Effective Impact of Dielectric Constant on Thermally Activated Delayed

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C: Energy Conversion and Storage; Energy and Charge Transport

Effective Impact of Dielectric Constant on Thermally Activated Delayed Fluorescence and Nonlinear Optical Properties: Through-Bond/-Space Charge Transfer Architectures Jin-Ting Ye, Li Wang, Hong-Qiang Wang, Xiu-Mei Pan, Haiming Xie, and Yongqing Qiu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05411 • Publication Date (Web): 27 Jul 2018 Downloaded from http://pubs.acs.org on July 29, 2018

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The Journal of Physical Chemistry

Effective Impact of Dielectric Constant on Thermally Activated Delayed Fluorescence and Nonlinear Optical Properties: Through-Bond/-Space Charge Transfer Architectures

Jin-Ting Ye,† Li Wang,† Hong-Qiang Wang,† Xiu-Mei Pan,†,‡ Hai-Ming Xie,†,‡ and Yong-Qing Qiu†,‡,∗ †

Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal

University, Changchun, 130024, China ‡

National & Local United Engineering Laboratory for Power Battery, Faculty of

Chemistry, Northeast Normal University, Changchun, 130024, China

∗ Corresponding Author. Fax: +86 431 85098768. E-mail addresses: [email protected] (Y. Q. Qiu).

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The Journal of Physical Chemistry 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 56 57 58 59 60

ABSTRACT Recently, three 9,9-dimethylxanthene-based donor (D)/acceptor (A) U-shaped space-through architectures, containing π−π intramolecular interactions between the D and A, exhibit unique advantage (i.e. a small singlet (S1) − triplet (T1) energy splitting (∆EST)) in thermally activated delayed fluorescence (TADF). To explore the TADF and second-order nonlinear optical (NLO) properties of U-shape compounds with through-space charge transfer (TSCT) between aligned D and A units compared with that of conventional conjugated D−A (L shape) ones, we theoretically investigated the geometric and electronic structures, through space D−A π−π interactions, CT properties, ∆EST, and first hyperpolarizabilities (βtot) of compounds 1-L ~ 5-U. The calculated ∆EST values of the U-shaped molecules are relatively smaller than that of L-shaped compounds in gas phase, indicating that the U-shaped derivatives are excellent thermally activated delayed fluorescent candidates. Furthermore, a noteworthy finding was that the conjugated D−A unit of L-shaped compounds was suggested to promote the performance in NLO due to the lower excited energy, and stronger oscillator strength for the crucial excited state. Especially, for compound 2-L, the βtot value is 8 times larger than that of 2-U in gas phase. In addition, we have quantitatively studied ∆EST and βtot values in the solid-state polarization for all studied molecules using the polarizable continuum model. Importantly, the results of polarization effects (ε from 1.0 to 3.0) show that the marked reduction in the ∆EST values of U-shaped derivatives due to the simultaneous presence of dominant 1TSCT and 3TSCT excited states in the solid-state polarization, which are favorable for TADF


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materials. In addition, the increment in the βtot values of L-shaped compounds are prefer for NLO applications. We hope this work may provide a theoretical understanding on the influence of the heteroatom and the π-π conjugation between D and A units and polarization effects on the ∆EST and βtot and novel design mentality of the efficiency-enhancing TADF and NLO materials.

1. Introduction The optimization of organic light emitting diode (OLED) technologies has been reported the first OLED in 1987 by Tang and Van Slyke,1 which have received extensive attention due to their applications in lighting, ultrathin displays for smart phones and televisions and in solid-state lighting.2-3 Recently, thermally activated delayed fluorescence (TADF) has evolved as a brand new mechanism used in OLEDs, because it can effectively utilizing triplet excitons through enhanced reverse intersystem crossing (RISC) process from the lowest triplet state (T1) to singlet state (S1) for OLED, which makes the realization of internal quantum efficiencies (IQE) up to 100%.4-5 Available experimental data for the effective TADF molecules indicate that the singlet−triplet splitting ∆EST can be as small as 0.1 eV,6-7 which can achieve an easier RISC at a given temperature (Figure S1). Moreover, the highly efficient TADF material requires spatial separation of electron densities of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) to gain a small ∆EST for rapid RISC process.



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Recently, numerous donor−acceptor (D−A) type TADF molecules with high quantum efficiency have been reported by Adachi et al..8-10 The majority of TADF materials

adopted

the

architecture

where

electron-donor

(D)

unit

and

electron-acceptor (A) unit are linked directly with the strong through-bond charge transfer (TBCT, L-shaped molecules)11 (Figure 1). Many studies have stated that these D-A compounds exhibit superior NLO properties, characterized by a large hyperpolarizability values (βtot) and good thermal and chemical stabilities.12 However, the strong TBCT effect in the conjugated architecture tends to induce a large red-shift of emission.11 In this regard, the twisted D−A configuration with through-space charge transfer (TSCT, U-shaped molecule) is one of the high efficiency molecular design strategies for efficient TADF emitter. There exists intramolecular through space D−A π−π interaction, minimizing the electron-exchange energy and yielding a small

∆EST.

