Adaptive Expansions of the Optimized Effective Potential in Physically Motivated Response Spaces

Abstract

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.