On Predicting the Excited-State Properties of Thermally Activated

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On Predicting the Excited State Properties of Thermally Activated Delayed Fluorescence Emitters Thomas James Penfold J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b03530 • Publication Date (Web): 19 May 2015 Downloaded from http://pubs.acs.org on June 2, 2015

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The Journal of Physical Chemistry

On Predicting the Excited State Properties of Thermally Activated Delayed Fluorescence Emitters Thomas J. Penfold∗ SwissFEL, Paul Scherrer Inst, CH-5232 Villigen, CH. E-mail: [email protected]

Abstract Limitations imposed by spin statistics governing exciton formation has meant that most efficient organic light emitting diodes (OLEDs) have relied upon complexes containing heavy metals. This can be overcome by exploiting thermally activated delayed fluorescence (TADF), which has opened the opportunity to design emitters composed only of lighter more abundant elements. For these complexes charge transfer excitations play a central role, meaning that modelling their properties within the framework of time-dependent density functional theory (TD-DFT) is challenging. Herein, two computational approaches to rectify this are explored. Firstly, an analysis based on the overlap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). This qualitative approach provides a satisfactory and very computationally efficient prediction of the energy gap between the lowest singlet and triplet excited states, crucial for TADF. In the second approach, the excited state properties are explicitly calculated using TD-DFT, by optimising the rangeseparation parameter within range-corrected functionals. This yields quantitative agreement with experimental results and can therefore be used to rationalise the photophysical properties of these complexes. ∗ To

whom correspondence should be addressed

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Introduction Organic light emitting diodes (OLEDs) have emerged within an ever increasing variety of lighting and display devices and consequently there is a strong driving force towards improving their performance and efficiency, while simultaneously reducing their manufacturing costs. The first generation of OLEDs were based upon organic fluorescent emitters. 1,2 Although these devices have been able to achieve high reliability, they suffer from an intrinsically low electroluminescence efficiency. This arises from the spin-statistics of exciton formation upon the electron-hole combination, shown in Figure 1. Because the lowest triplet state of organic molecules is not strongly dipole coupled to the molecular ground state, 75% of the excited states formed cannot emit, and consequently the energy is lost as heat or via other non-radiative decay channels. Second-generation phosphorescence-based OLEDs (PhOLEDs) overcame this limitation by doping the host layer with metal-organic emitters. 3 Through exploiting the large spin-orbit-coupling (SOC) of the metal centre, it becomes possible to also harvest the triplet excitons and consequently achieve a unity quantum efficiency. However, to date the only phosphorescent materials found practically useful are iridium and platinum complexes. 4 Unfortunately, lighter more abundant metal ions tend to have smaller SOC and therefore much lower T1 → S0 radiative rates making them again susceptible to non-radiative decay. 5 An alternative approach for effective harvesting of both the singlet and triplet excitons can be achieved by exploiting thermally activated delayed fluorescence (TADF) 6 as demonstrated by Adachi and co-workers. 7–9 For molecules with a small energy gap (∆ES1 −T1 ) between the emitting S1 and T1 states, thermal energy can induce reserve intersystem crossing (rISC) from the T1 to the S1 state. 7,8,10 Importantly, this provides a route to harvest the triplet excitons (via the singlet states) and because the radiative rate for the S1 →S0 transition is much greater than the T1 →S0 transition, reduces the reliance on heavy rare-earth metals, promoting the opportunity of exploiting exclusively organic materials. 9,11,12 In these cases, it is clear that to achieve effective TADF a careful control over ∆ES1 −T1 , preferably close to thermal energy at 300K (0.0257 eV), is required. This is accomplished by minimising electron-electron repulsion (electron-exchange term) between 2 ACS Paragon Plus Environment

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e-

p 1/ 2 (| "#i

h+

| ""i p | #"i) 1/ 2 (| "#i + | #"i) | ##i

S1

rISC T1

S0

Figure 1: Schematic showing the main principles for thermally activated delayed fluorescence emitters in OLEDs. Upon electron (e− ) and hole (h+ ) recombination, 25% of the corresponding excited states are singlets, while 75% are triplets. The triplet excitons are harvested though delayed fluorescence, following thermally promoted reverse intersystem crossing (rISC) from the T1 to the S1 state.