Very

recently,

three

twisted

TADF

compounds

9,9-dimethylxanthene-based D/A chromophores were synthesized and characterized by integrating D groups (phenothiazine for 1-U, carbazole for 2-U and 3,6-di-tertbutylcarbazole for 3-U) on the 4-carbon position of xanthenes.13 The only difference between TBCT and TSCT compounds (L-shaped and U-shaped molecules) is the bonding way of D/A segment, leading to their difference between structure and property. The experimental research mentions that higher quantum yields were observed in the solid state. However, TADF molecules in solid-state environment have so far been limited in theoretical studies. Sun group recently developed a methodology, the polarizable continuum model (PCM) -tuned approach.14-15


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In the present work, to investigate the effect of a strong electron-withdrawing substitution (CN) of the acceptor moiety and phenothiazine alternated by phenoxazine in the donor fragment on photophysical properties and CT cooperativity, we designed compounds 4-U and 5-U (Figure 1).13 The geometric structure, frontier molecular orbital, intramolecular through space D−A π−π interactions, ∆EST, and second-order NLO response would be performed to investigate the following issues: (i) the effects of

twisted

movement,

as

well

as

the

donors

(carbazole/3,6-di-tertbutylcarbazole/phenoxazine) and acceptors (cyano) on the structures, CT properties, ∆EST values, and NLO responses; (ii) the effects of a polarizable environment (especially for the solid-state polarization) on the distributions of hole and electron wave functions in the lowest singlet (S1) and triplet state (T1), CT pattern, ∆EST values and second-order NLO responses.

Figure 1. Molecular structures of 1-L ~ 5-U; conventional conjugated D−A (L shape) and U-shaped space-through architecture (U shape).

2. Computational details



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In this paper, the geometry optimizations and the electronic structures for the ground state were performed by using density functional theory (DFT) method. The ωB97XD16 functional is the functional from Chai and Head-Gordon,17 which uses a version of Grimme’s D2 dispersion model and performs well in understanding the π−π stacking interaction. Therefore, the optimized ground state geometries (S0) in the gas phase of all the studied compounds were obtained at ωB97XD/6-31G(d) level, which has successfully reproduces the experimental structures.13 The optimal tuned range-separated functional is referred as ωB97XD*, which the optimal ω values were obtained by the “optDFTω” procedure.18 The singlet and triplet excited-state geometries were optimized using the optimally tuned range-separated functional ωB97XD* with the 6-31G(d) basis set, which has been demonstrated to provide reliable descriptions of the excited-state property of organic molecular systems.15 The separation of the exchange term into a short-range DFT and a long-range HF is defined by the interelectronic distance r12 and the error function erf (x)19 as following formula:

r12 −1 = r12 −1erfc(ωr12 )+r12 −1erf(ωr12 )

(1)

The range-separation parameter ω represents the inverse of the distance at which the exchange changes from DFT-like to HF-like. In exact Kohn−Sham (KS) theory,20 the negative HOMO energy −εH(N) for an N-electron system should be equal to the vertical ionization potential (IP). This optimal tuning method, in brief, is determined nonempirically through minimizing the following equation:

J = ε H ( N ) + IP( N )


(2)

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A more refined target functional as shown below was proposed particularly for “better” description of HOMO−LUMO gap or transport gap: 2

1

J = ∑ [ε H ( N + i ) + IP ( N + i ) ] 2

(3)

i =0

The above equation simultaneously applies the IP criterion for both neutral (N) and anion (N + 1) systems. In addition, the IP, electron affinity (EA) and exciton binding energy (Eb)15 were studied at same level. The calculations of vertical excitation energies of the lowest singlet (Eo(S1)) and triplet (Eo(T1)) excited states and the vertical singlet−triplet gap (∆EST = Eo(S1) − Eo(T1)) have been calculated using the LR-TDDFT21 with Tamm-Dancoff approximation (TDA).22-23 In order to clarify the effect of the surrounding environment (such as “crystals”) on the

molecular

photophysical

properties,

the

polarizable

continuum

model

(PCM)-tuned RS functional approach was used to simulate the solvent effect,24-25 where the default integral equation formalism variant polarizable continuum model (IEFPCM) was imported by adding the “scrf(pcm, read)” keyword and defining the magnitude of the dielectric constant ε. The PCM description can experimentally determined parameters which reflect the response of the environments in their respective state (liquid or solid) due to it is based on these macroscopic, which can not only describe polarization effects in solution, but in general for any isotropic environment including amorphous thin films.26 The ε of a molecular crystal or thin-film was evaluated via the Clausius– Mossotti relation,27-28 which reads:

ε − 1 4π α = ε +2 3 V

(4)

where V is the volume occupied by a single molecule, and α term denotes the isotropic



