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C: Energy Conversion and Storage; Energy and Charge Transport

Charge Transfer and Delocalization in LadderType Fused Bithiophene Imide Oligomers Yujing Jin, Jing-Ai Qiao, Chang Liu, Ling Luo, Xin Chi, Yuexing Zhang, and Ming-Hua Zeng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04228 • Publication Date (Web): 30 Jul 2019 Downloaded from pubs.acs.org on July 31, 2019

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The Journal of Physical Chemistry

Charge Transfer and Delocalization in Ladder-Type Fused Bithiophene Imide Oligomers Yujing Jin, Jing-Ai Qiao, Chang Liu, Ling Luo, Xin Chi, Yuexing Zhang *, Ming-Hua Zeng* Hubei Collaborative Innovation Center for Advanced Organic Chemical Materials, Ministry of Education Key Laboratory for the Synthesis and Application of Organic Functional Molecules, College of Chemistry and Chemical Engineering, Hubei University, Wuhan 430062, P. R. China.

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Abstract On the basis of experimentally reported series of novel imide-functionalized ladder-type heteroarenes (fused bithiophene imide oligomers BTIn, n=1-5), expanded BTIn up to 24 rings with eight imide groups (n=6-8) as well as some heteroarenes derived from BTI are designed. Charge transfer and delocalization properties of BTIn (n=1-8) are studied theoretically by non-empirically optimal tuned range-separated density functional theory (LC-BLYP*), LCBLYP* combing polarizable continuum model (PCM) [LC-BLYP* (PCM, solid)], and traditional B3LYP functional. LC-BLYP* provides a good balance between localized and delocalized effects and reduces the electron self-interaction error (SIE) of traditional DFT method, while combing PCM model with TRS-DFT could accurately describe the properties of single crystals. The relationships between geometries, electronic properties, and semiconductor performances are explored. Due to the good planarity induced by the fused thienothiophene rings with imide, BTI oligomers show better performance than their derivatives with similar number of thiophene rings. It found that the BTI oligomers have very good planarity, large conjugation extent, fully delocalized polaron (over 16T units), and good semiconductor properties for both p- and n-types. BTI8 is good potential ambipolar semiconductor with very small charge injection barrier and large hole and electron mobilities of 16.60 and 3.02cm2V-1s-1. Different roles of thiophene and imide rings in making BTI series good semiconductor are also revealed by comparing BTI2 and BTI3 with thiophene-containing derivatives.


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I. INTRODUCTION Organic semiconductors have attracted substantial attentions owing to applications in optoelectronic devices, such as organic thin-film transistors (OTFTs) and organic photovoltaics (OPVs).1-2 π-conjugated oligomers for ladder-type heteroarenes, which reduce the skeleton torsion and enhance intermolecular carrier mobility, have aroused intensive interest as synthetic materials of organic semiconductor and molecular line.3-5 Among many ladder-type aromatic systems, bithiophene imide (BTI) with strong electron-withdrawing nature and good charge delocalization is considered to be the promising electron-deficient unit for building high performance n-types polymer semiconductors. BTI was firstly synthesized by Marks et al, which exhibited encouraging optoelectronic properties.6 Subsequently, the research on BTI-like analogues set off a wave of development in the field of organic semiconductor.7-12 In particular, a series of BTI analogues with well-defined building block as well as controllable conjugates length and up to 15 fused rings reported by Guo's group have shown great potential applications.13 Designing and synthesizing new materials with high charge-transfer mobility, high ambient stability, and good solubility in common organic solvents remains a great challenge. Toward this end, first-principles-based theoretical studies can help obtain a fundamental understanding of inherent charge transfer behavior, determine the corresponding properties for designing new semiconductors, and, therefore, shed new light into the performance of organic semiconductor devices. However, previous DFT studies on BTI series have only presented the electronic structures, while characterization of intramolecular charge transfer from a microscopic perspective has not yet been clearly explored, which is an obstacle to develop the potential application of BTI series. Charge delocalization should be achieved to ensure the π electrons flowing from one conjugate system to another, which need the orbitals extend to most of the atoms that make up the conjugate system instead of restricting to two carbon atoms.14,15 Due to the great significance of charge delocalization, many experimental and theoretical techniques have been tried to describe the range of charge delocalization.16 Successful appearance of charge delocalization required calculating the electronic structure of different ionized state of the oligomer. However, the longest experimentally reported BTI series only contain 15 fused rings, which are shorter than the delocalization length.14 To achieve further exploration on the charge delocalization and chain length effect for BTI series, we designed three new BTI-based molecules (BTI6-BTI8) and expanded the molecular to up to 24 fused rings.



