Bridges from Wavefunction Theory to Density Functional Theory

Density functional theory (DFT) is widely used to describe electronic structure in chemistry, physics, and materials science. Its accuracy is constrained by the exchange-correlation (XC) functional, which remains an approximation in all practical implementations. In contrast, wavefunction theory (WFT) offers a systematically improvable description of electron correlation, albeit at a higher computational cost. The complementary strengths of DFT and WFT have motivated efforts to connect the two. Historically, such connections have centered on total energies and electron densities, but recent advances have expanded these bridges to include XC potentials and energy densities. This review highlights strategies for translating quantities from WFT to DFT, with a focus on extracting XC potentials and energy densities from wavefunctions. Challenges in using finite basis sets, and potential solutions to this problem, are highlighted. These approaches offer insights into the structure of the exact XC functional and practical tools for developing next-generation approximations with improved accuracy and generalizability.