the ground and excited-state wavefunctions. This exchange interaction scales with the overlap of these wavefunctions 13 and consequently to date, the most promising TADF emitters have been dominated by charge transfer states. 9,14 To simulate the properties of these complexes, density functional theory (DFT) and timedependent density functional theory (TDDFT) 15,16 play a central role due their efficiency for simulating ground- and excited-state properties of larger molecules. However, the aforementioned importance of charge-transfer states is at odds with the widely document limitation of TDDFT for simulating these excitations. 17 To address these limitations, Huang et al., 18 adopted an approach whereby the exchange-correlation functional used to calculate the excited state was chosen according to the percentage of exact exchange required. This percentage was determined using a charge-transfer index that the authors defined following an analysis of the HOMO and LUMO orbitals. While the approach, which has since been applied to other complexes, 12,19,20 has yielded quantitative agreement with the experimental results, the main drawback is the number of differ-



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ent functionals used, 10 in total. As each functional does not only vary by the fraction of exact exchange, this approach does not necessarily yield a consistent description of the excited state properties. In a later study, later Moral et al. 21 proposed relating ∆ES1−T 1 to the electron-hole distance, calculated as the difference between the centroids of the HOMO and LUMO orbitals using double hybrid functionals. For a subset of 6 complexes, they found a correlation between of the experimental singlet-triplet splitting on the calculated electron-hole distance, which would be able to give an estimate of ∆ES1−T 1 . Besides providing a rationalisation for complexes studied experimentally, theory plays a crucial role in designing new complexes. 22 With this aim in mind, Shu et al 23 have recently implemented a genetic algorithm approach to identify new molecules. This methodology was able to identify nearly 4000 promising candidates, based upon a database of just over 1×106 . Importantly, their assessment of the suitability (fitness) of each candidate was based upon a calculation of ∆ES1−T 1 and the S1 →S0 oscillator strength using the range-separated CAM-B3LYP functional. 24 However, during this work, a calculation of a known complex, 4CzIPN yielded ∆ES1−T 1 =0.41 eV. This is just over 4 times greater than the experimentally determined value of 0.10 eV. 18 As the rISC relies on thermal energy (0.0257 eV at 300 K), this difference is hugely significant. Therefore for reliable predictions, accurate computations of ∆ES1−T 1 and the other excited state properties are essential. In this work two approaches for obtaining a description of the excited state properties of organic TADF complexes are studied. The first is a qualitative method that is focused upon achieving high computational efficiency by exploiting the correlation between ∆ES1 −T1 and the overlap between the HOMO and LUMO molecular orbitals. 25 The accuracy of this approach demonstrated herein for estimating ∆ES1 −T1 means that it can be expected to be very useful as a first step screening of potential high performing candidates. The second section explores tuning the range-separated functionals in order to achieve a quantitative description of the excited state energies, ∆ES1 −T1 and oscillators strengths. In this study 31 molecules are studied and these are shown in Figure 2. The full chemical names are given in the Supporting Information (SI).


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PhCz

PXZQ

NPh3!

PIC-TRZ

CBP DACQ CzT DTC-DPS: R=tBu DMOC-DPS: R=OCH3! DPA-DPS: R=H DTPA-DPS: R=tBu! 2PXD-TAZ: R=N-C6H5 2PXD-OXD: R=O 2PXD-TDZ: R=S

DMAC-DPS!

CC2TA

2CzPN: R=H 4CzPN: R=Cz

!

PXZ-TRZ DPA-AQ: R=H BBPA-AQ: R=C6H5 !

PhCzTAZ 4CzIPN

DTC-AQ

DMAC-AQ 4CzTPN

ACRFLCN

AcPmBPX

PxPmBPX

SpiroCN

ACRSA

Figure 2: Schematic of the complexes studied herein. The chemical names and abbreviations are given in the supporting information.



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Theory and Computations The geometry optimisations were performed using the ORCA quantum chemistry package. 26 In each case the structures were optimised at DFT(PBE) 27 level using a def2-TZVP basis set 28,29 for all of the atoms except hydrogen, for which a def2-SVP basis was used. To account for the weak π − π interactions, the calculations were supplemented with Grimme’s D3 dispersion correction with the Becke-Johnson damping scheme. 30,31 For the first subsection, the absolute overlap between the HOMO and LUMO orbitals was calculated as: O = h|φi ||φ j |i =

Z

|φi ||φ j |dr

(1)

This can be related to Tozers Λ diagnostic 32 used to characterised charge-transfer states within the framework of TDDFT. In their work, the absolute overlap between all the orbitals involved in the excited state were calculated and then weighted according to the occupied-virtual pair contribution to that excited state. However, so that this approach can be applied within a computational screening method, the principle aim of this aspect is computational efficiency and consequently we focus simply upon O. In the second section the excited state properties are simulated using a range-separated functional (LC-BLYP) 33 which has been optimally tuned. In these functionals the amount of exact exchange is weighted according to the inter electron distance, r12 : 1 −1 −1 = erfc(µ · r12 ) · r12 + erf(µ · r12 ) · r12 r12

