The article information
 Caibin Zhao, Zhihua Tang, Xiaohua Guo, Hongguang Ge, Jianqi Ma, Wenliang Wang
 赵蔡斌, 唐志华, 郭小华, 葛红光, 马剑琪, 王文亮
 Modeling Photovoltaic Performances of BTBPDPC_{61}BM System via Density Functional Theory Calculations
 BTBPDPC_{61}BM体系光伏性质的密度泛函理论计算
 Chinese Journal of Chemical Physics, 2017, 30(3): 268276
 化学物理学报, 2017, 30(3): 268276
 http://dx.doi.org/10.1063/16740068/30/cjcp1702016

Article history
 Received on: February 16, 2017
 Accepted on: April 7, 2017
b. Key Laboratory for Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi'an 710062, China
In the past 100 years, with the overconsumption for fossil energies (coal, petroleum, and natural gas), environmental pollution problems have received widespread attention, and actively exploring for the clean and renewable energy has being become a hot and focus issue [1, 2]. As one of the most promising longterm solutions for the clean and renewable energy, freemetal photovoltaic technology has attracted intense interests in recent years due to its numerous advantages compared to the commercial inorganic photovoltaic technology, such as low manufacturing cost, flexibility, ease of solvent processing, and largearea capability [36]. Previous studies indicated that the highperformance donor materials should meet the following requirements: (ⅰ) narrow optical band gap, (ⅱ) lowlying highest occupied molecular orbital (HOMO) level, and (ⅲ) high hole carrier mobility [79]. Unfortunately, electrondonating materials that simultaneously satisfy those three demands are still scarce up to date.
Recently, Cai et al. synthesized a novel small molecule material (BTBPD) with the donoracceptordonor (DAD) character, and found that the thinfilm field effect transistor fabricated with BTBPD had high hole mobility under natural ambient conditions [10]. More interestingly, BTBPD also exhibited the prominent capture to solar radiation, and its strongest absorption peak was found to redshift to 696 nm in solid state. In a word, all properties suggest that BTBPD should be an excellent electron donor candidate. In this work, taking BTBPD as donor and [6, 6]phenylC
To simplify calculations, the longalkyl chain (2ethylhexyl) in BTBPD was replaced with the CH
BTBPD and PC
$\begin{eqnarray}V_{\textrm{oc}} = \frac{1}{e} \left( {\left {E_{\textrm{HOMO}} \left(\textrm{D}\right)} \right  \left {E_{\textrm{LUMO}} \left(\textrm{A}\right)} \right} \right)  0.3\end{eqnarray}$  (1) 
where
As is wellknown, the charge binding energy (
$\begin{eqnarray}E_\textrm{b} = E_{\textrm{AIP}}  E_{\textrm{AEA}}  E_\textrm{m}\end{eqnarray}$  (2) 
As seen in Eq.(2), to calculate
As is known to all, the good harvest for solar radiation is essential for efficient dye sensitizers, which determines the shortcircuit current density
Shortcircuit current density
$\begin{eqnarray}J_{\textrm{sc}} = q\int_0^\infty {\eta _{\textrm{EQE}} (λ )} × S(λ )\textrm{d}λ\end{eqnarray}$  (3) 
where
$\begin{eqnarray}\eta _{\textrm{EQE}} = \eta _λ \eta _{\textrm{CT}} \eta _{\textrm{coll}}\end{eqnarray}$  (4) 
where
$\begin{eqnarray}FF=\frac{\nu_{\textrm{oc}}\textrm{ln}(\nu_{\textrm{oc}}+0.72) }{\nu_{\textrm{oc}}+1}\end{eqnarray}$  (5) 
where
$\begin{eqnarray} \nu_{\textrm{oc}}=\frac{qV_{\textrm{oc}}}{nk_\textrm{B}T}\end{eqnarray}$  (6) 
where
$\begin{eqnarray}\eta = \frac{{P_{\max } }}{{P_{\textrm{in}} }} = \frac{{V_{\textrm{oc}} J_{\textrm{sc}} }}{{P_{\textrm{in}} }}FF\end{eqnarray}$  (7) 
where
