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

在第一个供资期开展的基于精确交换能量密度的改进密度泛函的开发、实施和评价工作将得到延长。对于局部混合泛函（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以及渐近。将实施改进的校准功能，以处理LH的“量规问题”，并将改进优化程序。距离分离的本地混合动力（RSLH）将首次实现完整的功能，在一个有效的计算机代码，基态能量和梯度以及TDDFT激发能量。第一个有竞争力的RSLH将被优化和详细评估。改进的强相关校正的LH和RSLH（scLH和scRSLH）也将被实现和优化。在这种情况下，自动微分的例程将被集成，和新的TDDFT例程将被构造来处理包含非线性形式的确切交换能量密度的泛函。新的方法将评估大量的数据集，并将被应用到核心激发光谱和许多其他问题。该项目的主要目标是建立新的，实用的DFT方法，用于各种各样的应用。

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.