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component of the molecular polarizability. The V and α were calculated for all molecules at the ωB97XD/6-31G(d) level and listed in Supporting Information Table S1. Note that the molecular volume V here is van der Waals volume and was evaluated based on improved Marching Tetrahedra algorithm using Multiwfn software version 3.4.29 Thus, we employed the dielectric constant ε = 3.0 used in the PCM to simulate the solid environment.30 Considering accuracy and better connecting NLO properties and structures of all studied complexes, the two methods (CAM-B3LYP19 and ωB97XD*) with 6-31+G(d) basis set were used to calculate the total first hyperpolarizabilities (βtot). The βtot is calculated by analytical third energy derivatives using the following equation:

β tot = ( β x2 + β y2 + β z2 )

(5)

where β i is defined as: β i = (1 / 3 ) ∑ ( β ijj + β

jji

+ β jij )

i , j = { x , y , z}

(6)

j

Gradient isosurface (RDG) and Sign(λ2)*ρ are a pair of very important functions for revealing the weak interaction region.31

RDG ( r ) =

∇ρ (r )

1

2(3π 2 )

1

3

ρ (r )

4

(7)

3

It can be directly used to reveal the averaged weak interaction regions in the dynamics process and distinguish three different types of noncovalent interactions (hydrogen-bonding, π−π interaction, and steric hindrance) for the U-shaped compounds. All of the calculations were carried out by using the Gaussian 09W program package.32 RDG was obtained by employing the Multiwfn software version 3.4.29


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RDG were plotted using VMD 1.9.1.33

3. Results and discussion 3.1 Geometrical and electronic structures The structural parameters of compound 1-U (which has been synthesized experimentally) has been optimized by four different density functionals B3LYP, BHandHLYP, CAM-B3LYP and ωB97XD at 6-31G(d) basis set to obtain a reliable prediction. Generally, with respect to experimental values, the calculated intramolecular separation (d) of B3LYP, BHandHLYP, and CAM-B3LYP functionals were overestimated by ∼0.728, ∼0.513 and 0.346 Å, respectively. The calculation of ωB97XD functional (3.378 Å) seems to provide a reasonable agreement with experimental value (3.423 Å). Therefore, the geometry optimizations in the gas phase for compounds 1-L ~ 5-U obtained by ωB97XD/6-31G(d) level are summarized in Figure S2. The structures of compounds 1-U, 2-U, and 3-U were fully characterized via the single crystal X-ray diffraction analysis.13 The intramolecular separation of

2-U and 3-U are calculated as 3.375 Å (3.375 Å) and 3.372 Å (3.299 Å), respectively, which clearly demonstrate that the geometrical calculations are reliable for the current systems. The introduction of 3,6-di-tertbutyl on the D or cyano on the A groups have no effect on the configuration. Generally, it is important to suppress non-radiation decay by inhibiting the geometric changes between their ground (S0) and lowest singlet (S1) excited states for improving the luminescence efficiency of TADF material.6, 34 Figure S3 displays a geometric comparison between S0 and S1 states of



all studied compounds. The geometrical deviations between S0 and S1 states are mainly attributed to the twist between D unit and A unit. Among them, the deviation between S0 and S1 geometries for L-shaped compounds is more remarkable than U-shaped compounds.

3.2. Frontier molecular orbitals The frontier molecular orbitals (FMOs) plays an important part in judging the electronic and optical properties.35 The literatures mention that the conventional (semi) local exchange-correlation (XC) functionals (i.e., PBE36 and B3LYP37), which are the most frequently applied in organic donor−acceptor systems,38-40 fail in predicting the band gaps and especially the CT excitation energy. Therefore, considering the accuracy and computational cost, the orbital energy gap were calculated by using the ωB97XD*/6-31G(d) method. In order to research the effect of modifying the connected types between D and A units on their electronic properties, the HOMO and LUMO energy gaps of compounds 1-L ~ 5-U are plotted in Figure 2. As shown in Figure 2, the energy gaps between HOMO and LUMO of U-shaped compounds 1-U (6.01 eV) and 2-U (6.48 eV) are larger than that the corresponding L-shaped compounds 1-L (6.00 eV) and 2-L (6.30 eV). As a general rule, the smaller the energy gap, the larger the second-order NLO response,41 the L-shaped compounds should exhibit the better NLO property than that U-shaped compounds. Moreover, the energy gaps are reduced when introducing -CN to the acceptor fragment (4-U) compared to the value for compound 1-U, because the enhancement of the electron accepting


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ability of the A results in the lower energy gap.42 In addition, it is well-known that the HOMO and LUMO distributions are important for designing efficient TADF material, which dominates the ∆EST and subsequently the RISC.42 As depicted in Figure 2, the HOMOs

of

the

U-shaped

compounds

are

mainly

distributed

over

the

carbazole/3,6-di-tertbutylcarbazole/phenoxazine moieties, whereas the LUMOs are mainly located on the 2,4,6-triphenyl-1,3,5-triazine fragment, respectively. Such small overlap between HOMO and LUMO indicates that U-shaped compounds have small ∆EST and are potential TADF materials. In the 3.4 section, the ∆EST of all studied compounds will be discussed in detail. However, the distributions of LUMOs are located in the two phenyl links and the 2,4,6-triphenyl-1,3,5-triazine parts for compounds

1-L

and

2-L,

while

the

HOMO

originates

from

the

3,6-di-tertbutylcarbazole moiety and slight contribution comes from the phenyl ring for 2-L. Thus, the overlap between HOMO and LUMO is mainly centered on the connected phenyl in compound 2-L, indicating the bridge (conjugation and the heteroatom effect) have moderate influence on FMOs.