(2)

2 R where erf(x) = √ 0x exp(−t 2 )dt and erfc(x) = 1 − erf(x). The optimal value of µ was obtained π using the ∆SCF method. 34 This requires that we minimised the energy difference between energy of the HOMO (εHOMO ) and first ionisation potential (IP) of the neutral system and the energy difference between energy of the HOMO of the anionic system, (εHOMO (N+1) and the electron


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affinity (EA) of the neutral system. 34,35,35,36 These conditions are expressed as:

ω J0 (µ) = |εHOMO (N) + IPω (N)|

(3a)

ω J1 (µ) = |εHOMO (N + 1) + EAω (N)|

(3b)

Therefore our overall goal is to minimise the relationship:

J(µ) = J0 (µ) + J1 (µ)

(4)

Optimisation of the range-separated parameter, µ, using Equation 4 was performed within the approximation of the LC-BLYP exchange-correlation functional 33 using the Gaussian09 quantum chemistry package. 37 All calculations were performed using the same basis set as above. The effect of the solvent was included using the PCM approach 38 and the parameters of cyclohexane. This was only included during the calculation of the excited states and not during the tuning of µ. This is consistent with the conclusions of ref. 39 who reported that µ tuning within a continuum solvent model can result in unrealistic values due to a significant underestimation of vertical ionisation potential. Throughout this work all TD-DFT simulations were performed within the Tamm-Dancoff approximation (TDA) 40 to avoid any problems with triplet instability. 41,42 Finally it is noted that direct comparison with the experimental ∆ES1−T 1 requires calculating the S1 and T1 energies at the minimum energy geometries of these states. However, due to the computational expense of such excited state geometry optimisations, all of the calculations performed are at the ground state geometry. While this is an approximation, given the weak exchange interaction for these complexes, a requirement for efficient TADF, the S1 and T1 surfaces are expected to be parallel. This is a good approximation as recently discussed in refs. 18,23



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Results Overlap and ∆ES1 −T1 As discussed in the introduction, computational studies that rationalise and/or predict the photophysical properties of these molecules can significantly reduce experimental development time and costs. To achieve this, automated, high-throughput in silico characterisation frameworks, 22 such as the genetic algorithm approach of Shu et al. 23 are popular. For these to be used in the most efficient manner, they require multiple steps during which the accuracy may be increased in a stepwise manner, enabling unsuitable candidates to be accurately and efficiently eliminated. To estimate the energy gap between the lowest singlet and triplet excited states, crucial to the efficiency of TADF, the coulomb and exchange interactions between the electrons must be considered. The former lowers the energy of both states by the same amount and can therefore be neglected in terms of describing ∆ES1−T 1 . In contrast, the latter increases the singlet state energy and lowers the triplet state energy. 25 As a consequence, ∆ES1−T 1 is defined as twice the exchange energy, which can be approximated as the overlap of the ground and excited-state wavefunctions. 25 Assuming a simple HOMO-LUMO excitation, the exchange energy can be represented as the overlap between these orbitals. Because this is very computationally inexpensive, it therefore offers an attractive approach for screening complexes during in silico characterisation. Figure 3a shows the correlation between the experimentally determined ∆ES1−T 1 18 and absolute orbital overlap, O (Equation 1). The results are also shown in Tables 1 and 2. As expect a correlation between the variables is observed, those with larger overlap and consequently a larger ∆ES1−T 1 and those with a smaller overlap and therefore a smaller ∆ES1−T 1 . Using the linear fit of the initial 16 molecules shown in Table 1 (green line, shown in Figure 3a) we can estimate the ∆ES1−T 1 based solely on the overlap. The results are shown in Table 1 and yield an mean average error of 0.07 eV. As ∆ES1−T 1 for some of the complexes is as small as 0.01 eV this result should only be considered as qualitative, however this level of accuracy could be expect to be sufficient in order prioritise potential high performing complexes.


