Accurate TDDFT absorption spectra over full spectral range

全光谱范围内精确的 TDDFT 吸收光谱

• 批准号: 505191319
• 负责人: Dr. Matthias Kick
• 金额: --
• 依托单位: Department of Chemistry
• 依托单位国家: 德国
• 项目类别: WBP Fellowship
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/505191319?language=en
• 关键词: Accurate; TDDFT; absorption; spectra; over

Time dependent density functional theory (TDDFT) has proven to be a reliable work horse for obtaining absorption spectra and other related excited state quantities. Yet, calculation of entire absorption spectra can be very demanding and their evaluation is computationally prohibited for large system sizes. Roughly speaking TDDFT can be divided in two regimes, the linear-response or frequency domain time dependent density functional theory (LR-TDDFT) and in real-time time dependent density functional theory (RT-TDDFT). In the latter the time dependent Kohn-Sham states are explicitly propagated in time under the influence of a time dependent external potential. However, a large number of time steps is usually required to obtain the required accuracy and calculations for large systems becomes quickly unfeasible. LR-TDDFT aims to solve a non-hermitian eigenvalue problem in order to obtain the excited states. Generally speaking, the number of such excited states grows with system size and solving the linear algebra problem becomes also computational prohibited for large systems. Within the project we will develop a new approach for calculating full TDDFT spectra where the computational cost should not dramatically exceed the cost of the underlying ground state calculation. In particular we will obtain reliable approximated entire TDDFT spectra in combination with hybrid functional DFT. Thus our target is to provide accurate absorption spectra over a large spectral range and for large system sizes. For this purpose we suggest a method which combines the strengths of LR-TDDFT and RT-TDDFT to overcome the current limitations in system size. In order to reduce the computational cost to a minimum we aim at using very short time propagation in RT-TDDFT. As the resolution of the spectra significantly depends on the simulation time one can expect that this works already quite well for a spectrum which is characterized by a continuum or quasi continuum of states. However, it will fail if the spectrum also includes discrete excitations as the simulation time might be too short to achieve the desired resolution. Missing information about discrete excitations can be included using LR-TDDFT. Solving the eigenvalue problem associated with the linear-response formalism gives distinct excitation energies in form of eigenvalues of the particular problem. To keep the computational cost at a minimum we will approximately solve the LR equations using the so called small matrix approximation (SMA). The SMA will serve as a basis for more sophisticated approximations which will allow high accuracy in describing certain excitations or certain spectral regions. By this we envision an approach which guarantees the fast evaluation of entire TDDFT spectra in combination with high accuracy.

时间相关密度泛函理论（TDDFT）已被证明是获得吸收光谱和其他相关激发态量的可靠工具。然而，整个吸收光谱的计算可能是非常苛刻的，并且它们的评估在计算上被禁止用于大系统尺寸。粗略地说，TDDFT可分为线性响应或频域时变密度泛函理论（LR-TDDFT）和实时时变密度泛函理论（RT-TDDFT）两种。在后者中，时间相关的Kohn-Sham状态在时间相关的外部势的影响下显式地在时间中传播。然而，通常需要大量的时间步长来获得所需的精度，并且对于大型系统的计算很快变得不可行。LR-TDDFT旨在解决非厄米特征值问题，以获得激发态。一般来说，这种激发态的数量随着系统规模的增加而增加，求解线性代数问题对于大型系统来说也变得难以计算。在该项目中，我们将开发一种计算全TDDFT谱的新方法，其中计算成本不应显着超过底层基态计算的成本。特别是，我们将获得可靠的近似整个TDDFT光谱与混合泛函DFT相结合。因此，我们的目标是在大光谱范围和大系统尺寸上提供准确的吸收光谱。为此，我们提出了一种结合LR-TDDFT和RT-TDDFT优点的方法，以克服当前系统大小的限制。为了将计算成本降低到最小，我们的目标是在RT-TDDFT中使用非常短的时间传播。由于光谱的分辨率很大程度上取决于模拟时间，因此可以预期，对于以连续或准连续状态为特征的光谱，这种方法已经很好地起作用了。然而，如果频谱还包括离散激励，则会失败，因为模拟时间可能太短而无法达到所需的分辨率。离散激励的缺失信息可以用LR-TDDFT来包含。求解与线性响应形式相关的特征值问题，得到了特定问题的特征值形式的不同激励能。为了将计算成本保持在最小，我们将使用所谓的小矩阵近似（SMA）近似求解LR方程。SMA将作为更复杂的近似的基础，这将允许高精度地描述某些激发或某些光谱区域。通过这种方法，我们设想了一种保证快速评估整个TDDFT光谱并具有高精度的方法。