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Worth noting that many early theoretical studies have utilized standard hybrid density functional, such as B3LYP, which however tend to greatly overestimate delocalization due to the large (electron) self-interaction errors (SIE) connected with these functionalities and fail to predict electronic structures due to SIE, incorrect asymptotic behavior or derivative discontinuity (DD), and possible delocalization error (DE).17 In addition, there are obvious polarization effects and screening effects in the crystal or film, but the calculation is usually done in a vacuum environment, which will add difficulties to accurately predict of the experiment. Encouragingly, a non-empirically tuned range-separated density functional (TRS-DFT), which greatly mitigates the SIE and provides a good balance between localized and delocalized effects.18 To simulate solid-state environments, the optimal tuning approach could be combined with the polarization continuum model (PCM) to accurately describe the properties of organic molecules revealed by many researches.19-22 This approach is named as TRS-DFT (PCM, solid) in this work. Although TRS-DFT (PCM, solid) has accurately predicted the transport gaps of organic solids, Kummel et al. cautioned that  decreases dramatically with the system extended spatial size.23,24 The appropriate explanation is that molecular solids are embedded in the effective dielectric medium formed by surrounding molecules, and the system-dependent  decreases significantly with the increased intermolecular interaction of the extended π electron system. Exploration of the potential advantages and limitations of this approach remains to be done. Considering the range-separation parameter, a new and physical tuning strategy [named as TRS-DFT ()]25,26 is put forward that the long-range asymptotic potential tends to 1/εr rather than 1/r, and the optimal tuning of  is substituted by the effective scalar (static) dielectric constant in the LR potential, avoiding the collapse of the range-separation parameter . In this work, we studied the charge transfer and delocalization of series of ladder-type fused bithiophene imide oligomers (BTI-BTI8) with controllable conjugation lengths up to 24 fused aromatic rings by using TRS-DFT (PCM, solid). Structures and properties of BTI oligomers as well as some heteroarenes derived from BTI are also calculated with traditional B3LYP functional for the purpose of revealing the different roles of thiophene and imide segments. Our paper is organized as follows: after describing the essentials of the theoretical methods (section II), the results on the geometries, electronic structures, charge transfer integral, charge transfer mobility, and charge delocalization are presented and discussed in section III. Section IV extends the discussion and provides a general conclusion. This will be of great significance to the understanding and development of BTI based functional semiconductor materials.


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II. COMPUTATIONAL METHODOLOGY 1. Theoretical Methodology For the study of transport property of organic semiconductor, hopping mechanism works well and is widely used. In the hopping model, charge transfer can be regarded as self-exchange electron transfer reaction between a neutral molecule and a neighboring radical anion (n-type) or radical cation (p-type). The most critical parameter of charge transfer mobility is the transfer rate of charges between lattice points, which could be modeled by the standard Marcus-Hush theory27:

kij 

4 2 h

 V2   exp    4 k BT  4 k BT 

(1)

where V is the charge transfer integral (also called effective electronic coupling) between neighboring molecules 𝑖 and 𝑗 in the organic semiconductor materials and 𝜆 is the reorganization energy. T is the temperature, ℎ and 𝑘𝐵 are the Plank and Boltzmann constant, respectively. Reorganization energy λ and charge transfer integral V play important roles in the transport mechanism.28 Generally speaking, the internal and external parts of reorganization energy come from the intramolecular vibration (which reflects the strength of local electron-phonon coupling) and the contribution of the surrounding media, respectively. But the contribution of surrounding media is usually much smaller than the internal part, so unless otherwise stated, reorganization energy refers to the internal reorganization energy. The internal reorganization energy could be calculated using adiabatic potential energy surfaces.

