发表机构
Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń; Institute of Advanced Studies, Nicolaus Copernicus University in Toruń（托伦哥白尼大学物理、天文学与信息学学院物理研究所; 托伦哥白尼大学高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用现有模型交换势的物理响应函数作为自适应辅助方向，通过投影OEP方程确定系数，实现紧凑低维的交换-only OEP势表示，显著减少自由度。
AI 中文摘要
优化有效势（OEP）方法为在Kohn-Sham（KS）密度泛函理论（DFT）中纳入依赖于轨道的交换作用提供了一个精确框架。其实际实现需要在合适的辅助空间中表示交换响应势，然而传统选择未必适应OEP响应的物理结构。在此，我们引入一种通用的响应空间策略，其中来自现有模型交换势的物理动机响应函数被重新用作OEP方程的自适应辅助方向。具体而言，与Becke-Johnson（BJ）、Räsänen-Pittalis-Proetto（RPP）、Gritsenko-van Leeuwen-van Lenthe-Baerends（GLLB）、Krieger-Li-Iafrate（KLI）和局域Hartree-Fock（LHF）构造相关的响应函数被纳入紧凑的辅助空间，而其系数直接从投影的OEP方程确定，而非由底层模型势固定。这在模型交换势和有限基组OEP之间建立了系统联系：模型势提供物理信息丰富的响应方向，而OEP确定其依赖于系统的振幅。该框架涵盖一维和多维响应空间，包括占据轨道和占据对表示，而不修改底层OEP条件。我们表明，这些物理适应的空间以比传统辅助展开少得多的自由度捕获OEP交换响应的主要空间结构。因此，所提出的方法为交换-only OEP势的紧凑自适应表示提供了一般途径，并为从物理动机模型响应函数发展低维OEP近似提供了系统框架。
英文摘要
The optimized effective potential (OEP) method provides an exact framework for incorporating orbital-dependent exchange within Kohn-Sham (KS) density-functional theory (DFT). Its practical implementation requires representing the exchange-response potential in a suitable auxiliary space, yet conventional choices are not necessarily adapted to the physical structure of the OEP response. Here, we introduce a general response-space strategy in which physically motivated response functions from existing model exchange potentials are repurposed as adaptive auxiliary directions for the OEP equation. Specifically, response functions associated with the Becke-Johnson (BJ), R"as"anen-Pittalis-Proetto (RPP), Gritsenko-van Leeuwen-van Lenthe-Baerends (GLLB), Krieger-Li-Iafrate (KLI), and localized Hartree-Fock (LHF) constructions are incorporated into compact auxiliary spaces, while their coefficients are determined directly from the projected OEP equation rather than fixed by the underlying model potentials. This establishes a systematic connection between model exchange potentials and finite-basis OEP: model potentials provide physically informed response directions, while OEP determines their system-dependent amplitudes. The framework encompasses one- and multidimensional response spaces, including occupied-orbital and occupied-pair representations, without modifying the underlying OEP condition. We show that these physically adapted spaces capture the dominant spatial structures of the OEP exchange response with substantially fewer degrees of freedom than conventional auxiliary expansions. The proposed approach therefore provides a general route to compact, adaptive representations of exchange-only OEP potentials and a systematic framework for developing low-dimensional OEP approximations from physically motivated model response functions.