Generally, the charge transfer in organic photoelectric materials obeys the incoherent chargehopping mechanism, and the transfer rate constant between donor and acceptor,
$\begin{eqnarray}k_{\textrm{DA}} = \frac{{2\pi }}{h}\sqrt {\frac{\pi }{{λ k_\textrm{B} T}}} \left {V_{\textrm{DA}} } \right^2 \exp \left[{  \frac{{(\Delta G + λ )^2 }}{{4λ k_\textrm{B} T}}} \right]\end{eqnarray}$  (8) 
where
As seen in Eq.(8), the Gibbs free energy change,
$\begin{eqnarray}\Delta G_{\textrm{dis}} \hspace{0.15cm}&=&\hspace{0.15cm} E_\textrm{D}^ + (Q^ + ) + E_\textrm{A}^  (Q^  )  E_\textrm{D}^* (Q^* )  \nonumber \\&&\hspace{0.15cm}E_\textrm{A}^0 (Q^0 ) + \Delta E_{\textrm{coul}}\end{eqnarray}$  (9) 
where
$\begin{eqnarray}\Delta E_{\textrm{coul}} \hspace{0.1cm} = \hspace{0.1cm}\sum\limits_{\textrm{D}^ + } \hspace{0.1cm}{\sum\limits_{\textrm{A}^  } {\frac{{q_{\textrm{D}^ + }q_{\textrm{A}^  } }}{{4\pi \varepsilon _0 \varepsilon _\textrm{s} r_{\textrm{D}^ + \textrm{A}^  } }}} } \hspace{0.1cm}\hspace{0.1cm}\sum\limits_{\textrm{D}^* } \hspace{0.1cm}{\sum\limits_\textrm{A} {\frac{{q_{\textrm{D}^*}q_\textrm{A} }}{{4\pi \varepsilon _0 \varepsilon_\textrm{s} r_{\textrm{D}^*\textrm{A}} }}} }\end{eqnarray}$  (10) 
where
$\begin{eqnarray}\varepsilon _\textrm{s} = \left( {1 + \frac{{8\pi \overline{\alpha} }}{{3V}}} \right)\left( {1  \frac{{4\pi \overline{\alpha} }}{{3V}}} \right)^{  1}\end{eqnarray}$  (11) 
where
Generally, in organic solids the total reorganization energy (
$\begin{eqnarray}λ _1 \hspace{0.1cm}& =&\hspace{0.1cm} (E_\textrm{D}^* (Q^ + ) + E_\textrm{A}^0 (Q^ {} ))  (E_\textrm{D}^* (Q^* ) + E_\textrm{A}^0 (Q^0 ))\\ \end{eqnarray}$  (12) 
$\begin{eqnarray}λ _2 \hspace{0.1cm}& =&\hspace{0.1cm} (E_\textrm{D}^ + (Q^* ) + E_\textrm{A}^  (Q^0 ))  (E_\textrm{D}^ + (Q^ + ) + E_\textrm{A}^  (Q^\textrm{})) \end{eqnarray}$  (13) 
where
$\begin{eqnarray}\hspace{0.2cm}λ _{\textrm{ext}} \hspace{0.1cm} = \hspace{0.1cm}\frac{{(\Delta e)^2 }}{{8\pi \varepsilon _0 }}\left( {\frac{1}{{\varepsilon _{\textrm{op}} }} \hspace{0.1cm}\hspace{0.1cm} \frac{1}{{\varepsilon _\textrm{s} }}} \right)\hspace{0.2cm}\left( {\frac{1}{{R_\textrm{D} }}\hspace{0.1cm} +\hspace{0.1cm} \frac{1}{{R_\textrm{A} }} \hspace{0.1cm}\hspace{0.1cm} 2\sum\limits_\textrm{D} {\sum\limits_\textrm{A} {\frac{{q_\textrm{D} q_\textrm{A} }}{{r_{\textrm{DA}} }}} } } \right)\end{eqnarray}$  (14) 
where
$\begin{eqnarray}\varepsilon _{\textrm{op}} = n^2 = \frac{{V_\textrm{m} + 2R}}{{V_\textrm{m}  R}}\end{eqnarray}$  (15) 
where
As seen in Eq.(8), the
$\begin{eqnarray}V_{\textrm{D}(i)\textrm{A}(j)} = \frac{{T_{\textrm{D}(i)\textrm{A}(j)}  0.5(e_{\textrm{D}(i)} + e_{\textrm{A}(j)} )S_{\textrm{D}(i)\textrm{A}(j)} }}{{1  S_{\textrm{D}(i)\textrm{A}(j)}^2 }}\end{eqnarray}$  (16) 
where
$\begin{eqnarray} F^{\textrm{KS}} = SC\varepsilon C^{  1}\end{eqnarray}$  (17) 
where
As is known to all, the charge transport ability of donor remarkably affects the solar cell's performance. Thus, it is essential to discuss charge transport properties of BTBPD thinfilm. Generally, the charge transport ability of organic materials can be chartered with its carrier mobility,
$\begin{eqnarray}\mu = \frac{{eD}}{{k_{\rm{B}} T}}\end{eqnarray}$  (18) 
where
$\begin{eqnarray}D \approx \frac{1}{{2n}}\sum\limits_i {d_i^2 k_i P_i }\end{eqnarray}$  (19) 
where
In summary, BTBPDPC
Supplementary material: Detailed potentialsurface scan, optimized BTBPD geometry, calculated the lowestexcited energy for BTBPD, HOMO and LUMO of BTBPD, and detailed description for molecular dynamics simulation are shown.