hole   E *  E 0    E*  E  

(2)

electron   E *  E 0    E*  E  

(3)

where E0 and E + /E ― indicate the energies of neutral and cation/anion in the optimized ground-state potential energy surface, while E + ∗ /E ― ∗ and E ∗ + /E ∗ ― are expressed by the energies of the neutral states with the optimized cation/anion geometries and energies of cation/anion states with the optimized neutral geometries, respectively. According to Marcus-Hush charge transfer theory, the smaller the reorganization energy is, the faster the charge carrier transfer rate would be. Therefore, the design of compounds with low reorganization energy at the single molecule level is the primary task of materials with high carrier mobility.



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The charge transfer integral V can be calculated by the energy difference between the two adiabatic states in the charge transfer transition state. According to Koopmans’ theorem, when two interacting molecules exchange holes (electrons), the transfer integral V could be estimated by half of the energy difference between the HOMO(LUMO) orbital and the HOMO-1 (LUMO+1) orbital of neutral dimer. Alternatively, the transfer integrals for both holes and electrons could be calculated using the site-energy correction method.29 It is well known that the spatial factors such as the packing mode of molecules are crucial to the study of charge transfer properties of organic semiconductors. Predicting the crystal structure from a single molecule is an essential step in designing high performance charge transport materials. The crystal structures for BTI series were predicted using models described in our previous studies.30 According to the Cambridge Structural Database (CSD), about 90% of all organic and organometallic crystal structures are covered by the 17 most frequent space groups. Here, we select the ten most common spatial groups: P21/C, P-1, Pbca, P212121, P21, C2/c, Pna21, Cc, Pbcn and C2 for prediction. To ensure the integrity and accuracy of crystal prediction, we will repeat the prediction under the same setting two times. According to the above space groups, different criteria for density, van der Waals energy and so on are used to select the most stable crystal structures. The charge transfer in the organic single crystal is assumed as a Brownian motion (no any correlation between hopping events) and that charge motion and the diffusion coefficient D can be defined as:

1 x t  D  lim t  2n t

2



1  i 2Wi Pi  2n i

(4)

where n the spatial dimensionality, 𝑟𝑖 is the centroid distance of the hopping channel 𝑖, Wi is the nonadiabatic electronic hopping rate via the ith hopping pathway, and P is the hopping probability via the ith hopping pathway which is determined by

Pi  Wi / Wi i

(5)

the carrier mobility μ from charge hopping at a temperature T is then expressed by the Einstein relation, leading to the bulk (isotropic) mobility :



e D k BT

(6)


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For TRS-DFT method, the exchange items of RS hybrid functional are separated into a short-range (SR) and a long-range (LR) part and are expressed by the standard error function via

1/ r12  erfc  r12  / r12  erf  r12  / r12

(7)

The exchange item is further broken into LR component from the HF-exact-exchange and short-range component from the DFT. The range-separation parameter ω is intended as the inverse of a distance at which the functional transforms from short domain to HF-like. And a reduced ω value in the LC-BLYP functional indicates that the longrange domain HF-exchange will replace the short-range domain DFT-exchange at greater distance. In addition, it is crucial to remember that the default ω value of the RS-DFT functional is usually too large to consider extended πconjugated systems and therefore requires to be optimally tuned. The optimal ω is determined by non-empirically minimizing J(ω) = |εH (N) + IP(N)| for the neutral system. Then, a new objective equation31 is presented to better describe neutral (N) and anion (N+1): 1

J 2  [ H  N  i   IP  N  i ]2 i 0

(8)

Through the above formulas, “gap-tuning” of the isolated molecules are carried out. The above methods give credible descriptions for gas-phase isolated molecules,14 however, it is not applicable to solids. Here, we combine the polarization continuum model (PCM) into the above tuning procedure, where the default integral equation formalism variant polarizable continuum model (IEFPCM) was added by importing magnitude-equivalent dielectric constant (ε) of oligomer crystals [TRS-DFT (PCM, solid)]. On account of ω considered to be a function of density, studies have demonstrated that the effect of the dynamic dielectric constant ε on the single crystal is almost negligible which dynamic ε is not required for SCF ground-state calculation. And the static dielectric constant is given via Clausius–Mossotti equation:32

