Effects of Molecular Configuration on Charge Diffusion Kinetics within

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Effects of Molecular Configuration on Charge Diffusion Kinetics within Hole Transporting Materials for Perovskites Solar Cells Wei-Jie Chi, Quansong Li, and Ze-Sheng Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b02401 • Publication Date (Web): 01 Apr 2015 Downloaded from http://pubs.acs.org on April 6, 2015

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The Journal of Physical Chemistry

Effects of Molecular Configuration on Charge Diffusion Kinetics within Hole Transporting Materials for Perovskites Solar Cells

Wei-Jie Chi,a Quan-Song Li,*,a and Ze-Sheng Li*,a,b

a

Beijing Key Laboratory of Photoelectronic/Electrophotonic Conversion Materials,

Key Laboratory of Cluster Science of Ministry of Education, School of Chemistry, Beijing Institute of Technology, Beijing 100081, China b

The Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150080, China.

Corresponding Authors * E-mail: [email protected], [email protected]

ACS Paragon Plus Environment


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ABSTRACT: First principle calculations combined with Marcus theory were carried out to investigate the hole diffusion kinetics of two thiophene-based hole transporting materials 4,4’,5,5’-tetra[4,4’-bis(methoxyphenyl)aminophen-4”-yl]-2,2’-bithiophene (H112)

and

2,2’,5,5’-tetrakis[N,N-di(4-methoxyphenyl)amino]-3,3’-bithiophene

(KTM3) in perovskites solar cells (PSCs). The isomers H112 and KTM3 only differ in the almost planar or swivel-cruciform geometry, but give rise to significantly different power conversion efficiency (14.7% and 7.3%). We found the highest occupied molecular orbitals of H112 and KTM3 are on the same energy level, which explains why the two PSCs exhibit similar open-circuit voltage. We showed that the exciton binding energy of H112 is 23.6% smaller than that of KTM3, which indicates an easier generation of free charge carriers in H112. More importantly, the most stable crystal structure of H112 and KTM3 respectively belongs to P212121 and P21 space group, where the packing pattern is face-to-face and herringbone model. The face-to-face packing pattern leads to stronger hole couplings between the neighboring H112 molecules, and therefore results in substantial hole mobility (6.75×10-2cm2/V s), which is about four hundred times of that in KTM3. This clarifies the obvious enhancement of the short-circuit current density and therefore the overall performance of PSC with H112 as hole transporting material. Our work has provided new insights into the hole transporting properties that should be carefully considered for rational design of high-efficiency hole transporting materials.


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1. INTRODUCTION As cost-effective photovoltaic technology, dye-sensitized solar cells (DSSC) have attracted great scientific and technological attention in the past decades.1,2 In DSSC, the redox couple (usually I3-/I-) in electrolytes acts as electron and hole transporting medium. The solvent-based electrolytes have many advantages such as high dielectric constants and low viscosities, but involve the risk of leakage and volatilization.3 Recently, organic–inorganic hybrid solar cells based on organometal halide perovskites (RNH3)MX3 (R=alkyl, M=Pb, X=I, Br or Cl) have aroused considerable success with power conversion efficiencies (PCE) up to 20%,4-12 where the liquid electrolyte was replaced by solid-state hole transporting materials (HTM).13 The roles of HTM in PSCs can be summarized as enhancing the open-circuit voltage by decreasing recombination at the hole-collecting electrode and increasing the internal quantum efficiency independent of applied voltage and illumination wavelength by reducing losses of charges.14 Thus far, the most widely used HTM in perovskites solar cells (PSC) is 2,2′,7,7′ -tetrakis(N,N-p-dimethoxy-phenylamino)-9,9′-spirobifluorene (Spiro-OMeTAD).15-17 However,

the

onerous

synthesis18

and

low

charge-carrier

mobility19

of

Spiro-OMeTAD significantly limit its up-scaling applications in PSC. Therefore, the development of new HTM with low cost, facile synthesis and high charge-carrier mobility is of high priority. New types of HTM have been investigated for PSC, including

poly(3-hexylthiophene)

(P3HT),

20-22

2,4,6-tris[N,N-bis

(4-methoxyphenyl)-amino-N-diphenyl]-1,3,5-triazine(Triazine-Ph-OMeTPA),



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3,4-ethylenedioxythiophene(H101),2,4,6-tris[N,N-bis-(4-methoxyphenyl)amino-N-ph enylthiophen-2-yl]-1,3,5-triazine

(Triazine-Th-OMeTPA),

a-naphthylbutadienyl)-N,N-di(4-methoxyphenyl)-phenylamine

4-(4-phenyl-4and

9,9'-

([1,1'-biphenyl]-4,4'-diyl)Bis(N3,N3,N6-N6-tetrakis(4-methoxy-phenyl)-9H-carbazoe -3,6-diamine) (X51).23-27 Recently, a novel swivel-cruciform thiophene derivative KTM3 (see Figure 1) has been synthesized and applied in PSC, which shows a high open-circuit voltage (0.99 V), high fill factor (78.3%), moderate short-circuit current density (10.3 mA cm-2), and acceptable PCE (7.3%).

