State-specific density functionals for excited states from ensembles

Abstract

We present a first principles strategy for developing state-specific density functional approximations for excited states. We first clarify why approaches based on conventional ground state approximations miss density-driven correlations, by considering excited state physics through the lens of ensemble density functional theory. To solve this issue we gain insights on density driven correlations by exploiting the recently understood low-density limit of electrons in excited states. The theory developments are then combined to produce a proof-of-concept excited state approximation that resolves urgent paradigmatic failures (double excitations, charge transfer excitations, piecewise linearity) of existing state-of-art density-functional approaches, directly from differences of self-consistent field calculations; i.e., $\Delta$SCF. In light of its observed impressive performance, we conclude that the approach represents a major step toward unified and accurate modelling of neutral and charged excitations.

References in corpus (22)

• Recent developments in the PySCF program package
• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• Koopmans' condition for density-functional theory
• Perspectives on double-excitations in TDDFT
• Orbital Optimized Density Functional Theory for Electronic Excited States
• Benchmarking TD-DFT and Wave Function Methods for Oscillator Strengths and Excited-State Dipole Moments
• Reference Energies for Double Excitations
• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Charge-Transfer in Time-Dependent Density Functional Theory
• Band gaps of crystalline solids from Wannier-localization based optimal tuning of a screened range-separated hybrid functional
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Direct extraction of excitation energies from ensemble density-functional theory
• Excitations and benchmark ensemble density functional theory for two electrons
• Koopmans-compliant spectral functionals for extended systems
• Individual correlations in ensemble density-functional theory: State-driven/density-driven decompositions without additional Kohn-Sham systems
• Density-driven correlations in many-electron ensembles: theory and application for excited states
• The flexible nature of exchange, correlation and Hartree physics: resolving "delocalization" errors in a 'correlation free' density functional
• Electronic excited states in extreme limits via ensemble density functionals
• Ensemble density functional theory of ground and excited energy levels
• Stationary conditions for excited states: the surprising impact of density-driven correlations

Cited by in corpus (2)

• Freeze-and-release direct optimization method for variational calculations of excited electronic states
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities