Development of density functionals based on the exact-exchange energy density for wide application in chemistry, biophysics, and material sciences

将延长在第一个供资期间开展的基于精确交换能量密度的改进密度函数的发展、实施和评价。对于局部杂化泛函（LHs），改进的局部混合函数将被优化，从而改善核附近的精确交换混合，并渐近地改善。改进校正功能以解决LHs的“量规问题”，并改进优化程序。距离分离局部混合（RSLHs）将首次在高效的计算机代码中实现完整的功能，用于基态能量和梯度以及TDDFT激发能。将对首批具有竞争力的rslh进行优化和详细评估。改进的强相关校正LHs和RSLHs （scLHs和scRSLHs）也将实现和优化。在这种情况下，将集成自动微分例程，并构建新的TDDFT例程来处理包含精确交换能量密度非线性形式的泛函。新方法将在大量数据集上进行评估，并将应用于核心激发光谱和许多其他问题。这个项目的主要目标是为各种各样的应用建立新的、实用的DFT方法。

The development, implementation and evaluation of improved density functionals based on the exact-exchange energy density, carried out in the first funding period, shall be extended. For local hybrid functionals (LHs) improved local mixing functions will be optimized, which improve the exact-exchange admixture near the nuclei as well as asymptotically. Improved calibration functions to deal with the “gauge problem” of LHs will be implemented, and the optimization procedures will be improved. Range-separated local hybrids (RSLHs) will be implemented for the first time with full functionality in an efficient computer code, for ground-state energy and gradients as well as TDDFT excitation energies. The first competitive RSLHs will be optimized and evaluated in detail. Improved strong-correlation-corrected LHs and RSLHs (scLHs and scRSLHs) will also be implemented and optimized. In this context routines for automatic differentiation will be integrated, and novel TDDFT routines will be constructed to deal with functionals containing non-linear forms of the exact-exchange energy density. The new methods will be evaluated for a large number of data sets and will be applied to core-excitation spectra and to many other questions. The main goal of this project is to establish new, practical DFT methods for wide variety of applications.