Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states

Abstract

Gross-Oliveira-Kohn density functional theory (GOK-DFT) for ensembles is in principle very attractive, but has been hard to use in practice. A novel, practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The new model relies on two modifications of GOK-DFT: use of range separation and use of the slope of the linearly-interpolated ensemble energy, rather than orbital energies. The range-separated approach is appealing as it enables the rigorous formulation of a multi-determinant state-averaged DFT method. In the exact theory, the short-range density functional, that complements the long-range wavefunction-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) can be rationalized and that it effectively introduces weight dependence effects. As proof of principle, LIM has been applied to He, Be, H${}_2$ in both equilibrium and stretched geometries as well as the stretched HeH${}^{+}$ molecule. Very promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semi-local functionals. Even at the Kohn--Sham ensemble DFT level, that is recovered when the range-separation parameter is set to zero, LIM performs better than standard time-dependent DFT.

26 pages, 8 figures

References in corpus (11)

• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• Long-range-corrected hybrids including RPA correlation
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Density Matrix Renormalization Group with Efficient Dynamical Electron Correlation Through Range Separation
• Multi-configuration time-dependent density-functional theory based on range separation
• Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation
• Basis convergence of range-separated density-functional theory
• Excitation energies along a range-separated adiabatic connection
• Calculating excitation energies by extrapolation along adiabatic connections

Cited by in corpus (17)

• Reference Energies for Double Excitations
• Direct extraction of excitation energies from ensemble density-functional theory
• Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy
• Individual correlations in ensemble density-functional theory: State-driven/density-driven decompositions without additional Kohn-Sham systems
• Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• A weight-dependent local correlation density-functional approximation for ensembles
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Dynamical Kernels for Optical Excitations
• Ghost interaction correction in ensemble density-functional theory for excited states with and without range separation
• Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Excitation energies from G{ö}rling-Levy perturbation theory along the range-separated adiabatic connection
• Exact static linear response of excited states from ensemble density functional theory
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities