LCAO-TDDFT - $k$ - $ω$：光限光谱学
LCAO-TDDFT-$k$-$ω$: Spectroscopy in the Optical Limit
摘要：
理解、优化和控制低维系统中的光吸收过程、激子双生以及电子-空穴分离和传导是材料科学中的一个基本问题。然而，能够模拟低维大分子系统的吸光度并提供对所涉及过程的物理洞察的稳健且有效的方法仍然难以捉摸。我们采用了一个高效的线性组合原子轨道（LCAO）表示的Kohn-Sham（KS）轨道内的时间依赖密度泛函理论（TDDFT）在倒易空间（$k$）和频率（$ω$）域，在我们的LCAO-TDDFT- $k$ - $ω$代码内实现，并应用导数不连续校正的交换功能$Δ_x$的本征KS能量。在这样做，我们能够提供一个半定量描述的光学吸收，电导率和极化率光谱的原型0 D，1D，2D和3D系统的光学极限（$\|\bf{q}\|\to0^+$）相比，现有的测量和求解Bethe $-$ Salpeter方程与准粒子$G_0 W_0$本征值（$G_0 W_0$ -BSE）。具体而言，我们考虑了0 D富勒烯（C $_{60}$）、1D金属（10，0）和半导体（10，10）单壁碳纳米管（SWCNT）、2D石墨烯（GR）和磷烯（PN）以及3D金红石（R-TiO $_2$）和金红石（A-TiO $_2$）。对于每个系统，我们还采用空间分辨的电子-空穴密度来提供对其光学激发性质的直接物理洞察。这些结果表明，我们的LCAO-TDDFT- $k$ - $ω$代码的可靠性，适用性，效率和鲁棒性，并打开路径的光电，光伏和光催化应用$in$ $silico$的大分子系统的计算设计。
英文摘要：
Understanding, optimizing, and controlling the optical absorption process, exciton gemination, and electron-hole separation and conduction in low dimensional systems is a fundamental problem in materials science. However, robust and efficient methods capable of modelling the optical absorbance of low dimensional macromolecular systems and providing physical insight into the processes involved have remained elusive. We employ a highly efficient linear combination of atomic orbitals (LCAOs) representation of the Kohn--Sham (KS) orbitals within time dependent density functional theory (TDDFT) in the reciprocal space ($k$) and frequency ($ω$) domains, as implemented within our LCAO-TDDFT-$k$-$ω$ code, and apply the derivative discontinuity correction of the exchange functional $Δ_x$ to the KS eigenenergies. In so doing we are able to provide a semi-quantitative description of the optical absorption, conductivity, and polarizability spectra for prototypical 0D, 1D, 2D, and 3D systems within the optical limit ($\|\bf{q}\|\to0^+$) as compared to both available measurements and from solving the Bethe$-$Salpeter equation with quasiparticle $G_0 W_0$ eigenvalues ($G_0 W_0$-BSE). Specifically, we consider 0D fullerene (C$_{60}$), 1D metallic (10,0) and semiconducting (10,10) single-walled carbon nanotubes (SWCNTs), 2D graphene (GR) and phosphorene (PN), and 3D rutile (R-TiO$_2$) and anatase (A-TiO$_2$). For each system, we also employ the spatially resolved electron-hole density to provide direct physical insight into the nature of their optical excitations. These results demonstrate the reliability, applicability, efficiency, and robustness of our LCAO-TDDFT-$k$-$ω$ code, and open the pathway to the computational design of macromolecular systems for optoelectronic, photovoltaic, and photocatalytic applications $in$ $silico$.
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