Local-Excitation versus Charge-Transfer Characters in the Triplet

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Local Excitation vs. Charge Transfer Characters in the Triplet State: Theoretical Insight Into the Singlet–Triplet Energy Differences of CarbazolylPhthalonitrile-Based Thermally Activated Delayed Fluorescence Materials Kyungeon Lee, and Dongwook Kim J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10161 • Publication Date (Web): 21 Nov 2016 Downloaded from http://pubs.acs.org on November 26, 2016

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The Journal of Physical Chemistry

HOMO

h+ wfn

LUMO

CzPN

2CzPN

4CzPN

ACS Paragon Plus Environment

e- wfn


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Local Excitation vs. Charge Transfer Characters in the Triplet State: Theoretical Insight into the Singlet–Triplet Energy Differences of Carbazolyl-phthalonitrile-Based Thermally Activated Delayed Fluorescence Materials

Kyungeon Lee and Dongwook Kim*

Department of Chemistry Kyonggi University 154-42, Gwanggyosan-ro, Yeongtong-gu, Suwon 16227, Korea

*

E-mail: [email protected]

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Abstract The singlet–triplet energy differences, ∆EST, of a series of carbazolyl-phthalonitrile (CzPN) derivatives were calculated at the levels of density functional theory (DFT) and timedependent (TD) DFT using the gap-tuned, range-separated ωB97X functional. The studied CzPN derivatives include 4-(9H-carbazol-9-yl)-phthalonitrile (CzPN), 4,5-di(9H-carbazol-9yl)-phthalonitrile (2CzPN), 3,4,5-tris(9H-carbazol-9-yl)-phthalonitrile (3CzPN), and 3,4,5,6tetra(9H-carbazol-9-yl)-phthalonitrile (4CzPN). As additional Cz substituents are introduced, both the HOMO–LUMO energy gap, ∆EH-L, and ∆EST continuously decrease. Natural transition orbital analysis as well as a quantitative assessment of the local excitation (LE) and charge transfer (CT) contributions to the excited states consistently demonstrate that the S1 states of all the CzPN derivatives possess a predominantly CT nature. In contrast, in the T1 state, the LE feature is dominant, but the CT character increases with the number of Cz groups. The excitation energy decomposition discloses that in addition to the spatial separation of HOMO and LUMO, a significant CT nature in the T1 state is essential for further reduction in ∆EST. Moreover, the relative proportion of LE and CT characters in the T1 state of the CzPN derivatives can be modulated by ∆EH-L.

2


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I. Introduction As new-generation full-color displays and lighting appliances, organic light emitting diodes (OLEDs) have attracted enormous attention since their first invention.1 In OLEDs, an exciton, which can emit light, transfer to a neighboring molecule, or dissipate as heat, is generated by the recombination of an electron/hole pair. Such charges have no spin correlation when initially injected from the electrodes, and thus, according to spin statistics, triplet excitons are generated dominantly. In order to improve the performance of OLEDs, therefore, it is essential to exploit triplet excitons as light-emitting sources. To this end, phosphorescent molecules with heavy metal atoms (e.g., Ir and Pt) have been widely employed to fabricate efficient devices.2-4 Such phosphorescent materials, however, are generally expensive and still unreliable with regard to blue-light emission. In this regard, there is a great demand for cheap materials that are highly luminescent in their triplet state.

Thermally activated delayed fluorescence (TADF) has been demonstrated to be a viable alternative to phosphorescence for OLED applications.5-16 If molecules exhibit sufficiently small energy differences between the lowest-lying singlet (S1) and triplet (T1) excited states (∆EST), then they can undergo thermally activated up-conversion via intersystem crossing (UISC) from the triplet to the singlet excited state,17-20 and therefore, fluoresce. Hence, even pure organic molecules in the triplet state can luminesce at room temperature. The ∆EST of a given molecule is assumed as twice the exchange energy, 2K,21 which has been considered to be minimized by spatially separating its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and making the molecule ambipolar. Although this strategy has been successfully applied, from a theoretical perspective, some important facts have been ignored. First, the equivalence of ∆EST and 2K is based on the Hartree–Fock 3



