含时密度泛函理论及应用的最新发展

覃睿

doi:10.11858/gywlxb.20190747

含时密度泛函理论及应用的最新发展

doi: 10.11858/gywlxb.20190747

覃睿

中国工程物理研究院流体物理研究所冲击波物理与爆轰物理重点实验室，四川绵阳　621999

详细信息

作者简介:
覃　睿（1982－），男，博士，副研究员，主要从事计算材料研究. E-mail：qinrui@caep.cn

中图分类号: O521.2
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出版历程
- 收稿日期: 2019-03-25
- 修回日期: 2019-04-22

New Developments of Time-Dependent Density Functional Theory and Its Applications

QIN Rui

National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, Mianyang 621999, China

摘要

摘要: 密度泛函理论在材料计算研究领域得到了广泛的应用，然而它无法处理含时问题和材料的激发态性质。Runge-Gross定理奠定了含时密度泛函理论的基础，为研究这两类问题提供了有效的手段。经过三十多年的发展，含时密度泛函已被应用到量子化学、材料计算等多个领域，人们也更加了解其优势和不足。目前，含时密度泛函理论和方法仍在迅速发展。本文简要回顾含时密度泛函方法的发展历史，介绍近年来含时密度泛函在理论和应用方面的一些重要进展，总结当前在含时密度泛函领域存在的重要难题以及面临的挑战，展望其发展方向和趋势。
- 含时密度泛函 /
- 第一性原理计算 /
- 密度泛函 /
- 交换关联泛函
Abstract: Nowadays density functional theory which was introduced in the mid-1960s has wide applications in material simulations. However, it is not able to deal with time-dependent problems and excited properties of materials. Time-dependent density functional theory (TDDFT) based on Runge-Gross theorem, provides a viable way to deal with these two problems. After thirty years’ development, TDDFT has been widely applied to many fields, such as quantum chemistry and material simulation, and our understanding of its advantages and weaknesses also grows. To date, TDDFT theory and method still develop rapidly. Here a brief historical review of TDDFT is first introduced. Then it is followed by a discussion of recent important developments on theory and applications of TDDFT. Finally we summarize some important problems and challenges that TDDFT are facing and attempt to offer some thoughts about where TDDFT will be progressing.
- time-dependent density functional theory /
- first-principles calculations /
- density functional theory /
- correlation exchange functional

HTML全文

图 1 对CO₂分子的TDDFT研究（上图为偶极矩随时间演化，下图为通过傅里叶变换得到的谱（实线）与通过线性响应得到的谱（虚线）的比较）^[23]

Figure 1. TDDFT calculation for the CO₂ molecule (Top: time-dependent dipole moment. Bottom: dipole spectrum (full line) by Fourier transformation of dipole moment, compared with spectrum from LR-TDDFT (thin line).)^[23]

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图 2 乙炔在17.5 eV激光脉冲激发下的含时电子局域函数(TDELF)变化的快照^[28]

Figure 2. Snapshots of the time-dependent electron localization function (TDELF) for the excitation of acetylene by a 17.5 eV laser pulse^[28]

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图 3 偶极近似破坏了晶体哈密顿量的空间周期性

Figure 3. Spatial periodicity of the Hamiltonian destroyed by the dipole approximation

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图 4 块材硅的光吸收谱的RPA、TDDFT-ALDA计算和实验对比^[73]

Figure 4. Optical absorption spectrum of bulk Si: RPA, TDDFT-ALDA calculations and experiment^[73]

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图 5 采用bootstrap交换关联核的TDDFT计算各类半导体块材的光吸收谱及其与RPA计算、实验结果的对比^[74]

Figure 5. Optical absorption spectra of various bulk semiconductors calculated with TDDFT using the bootstrap xc kernel compared with the RPA calculations and experiments^[74]

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图 6 沿${\varGamma X}$和${\varGamma L}$方向的块材硅的高次谐波谱以及对应的联合态密度(JDOS) ^[76]

Figure 6. High harmonic spectra for the ${\varGamma X}$ polarization direction (red line) and the ${\varGamma L}$ direction (blue line); the bottom panel shows the corresponding joint density of states (JDOS) ^[76]

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图 7 计算得到的价电子动态结构因子与Sperling实验测量谱的对比^[78–79]

Figure 7. Calculated dynamic structure factor of valence electrons compared with the measured spectrum of Sperling et al. ^[78–79]

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表 1 一些气相Ar-TCNE体系的激发能E(单位eV)和振动强度f的计算和实验对比^[57]

Table 1. Excitation energies E (eV) and oscillator strengths f of several gas phase Ar-TCNE systems: theory and experiment^[57]

Ar	B3LYP		BNL ($\gamma $=0.5)	BNL $\gamma^* $			Exp.^[27]
Ar	E	f	E	$\gamma^* $	E	f	E	f
Benzene	2.1	0.03	4.4	0.33	3.8	0.03	3.59	0.02
Toluene	1.8	0.04	4.0	0.32	3.4	0.03	3.36	0.03
O-xylene	1.5	0	3.7	0.31	3.0	0.01	3.15	0.05
Naphthalene	0.9	0	3.3	0.32	2.7	0	2.60	0.01

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