28

Subsequently, Mhaisalkar and coworkers obtained a

planar thiophenes derivative H112 (see Figure 1),

29

which has the same chemical

composition with KTM3 except the position of the two thiophenes. When H112 was used as HTM in PSC, the corresponding performance parameters are as following: an open-circuit voltage of 1.07 V, a fill factor of 70%, a short-circuit current density of 19.70mA cm-2, and the overall PCE of 14.7%. Surprisingly, the small geometric structure change between KTH3 and H112 leads to a 100% increase in PCE. In the present work, based on the fact that small structure change gives rise to the massive gap in electrochemical properties, we fused our attention on ascertaining what effect, different geometric structures would have on their electronic structures, packing motifs and transport properties. The density functional theory, Marcus theory and Einstein relation were employed to calculate and evaluate these performances of H112 and KTM3. We hope these results can provide helpful guidelines for designing new HTMs for PSC.


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2. COMPUTATIONAL DETAILS The ground state structures were optimized by density functional theory (DFT) method with B3LYP functional and 6-31G(d,p) basis set, which can provide accurate description for neutral states in extended π-conjugated systems.30 The optimized structures have been confirmed to be minimum-energy points by harmonic frequency calculations, where all the frequencies are positive. All the calculations were performed using Gaussian 09 software package.31 The solvent effect was taken into consideration using the conductor-like polarizable continuum model (C-PCM)32 with the dielectric constants of chlorobenzene (ε=5.6968). To describe the carrier transport in HTM, we employed the thermally activated hopping and diffusion model because the intermolecular electronic couplings are relatively weak in organic semiconductors.33-35 The Marcus theory with the hopping model is an appropriate choice for the molecules system with a weekly coupling character. While the carrier mobility of perovskite itself may require the deformation potential theory to account for the phonon scattering and the electron-phonon coupling36. The charge hopping rate (k) is expressed as: 37 k=

 4π 2 2 1 λ  v exp  −  h 4πλk BT  4k BT 

(1)

where v is the transfer integral, λ is the reorganization energy, h is the Planck constant, T is the temperature in Kelvin, and kB is the Boltzmann constant, respectively. The internal reorganization energy (λ) was obtained from the adiabatic potential energy surface method: λ = λ0 + λ + / − = ( E 0 − E 0 ) + ( E + / − − E + / − ) *

*

(2)



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where E0 and E+/- respectively represent the energies of neutral and charged species in their lowest energy geometries, while E0* and E+/-* are respectively the energies of the neutral molecule at the geometry of charged molecules and the charged molecule at the geometry of neutral molecules. To achieve high carrier mobility, the reorganization energy and the transfer integral need to be minimized and maximized, respectively. The transfer integral, which shows the strength of electronic coupling between the donor and acceptor states, depends on the molecule arrangement in the solid state. In this work, we adopt a direct approach to get the transfer integral, which can be written as: 38-39 v = Ψi

HOMO / LUMO

F Ψf

HOMO / LUMO

(3)

where F is the Kohn-Sham-Fock matrix for the dimer; Ψi and Ψf represent the frontier orbitals of molecules 1 and 2 in the neutral dimer, respectively. The superscripts denote the frontier orbitals responsible for the charge hopping, that is, the HOMO for hole transfer and the LUMO for electron transfer. Assuming a Brownian motion of charge carrier in absence of applied electric field, the carrier mobility (µ) can be evaluated from the diffusion coefficient D with the Einstein equation.40 µ=

eD k BT

(4)

where e is the charge, D is the diffusion coefficient which can be calculated by41 D=

1 2d

∑r

i

2

vi Pi

(5)

i

where i is a given transfer pathway and ri represents the charge hopping centroid to centroid distance, d is 3 since the diffusion is considered in three dimension, and Pi


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( Pi = k i / ∑ik i ) is the relative probability for charge hopping to the ith pathway.