  1 4    2 3 V

(9)

where 𝛼 and V are the static isotropic polarizability and molecular volume of a single molecular, respectively. They are calculated at the B3LYP/6-31G(d,p) level and recognized by using Multiwfn software.33

2. Computational details



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All the geometric relaxation of the BTI-BTI8 oligomers and heteroarenes derivatives are firstly carried out using the B3LYP hybrid functional and the 6-31G(d,p) basis set in vacuum (which is accurate enough to describe the geometries of π-conjugation molecules).5 The long alkyl side chains were replaced by methyl groups to reduce the computation time.3,5,34 Studies have proved that side-chain has negligible influence on molecular properties. As exampled by BTI2 (Table S1, SI), the energy gap changes by only 0.01eV (which is almost ignored) and the reorganization energy is completely consistent when changing the alkyl side chains of BIT2 from methyl to n-butyl. ω tuning is first performed for LC-BLYP functional35 using the same 6-31G(d,p) basis set with the optimized geometries at B3LYP/6-31G(d,p) level. Then the -tuning-geometry-optimization self-consistent procedures14 are performed to get more reliable results. The LC-BLYP functional with optimized ω is named as LC-BLYP*. Considering the polarization and screening effects of solid crystals, LC-BLYP* (PCM, solid) method is performed. Based on the calculated static dielectric constant ε, LC-BLYP* ()]25,26 method is also used for BTI-BTI3. For the sake of comparison, the geometric structures, electronic structures, charge transfer mobility of molecular are also calculated at the LC-BLYP*/6-31G(d,p) and B3LYP/6-31G(d,p) level in gas-phase. To study charge delocalization, the various oxidized species including dipolarons and two separated polarons of BTI series are calculated with the tuned ω values in the film state and in vacuum. All calculations were carried out with the Gaussian 16 package.36 As shown in Table S3, the tuned  for LC-BLYP* method is 0.235, 0.186, 0.159, 0.143, 0.133, 0.125, 0.120 and 0.116 for BTI-BTI8, respectively. While for LC-BLYP* (PCM, solid) method, the ε/ are 3.61/0.066, 5.09/0.038, 7.41/0.025, 11.10/0.018, 17.23/0.013, 29.28/0.010, 64.67/0.008, and 498.00/0.006 for BTI-BTI8, respectively. LCBLYP* () approach obtains  of 0.14/0.2769/0.0001, 0.1622/0.1964/0.0001, and 0.3310/0.1349/0.0001 for BTI-BTI3, respectively.

III. RESULTS AND DISCUSSION 1. Molecular Structure


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Figure 1. Chemical structures of the BTI oligomers with varied conjugation lengths (BTI-BTI8) together with some heteroarenes derivatives. Figures 1 and S1 show the molecular geometries and optimized structures of BTI series at LC-BLYP* (PCM, solid)/6-31G(d,p) level. The calculated main structural parameters are tabulated in Table S2 together with those at LC-BLYP*/6-31G(d,p) and B3LYP/6-31G(d,p) level. The optimized structures of the BTI oligomers are fully conjugated adopting planar conformations (Figure S1). Generally, the planar backbone geometries typically are favorable for intramolecular charge delocalization and intermolecular charge transfer, because the C-C/C=C bond rotation in the planar conformation is prohibited and the infrared vibration coupling is closely related to lengthening/shortening the C-C/C=C bond. 14 Along with the increase of the π-conjugation length from BTI to BTI8, the bond length alternation (BLA, defined as the average value of single-bonds minus the average value of double-bonds for the conjugated C-C/C=C bonds thickened in Figure 1)37 of the neutral molecules calculated by LC-BLYP* (PCM, solid) decreased gradually



