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

Yichen Fan; Weitao Yang

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

Yichen Fan, Weitao Yang

Abstract

The $Δ$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 $Δ$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.

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

Abstract

The

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

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

cost, avoids separate SCF calculations for each excited state, and enables efficient large-scale excited-state simulations from ground-state calculations.

Paper Structure (15 equations, 2 figures)

This paper contains 15 equations, 2 figures.

Figures (2)

Figure 1: Occupancy extrapolation (OE@BLYP) energy surface for ethylene ($\rm{C_2H_4}$) as a function of fractional occupations of the HOMO and LUMO, computed with the BLYP functionalbeckeDensityfunctionalExchangeenergyApproximation1988leeDevelopmentColleSalvettiCorrelationenergy1988. Points A–D denote key electronic states: A, neutral ground state (0 eV); B, N+1 ground state (-EA = 2.14 eV); C, neutral triplet excited state $^{3}\mathrm{B}_{1u}$ (4.57 eV); D, N-1 ground state (IP = 10.44 eV). The color map represents total energy (yellow: higher, blue: lower). Convex energy behavior along A-B, A-D, C-B, and C-D reflects ground- and excited-state delocalization error of BLYP; they should be all straight lines for the exact functional perdewDensityFunctionalTheoryFractional1982ayangFractionalChargesLinear2024b The A-C convexity is physical and reflects particle-hole interaction.
Figure 2: Comparison of excitation energies obtained from OE@BLYP (blue markers) and $\Delta$ BLYP (yellow markers) with theoretical best estimates (TBE). The dashed line indicates perfect agreement with the reference values. OE closely reproduces $\Delta\mathrm{SCF}$ excitation energies across different excitation types, yielding comparable mean absolute errors (MAEs) for both singlet (S) and triplet (T) states.