Excitation energies along a range-separated adiabatic connection

Abstract

We present a study of the variation of total energies and excitationenergies along a range-separated adiabatic connection. This connectionlinks the non-interacting Kohn-Sham electronic system to the physicalinteracting system by progressively switching on theelectron-electron interactions whilst simultaneously adjusting aone-electron effective potential so as to keep the ground-statedensity constant. The interactions are introduced in arange-dependent manner, first introducing predominantly long-range,and then all-range, interactions as the physical system is approached,as opposed to the conventional adiabatic connection where theinteractions are introduced by globally scaling the standard Coulomb interaction.Reference data are reported for the He and Be atoms and the H2molecule, obtained by calculating the short-range effective potentialat the full configuration-interaction level using Lieb'sLegendre-transform approach. As the strength of the electron-electroninteractions increases, the excitation energies, calculated for thepartially interacting systems along the adiabatic connection, offerincreasingly accurate approximations to the exact excitation energies.Importantly, the excitation energies calculated at an intermediatepoint of the adiabatic connection are much better approximations tothe exact excitation energies than are the corresponding Kohn-Shamexcitation energies. This is particularly evident in situationsinvolving strong static correlation effects and states with multipleexcitation character, such as the dissociating H2 molecule. Theseresults highlight the utility of long-range interacting referencesystems as a starting point for the calculation of excitation energiesand are of interest for developing and analyzing practical approximaterange-separated density-functional methodologies.

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Cited by in corpus (8)

• Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states
• Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel
• Models and corrections: range separation for electronic interaction -- lessons from density functional theory
• Excitation energies along a range-separated adiabatic connection
• Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory
• Calculating excitation energies by extrapolation along adiabatic connections
• Coulomb effects on the photo-excited quantum dynamics of electrons in a plasmonic nanosphere
• Excitation energies from G{ö}rling-Levy perturbation theory along the range-separated adiabatic connection