Electronic Structure Modeling With the Strictly Correlated Electrons Density Functional

密度泛函理论(DFT)是生物、化学和物理中常用的电子结构计算方法。为了保证计算效率，我们采用了无相互作用电子的Kohn-Sham(KS)参考系，并使用泛函近似来模拟物理相互作用。当在不相互作用的框架内以强电子相关性为目标时，就会出现挑战，而传统的近似方法在这方面是不足的。作为泛函近似发展的最新突破，严格关联电子(SCE)泛函被引入KS-DFT中。它严格地源于DFT的强相互作用极限，在我的博士研究过程中，我确实证明了它可以从第一原理捕获强关联效应。此外，我确实证明了SCE泛函中的导数不连续。这一形式特征对于电子动力学的计算通常是至关重要的，但在传统的近似中却被忽略了。因此，动态过程的DFT建模有望得到改进，在这个项目中，我将在此背景下研究SCE泛函。将使用一维模型设置来从形式上分析姐妹资格委员会职能的能力。对于需要在泛函近似中引入导数不连续的现象，我们将特别关注。由于SCE的显著形式性质，在强关联系统之外的DFT建模中，泛函的改进是可望的。然而，在全面应用姐妹会议职能之前，需要在三个方面为其解决办法制定战略。为了设计一个三维的SCE解决方案，我将在下面分析SCE功能的构建块，即所谓的协同运动函数，在那里可以获得准确的参考数据。如果找不到重建协动函数的精确公式，将采用近似策略。最后，尝试用延拓方法来求解具有多个电子的双原子分子的SCE泛函。为了保证方法在所有相关区域都有良好的精度，可以考虑和改进对KS-SCE泛函的定量修正。随着该项目的发展，可以为密度泛函紧束缚方法(DFTB)等多尺度建模方法提供非经验参数。虽然需要对DFTB方法进行调整才能适当地结合SCE参数，但这些进展可以为模拟非常大的分子体系或复杂的固体提供可靠的方法。

Density functional theory (DFT) is routinely applied for electronic structure calculations in biology, chemistry and physics. To guarantee computational efficiency one employs the Kohn-Sham (KS) reference system of non-interacting electrons and functional approximations are used to model the physical interaction. Challenges arise when strong electronic correlation is targeted within the non-interacting framework with traditional approximations being deficient in this regard. As recent breakthrough in the development of functional approximations the strictly correlated electrons (SCE) functional was introduced in KS-DFT. It derives rigorously from the strong-interaction limit of DFT and in the course of my PhD research I did demonstrate that it can capture strong-correlation effects from first principles.Moreover I did demonstrate a derivative discontinuity in the SCE functional. This formal feature is often crucial for the computation of electron dynamics but is missed in traditional approximations . Hence, improvements are expected in the DFT modeling of dynamical processes and in this project I will investigate the SCE functional in this context. One dimensional model setups will be used to analyze the capabilities of the SCE functional from formal grounds. Special interest will be devoted to phenomena that require a derivative discontinuity in the functional approximation for a proper modeling.Due to the striking formal properties of the SCE functional improvements are expected in the DFT modeling beyond strongly correlated systems. Prior to a general application of the SCE functional, however, strategies are required for its solution in three dimensions. To devise a SCE solution in three dimensions I will analyze in the following the building blocks of the SCE functional, the so-called co-motion functions, for the Hydrogen molecule where accurate reference data is available. If no exact formulas for the reconstruction of the co-motion functions can be found approximate strategies will be pursued. Finally extensions will be attempted to solve the SCE functional for diatomic molecules with many electrons. To guarantee for a good accuracy of the method in all correlation regimes quantitative corrections to the KS-SCE functional can be considered and improved.With the developments of this project non-empirical parameters can be provided for multi-scale modeling methods like the density-functional tight-binding method (DFTB). Although adaptions of the DFTB method are required for a proper incorporation of the SCE parameters, the developments can lead to a reliable method for the modeling of very large molecular systems or complex solids.