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0.7

0.7

(a)

∆E(S1-T1) Energy gap (eV)

0.5 y=0.88x -0.03

0.4

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0.5 y=7.25x+0.04 0.4

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(b)

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0.0 0.00

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Overlap*(εHOMO-εLUMO)

Overlap (∫|ϕi|ϕj|)

Figure 3: O (a) and O · εgap (b) between the HOMO and LUMO orbitals against the experimental ∆ES1−T 1 for the 31 complexes studied herein. εgap =εHOMO -εLUMO The electronic structure has been calculated using DFT within the approximation of the PBE functional using the ground state geometry. The black dots are those complexes initially studied and used in the linear fit (green line). The red open circles are the second set of complexes (see table Table 2) used to assess the robustness of the correlation of O or O · εgap with ∆ES1−T 1 . As a test of the robustness of this simple approach, in Table 2 we show the estimated ∆ES1−T 1 based upon O and the respective errors from the experimental value for an additional 15 complexes not included in the linear fit of Figure 3a (red open circles). While the correlation between the two factors is maintained, there are significant outliers, especially DPA-AQ, BBPA-AQ, DTC-AQ and to a slightly lesser extent DMOC-DPS and 4CzPN. In all of these cases, ∆ES1−T 1 is much smaller than would be predicted from overlap between the HOMO and LUMO orbitals. These outliers significantly reduce the strength of the correlation between ∆ES1−T 1 and O and would make it difficult to eliminate high-performing candidates based solely on orbital overlap. The approach adopted thus far, ∆ES1−T 1 ∝ O addresses how the similarity of the HOMO and LUMO orbitals is related to the exchange energy and therefore the ∆ES1−T 1 . However, one key aspect which this does not consider is the (de)localisation and spatial confinement of these orbitals. Indeed it is perfectly reasonable to obtain the same overlap between the HOMO and LUMO for two different molecules, one which has the electronic density of both orbitals confined to one group



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Table 1: The O and O ·εgap between the HOMO and LUMO orbitals, predicted ∆ES1−T 1 (using the fit shown in Figure 3a), experimental ∆ES1−T 1 and error between the two. εgap = εHOMO -εLUMO . MAE: Mean average error. O NPh3 18 ACRFLCN 18 CBP 18 2PXZ-OXD 43 DPA-DPS 18 SpiroCN 18 CC2TA 18 4CzIPN 18 2CzPN 18 PhCz 18 CzT 18 DMAC-DPS 44 DTPA-DPS 18 4CzTPN 18 DTC-DPS 18 PXZ-TRZ 18 MAE

0.607 0.150 0.527 0.123 0.637 0.060 0.183 0.240 0.427 0.681 0.131 0.164 0.672 0.343 0.480 0.106

εgap (a.u.) 0.109 0.064 0.121 0.047 0.091 0.042 0.069 0.070 0.073 0.116 0.071 0.075 0.095 0.059 0.079 0.044

Expt. 0.57 0.24 0.71 0.15 0.52 0.06 0.20 0.10 0.31 0.55 0.10 0.09 0.46 0.09 0.36 0.06

∆ES1−T 1 (eV) Calc. (O) Error Calc. (O · εgap ) 0.50 0.07 0.52 0.10 0.14 0.11 0.43 0.28 0.50 0.08 0.07 0.08 0.53 0.01 0.46 0.03 0.03 0.06 0.13 0.07 0.13 0.18 0.08 0.16 0.34 0.03 0.26 0.57 0.02 0.61 0.09 0.01 0.16 0.11 0.02 0.13 0.56 0.10 0.50 0.27 0.18 0.19 0.39 0.03 0.31 0.06 0.00 0.07 0.07

Error 0.02 0.13 0.21 0.07 0.06 0.00 0.07 0.06 0.05 0.06 0.06 0.04 0.04 0.10 0.05 0.01 0.06

of the molecule and a second for which the density of both orbitals is delocalised over the whole molecular scaffold. This degree of spatial confinement is important, as it will alter the coulomb and exchange energies. Indeed, since the singlet excited state is generally more extended than the triplet excited state, any confinement increases the singlet excited state more than the triplet. 13,45,46 Consequently, while the overlap may be the same for two molecules, it is the one with the more delocalised orbitals that will exhibit the smallest ∆ES1−T 1 . This is not addressed by the relation ∆ES1−T 1 ∝ O. An indication of the degree of spatial confinement can be obtained from the energetic gap between the HOMO and the LUMO, which becomes larger with increasing localisation. From this description we would therefore expect that a larger HOMO-LUMO gap would lead to a larger ∆ES1−T 1 , as confinement increases the singlet excited state more than the triplet. Indeed this trend is demonstrated in Figure 4 which shows the experimental S1 and T1 energies from ref. 18 plotted 10 ACS Paragon Plus Environment

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3.6

3.4

S1

3.2

Energy (eV)

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3.0 T1 2.8

2.6

2.4 1.5

2.0

2.5

3.0

HOMO-LUMO gap (eV)