Figure 2. Contour plots of the HOMO and LUMO of compounds 1-L ~ 5-U.



3.3 Noncovalent Interaction. The reduced density gradient (RDG) map43 based on the analysis of the electron densities (r) and their reduced gradients (s), as a new approach to visualize noncovalent interactions, is an important tool to distinguish three different types of noncovalent interactions (red signifies strong repulsion, green represents π−π interactions, and blue denotes strong attraction). The computed plots of SRDG versus sign(λ2)ρ (the electron density multiplied by the sign of the second Hessian eigenvalue) and the gradient isosurfaces with s = 0.5 au for U-shape compounds were showed in Figure 3. According to Yang et al,43 the existence of a spike with low electron density marked by pink circle (-0.005 < sign(λ2)ρ < 0.005) indicate the weak noncovalent interactions. Likewise, the two spikes of all the U-shape compounds (pink circle in Figure 3) are correlating with intramolecular through space D−A π−π interactions. Moreover, in accordance with the experimental results that crystal structures have the π−π intramolecular interactions between D and A.13 In addition, the green-gray area can represent the dispersion range of the π−π interaction. The dispersion range of compound 3-U more scattered than that of other compounds, because the introduction of methyl groups makes that space steric hindrance increase.


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Figure 3. Plots of the SRDG versus sign(λ2)ρ and the gradient isosurfaces (s = 0.5 a.u.) of U-shape compounds 1-U-5-U.

3.4 Singlet-triplet energy gap (∆EST) For efficient TADF material, a small ∆EST value is beneficial to the RISC process from the T1 to S1 states and the enhancement of luminescence efficiency. The exciton binding energies (Eb) is defined as the difference between the transport gap (Eg ≡ IP − EA) and the optical gap (E0). We calculated the IPs, EAs, Eg, E0, and Eb values from the gas-phase to the solid environment as shown in Table 1. Sun et al. proved that reducing the Eb of the D layer is a useful approach to simultaneously achieve efficient exciton separation efficiency.44 In gas phase, the Eb values are in the range of 2.064 to 2.795 eV for 1-L and 2-U. For solid thin films (ε = 3), all the exciton binding energies are significantly reduced as expected, which decrease to ∼0.628 eV for 1-L and

∼1.308 eV for 2-U indicate that the solid-state polarization effects can result in an easier separation of hole−electron pairs.15, 30



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Table 1. Calculated ionization potential/electron affinity (IP/EA), transport gap (Eg), lowest singlet and triplet excitation energy (E0(S1) and E0(T1)), exciton binding energy (Eb = Eg - E0(S1)), and vertical singlet−triplet gap (∆EST) (in eV) of all the studied compounds in both gas and solid phases at the ωB97XD*/6-31G(d) level gas phase 1-L 1-U 2-L 2-U 3-U 4-U 5-U solid film 1-L 1-U 2-L 2-U 3-U 4-U 5-U

ω 0.146 0.141 0.143 0.138 0.125 0.138 0.139

IP 6.55 6.13 6.85 6.60 6.31 6.25 5.92

ω 0.029 0.032 0.027 0.030 0.028 0.031 0.032

IP 5.06 5.13 5.77 5.70 5.48 5.21 5.03

ωB97XD*/6-31G(d) EA Eg E0(S1) E0(T1) Eb 0.56 5.99 3.926 3.357 2.064 0.14 5.99 3.237 3.162 2.753 0.53 6.32 4.165 3.308 2.155 0.08 6.52 3.725 3.435 2.795 0.15 6.16 3.469 3.388 2.691 0.82 5.43 2.698 2.668 2.732 0.11 5.81 3.025 2.966 2.785 PCM (ε = 3.0) ωB97XD*/6-31G(d) EA Eg E0(S1) E0(T1) Eb 1.54 3.52 2.8916 2.8846 0.628 1.22 3.91 2.6292 2.6289 1.281 1.52 4.25 3.2732 3.1197 0.977 1.21 4.49 3.1820 3.1816 1.308 1.21 4.27 3.0234 3.0232 1.247 1.85 3.36 2.1325 2.1324 1.228 1.21 3.82 2.4963 2.4962 1.324