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(HF)/configuration interaction singles (CIS) theories, which do not take the electron correlation properly into account.22-23 In general, electron density distributions are notably different for singlet and triplet states and thus the effects of electron correlation on the energies of those states should also be dissimilar.23 Furthermore, even in this oversimplified picture, such an estimation of ∆EST is valid only if both the singlet and triplet states exhibit the same nature.22-24 More notably, K has a different impact on the stability of the singlet and triplet states; small K values tend to stabilize singlet states, but destabilize triplet ones.22-23 This effect explains why the T1 states of many ambipolar host molecules for blue phosphorescent OLEDs have local excitation (LE) character which corresponds to large K values.24-26 Therefore, this behavior strongly suggests that separating the HOMO and LUMO is not sufficient to realize ∆EST comparable to thermal energy. In this vein, a deeper understanding of the nature of such excited states and the associated energy differences is critical for the design and development of efficient TADF materials.

A plethora of TADF materials have been synthesized and successfully applied in OLEDs.5-16 Adachi and coworkers recently reported that OLEDs with internal quantum efficiencies of almost unity could be fabricated by employing carbazolyl-phthalonitrile (CzPN)-based TADF molecules: 4,5-di(9H-carbazol-9-yl)-phthalonitrile (2CzPN), 3,4,5,6-tetra(9H-carbazol-9-yl)phthalonitrile (4CzPN), 2,4,5,6-tetra(9H-carbazol-9-yl)-isophthalonitrile (4CzIPN), and 2,3,5,6-tetra(9H-carbazol-9-yl)-terephthalonitrile (4CzTPN).7 In their subsequent study, the T1 states of some of these molecules, e.g., 4CzIPN and 4CzTPN, were found to be of charge transfer (CT) character, giving rise to insignificant K values and hence marginal ∆EST values; in the case of 4CzPN, triplet LE and CT states were reported to be nearly isoenergetic.27 This result is highly notable in the sense that, as mentioned above, triplet states tend not to favor 4


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small K values. Therefore, studying these CzPN derivatives should provide insights into how to manipulate ∆EST.

Figure 1. Chemical structures of the carbazolyl-phthalonitrile (CzPN) derivatives investigated in this study.

In this context, we aim to gain a better understanding of the relationships between molecular structure and ∆EST for TADF materials. In the present report, we detail density functional theory (DFT) and time-dependent (TD) DFT calculation results for CzPN derivatives, including those reported by Adachi and coworkers (see Figure 1).7 Further, we discuss the effects of the number of carbazolyl subunits on the system energetics, focusing on the S1/T1 excited states and ∆EST. We then draw important conclusions that are helpful for designing efficient TADF molecules. 5



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II. Computational Details A recent study suggested that DFT with gap-tuned, range-separated exchange-correlation (XC) functionals can reliably assess ∆EST of TADF materials.28-29 Thus, the ωB97X functional was chosen as a range-separated XC functional in conjunction with 6-31G(d) basis set. The rangeseparation parameter, ω, of the ωB97X functional was modulated to optimize the HOMO– LUMO energy gap by minimizing parameter I2, which is defined as29-30

1

I 2 = ∑ ε H ( N + i ) + IP ( N + i ) 

2

(1)

i=0

where ε H and IP denote the orbital energy of HOMO and the ionization potential of a given molecule, respectively. Unlike in previous studies,29,

31

however, the ground-state (S0)

geometry and ω value were optimized simultaneously for all molecules in this study. The excited state geometries were then optimized at the TD-DFT level of theory using the ground-state ω value,32 and the adiabatic ∆EST values were evaluated. To shed additional lights on the features of the excited states, natural transition orbital (NTO) analyses33 were conducted. The excitation energies were further examined in detail via their decompositions.22-23,

