The state of the art in the development, implementation, validation, and application of local hybrid functionals with position‐dependent exact‐exchange admixture is reviewed comprehensively. Starting from the general formulation of a local hybrid functional, possible constructions of local mixing functions to determine the position dependence are scrutinized in terms of their exact properties as well as their desirable features. The gauge problem pertaining to the ambiguity of exchange‐energy densities is discussed. “Smoking guns” for the gauge problem are identified, and the first calibration functions to improve the match of the exact and semi‐local exchange‐energy densities are compared. In view of the appearance of nonstandard exact‐exchange integrals, a crucial aspect is the efficient implementation of local hybrid functionals. This has been achieved recently using a resolution of the identity and/or semi‐numerical techniques, both for ground‐state energies and gradients, and for linear‐response time‐dependent density functional theory. The validation and early applications of local hybrids are reviewed, including thermochemistry, reaction barriers, structures and vibrational frequencies, electric and magnetic properties, as well as electronic excitation spectra.

中文翻译：

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局部混合功能：量子化学及其他方面新兴的新工具的理论，实现和性能

全面审查了具有位置依赖的精确交换混合物的本地混合功能的开发，实施，验证和应用的最新技术。从局部混合功能的一般公式开始，根据位置精确的特性和所需的特征来研究确定位置依赖性的局部混合功能的可能构造。讨论了与交换能量密度的歧义有关的规范问题。确定了解决量规问题的“烟枪”，并比较了用于提高精确和半局部交换能量密度的匹配度的第一个校准功能。考虑到非标准精确交换积分的出现，一个关键方面是局部混合功能的有效实现。最近，这已经通过对基态能量和梯度以及线性响应时间相关的密度泛函理论的恒等式和/或半数值技术的解析来实现。审查了本地混合动力车的验证和早期应用，包括热化学，反应障碍，结构和振动频率，电和磁性能以及电子激发光谱。