Ⅴ. ACKNOWLEDGMENTSThis work was supported by the National Natural Science Foundation of China (No.21373132, No.21502109, No.21603133), the Education Department of Shaanxi Provincial Government Research Projects (No.16JK1142, No.16JK1134), and the Scientific Research Foundation of Shaanxi University of Technology for Recruited Talents (No.SLGKYQD213, No.SLGKYQD210, No.SLGQD1410).
General Comments The detailed description for molecular dynamics simulationAs seen in Eq(14), to estimate the external reorganization energy λ_{ext}, the optical dielectric constant of medium, ε_{op}, need to be firstly calculated by means of Eq(15), that is to say, we firstly need to estimate the material's density ρ. Here, in order to simulate the ρ, Materials Studio 5.5 software package is applied. The whole simulation process can be described as the following steps.
Firstly, the object molecule (BTBPD) was optimized at the B3LYP/631G(d) level with the aid of the Gaussian 09 software (Fig.S4), and the stable molecular structure was introduced the Materials studio 5.5 software package. Then, keep the molecular rigid, and apply the Dreiding force field and the Amorphous Cell module to establish a cubic lattice amorphous cell containing 100 molecules (The starting cubic cell parameter was selected to make the density close to 1.0g· cm^{3}). In the practical calculation, the summation method of atomic charges was used in evaluating the electrostatic and van der Waals interactions, and the quality of energy calculation was selected as fine. And then, the Discover module and smart minimizer method were used to roughly optimize the amorphous cell more than 3000 iterations. In the smart process, all options were selected as the default values. Thus, a relatively reasonable amorphous cell (Ⅰ) was obtained (Fig.S5).
Secondly, the amorphous cell (Ⅰ) was introduced into the Forcite Module, and an anneal dynamics calculation was carried out. Here, the cell temperature was firstly increased from 300 K to 600 K, and then was decreased from 600K to 300 K. After the twostep annealing processing including 8 cycles, the unreasonable structures can be efficiently eliminated. Then, the stable cell (Ⅱ) was obtained, which provides a relatively balance geometry for the subsequent molecular dynamics simulation. Fig.S6 showed the energy variation of amorphous cell with the simulated time. Fig.S7 exhibited the temperature change with the simulated time.
Thirdly, in order to achieve balance as soon as possible, a molecular dynamics simulation with 50ps under the condition of constant temperature and volume (NTV) was firstly carried out. In the practical simulation, the Dreiding force field, the current charge, and the Andersen method of temperature control were applied. In addition, the total simulated time was selected to 50ps. Finally, the amorphous cell (Ⅲ) was obtained. Fig.S8 showed the energy variation of amorphous cell with the simulated time. Fig.S9 exhibited the temperature change with the simulated time. As seen, when the simulated time was 5ps, the cell was close to the balance.
Fourthly, based on the cell structure obtained by means of the step 3, then a molecular dynamics simulation for 100ps under the condition of constant temperature and pressure (NTP), after 50ps system was balanced, finally, the density of material was obtained (Fig.S11). In the practical simulation, the Dreiding force field, the current charge, and the Berendsen method of temperaturebath coupling were used. In addition, the total simulated time was selected to 100ps. Fig.S10 showed the temperature variation of amorphous cell with the simulated times. Fig.S11 exhibited the material's density change with the simulated times. As seen, when the simulated time was 10ps, the cell trended toward to be a balance structure.
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b. 陕西师范大学化学化工学院, 陕西省大分子科学重点实验室, 西安 710062