. Introduction
The TADF mechanism is based on a second-order spin-vibronic coupling between a charge
transfer triplet state (3CT) and a local excited triplet (3LE) to mediate the up-conversion reverse
intersystem crossing (rISC) of the coupled 3LE/3CT triplet(s) to the emissive charge transfer singlet
(1CT) 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 ΔEST 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].
*IVUS2024: Information Society and University Studies 2024, May 17, Kaunas, Lithuania
1,∗
Corresponding author
†
CEUR
ceur-ws.org
These author contributed equally.
Workshop
Proceedings
ISSN 1613-0073
gudeika.dalius@gmail.com (D. Gudeika)
0000-0001-5718-8583 (D. Gudeika)
©️ 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
2. 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 1CT, 3CT, and 3LE states. Some researches attempted to relate D-
A dihedral angle with S1 and T1 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 S1/T1 states, or (3) mixed
level of theory for S1 and T1 leading to inverted S1/T1 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].
2.2. 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 S1 state [9].
3. Results and Discussion
3.1. 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 (S1) is lower in energy than that associated with the meta- donor CT state (S2).
This is in agreement with expectations and the trends established for oDA and mDA. In (o,o)ACA
the S1 and S2 states are much closer in energy, and each involves both of the ortho- donor units.
These represent symmetric (S1) and antisymmetric (S2) 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.
a)
(o,m)ACA (o,o)ACA
3.50
T3
T3
3.25
Energy / [eV]
S2 T2
3.00
2.75 S2 T2
S1 S1 T1
2.50 T1
Figure 1: a) Adiabatic singlet / triplet energy diagram of (o,m)ACA and (o,o)ACA (TDA-DFT
rBMK/6- 31G(d)); b) selected set of natural transition orbitals (NTO) of (o,m)ACA and (o,o)ACA
(TDA-DFT rBMK/6-31G(d)) (isovalue = 0.01)).
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 T3 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 T3 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 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 T3 energies compared to experiment. Accurately accounting for such interactions with
unoccupied states would instead require more advanced multireference or complete active space ab-
initio 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 3LE state
associated with the A unit (3LEA) in (o,m)ACA as compared to mD-D in (o,o)ACA. The resulting
state mixing between D-D and 3LEA 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 3LEA 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.
Figure 2: State diagrams showing: a) Formation of symmetric and antisymmetric molecular orbitals
from pairs of degenerate atomic orbitals. b) Analogous proposed formation of D-D states with
different energies due to stronger or weaker conjugation across meta- or para- bridges in (o,m)ACA
(pD-D) and (o,o)ACA (mD-D). c) Different D-D energies and extents of interaction with the
acceptor- centred LE triplet state (3LEA) lead to different experimental triplet energies. All orbital
representations and implied relative state energies are indicative only.
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).
1
1
(o,o)ACA _DCM (o,m)ACA _DCM (o,o)ACA _TOL (o,m)ACA _TOL
Norm Absorbance
Norm Absorbance
0
0 300 350 400 450
250 300 350 400 450
Wavelength (nm)
Wavelength (nm)
1
1
(o,o)ACA _CHX (o,m)ACA _CHX (o,o)ACA _CFM (o,m)ACA _CFM
Norm Absorbance
Norm Absorbance
0
0
250 300 350 400 450
250 300 350 400 450
Wavelength (nm) Wavelength (nm)
1
(o,o)ACA _DPEPO
(o,m)ACA _DPEPO
Absorbance
Norm
0
300 350 400 450
Wavelength (nm)
Figure 3: Absorbance spectra in DPEPO films and various dilute solutions (dichloromethane,
toluene, cyclohexane, chloroform). The low energy edge of the main donor band is redshifted for
(o,m)ACA (~300 to 325 nm) in all cases, attributed to the underlying pD-D state.
In DPEPO films and a range of solvents a redshift in the main absorbance band (peak at ~275
nm, attributed to DMAC) in (o,m)ACA compared to (o,o)ACA was observed. This redshift is due to
the presence of a weak underlying band associated with excitation of the pD-D singlet state. In
(o,o)ACA
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 ΔEST, 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.
4. 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 3LE 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.
5. Acknowledgements
This project was funded by the European Union (project No [S-ST-23-224], title “Artimo gamtai
miškininkavimo modelių vystymas naudojant miškininkavimo sprendimų paramos sistemą
Heureka”) under the agreement with the Research Council of Lithuania (LMTLT).
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