Hillenbrand Christopher, Li Jiachen, Zhu Tianyu
Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA.
J Chem Phys. 2025 May 7;162(17). doi: 10.1063/5.0260895.
We present an energy-specific Bethe-Salpeter equation (BSE) implementation for efficient core and valence optical spectrum calculations. In the energy-specific BSE, high-lying excitation energies are obtained by constructing trial vectors and expanding the subspace targeting excitation energies above the predefined energy threshold in the Davidson algorithm. To calculate optical spectra over a wide energy range, energy-specific BSE can be applied to multiple consecutive small energy windows, where trial vectors for each subsequent energy window are made orthogonal to the subspace of preceding windows to accelerate the convergence of the Davidson algorithm. For seven small molecules, energy-specific BSE combined with G0W0 provides small errors around 0.8 eV for absolute and relative K-edge excitation energies when starting from a hybrid PBEh solution with 45% exact exchange. We further showcase the computational efficiency of this approach by simulating the N 1s K-edge excitation spectrum of the porphine molecule and the valence optical spectrum of silicon nanoclusters involving 6000 excited states using G0W0-BSE. This work expands the applicability of the GW-BSE formalism for investigating high-energy excited states of large systems.
我们提出了一种针对高效计算芯能级和价带光谱的能量特定型贝塞耳-萨尔皮特方程（BSE）实现方法。在能量特定型BSE中，通过构建试探向量并在戴维森算法中扩展目标激发能高于预定义能量阈值的子空间来获得高能激发能。为了在宽能量范围内计算光谱，能量特定型BSE可应用于多个连续的小能量窗口，其中每个后续能量窗口的试探向量与前一个窗口的子空间正交，以加速戴维森算法的收敛。对于七个小分子，当从具有45%精确交换的混合PBEh解开始时，能量特定型BSE与G0W0相结合，对于绝对和相对K边激发能，能提供约0.8 eV的小误差。我们通过使用G0W0 - BSE模拟卟吩分子的N 1s K边激发光谱和涉及6000个激发态的硅纳米团簇的价带光谱，进一步展示了这种方法的计算效率。这项工作扩展了GW - BSE形式体系在研究大系统高能激发态方面的适用性。
