Occupancy Extrapolation: Reaching Many Excited Electronic States from Ground State Calculations

The $\Delta$SCF DFT approach defines the system energy as a function of orbital occupancy. Inspired by Landau Fermi liquid theory, we develop an occupancy extrapolation (OE) method that captures excited-state energies via a Taylor expansion of the energy with respect to occupation fluctuation from a reference state. OE retains the physics of $\Delta$SCF while offering a physical interpretation of excitation energies as sums of quasiparticle energies and their generalized screened interactions. It yields accurate valence, Rydberg, and charge-transfer excitation energies at $O(N^3)$ cost, avoids separate SCF calculations for each excited state, and enables efficient large-scale excited-state simulations from ground-state calculations.