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from 0.051 Å for BTI to, 0.031 Å for BTI3, 0.026 Å for BTI5, and 0.024 Å for BTI8. More precisely, the average single-bond length on the conjugation groups decreases from 1.435 Å in BTI to 1.428 Å in BTI8, while the average double-bond length increases from 1.383 Å in BTI to 1.405 Å in BTI8, resulting in the decreased BLA with the oligomer conjugate length. The BLA of anion first decrease from 0.022 Å for BTI to 0.017 Å for BTI2 and then almost do not change till BTI8. On the contrary, the average single-bonds length of cations increase from 1.405 Å for BTI to 1.422 Å for BTI8 while the average double-bonds length slightly decrease from 1.410 Å in BTI to 1.409 Å in BTI8 and resulting increased BLA for cations from -0.005 Å to 0.013 Å (Figure S4). The single-bonds tend to decrease while the double-bonds increase upon both oxidation and reduction, resulting much smaller BLA for cation and anion in comparison with the neutral, indicating that the cation and anion have larger conjugate extent than neutral. The average bond lengths change of cations/anions relative to neutrals could be used to estimate and rationalize the reorganization energy for hole/electron (Table S2). With the increase of the oligomer length from BTI to BTI8, the average bond lengths change of cations relative to neutral decrease from 0.0143 Å for BTI to 0.0028 Å for BTI8, and the average bond lengths change of anions relative to neutral decrease from 0.0149 Å for BTI to 0.0028 Å for BTI8. These results suggest that both hole and electron reorganization would be very small and decrease from BTI to BTI8 (vide infra). Comparing the calculated results with LC-BLYP* (PCM, solid), LC-BLYP*, and B3LYP shows that (a) LCBLYP* (PCM, solid) has much smaller BLA than LC-BLYP* and B3LYP, (2) LC-BLYP* has slightly smaller BLA than B3LYP for BTIn with n> 3 but shows larger BLA for shorter oligomers with n10-3 and 0.013 cm2V-1s-1, respectively, which are several orders of magnitude smaller than theoretical predicted ones (9.70 and 0.46 cm2V-1s-1). Many factors cause this: on one hand, experimental mobility can be significantly affected by many factors such as purity of the sample, preparation process and energy level barrier of the electrode. For example, changing annealed temperature from 240 to 80 ℃ increases the electron mobility of BTI5 by 6 times.13 On the other hand, our theoretical predicted mobilities are intrinsic mobilities based on highly ordered single crystal structures of simplified molecular models without considering boundary between crystals and purity of the sample while experimental devices are fabricated from thin film. Nevertheless, our simulated electron mobilities of the order BTI5 < BTI3 < BTI4 are also consistent well with the experimental trend. For comparison, the charge transfer mobilities of the BTI series are also predicted under vacuum conditions at the LC-BLYP*/6-31G(d,p) and B3LYP/6-31G(d,p) levels (Figure S6d). The results show that the LC-BLYP* and B3LYP functionals predict larger charge injection barrier and larger reorganization energy and thus smaller charge transfer mobilities than LC-BLYP* (PCM, solid). However, the above results show that the relative values of charge mobility between molecules calculated by different methods are consistent.

5. Charge delocalization Because of the great significance of charge delocalization in organic semiconductor devices, many efforts have been made to describe its extent using both experimental and theoretical techniques.16,42 For the radical- cation (positive polaron) with different oxidation states, it allows for a certain extent charge delocalization over a certain molecules chain length. Both geometry and spin density indexes could be used to describe the charge delocalization. The significant differences between the neutral and cation geometries can be used to study the extent of charge delocalization. Since the series BTI molecules are planar with all the rings fused, we could not use the dihedral angles between each ring as index for delocalization as done in refer.14 Alternatively, the bond length modification upon oxidation is chosen as one index for hole delocalization. As can be seen from Figure S3 and Table S2, both the single and double bonds in the molecular center have very large changes upon oxidation and the change extent decreases from center to edge. If taking 0.005 Å as the threshold for geometry index, radical delocalizes over five thienothiophene(TT) units (or counting as 10T) from center for BTI7 and BTI8. This consists well with the charge delocalization extent over 3TT−4T or 2TT−6T (total 10T) for BTTT5 and BTTT6.14 However, since BTI oligomers all have planar structure, charge delocalization would be more comparable to the co-planar BTTT6’, in which the