Figure 4: The dependency of the experiment S1 and T1 energies 18 on the calculated DFT(PBE) Kohn-Sham (KS) HOMO-LUMO gap. against the Kohn-Sham (KS) HOMO-LUMO gap. Here a clear trend is observed and for molecules with a larger HOMO-LUMO gap, a larger ∆ES1−T 1 is found, as the T1 state does not increase with the HOMO-LUMO gap at the same rate as the S1 state. To address the effect of the spatial delocalisation, we investigate the correlation between the experimentally determined ∆ES1−T 1 and O · εgap , where εgap =εHOMO -εLUMO . It is stressed that inclusion of the HOMO-LUMO gap could introduce a stronger functional dependence than simply using the overlap, O, as this quantity is typically more sensitive to the functional, especially when exact exchange is included. This was assessed by comparing the results below obtained using PBE with PBE0, as shown in the SI. This shows that the trends remain strong supporting the used of O · εgap . The results are shown in Figure 3b and Tables 1 and 2. For the initially studied complexes (filled black circles), as demonstrated by the slight reduction in the MAE, we observe a slightly stronger correlation between the experimental ∆ES1−T 1 and the one estimated using the linear fit.



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Table 2: The O and O · εgap between the HOMO and LUMO orbitals, predicted ∆ES1−T 1 , experimental ∆ES1−T 1 and error between the two. εgap = εHOMO -εLUMO . These complexes are those that are not part of the linear fits shown in Figure 3 and therefore test the robustness of the approach. MAE: Mean average error.

4CzPN 18 PXZ-TDZ 47 PIC-TRZ 18 DMOC-DPS 19 2PXZ-TAZ 14 PhCzTAZ 48 DACQ 49 PXZQ 49 DPA-AQ 20 BBPA-AQ 20 DTC-AQ 20 DMAC-AQ 20 ACRSA 50 AcPmBPX 51 PxPmBPX 51 MAE

O

εgap (a.u.)

0.365 0.093 0.279 0.414 0.120 0.214 0.223 0.105 0.628 0.610 0.484 0.152 0.128 0.049 0.036

0.067 0.040 0.068 0.079 0.060 0.078 0.045 0.038 0.057 0.052 0.049 0.023 0.072 0.053 0.035

Expt. 0.15 0.11 0.18 0.21 0.23 0.20 0.08 0.19 0.27 0.26 0.19 0.11 0.03 0.05 0.02

∆ES1−T 1 (eV) Calc. (O) Error Calc. (O · εgap ) 0.29 0.14 0.22 0.05 0.06 0.07 0.22 0.04 0.18 0.33 0.12 0.28 0.08 0.15 0.09 0.16 0.04 0.16 0.16 0.08 0.11 0.06 0.13 0.07 0.52 0.25 0.30 0.50 0.24 0.27 0.39 0.20 0.21 0.10 0.01 0.07 0.08 0.05 0.06 0.01 0.04 0.05 0.00 0.02 0.11 0.10

Error 0.07 0.04 0.00 0.07 0.12 0.07 0.01 0.12 0.03 0.01 0.02 0.04 0.03 0.00 0.09 0.05

This is mostly associated with the improvement in the estimation of CBP which has a large εgap because of the LUMO orbital confined on the central phenyl groups (See Figure 2). For the second set of complexes (Table 2) we observe a significant improvement in the correlation, especially for anthraquinone based complexes, DPA-AQ, BBPA-AQ and DTC-AQ. In this case the MAE is only 0.05 eV. The improvement observed for the anthraquinone based complexes is because, although these complexes have a rather significant overlap between the HOMO-LUMO orbitals they have a comparatively small εgap , arising from the delocalised nature of the HOMO and LUMO orbitals which leads to smaller estimated ∆ES1−T 1 gap than would be predicted by O alone. Optimising the range separated parameter: µ tuning In the previous section we have demonstrated a qualitative approach for estimating ∆ES1−T 1 based upon the the overlap and energy gap between the HOMO and LUMO orbitals. However, towards 12 ACS Paragon Plus Environment

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achieving a more detailed understanding and rationalisation of the photophysical properties of these molecules, it is important to explicitly simulate the excited state. Given the size of many of the molecules studied herein, TDDFT represents the only realistic approach. However, as previously discussed, this is at odds with the widely documented limitations of TDDFT for describing charge-transfer excitations. 0.04 ACRFICN 2PXD-OXD PXZ-TRZ CC2TA

0.03

J(µ) (hartree)

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µ (bohr

)

