We study the dependence of kinetic energy densities (KED) on density-dependent variables that have been suggested in previous works on kinetic energy functionals (KEF) for orbital-free DFT (OF-DFT). We focus on the role of data distribution and on data and regressor selection. We compare unweighted and weighted linear and Gaussian process regressions of KED for light metals and a semiconductor. We find that good quality linear regression resulting in good energy-volume dependence is possible over density-dependent variables suggested in previous literature. This is achieved with weighted fitting based on KED histogram. With Gaussian process regressions, excellent KED fit quality well exceeding that of linear regressions is obtained as well as a good energy-volume dependence which was somewhat better than that of best linear regressions. We find that while the use of the effective potential as a descriptor improves linear KED fitting, it does not improve the quality of the energy-volume dependence with linear regressions but substantially improves it with Gaussian process regression. Gaussian process regression is also able to perform well without data weighting.
Development of Kinetic Energy Density Functional Using Response Function Defined on the Energy Coordinate
在密度泛函理论的基础上，为了实现无轨道密度泛函理论，提出了一种基于能量电子密度的动能泛函Ee.该泛函包括用参考系的线性响应函数（LRF）描述的非局部项。作为本方法的一个显著特征，LRF表示在针对每个感兴趣系统定义的能量坐标ε上。此外，采用原子系统作为构造LRF的参考系，这与传统的基于均匀电子气的方法有明显的区别。利用耦合参数积分法，给出了泛函Ee的显式表达式。应用泛函Ee kin kin方法计算了模拟H、He、Ne和Ar的赝原子的动能。由此可以解释，每个原子的动能是用泛函Ee相对于每个原子的价电荷Zv的变化来计算的。在这些计算中，采用Kohn-Sham DFT优化的电子密度n作为泛函的自变量。计算结果与Kohn-Sham密度泛函理论的计算结果吻合得很好。我们还设计了一种方法来执行自洽场计算利用功能Ee。用这种方法计算了赝Ne和Ar原子中电子的径向分布函数。结果表明，所得结果与Kohn-Sham密度泛函理论的结果基本一致。
Nonlocal Kinetic Energy Functionals By Functional Integration
Since the seminal works of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting Kinetic Energy , $T_s[ρ]$ , the subject of this work. The typical paradigm is to first approximate the energy functional, and then take its functional derivative, $\frac{δT_s[ρ]}{δρ(r)}$ , yielding a potential that can be used in orbital-free DFT, or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-function…
Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via machine learning
Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes
我们提出了将精确交换结合到热辅助占据密度泛函理论（TAO-DFT）中的混合方案[J. - D. Chai，J.Chem.Phys.136，154104（2012）]，以改进对非局部交换效应的描述。通过一些简单的修改，Kohn-Sham密度泛函理论（KS-DFT）中的整体和距离分离的杂化泛函可以与TAO-DFT无缝结合。与KS-DFT中的全局混合泛函相比，TAO-DFT中所得的全局混合泛函对于具有强静态相关效应的系统（例如，H2和N2的解离、扭曲乙烯和线性并苯的电子性质），同时对于没有强静态相关效应的系统保持类似的性能。此外，通过在混合TAO-DFT中引入色散校正，可以有效地实现对非共价相互作用的合理准确描述。相对于TAO-DFT中的半局域密度泛函，TAO-DFT中的全局杂化泛函在热化学、动力学、反应能和优化几何结构等广泛的应用中表现出优越的性能.
Electronic transport calculations for lightly-doped thermoelectrics using density functional theory: Application to high-performing Cu-doped zinc antimonides
NeuralNEB -- Neural Networks can find Reaction Paths Fast
DTU Compute, Technical University of Denmark (DTU)（丹麦技术大学（DTU）计算系）；DTU Energy, Technical University of Denmark (DTU)（丹麦技术大学（DTU）能源系）；Department of Biology, University of Copenhagen (UCph)（哥本哈根大学（UCph）生物系）；Genomic Medicine, Copenhagen University Hospital, Rigshospitalet（哥本哈根大学医院（Rigshospitalet）基因组医学部）
Easy representation of multivariate functions with low-dimensional terms via Gaussian process regression kernel design: applications to machine learning of potential energy surfaces and kinetic energy densities from sparse data
