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物理化学学报  2017, Vol. 33 Issue (6): 1171-1180    DOI: 10.3866/PKU.WHXB201704071
论文     
有机半导体的电子电离能、亲和势和极化能的密度泛函理论研究
郭姿含,胡竹斌,孙真荣,孙海涛*()
Density Functional Theory Studies on Ionization Energies, Electron Affinities, and Polarization Energies of Organic Semiconductors
Zi-Han GUO,Zhu-Bin HU,Zhen-Rong SUN,Hai-Tao SUN*()
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摘要:

准确预测有机半导体的能级(如电子电离能和亲和势等)对设计新型有机半导体材料和理解相关机理至关重要。从理论计算的角度看,主要挑战来自于缺少一种不仅能够在定性上合理而且在定量上精确预测,同时并不显著增加计算成本的理论方法。本文中,我们证明了通过结合极化连续介质模型(PCM)和“最优调控”区间分离密度泛函方法能够准确预测一系列有机半导体的电子电离能(IP)、亲和势(EA)和极化能,其预测结果与实验数据吻合得很好。重要的是,经过调控后分子的前线分子轨道能量(即-εHOMO和-εLUMO)与对应的IP和EA计算值很接近。调控方法的成功可以进一步归因于其能够根据不同分子体系或同种分子所处的不同状态(气态和固态)“最优”地平衡泛函中分别用于描述电子局域化和离域化的作用。相比而言,其它常见的密度泛函方法由于包含的HF%比例过低(如PBE)或过高(如M06HF和未调控的区间分离泛函),均不能给予合理的预测。因此,我们相信这种PCM-调控的方法能够为研究其它更加复杂的有机体系的能级问题提供一种更加可靠和便捷的理论工具。

关键词: 有机半导体密度泛函理论最优化调控区间分离泛函带隙    
Abstract:

Accurate prediction of the energy levels (i.e. ionization potential and electronic affinity) of organic semiconductors is essential for understanding related mechanisms and for designing novel organic semiconductor materials. From a theoretical point of view, a major challenge arises from the lack of a reliable method that can provide not only qualitative but also quantitative predictions at an acceptable computational cost. In this study, we demonstrate an approach, combining the polarizable continuum model (PCM) and the optimally tuned range-separated (RS) functional method, which provides the ionization potentials (IPs), electron affinities (EAs), and polarization energies of a series of molecular semiconductors in good agreement with available experimental values. Importantly, this tuning method can enforce the negative frontier molecular orbital energies (-εHOMO, -εLUMO) that are very close to the corresponding IPs and EAs. The success of this tuning method can be further attributed to the fact that the tuned RS functional can provide a good balance for the description of electronic localization and delocalization effects according to various molecular systems or the same molecule in different phases (i.e. gas and solid). In comparison, other conventional functionals cannot give reliable predictions because the functionals themselves include too low (i.e. PBE) or too high (i.e. M06HF and non-tuned RS functionals) HF%. Therefore, we believe that this PCM-tuned approach represents an easily applicable and computationally efficient theoretical tool to study the energy levels of more complex organic electronic materials.

Key words: Organic semiconductor    Density functional theory    Optimally-tuned    Range-separated (RS) functional    Energy level
收稿日期: 2016-12-27 出版日期: 2017-04-07
中图分类号:  O641  
基金资助: 国家自然科学基金(21603074);国家自然科学基金(11474096);上海市国际科技合作(16520721200)
通讯作者: 孙海涛     E-mail: htsun@phy.ecnu.edu.cn
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引用本文:

郭姿含,胡竹斌,孙真荣,孙海涛. 有机半导体的电子电离能、亲和势和极化能的密度泛函理论研究[J]. 物理化学学报, 2017, 33(6): 1171-1180.

Zi-Han GUO,Zhu-Bin HU,Zhen-Rong SUN,Hai-Tao SUN. Density Functional Theory Studies on Ionization Energies, Electron Affinities, and Polarization Energies of Organic Semiconductors. Acta Physico-Chimica Sinca, 2017, 33(6): 1171-1180.

链接本文:

http://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201704071        http://www.whxb.pku.edu.cn/CN/Y2017/V33/I6/1171