3. RESULTS AND DISCUSSION 3.1 Geometric Structures and Molecular Orbitals The optimized geometric structures of H112 and KTM3 are given in Figure 1. We can see that the C1-C2-C3-C4 dihedral angle is 5.1° in H112, but increases to 60.2° in KTM3. As for the bond lengths, the C2-C3 distance of H112 (1.447 Å) is slightly shorter than that of KTM3 (1.485 Å), while other bonds are slightly affected by the position of C-C linking. With respect to the neutral molecules, the C2-C3 bond in H112 and KTM3 cations decreases to 1.452 Å and 1.478 Å, respectively. In addition, the C1-C2-C3-C4 dihedral angle is 15.90° for H112 and 55.55° for KTM3 in cation states. Since the geometric structure of the isolated molecule plays the key role in determining the molecular arrangement of the single crystal, we conjecture that H112 and TKM3 may have different packing model in crystal structures. To characterize the electronic structures, we took a closer look at the frontier orbitals of H112 and KTM3. The highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) in conjunction with the energy levels and the HOMO-LUMO gaps are shown in Figure 2. It can be seen that the HOMOs and the LUMOs are of π character. The HOMOs are delocalized over the molecule skeleton of H112 and KTM3, while it is not the case for the LUMOs. The LUMO of H112 is mainly located over the two conjugated thiophenes rings and the two benzene rings adjacent to the sulfur atoms, while the LUMO of KTM3 is mainly delocalized over the two conjugated thiophenes rings and the four neighboring



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benzene rings. This shows that the LUMO distribution of KTM3 is more widespread than that of H112. As for the energy level, the HOMO and the LUMO in H112 are -4.55 eV and -1.64 eV at B3LYP/6-31G(d,p) level, while they are -4.52 eV and -1.32 eV in KTM3. The calculated energy levels are not in excellent agreement with the electrochemical experiment results by cyclic voltammetry, where the HOMO levels are measured to be -5.29 eV and -5.13 eV for H112 and KTM3.23,24 Meanwhile, the calculated energy gaps and the varying trend of the HOMO and the LUMO energy levels between H112 and KTM3 match well with the experimental observations. 28,29 The energy gap is estimated by the energy difference between the HOMO and the LUMO. The calculated energy gap of H112 is 2.91 eV, which is about 0.3 eV smaller than that of KTM3. This difference mainly comes from the different LUMO energy levels since the HOMO energy levels of H112 and KTM3 are almost equal. Moreover, the equivalence of the HOMO levels also explains why there is no evident difference in open-circuit voltage for H112 PSC and KTM3 PSC, since the open-circuit voltage of a solar cell is determined by the difference between the quasi-Fermi levels of the TiO2 and the HOMO energy level of HTMs.

3.2 Partial Charge Difference on Conjugated Backbone and Reorganization Energy The partial charge difference value ∆qC on the conjugated backbone is defined as42: ∆qC = ∑ qCi + − ∑ qCi i

0

i


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where qCi + and qCi 0 denote the partial charge of the ith C atom on the conjugated backbone in the cation and neutral state, respectively. The charges are derived from the Mulliken population in DFT calculations. Similarly, we can obtain the partial charge difference values on hydrogen atom ( ∆qH ), oxygen atom ( ∆qO ), nitrogen atom ( ∆qN ), and sulfur atom ( ∆qS ). Table 1 presented the partial charge difference values of different types of atoms between the cation and the neutral states, and the hole reorganization energy of H112 and KTM3 at B3LYP/6-31G(d,p) level. We can see the ∆qH value for H112 is slightly larger than ∆qC , and the ∆qC and ∆qH are much larger than those of ∆qO , ∆qN , and ∆qS . These results indicate that the charge transfer mainly occurs on the C and H atoms of the conjugated backbone of H112. As for KTM3, although the charge transfer also mainly occurs on the C and H atoms of the conjugated backbone, the difference between ∆qH and ∆qC is much larger than that in H112. This means that H atom plays more important role in charge transfer than C atom in KTM3. The ∆qC for molecules H112 and KTM3 are 0.404 e and 0.293 e, respectively. Meanwhile, the

∆qH increases from 0.446 e to 0.526 e when the planar structure of conjugated thiophenes is broken. In contrast, there are no obvious differences in ∆qO , ∆qN and

∆qS values between the planar H112 and the swivel-cruciform KTM3 structures. Our calculations illustrate that the differences in geometric structures of isomeride can be reflected in the partial charge difference values between the neutral and corresponding cation states. The reorganization energy (λ) is one of the important parameters governing the



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hole mobility. Generally, a lower reorganization energy ensures a faster hole transfer. In this work, the inner-sphere reorganization energies (λh) for hole transfer of H112 and KTM3 were considered at B3LYP/6-31G(d,p) level and the obtained results are listed in Table 1. The λh values for H112 and KTM3 are 0.172 and 0.158 eV, which are smaller than that (0.332 eV) of the typical hole transporting material N,N’-diphenyl-N,N’-bis(3-methylphenyl)-(1,1’-biphenyl)-4,4’-diamine calculated at the same level.

