用半正定顶点修正自能逼近耦合簇精度
Approaching Coupled Cluster Accuracy with Positive Semidefinite Vertex Corrected Self-Energies
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中文总结 AI 辅助
本研究基于非平衡格林函数形式体系推导半正定顶点修正自能，解决了原方法的正定性缺陷，在标准分子基准测试中其准粒子能量精度可与耦合簇参考计算媲美。
中文摘要 AI 辅助
Hedin的泛函导数形式体系是构建关联电子理论最知名的系统方法，这主要得益于其最低阶自能展开——GW近似的成功。超越GW的图示重求和方案试图同时在所有粒子-粒子和粒子-空穴通道混合关联作用，但这种全面处理对真实分子体系计算成本过高，因此一种高效替代方案是仅在一个特定通道（通常是粒子-空穴通道）中完全考虑电子关联。该思路近期已应用于分子体系[1]，得到的自能由Bethe-Salpeter方程求解得到的激发态能量和跃迁振幅表示，而非GW所用的随机相位近似。尽管该方法具有预测性且数值高效，但它在某些能量范围内违反了电子谱函数的基本正定性约束。本研究中，我们基于非平衡格林函数形式体系的严格框架，推导了该理论的半正定（PSD）扩展，解决了这一物理缺陷。PSD约束引入了新的散射通道和三重态中间态，恢复了正确的物理行为。我们在标准分子基准测试中证明，它能持续改进准粒子能量，精度可与耦合簇参考计算媲美。
英文摘要
Hedin's formalism of functional derivatives is the best-known method for systematically constructing correlated electronic theories, largely due to the success of its lowest-order self-energy expansion, the $GW$ approximation. Beyond $GW$, diagrammatic resummation schemes attempt to mix correlations simultaneously across all particle-particle and particle-hole channels. Because such a comprehensive treatment is computationally prohibitive for realistic molecular systems, a highly effective alternative is to fully account for electronic correlations in one specific channel, typically the particle-hole channel. This idea was recently implemented for molecular systems [1], yielding a self-energy expressed in terms of excited-state energies and transition amplitudes from the solution of the Bethe-Salpeter equation, rather than the random phase approximation used in $GW$. While this approach is predictive and numerically efficient, it violates the fundamental positive-definiteness constraint of the electron spectral function in certain energy ranges. In this study, we resolve this physical flaw by deriving a positive semidefinite (PSD) extension of the theory using a rigorous framework based on the nonequilibrium Green's function formalism. The PSD constraint introduces new scattering channels and triplet intermediate states and restores the correct physical behavior. We demonstrate that it consistently improves quasiparticle energies across standard molecular benchmarks, with an accuracy comparable to coupled-cluster reference calculations.
