用随机相位近似模拟伦敦色散力：方法学的发展
Modelisation of London dispersion forces by random phase approximation: methodological developments
摘要：
在这篇论文中，我们展示了在距离分离理论的背景下，无规相位近似（RPA）的发展。我们目前的RPA的一般形式主义的进展，特别是在“电介质矩阵”制定RPA，这是详细探讨。我们显示的RPA方程与本地化轨道，特别是虚拟本地化轨道的发展，是“投影振荡轨道”（POO）的工作总结。已经编写了一个程序来计算函数，如交换孔，响应函数等在真实空间网格（平行六面体或“DFT”类型）上;这里显示了其中一些可视化。在实空间中，我们提供了一个适应的有效能量分母近似（EED），最初发展在倒易空间中的固体物理。推导了距离分离背景下RPA相关能的解析梯度。这里用拉格朗日量发展的形式主义允许在梯度的表达式中出现的短期和长期项的一体化推导。这些术语显示出有趣的相似之处。显示了在RSH+dRPA-I和RSH+SOSEX水平上对一组16个分子的几何优化，以及在RSH+dRPA-I水平上相关密度的计算和可视化。
英文摘要：
In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localised orbitals, especially developments of the virtual localized orbitals that are the "projected oscillatory orbitals" (POO). A program has been written to calculate functions such as the exchange hole, the response function, etc on real space grid (parallelepipedic or of the "DFT" type) ; some of those visualisations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developped in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developped here with a lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimisations at the RSH+dRPA-I and RSH+SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualisations of correlated densities at the RSH+dRPA-I level.
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