43

(TPD)

This implies better hole transfer ability of H112 and

KTM3 than that of TPD in terms of reorganization energy. In addition, the reorganization energy of H112 is 0.014 eV higher than that of KTM3. This difference has some clues in the torsion angle of the two thiophene rings. The variation of the C1-C2-C3-C4 dihedral angle between the neutral state and the cation state is 10.8° for H112 and 4.65° for KTM3, respectively. A larger structure distortion between the neutral state and the cation state requires more reorganization energy. 3.3 Charge Density Difference and Exciton Binding Energies It is known that three-dimensional charge density difference (CDD) analysis between the excited state and the ground state is capable of providing useful information on the spatial location of the excitons and the possibility of these excitons escaping from the Coulomb well. The CDD analysis at TD-B3LYP/6-31G(d,p) level was carried out for H112 and KTM3, and the obtained charge transfer morphology upon excitation and the amount of intramolecular charge transfer are presented in Figure 3. The CDD map displays that there is apparent charge transfer from the triphenylamine moieties to the thiophene rings upon S0→S1 transition in H112 and


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KTM3. Moreover, the amount of charge transfer is 0.672 e in H112 and 0.611 e in KTM3. In general, the more the amount of intramolecular charge transfer is, the weaker the Coulomb attraction and the easier the separation of the exciton are. In this context, the exciton of H112 which has larger amount of transferred charge may be easier to generate the separated charges and thus the H112 PSC may be more efficient than that of KTM3 PSC. To further probe the properties of the excitons of the investigated systems, we have computed the electron-hole binding energy (Eb), which is the energy difference between the neutral exciton and the two free charge carriers (the electron and the hole). The employed expression is Eb=Eg-Ex=∆EH-L-E1, where Eg is the electronic band gap that is replaced by the HOMO-LUMO energy gap (∆EH-L), and Ex is the optical gap which is defined as the first singlet excitation energy (E1).44 The E1 is obtained at the optimized geometry of S1 state by time-dependent density function theory (TDDFT) method at TD-B3LYP/6-31G(d,p) level. TDDFT is a powerful tool on description of the optical properties involving many-body effect. The calculated exciton binding energies are 0.55 and 0.72 eV for H112 and KTM3, respectively. This implies that the electron-hole pairs of H112 are easier to dissociate into free charge carriers than those in KTM3, which is in accordance with the CDD analysis mentioned above. We speculated that the exciton binding energy of HTM is an important parameter in determining the short-circuit current density of the solar cell. Remind that there exists huge difference in the short-circuit current density of PSC using H112 (19.70 mA cm-2) and KTM3 (10.3 mA cm-2). A smaller exciton binding



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energy of HTM is beneficial for a larger short-circuit current density in solar cells. 3.4 Charge Transfer Integral and Hole Mobility The charge transfer integral is another important parameter in determining the charger carrier mobility. The transfer integral value is dependent on the relative position of interacting molecules and the distribution patterns of the frontier molecular orbitals (HOMO and LUMO). It has been reported that in organic transporting materials there are mainly four possible packing motifs in solid state, which are the typical herringbone packing, the non-classical herringbone packing, the one-dimensional π-stacking, and the two-dimensional π-stacking.45 The crystal structures of H112 and KTM3 were predicted by the Polymorph module in Materials Studio package.46 The module has provided sound description on the crystal structures of tetrathiafulvalene derivatives.33 Accordingly, the single crystal structures were used to generate the possible intermolecular hopping pathways between the neighboring molecules. After that, the transfer integral was calculated through a direct approach by evaluating the hole coupling between the two neighboring molecules at M06-2X/6-31g(d,p) level. The M06-2X functional has been verified as the best choice for noncovalent interactions by comparing with twelve other functionals and the Hartree-Fock theory.47 The calculated crystal structures (see Figure S1 in Supporting Information) with the lowest total energies of H112 and KTM3 belong to P212121 and P21 space group, respectively. The corresponding lattice parameters are Z=4, a=15.596 Å, b=25.607 Å, c=21.154 Å, and α=β=γ=90° for H112, while they are Z=2, a=14.514 Å, b=26.049 Å,