∆EST 0.569 0.075 0.857 0.290 0.080 0.030 0.058 ∆EST 0.0071 0.0003 0.1535 0.0004 0.0002 0.0001 0.0001

In order to obtain a pictorial description of the excited state property, the hole (h) and electron (e) distributions of S1 and T1 state were also analyzed using Multiwfn software. The hole−electron wave function overlap (Oh,e) and the distance (∆r)45 between the centroids of hole and electron wave functions in the lowest singlet (S1) and triplet state (T1) are listed in Table 2. A smaller Oh,e value and a larger ∆r value generally point to a stronger charge-transfer character.30 For comparison, the calculated

∆EST

values

of

all

the

studied

compounds

at

the

TDA-ωB97XD*/6-31G(d)/PCM level are described in Figure 4. The optimal ω values are in the range from 0.125 (3-U) to 0.146 (1-L) Bohr−1, which are significantly


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smaller than the default ω value for ωB97XD (0.20 Bohr−1), indicating that the tuned functional switches from DFT to exact-exchange (eX) at larger interelectronic distances. The smaller ω values in the case of the simulated solid-state environment can be explained by the fact that the electron density in crystal has a more spatial delocalization than that in the gas-phase isolated molecule.14, 46-47 For the gas phase, Figure 4 shows that the calculated ∆EST values of U-shaped compounds (0.0298−0.2901 eV) are smaller than that the corresponding L-shaped compounds (0.5695−0.8570 eV). As a matter of the fact, the difference between S1−T1 energy gaps in gas phase is very small due to their sufficient separation of the HOMO and LUMO for the U-shaped molecules. The molecular structures are such that rigid placement of a donor and an acceptor with cofacial alignment at distances of 3.3−3.5 Å produces quantitative formation of a charge transfer excimer structure, which are prone to lead to spatial separations of HOMOs and LUMOs, and lead to small ∆EST values. Therefore, the style of connection between D and the A moieties are expected to play the crucial roles in the CT character and singlet-triplet energy gap. In addition, the U-shaped D-A compounds are more promising to be effective TADF material than that the corresponding L-shaped D-A compounds.



Figure 4. Calculated vertical ∆EST of U-shaped and L-shaped compounds using the (PCM-)tuned ωB97XD* and B3LYP functional in both gas and solid phases (ε = 3.0). As shown in Figure 5 (ε = 1.0), for the S1 state of 1-L, the electron is mainly localized on the carbazole and phenyl groups showing a typical π* character, while the hole is distributed on the carbazole fragment and displays both π character. Meanwhile, the calculated the Oh,e and ∆r (a smaller Oh,e and a larger ∆r values, a stronger charge-transfer character) are 0.89 and 2.83 Å, respectively. Thus, the S1 exhibit the outstanding through-bond charge transfer and local excitation transitions ππ*(1TBCT+1LE). For the T1 state, the e-h are mainly localized in the central part of the molecule, which corresponds to a greater 3LE character with an Oh,e value of 0.98 and ∆r of 0.74 Å. For the S1 and T1 states of 1-L in the solid phase, the electron is mainly distributed over the central part of the molecule, and the hole delocalizes along the A segment, which exhibits the clearly TSCT transitions than that in gas phase. The result is in good agreement with the calculated Oh,e and ∆r values for both S1 state become 0.73 and 6.75 Å (0.74 and 6.63 Å for T1 state), respectively. For compound

1-U, there are significant ππ* through-space charge transfer (TSCT) characters for both S1 and T1 states in both gas phase and solid state. Interestingly, the T1 state of the


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molecule has partial 3LE character in the gas phase with the Oh,e value of 0.94 and the ∆r of 1.22 Å, which results the ∆EST value significantly greater than that in solid state. Very similar observations can be made in the case of the compounds 2-U and 3-U.

Figure 5. Distributions of hole and electron wave functions in the lowest singlet (S1) and triplet state (T1) of 1-L and 1-U in both gas phase and solid film (ε = 3.0) calculated at the PCM-tuned ωB97XD*/6-31(d) level. Superscripts “1” or “3” indicate a singlet or triplet state. Blue and purple isosurfaces refer to hole and electron, respectively. For the S1 state of 2-L in the gas phase (Figure 6), the electron localizes on the central part of the molecule with a wave function showing a typical π* character and hole localizes on the carbazole and phenyl groups and displays both π character, which is made of significant ππ*(1TBCT+1LE) transitions with an Oh,e value of 0.24 and ∆r of 2.40 Å. For T1 state, the electron and hole localize on the central part of the molecule showing a typical ππ*(3LE) character with an Oh,e value of 0.94 and ∆r of 1.29 Å. For the solid state, the S1 and T1 states of compound 2-L tend to have substantial ππ*(TBCT) character than that in vacuum, which promotes further



reduction of ∆EST. In addition, the calculated results demonstrate that the ∆EST value for the molecule 4-U is reduced from 0.0748 eV to 0.0298 eV, because the introduction of -CN on the 2,4,6-triphenyl-1,3,5-triazine fragment enhances its electron accepting ability.48 These results are also in line with the previous findings of Zhang et al.42. Obviously, for the S1 and T1 states of 4-U/5-U in gas phase (Figure S4), the electron and hole are mainly distributed over A and the D fragments, respectively, which exhibits TSCT character. The decrease of ∆EST value of compounds 4-U and