图1  有机半导体分子在气态(左)和固态(右)下的前线分子轨道(HOMO和LUMO)能级以及电离能(IP)和亲和势(EA)的示意图
图2  本文中所计算的13种有机半导体分子
Molecule V/nm3 α/nm3 ε ωg/bohr?1 ωs/bohr?1
1TPD0.670.0703.370.1730.048
2NPD0.730.0793.440.1810.042
3YCP0.590.0593.180.1900.045
4Alq30.510.0493.010.1910.055
5mCP0.500.0503.190.1940.048
6BCP0.450.0453.160.1890.060
7Bphen0.410.0413.180.1980.063
8DPNTCI0.460.0453.110.2100.067
9TCNQ0.240.0304.100.2400.059
10MPMP0.600.0512.650.2030.063
11NTCDA0.260.0242.900.2500.077
12mPTCDI0.440.0544.150.2010.044
13PTCDA0.390.0484.120.2030.048
表1  在B3LYP/6-31G(d)水平下计算的13种有机半导体分子的分子体积V,静态极化率α和介电常数ε,以及在气态(g)和固态(s)下调控的最优ω参数值
Molecule ?εHOMOg IPVg ?εLUMOg EAVg ?εHOMOS IPVS ?εLUMOS EAVS IPUPS EAIPES
1TPD6.046.06?0.47?0.454.844.800.850.855.1050
2NPD6.136.10?0.20?0.274.804.811.271.275.20511.5252
3YCP6.736.73?0.71?0.755.295.300.760.785.6151
4Alq36.746.770.250.265.495.441.591.555.57501.9652
5mCP7.037.05?0.65?0.655.565.550.790.825.9851
6BCP7.347.34?0.06?0.066.086.131.201.246.30531.5654
7Bphen7.607.610.070.076.246.281.351.396.4055, 56
8DPNTCI8.588.581.861.867.027.052.912.937.4050
9TCNQ8.928.903.403.407.297.284.134.127.40574.2058
10MPMP6.436.47?1.70?1.655.045.08?0.21?0.185.40590.0559
11NTCDA9.539.522.362.347.877.883.263.307.97544.0254
2mPTCDI7.457.422.152.176.016.023.193.196.60603.9560
13PTCDA7.927.922.572.566.386.363.453.496.60613.9061
MAD0.280.270.410.40
表2  在LC-ωPBE*/6-31G(d)水平下计算的固态和气态下各分子轨道能量(?εHOMOS, ?εLUMOS和?εHOMOg,?εLUMOg)、垂直电离能(IPVS和IPVg)、亲和势(EAVS和EAVg)以及由UPS和IPES测得的实验值(IPUPS和EAIPES)(其中上标s和g代表固态和气态)
?εHOMOS vs IPUPS ?εLUMOS vs EAIPES IPVS vs IPUPS EAVS vs EAIPES
PBE1.090.430.320.41
B3LYP0.410.270.130.51
BMK0.350.750.230.64
M062X0.840.900.450.58
M06HF2.441.931.000.66
CAM-B3LYP0.841.270.400.70
LC-ωPBE2.082.040.620.68
ωB97XD1.441.780.480.72
HF1.573.420.751.46
LC-ωPBE*0.28(1.15)b0.41(1.55)b0.27(1.15)b0.40(1.55)b
表3  各种密度泛函方法计算的固态下分子轨道能量(?εHOMOS和?εLUMOS)、垂直电离能(IPVS)、亲和势(EAVS)相对于实验值的平均绝对误差(MAD)a
图3  在LC-ωPBE*/6-31G(d)水平下计算的13种分子在固态下分子轨道能量?εHOMOS和电离能IPVS与实验值IPUPS的关系图
图4  与实验值相比,各种密度泛函方法计算的(固态下)分子轨道能量(?εHOMOS和?εLUMOS)、垂直电离能(IPVS)、亲和势(EAVS)的平均绝对误差
MoleculePBEB3LYPBMKM062XM06HFCAM-B3LYPLC-ωPBωB97XDHFLC-ωPBE*
1TPD0.700.720.710.710.690.720.720.720.821.26
(?0.10)(?0.09)(?0.11)(?0.12)(?0.15)(?0.11)(?0.12)(?0.11)(?0.12)(1.20)
2NPD0.690.700.700.700.680.720.720.710.801.29
(?0.10)(?0.10)(?0.12)(?0.12)(?0.15)(?0.11)(?0.12)(?0.12)(?0.13)(1.33)
3YCP0.770.790.770.770.750.790.780.770.781.43
(?0.08)(?0.06)(?0.08)(?0.08)(?0.12)(?0.07)(?0.09)(?0.08)(?0.09)(1.44)
4Alq30.750.740.710.710.670.720.690.700.691.33
(?0.15)(?0.16)(?0.18)(?0.19)(?0.23)(?0.17)(?0.20)(?0.18)(?0.21)(1.25)
5mCP0.870.850.830.840.830.840.850.830.841.50
(?0.05)(?0.05)(?0.07)(?0.06)(?0.09)(?0.05)(?0.07)(?0.07)(?0.07)(1.47)
6BCP0.820.850.850.850.830.870.870.860.911.21
(?0.22)(?0.14)(?0.15)(?0.16)(?0.19)(?0.15)(?0.16)(?0.16)(?0.17)(1.26)
7Bphen0.850.900.900.910.900.920.930.910.961.33
(?0.23)(?0.11)(?0.13)(?0.13)(?0.16)(?0.12)(?0.14)(?0.13)(?0.15)(1.36)
8DPNTCI0.810.870.931.021.031.061.061.031.091.53
(?0.10)(0.00)(?0.01)(?0.01)(?0.04)(0.01)(0.00)(0.00)(0.02)(1.56)
9TCNQ1.501.521.531.511.491.531.541.521.591.62
(0.25)(0.26)(0.26)(0.25)(0.23)(0.26)(0.26)(0.26)(0.27)(1.63)
10MPMP0.720.730.730.710.700.720.720.720.731.39
(?0.09)(?0.09)(?0.10)(?0.10)(?0.12)(?0.09)(?0.11)(?0.10)(?0.10)(1.39)
11NTCDA1.201.341.351.341.331.121.341.121.361.64
(0.06)(0.21)(0.22)(0.21)(0.20)(0.21)(0.21)(0.20)(0.26)(1.66)
12mPTCDI1.141.181.181.171.151.181.181.171.261.40
(0.07)(0.10)(0.09)(0.09)(0.06)(0.10)(0.09)(0.09)(0.13)(1.44)
13PTCDA1.321.351.361.351.341.361.351.351.421.56
(0.22)(0.25)(0.26)(0.24)(0.23)(0.26)(0.24)(0.24)(0.29)(1.54)
表4  各种密度泛函方法计算的气态下分子电子电离能IPVg与固态下电子电离能IPVS的差值,即极化能P+(公式(6))
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