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c=21.209 Å, α=γ=90°, and β=93.05° for KTM3. In the crystal structure, one molecule was arbitrarily chosen as the center to diffuse charge. Then, the possible hole transfer pathways between the center molecule and the neighboring one were identified and shown in Figure 4. The centroid to centroid distance of the correlated dimer, the hole transfer integrals, the hole hopping rates, and the hole mobilities of the main hopping pathways were listed in Table 2. Seven and eight nearest neighboring pathways were recognized for H112 and KTM3. Among the possible charge hopping routes of H112 and KTM3, we have tried to obtain the most effective ones based on the kinetics parameters including the hole transfer integral, the hole hopping rate, and the hole mobility. As can be seen in Table 2, the hole transfer integrals on pathways 3 and 4 of H112 are almost equal and much larger than those on other pathways. The reason is that the two H112 molecules on pathway 3 and 4 assemble in a face-to-face way which results in a smaller intermolecular distance of 14.513 Å. The most compact structure leads to the largest hole coupling. While for KTM3, the two molecules on pathway 7 and 8 have the largest intermolecular distance but possess the strongest coupling integrals. The abnormal case can be explained by the packing model and the coupling region of the hole. The coupling region of the hole is mainly located between the two adjacent triphenylamines on each molecule. Although the two KTM3 molecules on pathways 7 and 8 have the largest centroid to centroid distance, the distance between the two neighboring triphenylamines is the smallest (see Table S1 in Supporting Information), which results in the largest hole coupling integral. It is worth noting that the two H112 molecules stack in a face-to-face mode while



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the two KTM3 molecules exhibit a herringbone packing style, which may be the most important reason for their different hole mobilities. To better understand the intermolecular hole coupling, the HOMO-HOMO orbitals overlap in pathway 3 of H112 and pathway 7 of KTM3 are shown in Figure 5. The green and blue mesh regions represent the overlapping area with the same and opposite phase, respectively. As the HOMO wave function is more associated to hole transfer, the central spatial overlap area is thought to be responsible for hole migration. Compared with H112, the interorbital overlaps in HOMOs of KTM3 are very small, which explains why the coupling integral of KTM3 is only 1/25 of that of H112. In other words, the large overlap area of π orbital between the neighboring molecules contributes to the larger transport integral of H112. This finding confirms the common rule that the pathway with face-to-face mode in general possesses relatively larger transfer integral than other pathways with edge-to-face or edge-to-edge stacking. Combining the Einstein equation with the Marcus formula, the hole mobilities of H112 and KTM3 were calculated based on their crystal structures. It can be seen from Table 2 that H112 has relatively large hole mobility (6.75×10-2 cm2/V s) due to better π-π overlap. As for KTM3, the herringbone model leads to much smaller hole mobility (1.71×10-4 cm2/V s). The noticeable difference of hole mobilities originates from isolated molecular structure. H112 with plane structure of the bithiophene region leads to better stacking mode than KTM3 with across structure in crystal structures. Remind that the reorganization energy of H112 is 0.014 eV higher than that of KTM3, which indicates a slower hole mobility in H112. Therefore, the factors of the transfer


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integral and the reorganization energy offset each other, resulting in a much faster hole mobility in H112 owing to the dominating role of the transfer integral in the exponential term of Eq (1). According to the calculated hole mobilities and the observed short-circuit current density from experiment of perovskites solar cells with H112 and KTM3 as HTM, we speculate that the hole mobilities of HTMs play the key role in determining the short-circuit current density of the device. The hole mobility of HTM is proportional to the short-circuit current density. For example, the observed short-circuit current density of perovskites solar cells with Spiro-OMeTAD, Triazine-Th-OMeTPA and Triazine-Ph-OMeTPA as HTMs is 21.37, 20.74 and 19.14 mA cm-2, respectively. The hole mobilities are 4.43×10-4, 1.74×10-4 and 1.50×10-4 cm-2/VS for Spiro-OMeTAD, Triazine-Th-OMeTPA and Triazine-Ph-OMeTPA, respectively.48 Moreover, similar trend has been reported in recent work on perovskite solar cells with butadiene as hole-transporting materials. 49