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charge delocalize over 3.5−4 T−TT−T units (14-16 T). The bond-length-modification threshold of 0.005 Å thus may be too large. If taking 0.001 Å as the threshold for geometry index, charge delocalization would increase to 16T (2T7TT) of BTI8. That is, charge delocalizes over the whole molecules of the longest oligomers studied in this work. Spin density is a direct reflection for charge delocalization. Here, we calculated Mulliken spin density at the

LC-BLYP* (PCM, solid)/6-31G(d) level and for each T or TT unit on BTI-BTI8 (for BTI series molecules, thiophene ring is a T unit and thienothiophene is a TT unit, as illustrated in Figure 6, Figure 7 and Table S7). As illustrated in Figure 6 for the charge delocalization diagram of the cations of BTI series, the spin electrons mainly distribute on C=C double-bonds and have similar feature as HOMO. However, even for the longest oligomer BTI8, there are still clear spin density on the terminal thiophene units. As listed in Table S7, the spin density of these oligomers is delocalized effectively on the whole molecule and each unit is greater than 0.01e (the threshold for spin density on each T or TT unit chosen in reference 14). Moreover, Figure 7a indicates that the spin density of the cation decreases relatively from the center to the terminal unit for BTI-BTI8 cations and the sum of the spin density on half of the chain is almost 0.5e at the same time, which prove that polaron occupies the center of molecules. To compare the methods, we also calculated the spin densities at LC-BLYP* and B3LYP levels under vacuum conditions. The results of cations calculated by the two methods are consistent with the film state. With the increase of molecular conjugate length, the charge delocalization is over the entire skeleton for threshold of 0.01e. The charge delocalization extents for different method have the order of LC-BLYP* (PCM, solid) > B3LYP > LCBLYP*. As B3LYP functional tends to overestimate the delocalization extent, LC-BLYP* thus greatly mitigates the SIE and provides a good balance between localized and delocalized effects. However, polarization effect under the condition of film state promotes charge delocalization.


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Figure 6. Spin density map in BTI4-BTI8 cations calculated at the LC-BLYP* (PCM, solid)/6-31G(d,p) level. When two positive charges are contained on the oligomer, it may take two possible configurations for the dication: one is to make two polarons couple and form a bipolaron corresponding to singlet; the other is two separated polarons, corresponding to triplet or spin-polarized singlet. Whether the dication ends up as a bipolaron or two polarons depends on a subtle balance between the charge pairing effects (two charges sharing the same region of space) and the geometry relaxation effects. Due to the good planarity and very long charge delocalization distance, two separated polarons may be hard to be formed. For possible two separated polarons, spin-polarized singlet is advantage than triplet because the couple between  and  spin electrons in the former could reduce the overlap between the two polarons. In addition, the electron density transfers between the fragments and the polarization effect occurs under the condition of film state, promoting the formation of bipolarons (the spin-polarized single state cannot be formed side by side).



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Figure 7. Distribution of spin density on each T or TT units in the BTI-BTI8 cations (a) and the bipolarons of BTI2, BTI4, BTI6, and BTI8 (b) as well as the bipolarons of BTI3, BTI5, and BTI7 (c) calculated at the LC-BLYP* (PCM, solid)/6-31G(d,p) level. The calculated results of dipolarons at LC-BLYP* (PCM, solid)/6-31G(d,p) level show that (a) polarized singlet could not form for BTI due to the too short conjugate length; (b) the spin electrons in the polarized singlets of BTI2-BTI8 couple and result to almost the same total energy as normal closed-shell singlet configurations, indicating even the longest oligomer BTI8 could not afford two uncoupled separated polarons to delocalized freely due to the good molecular planarity of BTI oligomers; (c) singlets or spin polarized singlets of BTI2-BTI8 are more stable than the corresponding triplets and the energy differences decrease from 0.73 eV for BTI2 to 0.14 eV for BTI8, indicating the series of BTI oligomers tend to form bipolaron instead of separated polarons; (d) the triplets of BTI4-BTI8 have some separated polaron characteristic with largest spin density being found at center TT units of half-molecule and decreasing to terminal and center units of the whole molecule.


