Holzer Christof
Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany.
J Chem Phys. 2020 Nov 14;153(18):184115. doi: 10.1063/5.0022755.
A seminumerical algorithm capable of performing large-scale (time-dependent) density functional theory (TD-DFT) calculations to extract excitation energies and other ground-state and excited-state properties is outlined. The algorithm uses seminumerical integral techniques for evaluating Coulomb and exchange parts for a set of density matrices as occurring in standard TD-DFT or similar methods for the evaluation of vibrational frequencies. A suitable optimized de-aliasing procedure is introduced. The latter does not depend on further auxiliary quantities and retains the symmetry of a given density matrix. The algorithm is self-contained and applicable to any orbital basis set available without the need for further auxiliary basis sets or optimized de-aliasing grids. Relativistic two-component excited-state TD-DFT calculations are reported for the first time using the developed seminumerical algorithm for standard and local hybrid density functional approximations. Errors are compared with the widely used "resolution of the identity" (RI) approximations for Coulomb (RI-J) and exchange integrals (RI-K). The fully seminumerical algorithm does not exhibit an enlarged error for standard DFT functionals compared to the RI approximation. For the more involved local hybrid functionals and within strong external fields, accuracy is even considerably improved.
概述了一种能够执行大规模（含时间依赖性）密度泛函理论（TD-DFT）计算以提取激发能及其他基态和激发态性质的半数值算法。该算法使用半数值积分技术来评估标准TD-DFT或类似振动频率评估方法中出现的一组密度矩阵的库仑部分和交换部分。引入了一种合适的优化去混叠程序。后者不依赖于其他辅助量，并保留给定密度矩阵的对称性。该算法自成体系，适用于任何可用的轨道基组，无需额外的辅助基组或优化的去混叠网格。首次使用所开发的半数值算法对标准和局域杂化密度泛函近似进行相对论双分量激发态TD-DFT计算。将误差与广泛使用的库仑（RI-J）和交换积分（RI-K）的“单位分解”（RI）近似进行比较。与RI近似相比，全半数值算法对于标准DFT泛函并未表现出更大的误差。对于更复杂的局域杂化泛函以及在强外场中，精度甚至有显著提高。