Figure 5: J(µ) as a function of the range separation parameter µ for 4 complexes, ACRFLCN, 2PXD-OXD, PXZ-TRZ and CC2TA. The minimum displays the optimal value of µ. In this section we seek to explicitly calculate the excited state properties and achieve a quantitative description of the excited state energies and ∆ES1 −T1 by optimising the range separated parameter, µ using the ∆SCF approach described above. The optimal value of µ for the 11 molecules studied are shown in Table 3. The molecules chosen are those with a small ∆ES1 −T1 (i.e. a significant charge transfer character making them most challenging for TDDFT) and for which literature values for the lowest singlet excited state (ES1 ) and ∆ES1−T 1 in solution are reported. Figure 5 shows, as a demonstration of the tuning procedure, the magnitude of J as a function of µ for ACRFLCN, 2PXD-OXD, PXZ-TRZ and CC2TA. Usually, because J0 (µ) and J1 (µ) describe different systems (i.e the n and n+1 electron systems), their minima do not coincide. This can give rise to a rather flat J(µ), whose minimum is ill defined. However in all of the cases studied herein 13 ACS Paragon Plus Environment


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this was found not to be the case and a distinct minimum could be identified as highlighted by the prototypical examples shown in Figure 5. As shown in Table 3, for all of the complexes studied we find an optimal µ between 0.15-0.19 bohr−1 . This is about a factor of 2 smaller than the standard system-independent µ=0.33 bohr−1 for LC-BLYP, 52 indicating that these systems require less exact exchange to fulfil Equation 4. This optimal µ is also in close agreement with the one determined in similar work on organic dye molecules, 53 and suggests that it would be possible to define a general µ for these systems. Using the LC-BLYP functional and employing the optimal µ, Table 3 shows both the energy of the lowest excited state (ES1 ), the S1 →S0 oscillator strength and ∆ES1−T 1 . For both ES1 and and ∆ES1−T 1 we find very good agreement with the experimentally determined values. Indeed, for ES1 the MAE is 0.09 eV, while for ∆ES1−T 1 it is 0.05 eV. In particular, the ∆ES1−T 1 calculated for 2PXZ-OXD (0.06 eV) and 4CzIPN (0.14 eV) is significantly closer to the experimental value than previously reported using the CAM-B3LYP functional for which ∆ES1−T 1 was reported to be 0.57 eV for 2PXZ-OXD 43 and 0.41 eV for 4CzIPN. 23 In general, these results are comparable in accuracy to the work of Huang et al., 18 who as described in the introduction adopted a slightly different approach, based upon the definition of a charge transfer index and an empirical selection of the exchange-correlation functional. While both this work and the present results show good agreement with experiments, the distinct advantage of the present tuning methodology is that all calculations are performed within the same functional for which the tuning of the range-separation parameter is not performed in an empirical manner. This provides a consistent description of the excited state. The one exception of the agreement between this work and ref. 18 is the ∆ES1−T 1 for CC2TA. In their work, Huang et al 18 calculated the energy gap to be 0.43 eV, while we find 0.32 eV. Although in the present case, this displays the largest error (0.12 eV) compared to the experimental values it is still ∼0.1 eV closer than ref. 18 The biggest errors in the calculated values for ES1 are found for PXZ-TRZ and DMAC-DPS. Indeed in both cases the error is >0.2 eV. For the latter the error is almost identical to that reported in ref. 44 using the method of Huang et al. 18 In contrast the calculated absorption energy for


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Table 3: Optimised range separated parameter (µ), the lowest singlet excitation and ∆ES1−T 1 for selected complexes, i.e. those with literature values for ES1 and ∆ES1−T 1 (eV). All calculations were performed at the Franck-Condon geometry and are compared to the experimental values for the complexes in cyclohexane. ES1 was determined in ref 18 from the emission energy of S1 and the onset of absorption and emission edges utilising the mirror image rule.

DPA-DPS 18 ACRFLCN 18 2PXZ-OXD 43 SpiroCN 18 CC2TA 18 PXZ-TRZ 18 DMAC-DPS 44 4CzIPN 18 4CzTPN 18 PIC-TRZ 18 4CzPN 18 MAE

µ 0.17 0.18 0.18 0.17 0.17 0.19 0.18 0.15 0.16 0.19 0.17

Calc. 3.57 3.06 2.78 2.69 3.65 2.95 3.28 2.70 2.49 3.30 2.84

ES1 (eV) f Expt. 0.8807 3.53 0.0014 3.05 0.0235 2.73 0.0033 2.69 0.7056 3.64 0.0005 2.73 0.0089 3.00 0.0745 2.85 0.1766 2.61 0.0523 3.35 0.0338 2.82