34

All calculations were carried out using the Gaussian 09 program

package,35 except for the excitation energy decomposition analysis22-23,

34

which was

performed using the Q-Chem program suite (version 4.2).34, 36-37

Pairs of hole and electron NTOs were analyzed to assess the LE and CT contributions to a given excited state.38 These NTO pairs are obtained from the singular-value decomposition of 6


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a one-particle transition density matrix, T, i.e.,33

( U TV ) †

ij

= δ ij λi

(2)

where δij is the Kronecker delta, λ is the square of the singular value, and U and V are unitary square matrices with dimensions Nocc × Nocc (the number of occupied orbitals) and Nvirt × Nvirt (the number of virtual orbitals), respectively. Matrices U and V further convert the canonical occupied and virtual molecular orbitals into hole and electron NTOs, respectively:

ChNTO = UCocc ;

CeNTO = VC virt

(3)

where ChNTO and CeNTO represent orbital coefficient matrices in the atomic orbital (AO) basis for hole and electron NTOs, respectively; likewise, Cocc and Cvirt are the orbital coefficient matrices for the respective canonical occupied and virtual molecular orbitals (MOs) in the AO basis. The atomic populations of the hole and electron NTOs can then be computed via Löwdin population analysis.39

µ PNTO = ∑ ( S1/ 2 DNTOS1/ 2 )

ii

i∈µ

(4)

where DNTO is the density matrix for the NTO, D NTO = C †NTO C NTO , and S denotes the overlap matrix in the AO basis. The LE and CT contributions to a given excited state can then be calculated as

7



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N occ .

∑ λ Pµ

Pν

i hNTO eNTO

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(5)

i =1

That is, if atoms µ and ν constitute the same molecular unit, e.g., electron-donor (D) or electron-acceptor (A), then the value above contributes to an LE character; otherwise, it is associated with CT contribution.

III. Results and Discussion ∆EST: calculation vs. experiment Table 1 collects the calculated adiabatic transition energies for respective singlet and triplet excited states and the energy difference between them, ∆EST. For comparison, the corresponding data from previous theoretical and experimental studies are listed.7, 27, 29 The computational results in this study underestimated the S1- and T1-state energies by ca. 0.15 eV or less, except for the S1 energy of 2CzPN, which is calculated to be around 0.1 eV higher than the experimental value. Although the calculated ∆EST value for 2CzPN is considerably larger than the experimental one (ca. 0.49 vs. ca. 0.31 eV) due to the overestimated S1 and underestimated T1 energies, the values for compounds with four carbazolyl (Cz) substituents are in markedly better agreement (Table S3 in the Supporting Information), with differences between the computational and experimental values of less than ca. 40 meV. More importantly, our results are in good agreement with previous studies, in that more Cz substituents lead to both smaller S1 and T1 energies, and smaller ∆EST. We also calculated the S1- and T1-state energies for CzPN and 3CzPN, and the difference between them, which, to the best of our knowledge, have not been reported previously, either experimentally or theoretically. These calculations are expected to provide reliable missing values, which will 8


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aid in understanding the effect of the number of Cz subunits.

Table 1. Calculated and experimental adiabatic S1- and T1-state energies (Ead(S1) and Ead(T1), respectively) of carbazolyl-phthalonitrile (CzPN) derivatives and the energy difference between them (∆EST)a Ead(S1) Calc.

a

CzPN

3.50

2CzPN

3.04, 2.94b

3CzPN

2.67

4CzPN

2.52, 2.59b

∆EST

Ead(T1) Expt.

Calc.

Expt.

2.59 2.94b

2.55, 2.57b

2.37, 2.45b

Expt.

0.91 2.63b

2.47 2.60b

Calc.

0.49, 0.37b, 0.24c

0.31b

0.20 2.45b

0.15, 0.14b, 0.00c

0.15b

All the values are in eV. b Ref. 27. c Ref. 29.