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The cases for calculated results with LC-BLYP* and B3LYP functions are somewhat different from that with LC-BLYP* (PCM, solid)/6-31G(d,p) method due to the lack of polarization effect in the former methods. Closedshell singlets of BTI and BTI2 with LC-BLYP* method and BTI, BTI2, BTI3 with B3LYP method are reveal to be the most stable configurations while the spin polarized singlets of the other oligomers are most stable configurations. Triplets of BTI2-BTI8 are less stable than the spin polarized singlets but the energy differences decrease rapidly from 1.17 eV for BIT2 to only 0.015 eV for BTI8 according to the calculated results with LC-BLYP* method. These results indicate that dipolarons tend to take spin polarized singlet state in long oligomers and the coupling extent between and spins decreases with increasing oligomer length. Worth-noting that the spin density on the center TT unit of BTI8 with spin polarized singlet state calculated with both LC-BLYP* and B3LYP is negligible small and the two half-molecules each have spin above 0.8 e. This together with the fact that energy difference between triplet and spin polarized singlet is quite small (0.015 eV) reveals the two polarons in dication of BTI8 are almost completely separated. This indicates that though charge of BTI8 cation could delocalize over the whole molecule, BTI8 dication prefer to be two separated (side-by-side) polarons and compress polaron delocalization to only 8T units does not significantly increase the energy. In consistent with the calculated charge delocalization extent with the order of LC-BLYP* (PCM, solid) > B3LYP > LC-BLYP* for cation, all oligomers are singlet bipolar with LC-BLYP* (PCM, solid) method but BTI3 and shorter oligomers take singlet bipolar with B3LYP method while only BTI2 and BTI are singlet bipolar with LC-BLYP* method. That is, the longer charge delocalization extent is, the more possible the two polarons tend to couple for certain oligomer.

CONCLUSIONS Charge transfer and delocalization properties of a series of novel imide-functionalized ladder-type heteroarenes up to 24 rings with eight imide groups are studied theoretically with non-empirically optimal tuned range-separated density functional theory combined with the polarizable continuum model. The oligomers are found to have very good planarity, large conjugation extent, fully delocalized polaron (over 16T units), and good semiconductor properties for both p- and n-type. Associated with the decreased hole and electron injection barrier and reorganization energy, charge transfer mobilities tend to increase with increasing oligomer length. BTI8 is better potential good ambipolar semiconductor with very small charge injection barrier and large hole and electron



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mobilities of 16.60 cm2V-1s-1 and 3.02 cm2V-1s-1. The novel performance of BTI oligomers in comparison with their derivatives with similar number of thiophene rings is attributed to the good planarity induced by the fused thienothiophene rings with imide. LC-BLYP* greatly reduces the SIE of B3LYP functional and provides a good balance between localized and delocalized effects, while combining PCM model with TRS-DFT could accurately describe the properties of single crystals. This study marks a significant advance for the further development of ladder molecules and organic semiconductors in the application of organic electronics. ASSOCIATED CONTENT Supporting Information. Detailed descriptions and corresponding figures for the chain length effect, geometries and electronic structures of the BTI-BTI8 series molecules, and the lateral displacements of the stacking pairs along the short-axis and the long-axis as well as the vertical distances and predicted crystal charge transport paths for BTIBTI8 and Mulliken spin densities for the cations of BTI-BTI8, and the multiply oxidized systems [BTI2+- BTI82+] in both vacuum and single crystals at the TD-DFT (LC-BLYP*) and B3LYP levels. AUTHOR INFORMATION Corresponding Author *Email: [email protected] (YZ), [email protected] (MZ) Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was supported by the National Science Foundation for Distinguished Young Scholars of China (No. 21525101), the NSF of Hubei Province innovation group project (2017CFA006), and Hubei University. This work is also supported by BAGUI Talent (201904), and NSFGX (Grants 2014GXNSFFA118003, 2017GXNSFDA198040).


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