Error 0.04 0.01 0.05 0.00 0.01 0.22 0.28 0.15 0.12 0.05 0.02 0.09

∆ES1−T 1 (eV) Calc. Expt. Error 0.55 0.52 0.03 0.26 0.24 0.02 0.06 0.15 0.09 0.09 0.06 0.03 0.32 0.20 0.12 0.12 0.06 0.06 0.06 0.09 0.03 0.14 0.10 0.04 0.13 0.09 0.04 0.28 0.18 0.10 0.21 0.15 0.06 0.05

the former (PXZ-TRZ) reported in ref. 18 is much closer to the experimental value than reported here. However, despite the disagreement with the ES1 the calculated absorption spectra shown in the Supporting Information (SI) show good agreement between the experimental and calculated spectra. Finally, an additional assessment of the optimally tuned range separated functionals for calculating the excited state properties is to compared the calculated and experimental absorption spectra. Figure 6 shows these results for DPA-DPS, ACRFLCN, 2PXZ-OXD. The absorption spectra for the remaining complexes reported in Table 3 are shown in the SI. Overall, the simulated spectra reproduce the main features of the absorption spectrum, making it possible to assign each band. For DPA-DPS the lowest (S1 ) state is a strong dipole allowed π − π ∗ transition occurring at ∼345 nm. This lowest transition is dominated by the HOMO and LUMO orbitals, which are delocalised over the whole molecule (Figure 7a). While this spatial overlap of the orbitals is responsible for the strong oscillator strength ( fS1 =0.96) of the transition, it is also this overlap which is responsible for the large ∆ES1−T 1 which is typical for π − π ∗ systems 9 and which makes these complexes not 15 ACS Paragon Plus Environment


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Figure 6: The experimental (solid) and computed (dashed) a absorption spectra of DPA-DPS (a), ACRFLCN (b) and 2PXD-OXD (c). The experimental spectra have been recorded in cyclohexane at 300 K. The theoretical absorption spectra are generated using the Molden program 54 with a half-bandwidth of 5 nm. very suitable for TADF. (a)

HOMO$

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Figure 7: The structure and important frontier orbitals of DPA-DPS (a), ACRFLCN (b) and 2PXDOXD (c). Figure 7b and c show, as expected for the smaller reported ∆ES1−T 1 , that the overlap between the HOMO and LUMO orbitals for ACRFLCN and 2PXD-OXD is small. In both cases this leads to a S0 →S1 transition that is very weak. For ACRFLCN the oscillator for S1 is zero and the first optically bright state is S3 whose oscillator strength is 0.5. For 2PXD-OXD, the oscillator


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for S1 is 0.02, and the first strong transition observed at ∼300 nm corresponds to transitions into the S7 state. As observed for DPA-DPS, the calculated absorption spectrum for ACRFLCN is in good agreement with the experimental one. However, this agreement is not so good for 2PXDOXD, which appears rather over structured in comparison to the experiment. This would appear to suggest that 2PXD-OXD is more susceptible to a large number of ground state configurations arising from dynamics driven by thermal energy.

Conclusions In conclusion this present work has studied two approaches, of varying accuracy and computational expense, that can be employed to characterise and design new TADF molecular emitters. The first correlates the overlap and energy gap between the HOMO and LUMO orbitals with the experimental ∆ES1−T 1 . Here we observe strong correlation which makes it possible to estimate ∆ES1−T 1 based purely on these simple ground state quantities. In the context of charge transfer states within time-dependent density functional theory, it is noted that a number of metrics used to assess the extend of charge transfer have been developed 32,55–57 and used to effectively describe the extent of electron-hole delocalisation in the excited state. While very effective and, in contrast to the qualitative approach presented herein, all of these require explicit calculation of the excited state using TDDFT. Importantly, while these former method are likely to yield a more higher level description of the excited state delocalisation, the approach presented here has the advantage that it simply requires one ground state density functional calculation, it may be used in a computationally efficient manner to screen high numbers of potential candidates in a timely manner. It is also important to bear in mind that besides ∆ES1−T 1 , a large S1 →S0 oscillator strength is also important. Remaining within the simple single particle excitation framework, this can be approximated using the off-diagonal position matrix element between the HOMO and LUMO, i.e hφ j |r|φi i, providing the opportunity to obtain qualitative insight into both quantities form a single DFT calculation. In the second approach, we have demonstrated that optimising the range-separation parameter 17 ACS Paragon Plus Environment


