We report unphysical irregularities and discontinuities in some key experimentally measurable quantities computed within the GW approximation of many-body perturbation theory applied to molecular systems. In particular, we show that the solution obtained with partially self-consistent GW schemes depends on the algorithm one uses to self-consistently solve the quasiparticle (QP) equation. The main observation of the present study is that each branch of the self-energy is associated with a distinct QP solution and that each switch between solutions implies a significant discontinuity in the quasiparticle energy as a function of the internuclear distance. Moreover, we clearly observe “ripple” effects, i.e., when a discontinuity in one of the QP energies induces (smaller) discontinuities in the other QP energies. Going from one branch to another implies a transfer of weight between two solutions of the QP equation. The cases of occupied, virtual, and frontier orbitals are separately discussed on distinct diatomics. In particular, we show that multisolution behavior in frontier orbitals is more likely if the HOMO–LUMO gap is small.

中文翻译：

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GW方法中的非物理不连续性

我们报告了一些物理上可测量的关键非物理不规则性和不连续性，这些可量化的数量是在应用于分子系统的多体摄动理论的GW近似值内计算的。特别是，我们表明，使用部分自洽的GW获得的解决方案方案取决于一种用于自洽求解拟粒子（QP）方程的算法。本研究的主要观察结果是，自能量的每个分支都与一个不同的QP解相关，并且每个解之间的切换都暗示了准粒子能量的显着不连续性，该不连续性是核间距离的函数。此外，我们清楚地观察到“波纹”效应，即，当一个QP能量的不连续性引起（较小的）其他QP能量的不连续性时。从一个分支到另一个分支意味着在QP方程的两个解之间转移了权重。在不同的双原子论上分别讨论了占据轨道，虚拟轨道和边界轨道的情况。特别是，我们表明，如果HOMO-LUMO间隙较小，则边界轨道上的多解行为更有可能发生。