5-U in the solid phase are related to the fact that S1 and T1 possess the more obvious TSCT characters, which explains that the smaller Oh,e value and a larger ∆r value generally point to a stronger CT character. The small singlet−triplet gaps obtained when considering the polarizable medium point to U-shaped compounds as potentially efficient TADF materials. When the distance ∆r is large, indicating that the separation of electron and hole is more obvious. In this case, natural transition orbital (NTO, hole and electron wave functions) for the S1 and T1 states were calculated. When the electron is excited from i state to j state, the transition dipole moment is µij = i −r j . Generally, we can see that the pairs of hole and electron NTOs distributions with the largest eigenvalue exhibit larger variations and their overlap degree are low, which leads to the transition dipole moment between two NTOs

NTO − r NTO '

integral smaller. Accordingly, the transition dipole moment

between the correspondingly electronic states is small. In this work, for 2-U molecule, the more effective separation of electron-hole for the S1 state can be found with the calculated Oh,e (0.92) and ∆r values (1.81 Å) in gas phase, which confirm a significant


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TSCT character (Figure 6). However, for correspondingly L-shaped molecule 2-L, the hole and electron distribution of the S1 state corresponds to a greater 1LE character with an Oh,e value of 0.77 and ∆r of 4.50 Å, which showing a smaller Oh,e and a larger ∆r (a smaller transition dipole moment) than 2-U molecule. However, the 2-U molecule exhibits smaller ∆EST values (0.290 eV) than the 2-L molecule (∆EST = 0.857 eV) in gas phase. Therefore, the results show that the transition dipole moment is not the only criterion to obtain a small ∆EST value when the comparable molecular configuration is different (U-shaped and L-shaped configurations). However, for all studied U-shaped molecules, 4-U molecule with smaller Oh,e and larger ∆r (a smaller transition dipole moment) is significantly enhance the TADF property than other donor substitution systems in gas phase, thus, the smaller transition dipole moment is important for the photophysical properties of TADF when the comparable molecules exhibit the same architectures (only one configuration, U shape or L shape).



Figure 6. Distributions of hole and electron wave functions in the lowest singlet (S1) and triplet state (T1) of 2-L and 2-U in both gas phase and solid film (ε = 3.0) calculated at the PCM-tuned ωB97XD*/6-31(d) level. Superscripts “1” or “3” indicate a singlet or triplet state. Blue and purple isosurfaces refer to hole and electron, respectively.

Our results in Figure 4 show that, in comparison to the gas phase (with ∆EST values of 0.8570 eV for 2-L and 0.0298eV for 4-U), the solid thin films (ε = 3) can significantly reduce the singlet−triplet gaps, with ∆EST values of 0.1535 eV for 2-L and 0.0001eV for 4-U and 5-U. Compared to ωB97XD*, hybrid functional B3LYP overall give reasonable predictions for the ∆EST values (see Figure 4 and Table S2). However, the performance in predicting the gas-to-solid change in singlet−triplet gaps using B3LYP cannot be captured due to a simultaneous over/underestimation of the lowest singlet and triplet excitation energies.49 This finding is also consistent with a recent study by Phillips et al. and Sun et al..30, 50


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Table 2. Hole-electron wave function overlap (Oh,e) and distance between the centroids of the hole and electron distributions (∆r) in the lowest singlet and triplet states (S1 and T1) for the seven molecules in both gas and solid phases (ε = 3.0)

S1 (gas) T1 (gas) S1 (solid) T1 (solid)




1-L Oh,e 0.89 0.98 0.73 0.74 2-L Oh,e 0.77 0.94 0.71 0.88 3-U Oh,e 0.94 0.98 0.84 0.84 5-U Oh,e 0.90 0.92 0.79 0.79

∆r 2.83 0.74 6.75 6.63

character ππ*(1TBCT+1LE) 3 LE(ππ*) 1 TBCT(ππ*) 3 TBCT(ππ*)

Oh,e 0.89 0.94 0.78 0.78

∆r 4.50 1.29 6.88 2.88

character ππ*(1TBCT+1LE) 3 LE(ππ*) 1 TBCT(ππ*) ππ*(3TBCT+3LE)

Oh,e 0.92 0.98 0.78 0.78

∆r 1.73 0.75 2.99 2.99

character TSCT(ππ*) ππ*(3ICT+3LE) 1 TSCT(ππ*) 3 TSCT(ππ*)

