Reduced Density Matrix Functional Theory Across Molecules and Periodic Systems: Screening and Coupled Optimization

Abstract

Reduced density matrix functional theory (RDMFT) provides a rigorous framework for treating strong electron correlation, yet its application to periodic systems has long been hindered by two fundamental challenges: the lack of transferable approximate functionals and the poor efficiency of orbital-occupation optimization. Here we show that these two longstanding obstacles can be overcome simultaneously. We develop a periodic implementation of RDMFT based on a coupled optimization framework that enables the efficient simultaneous optimization of natural orbitals and occupation numbers under periodic boundary conditions. Using this implementation, we demonstrate that physically motivated short-range screening transforms the Power functional into a transferable functional applicable to both molecules and periodic solids. Remarkably, short-range screening is found to play a dual role: besides substantially improving energetic accuracy, it fundamentally reshapes the optimization landscape, producing robust optimization step sizes and dramatically accelerating convergence. The coupled optimization framework consistently requires substantially fewer optimization iterations than conventional decoupled optimization for periodic calculations, while the screened $\omega$P22 functional outperforms semilocal and hybrid density functionals in predicting representative surface reaction barriers. These results establish a computationally efficient periodic RDMFT framework and identify short-range screening as a promising design principle for developing transferable one-body reduced-density-matrix functionals.