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(µ) within the LC-BLYP functional provides excellent agreement between the calculated absorption energy (ES1 ), ∆ES1−T 1 and absorption spectra. Thus this can be use to achieve a quantitative agreement with experimental allowing theory to provide a understanding and rationalisation of the electronic structure of these complexes. Something that has not been addressed within this work is the effect of the spin-orbit coupling between the singlet and triplet states and nonadiabatic couplings within the triplet manifold. 58 The former plays an important role in determining the rate of ISC and rISC. Given the presence of only light elements this can be expected to be only a small perturbation, it is important that a non-zero value is obtained, even if the energy gap between the states is small. 59–61 In this respect the spin orbit coupling within organic systems is usually cast in terms of El-Sayed rules, 62 which demonstrates that spin orbit coupling is most significant between states of different character e.g. S(n,π ∗ ) and T(π,π ∗ ) and therefore design of new complexes should also bear this in mind. For the latter, nonadiabatic couplings between low-lying triplet states increases state mixing and has also been implicated in enhancing the efficiency of T1 →S1 upconversion for TADF emitters. 58 Finally, it is stressed that this is a first, necessary step for computational studies of TADF molecular emitters. Indeed, complexes identified computationally by their electronic and structural properties may display promising properties in the gas phase or with implicit solvation. However, these single molecule studies are not a guarantee for efficient device performance and indeed many often do not deliver when incorporated into the solid state. The reason for this is the role of interactions with the environment that can somewhat alter its properties. Importantly, in terms of TADF materials, the electron-hole wavefunction is smaller for the triplet than the singlet state because of stronger electron correlation in the triplet state. Consequently, the triplet state is less susceptible to fluctuations in the environment and this will influence the average ∆ES1−T 1 . Therefore, studies of these complexes with an explicit atomic description of their native environment will be crucial.


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Supporting Information The chemical names of the complexes studies, correlation between O and O·εgap and ∆ES1−T 1 for the PBE0 functional and the absorption spectra for 8 additional complexes can be found in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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0.02

0.04

0.06

0.08



Page 26 of 36

Page 27 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

p 1/ 2 (| "#i

e-

h+


| ""i

p | #"i) 1/ 2 (| "#i + | #"i)

| ##i

S1

rISC T1

S0 ACS Paragon Plus Environment

PhCz


1 2 3 4 5 CzT 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21CC2TA 22 23 24 25 PXZ-TRZ 26 27 28 29 30 31 32 33 34 35 36 37 38 DMAC-AQ 39 40 41 42 43 44 45 46 47 48 49 ACRFLCN 50

Page 28 of 36

PXZQ

NPh3!

PIC-TRZ

CBP DACQ DTC-DPS: R=tBu DMOC-DPS: R=OCH3! DPA-DPS: R=H DTPA-DPS: R=tBu! 2PXD-TAZ: R=N-C6H5 2PXD-OXD: R=O 2PXD-TDZ: R=S

DMAC-DPS!

2CzPN: R=H 4CzPN: R=Cz

PhCzTAZ 4CzIPN

DPA-AQ: R=H BBPA-AQ: R=C6H5 !

4CzTPN

!

DTC-AQ

SpiroCN

ACS Paragon Plus Environment

AcPmBPX

PxPmBPX

ACRSA

Page 29 of 36


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

0.7


(a)

0.6

0.5 y=0.88x -0.03

0.4

0.3

0.2

0.1

0.0 0.0

0.1

0.2

0.3

0.4


Overlap (∫|ϕi|ϕj|)

0.5

0.6

0.7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

0.7

Page 30 of 36

(b)

0.6

0.5 y=7.25x+0.04 0.4

0.3

0.2

0.1

0.0 0.00

0.02

0.04 ACS Paragon Plus Environment


0.06

0.08

Page 31 of 36

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55


3.6

3.4

S1

3.2

3.0 T1 2.8

2.6

2.4 1.5

2.0

2.5


HOMO-LUMO gap (eV)

3.0

0.04

J(µ) (hartree)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50


Page 32 of 36

ACRFICN 2PXD-OXD PXZ-TRZ CC2TA

0.03

0.02

0.01

0.00 0.10

0.15

0.20

0.25


-1

µ (bohr

)

0.30

Page 331.0 of 36

Absorbance (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41


Expt. DPA-DPS Calculated

(a)

0.8

0.6

0.4

0.2

0.0 260

280

300 340 ACS Paragon320 Plus Environment Wavelength (nm)

360

380

400


Absorbance (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Page 34 of 36

(b) 0.8 Expt. ACRFLCN Calculated

0.6

0.4

0.2

0.0 260

280

300 340 ACS Paragon 320 Plus Environment Wavelegnth (nm)

360

380

400

Page 35 of 36

Absorbance (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41


(c)

1.5

Expt. 2PXD-OXD Calculated

1.0

0.5

0.0 300

350 ACS Paragon Plus Environment Wavelength (nm)

400

450

(a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40


Page 36 of 36

HOMO$

LUMO$

(b)

(c)

HOMO'1$

HOMO$


HOMO$

LUMO$

LUMO$

On Predicting the Excited-State Properties of Thermally Activated

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