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Small-wavevector excitations in Coulomb-interacting systems can be decomposedinto the high-energy collective longitudinal plasmon and the low-energysingle-electron excitations. At the critical wavevector and correspondingfrequency where the plasmon branch merges with the single-electron excitationregion, the collective energy of the plasmon dissipates into singleelectron-hole excitations. The jellium model provides a reasonable descriptionof the electron-energy-loss spectrum (EELS) of metals close to thefree-electron limit. The random phase approximation (RPA) is exact in thehigh-density limit but can capture the plasmonic dispersion reasonably even fordensities with rs > 1. RPA and all beyond-RPA methods investigated here, resultin a wrong infinite plasmon lifetime for a wavevector smaller than the criticalone where the plasmon dispersion curve runs into particle-hole excitations.Exchange-correlation kernel corrections to RPA modify the plasmon dispersioncurve. There is however a large difference in the construction and form of thekernels investigated earlier. Our current work introduces recent modelexchange-only and exchange-correlation kernels and discusses the relevance ofsome exact constraints in the construction of the kernel. We show that, becausethe plasmon dispersion samples a range of wavevectors smaller than the rangesampled by the correlation energy, different kernels can make a strongdifference for the correlation energy and a weak difference for the plasmondispersion. This work completes our understanding about the plasmon dispersionin realistic metals, such as Cs, where a negative plasmon dispersion has beenobserved. We find only positive plasmon dispersion in jellium at the densityfor Cs.

physical review. b./physical review. b

Understanding plasmon dispersion in nearly-free-electron metals: the  relevance of exact constraints for novel exchange-correlation kernels within  time-dependent density functional theory