Oh,e 0.90 0.90 0.78 0.78

∆r 1.83 1.75 2.99 2.99

1

1-U ∆r 1.87 1.22 3.05 3.05 2-U ∆r 1.81 0.56 2.96 2.96 4-U ∆r 1.87 1.87 3.25 3.25

character TSCT(ππ*) ππ*(3TSCT+3LE) 1 TSCT(ππ*) 3 TSCT(ππ*) 1

character TSCT(ππ*) ππ*(3ICT+3LE) 1 TSCT(ππ*) 3 TSCT(ππ*) 1

character TSCT(ππ*) 3 TSCT(ππ*) 1 TSCT(ππ*) 3 TSCT(ππ*) 1

character TSCT(ππ*) 3 TSCT(ππ*) 1 TSCT(ππ*) 3 TSCT(ππ*) 1

3.5 Static first hyperpolarizabilities It is known that the obvious intramolecular CT and intrinsic nonsymmetrical electronic structures of the studied compounds are the potential second-order NLO materials.41, 51-52 For these studied compounds, the origin of the Cartesian coordinate system is located at the centre of D and A moieties for TBCT type (the centre of the 9,9-dimethylxanthene scaffold for TBCT type), and A moieties are placed in the xy-plane with the longitudinal x axis points to A moieties (Figure 1). As a ACS Paragon Plus Environment


consequence, we investigated their second-order NLO properties by ωB97XD* and CAM-B3LYP functionals.35,

53

Among the considered functional (Table S3), the

ωB97XD* produces the smaller βtot values than CAM-B3LYP. Similar trends are seen in the previous theoretical research.54 Thus, for a more detailed analysis of our results, we selected the βtot values of ωB97XD* method in the following discussion. The basis-size effects were tested by extending the basis sets from 6-31G(d) to 6-31+G(d), 6-311G(d), and 6-311+G(d) (see Table S4). The results obtained from the calculations using 6-31+G and 6-311+G(d) basis sets are nearly the same. Therefore, we discuss the results of the 6-31+G(d) basis in this section because this basis set shows a good balance between accuracy of the results and reasonable computational cost. Figure 7 shows that the calculated static βtot values of L-shaped compounds are larger than that of U-shaped compounds. For example, at gas phase, compound 1-L exhibits almost 7 times higher static βtot values (βtot =15.6 × 10−30 esu) as compared with compound 1-U (βtot =2.2 × 10−30 esu). Meanwhile, the first hyperpolarizabilities for compound 2-L is also higher (about 8 times) than 2-U (βtot, 2-U =4.3 × 10−30 esu and βtot, 2-L =35.3 × 10−30 esu). Further, the static βtot value can be effectively enhanced when the carbazole was installed on the 4-carbon position of xanthenes (2-L and 2-U). It is indicates that subtle structural modifications can substantially enhance the second-order NLO response. Amazingly, the introduction of the CN and CH3 can enhance the first hyperpolarizability. Further, the effect of phenoxazine (5-U) on the static βtot values was found to be negligible as compared with compound 1-U. Turning our attention to the magnitude of the hyperpolarizability results embedded


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in a polarizable environment, as shown in Figure 7, the static βtot values of all studied compounds increase significantly as the dielectric constant from 1.0 (vacuum) to 3.0 except for compound 4-U. Especially, compound 1-L exhibits twice as high static βtot values (βtot =32.5 × 10−30 esu) as compared with that in the gas phase (βtot =15.6 × 10−30 esu), which indicates that a polarizable environment can also play a dramatic role in the second-order NLO response.

Figure 7. The calculated βtot values of all studied compounds as a function of dielectric constant. In order to gain deeper insight and accurate explanation of the trend in the NLO behaviors for L-shaped and U-shaped compounds, electronic absorption spectra of the compounds 1-L, 1-U, 2-L, and 2-U were carried out at the TDA-ωB97XD*/6-31G(d) level in dichloromethane solution. The reason why we choose dichloromethane solution is that it was used in the related experiments.13 The simulated spectrum of compound 1-U (258 nm) is consistent with the experimental absorption bands (272 nm,), confirming that the adopted method is suitable. The excitation energies (∆E), oscillator strengths (fos,), and transition dipole moment (∆µ) calculated for the crucial singlet excited states are summed in Table 3, together with the transferred charge (qCT)



and the distance of transferred charge (dCT). The results show that the absorption spectra of compounds 1-L and 2-L have the obvious bathochromic-shift, partially for complex 2-L, with respect to the corresponding U-shaped compounds, suggesting the possibility of a strong second-order NLO response under the right conditions.55 The L-shaped compounds decreases the electronic excitation energies (4.444 eV for 1-L vs 4.806 eV for 1-U; 4.154 eV for 2-L vs 4.440 eV for 2-U) and meanwhile increases the oscillator strengths compared with the corresponding U-shaped series. In addition, moderately stronger CT transitions of L-shaped compounds with higher electron transfers (from 0.622e to 1.299e) were detected in Figure 8. Further, the D−A structures with a planar conformation that minimizes the bond twisting observed in linear conjugated structures, which can offer an effective way to improve properties.56 Conjugated molecules, composed of a conjugated bridge that separates D from A, were extensively investigated due to the large optical nonlinearity. Recently, highly unsaturated organic frameworks have gained special attention in the attempt to optimize their nonlinear responses, aiming for large dipole moments and (hyper)polarizabilities.57-61 Under these circumstances a higher transition dipole moment suggests a better coupling/interaction between the D−A junctions.62 This subsequently will lead to a better energy transfer between the two moieties. In this work, the analogy with a classical dipole moment model gives that the larger transition dipole moment of the L-shaped molecules comes from the longer CT distance due to the widening at the D/A interface, which are in agreement with the reference.62 In addition, the relevant literature showed that the NLO response has a


