Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom.
J Chem Phys. 2013 Aug 14;139(6):064104. doi: 10.1063/1.4817330.
We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on (10,0) carbon nanotubes of different lengths.
我们提出了一种线性响应形式的含时密度泛函理论（TDDFT）的实现，能够计算大分子和纳米结构的低能光吸收光谱。该方法避免了对占据或虚拟 Kohn-Sham 态的任何显式规范表示，从而实现了与系统规模线性比例的计算工作量。与传统的局域轨道公式不同，后者使用单个局域函数集来跨越占据态和未占据态流形，我们使用了两组原位优化的局域轨道，一组用于占据态，一组用于未占据态。这种双表示方法避免了用最小化的局域轨道来跨越未占据 Kohn-Sham 态空间的已知问题，同时原位优化过程允许使用最小数量的函数进行高效计算。该方法应用于一些中等大小的有机分子，并观察到与传统 TDDFT 方法的良好一致性。此外，还在不同长度的（10,0）碳纳米管上证明了计算成本与系统规模的线性比例。
