The GW approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is $\mathcal{O}(N^4)$ in the system size N, which prohibits its application to many systems of interest. We present a full-frequency GW algorithm in a Gaussian-type basis, whose computational cost scales with N² to N³. The implementation is optimized for massively parallel execution on state-of-the-art supercomputers and is suitable for nanostructures and molecules in the gas, liquid or condensed phase, using either pseudopotentials or all electrons. We validate the accuracy of the algorithm on the GW100 molecular test set, finding mean absolute deviations of 35 meV for ionization potentials and 27 meV for electron affinities. Furthermore, we study the length-dependence of quasiparticle energies in armchair graphene nanoribbons of up to 1734 atoms in size, and compute the local density of states across a nanoscale heterojunction.

中文翻译：

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向GW上的数千个原子计算

多体摄动理论的GW近似是计算分子和固体的电子加成和去除能的准确方法。但是，在规范的实现中，其计算成本为$\mathcal{Ø}（{ñ}^4）$在系统大小N中，它禁止将其应用于许多关注的系统。我们在高斯类型的基础上提出了一种全频GW算法，其计算成本范围为N ²至N ³。该实现经过优化，可在最先进的超级计算机上大规模并行执行，并且适用于使用伪电势或所有电子的气相，液相或凝聚相中的纳米结构和分子。我们在GW上验证算法的准确性100个分子测试仪，发现电离势的平均绝对偏差为35 meV，电子亲和力的平均绝对偏差为27 meV。此外，我们研究了尺寸高达1734个原子的扶手椅石墨烯纳米带中准粒子能量的长度依赖性，并计算了纳米级异质结上的局部态密度。