多体GW形式体系中静态与动态可极化环境的比较
Static versus dynamically polarizable environments within the many-body $\bf{GW}$ formalism
AI总结：
本文在嵌入GW形式体系中比较静态绝热与动态介电环境，提出正确取静态极限的方法，并通过C60分子和水分子体系验证绝热近似对能隙极化能的误差通常低于10%。
摘要：
用于研究嵌入子系统光电过程的连续或离散可极化模型，大多依赖于将周围电子介电响应限制在其低频极限。这种描述基于如下假设：周围介质中的电子对中心子系统中的任何激发瞬时响应，从而在绝热极限下处理环境。利用最近发展的嵌入GW形式体系，并在完全从头算水平上描述环境，我们评估了绝热极限相对于考虑介电响应完整动力学的环境的优劣。进一步，我们展示了如何正确取环境极化率的静态极限，引入所谓的库仑空穴和屏蔽交换对反应场的贡献。作为第一个应用，我们考虑了C60晶体表面的C60分子，即嵌入子系统与周围子系统的动力学相似的情形。常见的绝热假设在得到适当处理时，对前沿能级及相关能隙的极化能产生的误差低于10%。最后，我们考虑了金属纳米管内的水分子，这是环境绝热极限的最不利情形。即使前沿轨道极化能的误差可达十分之几电子伏特，能隙极化能的误差仍保持在10%以下。
英文摘要：
Continuum or discrete polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, treating thus the environment in the adiabatic limit. Exploiting a recently developed embedded $GW$ formalism, with an environment described at the fully ab initio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response is considered. Further, we show how to properly take the static limit of the environment susceptibility, introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C$_{60}$ molecule at the surface of a C$_{60}$ crystal, namely a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below $10\%$ on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment adiabatic limit. The error on the gap polarization energy remains below $10\%$, even though the error on the frontier orbitals polarization energies can reach a few tenths of an electronvolt.
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