ABSTRACT Functional theories reformulate the many‐electron problem by expressing electronic properties as functionals of reduced quantities, providing efficient alternatives to wave function‐based correlation methods. Kohn‐Sham density functional theory (KS‐DFT) and reduced density matrix functional theory (RDMFT) exemplify this philosophy but remain limited by their single‐determinant nature and numerical complexity, respectively. This review presents hierarchically correlated orbital functional theory (HCOFT), a unified framework developed to overcome these limitations. By extending orbitals into tunable hypercomplex spaces and deriving hierarchically correlated orbitals (HCOs) with fractional occupations through Clifford algebra, HCOFT establishes the corresponding variational foundation and a continuous dimensional hierarchy that spans KS‐DFT, RDMFT, and the intermediate 1‐HCOFT—a third formal functional theory featuring paired HCOs that naturally capture strong correlation while maintaining computational stability. Further advances, including the explicit‐by‐implicit scheme for stable occupation optimization, the coupled optimization strategy for accelerated convergence through simultaneous orbital and occupation updates, and the development of short‐range screened, occupation‐dependent orbital functionals for balanced treatment of dynamical and strong correlation, further strengthen the practical applicability of HCOFT. By integrating mathematical rigor, algorithmic efficiency, and a flexible platform for functional construction, HCOFT provides a systematically improvable foundation for electronic‐structure modeling and offers a promising pathway toward a versatile and unifying paradigm for accurate first‐principles calculations. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory
Zhang et al. (Sun,) studied this question.