CPMOH/LOMA, Université de Bordeaux 1, 351 Cours de la Liberation, 33405 Talence, France.
J Chem Phys. 2011 Aug 21;135(7):074105. doi: 10.1063/1.3624731.
We describe an implementation of Hedin's GW approximation for molecules and clusters, the complexity of which scales as O(N(3)) with the number of atoms. Our method is guided by two strategies: (i) to respect the locality of the underlying electronic interactions and (ii) to avoid the singularities of Green's functions by manipulating, instead, their spectral functions using fast Fourier transform methods. To take into account the locality of the electronic interactions, we use a local basis of atomic orbitals and, also, a local basis in the space of their products. We further compress the screened Coulomb interaction into a space of lower dimensions for speed and to reduce memory requirements. The improved scaling of our method with respect to most of the published methodologies should facilitate GW calculations for large systems. Our implementation is intended as a step forward towards the goal of predicting, prior to their synthesis, the ionization energies and electron affinities of the large molecules that serve as constituents of organic semiconductors.
我们描述了一种用于分子和团簇的 Hedin GW 近似的实现方法，其复杂度随原子数量呈 O(N(3)) 增长。我们的方法遵循两个策略：(i) 尊重基础电子相互作用的局部性，(ii) 通过使用快速傅里叶变换方法来操纵其光谱函数，而不是直接处理格林函数的奇点。为了考虑电子相互作用的局部性，我们使用原子轨道的局部基和它们乘积的局部基。我们还将屏蔽库仑相互作用压缩到更低维的空间中，以提高速度并降低内存需求。与大多数已发表的方法相比，我们的方法的改进缩放应该有助于对大型系统进行 GW 计算。我们的实现旨在朝着在合成之前预测作为有机半导体组成部分的大型分子的电离能和电子亲和能的目标迈出一步。