Effect of the number of carbazolyl substituents: ∆EST vs. ∆EH-L As stated above, increasing the number of Cz subunits reduces both the singlet and triplet energies. In going from the molecule with a single Cz substituent (CzPN) to the molecule with four Cz subunits (4CzPN), the S1 energy monotonously decreases from ca. 3.50 eV to 2.52 eV. Similarly, the energy of the T1 state decreases from ca. 2.59 eV to 2.37 eV, as more Cz substituents are appended onto the core phthalonitrile (PN) unit. The reduction in the S1 energy is, however, more significant than that in the T1 energy (ca. 0.98 eV vs. 0.22 eV), and therefore, ∆EST decreases as the number of Cz subunits increases. This result indicates that Cz substituents have a more direct impact on the S1-state energy than the T1-state energy. Penfold recently suggested that the HOMO–LUMO energy gap, ∆EH-L, of TADF molecules is one of the factors that determines ∆EST.28 Given the electron-pulling character of a Cz group 9



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attached via its N atom,24-26 additional Cz groups are expected to stabilize the LUMO of a molecule and hence reduce ∆EH-L. To justify this assumption, the IPs and electron affinities (EAs) of the CzPN derivatives were evaluated, as shown in Table 2.40 As clearly observed, the substitution of additional Cz groups on the core PN unit has different effects on the IP and EA values of the CzPN derivatives. Additional Cz units induce a decrease in the EA values of CzPN analogs, consistent with the expected lower LUMO levels. In contrast, increasing the number of Cz units leads to a reduction in the IP values, corresponding to elevated HOMO levels. Consequently, introduced Cz substituents decrease the IP + EA value of the CzPN derivatives, corresponding to a reduction in ∆EH-L.

Table 2. Calculated adiabatic ionization potentials (IPs) and electron affinities (EAs) (in eV) of carbazolyl-phthalonitrile (CzPN) derivatives

a

IP

EAa

IP + EA

CzPN

7.43

-0.89

6.54

2CzPN

7.14

-1.17

5.97

3CzPN

6.87

-1.34

5.53

4CzPN

6.73

-1.49

5.24

EA = E(anion) - E(neutral)

Thus, the following question arises: Why does the reduced ∆EH-L value influence the S1-state and T1-state energies in a different fashion? To better understand such dissimilar effects, the natures of the S1 and T1 states for the CzPN derivatives should be compared. In this regard, the pairs of hole and electron NTOs for the S1 and T1 state were calculated, as depicted in Figure 2 and 3, respectively. In Figure 2, the HOMO and LUMO of each CzPN derivative are 10


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also displayed. As clearly demonstrated, the HOMO and LUMO are effectively separated in all the CzPN derivatives; the HOMO is located mostly on the peripheral Cz subunits and the LUMO is localized almost exclusively within the core PN moiety. The hole and electron wave functions for the S1 state of the CzPN derivatives are separated in the same manner. Therefore, the S1 state of the CzPN analogs, even that with a single Cz substituent, is dominated by CT character from the HOMO-like orbital of the peripheral Cz groups to the LUMO-like orbital of the core PN unit. Consequently, the corresponding excitation energy is directly influenced by ∆EH-L. On the other hand, Figure 3 unambiguously shows that the T1 state of CzPN is characterized predominantly by LE within the core PN unit, and even that of 4CzPN exhibits a significant LE character. The energies of such LE states are readily expected not to be influenced by ∆EH-L. However, we also note that the CT feature is considerably enhanced in 4CzPN. To confirm this observation, the LE vs. CT contributions to both the S1 and T1 states of the CzPN derivatives were calculated, as listed in Table 3; the PN core unit is set to be the electron-acceptor and the peripheral Cz groups constitute the electron-donor. As consistent with Figures 2 and 3, CT character (>90%) dominates the S1 states of all the CzPN analogs. On the other hand, the T1 states have a rather mixed nature, with the CT character monotonously growing from ca. 24% to ca. 49% in going from CzPN to 4CzPN. With the limited CT character of the T1 state, its energy is expected to be considerably less affected by ∆EH-L than the S1-state energy. However, the increase in the CT character with the number of Cz groups suggests that the reduced ∆EH-L enhances the CT contribution to the T1 state, and thus, the T1-state energy become more sensitive to ∆EH-L. As

∆EST also decreases as the number of Cz substituents increases, the correlation between the CT contribution to the T1 state and ∆EST can be easily deduced.