4. CONCLUSIONS In summary, the geometries, electronic properties, partial charge differences, and hole mobilities of two recent reported hole transporting materials H112 and KTM3 have been theoretically investigated using Marcus theory combined with quantum chemistry method. We find that the HOMO energy levels of H112 and KTM3 are almost equivalent, while the reorganization energy of H112 is slight higher than that of KTM3 due to the large difference of twist angle between the neutral state and the



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cation state. Furthermore, the exciton binding energy of H112 is 23.6% smaller than that of KTM3, which suggests that the electron-hole pairs are easier to dissociate into free charge carriers in H112. More importantly, the hole mobility of H112 is up to 6.75×10-2cm2V-1s-1, which is nearly four hundred times larger than that of KTM3. The significant difference is attributed to that the face-to-face packing pattern of H112 that leads to stronger hole couplings than herringbone packing of KTM3. Based on these results, we believe that the small exciton binding energy and the large hole mobility of H112 contribute to the enhancement of the short-circuit current density of the device. These findings are expected to be helpful for further rational design of novel HTMs for high performance perovskites solar cells. Supporting Information Information on crystal structures with the lowest total energies of H112 and KTM3 and The distances between the two neighboring triphenylamines of pathways 1-8 for KTM3. This information is available free of charge via the Internet at http://pubs.acs.org. ACKNOWLEDGEMENTS This work is financially supported by the Major State Basic Research Development Programs of China (2011CBA00701), the National Natural Science Foundation of China (21473010, 21303007), and Beijing Key Laboratory for Chemical Power Source and Green Catalysis (2013CX02031). This work is also supported by the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (ZDKT12-03).


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Table 1. Partial charge difference values (between the cation and neutral states) on the C atoms ( ∆qc , e), O atoms ( ∆qO , e), H atoms ( ∆q H , e), N atoms ( ∆q N , e), and S atoms ( ∆q S , e), and reorganization energy (λ, eV) of the H112 and KTM3 molecules on the conjugated backbone. Compounds

∆qC

∆q H

∆qO

∆q N

∆q S

λ

H112 KTM3

0.404 0.293

0.446 0.526

0.052 0.043

0.054 0.059

0.044 0.078

0.172 0.158


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Table 2. The centroid to centroid distances (d, Å), the hole transfer integrals v (meV), hole hopping rate kij (s-1), and hole mobilities (u, cm2v-1s-1) of main hopping pathways selected based on the predicted crystalline structures. Compounds

H112

KTM3

pathway

d

v

kij

1

15.840

-0.282

1.97×109

2

15.869

0.605

9.08×109

3

14.513

4.74

5.57×1011

4

14.513

4.73

5.57×1011

5

15.596

-1.63

6.59×1010

6

15.699

0.281

1.97×109

7

15.869

0.605

9.08×109

1

14.513

0.0856

2.03×108

2

14.513

0.0856

2.03×108

3

17.702

0.0257

1.83×107

4

16.638

0.0699

1.35×108

5

17.702

0.0257

1.83×107

6

16.638

0.0699

1.35×108

7

18.858

0.189

9.79×108

8

18.858

0.189

9.79×108


u

6.75×10-2

1.71×10-4


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Figure 1. Chemical structures of H112 and KTM3. Figure 2. The calculated frontier molecular orbitals of H112 and KTM3 (HOMO: highest occupied molecular orbital; LUMO: lowest unoccupied molecular orbital). The energy gaps between in HOMO and LUMO are also listed. The values in brackets denote experimental values. Figure 3. CDD maps and transferred charge of H112 and KTM3. The purple represents where the electrons are coming from, and the green represents where the electrons are going. Figure 4. Main hole hopping pathways selected based on the predicted crystal structures for molecules H112 and KTM3. Figure 5. HOMO-HOMO orbital overlap of face to face model and herringbone model in H112 and KTM3 crystals.


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Figure 1. Chemical structures of H112 and KTM3.



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Figure 2. The calculated frontier molecular orbitals of H112 and KTM3 (HOMO: highest occupied molecular orbital; LUMO: lowest unoccupied molecular orbital). The energy gaps between in HOMO and LUMO are also listed. The values in brackets denote experimental values.


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Figure 3. CDD maps and transferred charge of H112 and KTM3. The purple represents where the electrons are coming from, and the green represents where the electrons are going.



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Figure 4. Main hole hopping pathways selected based on the predicted crystal structures for molecules H112 and KTM3.


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Figure 5. HOMO-HOMO orbital overlap of face to face model and herringbone model in H112 and KTM3 crystals.



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Effects of Molecular Configuration on Charge Diffusion Kinetics within

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