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linear relationship with the lower dihedral angles between the donor-linker-acceptor of the molecules.62 Our results agree with previous studies, the L-shaped molecules are more planar, which are different from their corresponding U-shaped compounds with a cofacial arrangement, and have a higher CT character. For example, the transition dipole moment of 2-L is transferred upon light excitation (qCT = 1.299 |e|) and the large associated charge-transfer distance (dCT = 6.797 Å) than that of 2-U compound (qCT = 0.649 |e| and dCT = 0.757 Å), presenting the maximum CT and obvious charge separation, which is the indispensable requirements to obtain high NLO response. Therefore, this indicates that conjugated linear molecules with longer charge transfer distance will have obvious charge transfer characteristics and larger transition dipole moments, which will result in a large NLO response.

Table 3. The major absorption wavelengths (λ, nm), Energies (∆E, eV), oscillator strengths (fos,), transition dipole moment (∆µ, Debye), charge transfers (qCT, |e|), and charge transfer distances (dCT, Å) for 1-L, 1-U, 2-L, and 2-U at the ωB97XD*/6-31G(d) level in dichloromethane solution Complex 1-L 1-U 2-L 2-U

State λ ∆E fos ∆µ qCT S4 279 4.444 1.557 2.580 0.662 a S15 258 (272) 4.806 0.330 2.183 0.649 S1 298 4.154 1.539 3.589 1.299 S8 279 4.440 0.135 1.429 0.649 a The main absorption wavelength in experiment.


dCT 1.366 1.155 6.797 0.757


Figure 8. Electron density difference of the L-shaped system and with corresponding U-shaped molecules from the ground state to the crucial excited state calculated at the TDA-ωB97XD*/6-31G(d) level in dichloromethane.

4. Conclusions In conclusion, based on the synthesized thermally activated delayed fluorescence (TADF) through-space conjugation (U-shaped molecules) system comprising D and A bridged by the heteroatom, the conventional conjugated D−A molecules (L shape) have been designed to investigate the effect of modifying the connected bridge (conjugation and the heteroatom) between D and A units on the TADF and second-order NLO properties in detail. The calculated U-shaped compounds with a cofacial arrangement at a distance of 3.375−3.410 Å produces the intramolecular through space D−A π−π interactions. In addition, the ∆EST and βtot values as a function of dielectric constant ε (especially for the solid-state polarization) for all studied molecules using the polarizable continuum model have been demonstrated. The results indicate that the theoretical calculated singlet−triplet gaps of the U-shaped molecules in a polarizable environment are reduced with respect to that in vacuum, indicating that they exhibited delayed fluorescence in solid state, which are in


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excellent agreement with the experimental consequence. It is attributes to the fact that the more obvious TSCT character possesses in the solid-state environment. Importantly, a noteworthy finding was also that in compound 2-L the conjugated D−A was suggested to promote the performance in NLO due to the larger dipole moment variation of the S0 → S1 transition. Thus, the polarization effects can lead to the marked reduction in the ∆EST values for U-shaped derivatives and increment in the βtot values for L-shaped compounds, which are favorable for TADF and NLO applications, respectively. In addition, the polarization effect between the gas-phase isolated molecule and crystals can be well described using the (PCM-)tuned approach. The present work provides a theoretical understanding on the influence of the connected bridge (conjugation and the heteroatom) between D and A units and polarization effects on the ∆EST and βtot, which might be helpful to the theoretical and experimental design of new functional organic materials.

ASSOCIATED CONTENT Supporting Information. Computational details regarding the RDG methodology described in this work; Calculated the volume (Bohr3), polarizabilities (Bohr3) and dielectric constant ε simulated the solid thin-film environment for all molecules; calculated vertical singlet−triplet gap (∆EST) and total first hyperpolarizabilities (10−30 esu) of all studied molecular materials as a function of dielectric constant; schematic representation of vertical ∆EST using potential energy surfaces; a comparison between the ground state and lowest singlet excited state geometries; distributions of electron



and hole in the lowest singlet and triplet state of 3-U, 4-U and 5-U in both gas phase and solid film.

AUTHOR INFORMATION Corresponding Author *Y. Q. Qiu: E-mail: [email protected] Telephone: +86 431 85099291

Notes The authors declare no competing financial interest.

Acknowledgments The authors gratefully acknowledge the financial support from the “12th Five-Year” Science and Technology Research Project of the Education Department of Jilin Province ([2016] 494) and the National Natural Science Foundation of China (No. 21173035).

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TOC Graphic


Effective Impact of Dielectric Constant on Thermally Activated Delayed

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