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Figure 2. Frontier molecular orbitals (FMOs) of ground-state carbazolyl-phthalonitrile (CzPN) derivatives and natural transition orbital (NTO; hole and electron wave functions) pairs for the S1 states. The calculated square of singular values, λ, are 0.9994, 0.9989, and 0.9968 for CzPN, 2CzPN, and 4CzPN, respectively.

12


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Figure 3. Natural transition orbital (NTO: hole and electron wave functions) pairs for the T1 states of carbazolyl-phthalonitrile (CzPN) derivatives. λ denotes the square of singular value for a given NTO pair.

Table 3. Calculated local excitation (LE) and charge transfer (CT) contributions to the lowestlying singlet (S1) and triplet (T1) excited states of carbazolyl-phthalonitrile (CzPN) derivatives S1

T1

LE

CT

LE

CT

CzPN

0.083

0.917

0.764

0.236

2CzPN

0.081

0.919

0.645

0.355

3CzPN

0.077

0.923

0.593

0.407

4CzPN

0.089

0.911

0.508

0.492

CT vs. LE characters in the T1 state: orbital energy difference vs. exciton binding energy 13



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As the CT feature in the excited state was found to play a pivotal role in ∆EST, we explored the factors governing the nature of a given excited state in more detail. Thus, for both the S1 and T1 states, excitation energy decomposition analyses were performed at their respective geometries (Table S5 and Table 4, respectively). The vertical excitation energy (∆E) is composed of the orbital energy difference (∆ε), 2K, the Coulomb integral (–J) between the hole and electron, and an additional 2-electron integral energy term from the DFT exchangecorrelation kernel (XC2):34

∆E = ∆ε + 2 K − J + XC 2 Note that the latter three terms constitute the exciton binding energy (Eex). As such analyses can be conducted only within the Tamm–Dancoff approximation (TDA), the total sum of the excitation energy components, ∆ETDA, could be different than the excitation energy evaluated within the random phase approximation (RPA, i.e., TD-DFT), ∆ETD, which we have relied on thus far.32 As discussed above, the S1 state of all the CzPN derivatives corresponds to the HOMO-to-LUMO CT transition. Among all possible electronic excitations, this is associated with the smallest ∆ε and negligible K, both of which are favored by singlet states. As expected, the ∆ε values correspond well with ∆EH-L; the differences between them are less than 0.2 eV (less than ca. 4 % with respect to ∆ε). In addition, the 2K values are as negligibly small as ca. 1~2 meV.

On the other hand, as mentioned earlier, the triplet states of the CzPN derivatives are of mixed character, and thus it would be helpful to understand the difference in the excitation energy components for different states, i.e., LE vs. CT states. As the contribution of K to the triplet state is buried in ∆ε and computed as zero,22-23, 41 it is more straightforward to compare singlet CT and LE states. The vertical excitation energies for the LE state were obtained for 14


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the corresponding PN group by replacing all the Cz substituents with H atoms. For example, this calculation gives∆ε, 2K, –J, and XC2 values for the LE state of CzPN as ca. 8.72, 1.34, 4.69, and -0.39 eV, respectively, whereas these terms for the CT state are distinctively smaller (ca. 6.76, 0.41, -3.55, and -0.09 eV, respectively). The differences in ∆ε and 2K are obvious and those in –J and XC2 can also be readily understood. When localized within the same unit (LE state), the wave function overlap between the hole and electron will be large (see the larger 2K value) and thus the distance between them is expected to be shorter on average, giving rise to a –J value larger in magnitude. In addition, the correlation between charges that are already sufficiently separated would be relatively small, leading to a smaller XC2 value in the CT state.

Donor

Donor

EexCT

EexLE

∆εCT

∆εLE ∆ECT

>

∆ELE

∆εCT

EexCT

∆εLE ∆ECT

Acceptor

EexLE

Local-Excitation versus Charge-Transfer Characters in the Triplet

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