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We use excited-state quantum chemistry techniques to investigate theintraband absorption of doped semiconductor nanoparticles as a function ofdoping density, nanoparticle radius, and material properties. The excesselectrons are modeled as interacting particles confined in a sphere. We comparethe predictions of various single-excitation theories, including time-dependentHartree-Fock, the random-phase approximation, and configuration interactionwith single excitations. We find that time-dependent Hartree-Fock mostaccurately describes the character of the excitation, as compared toequation-of-motion coupled-cluster theory with single and double excitations.The excitation evolves from confinement-dominated, to excitonic, to plasmonicwith increasing number of electrons at fixed density, and the threshold numberof electrons to produce a plasmon increases with density due to quantumconfinement. Exchange integrals (attractive electron-hole interactions) areessential to properly describe excitons, and de-excitations (i.e.~avoidance ofthe Tamm-Dancoff approximation) are essential to properly describe plasmons. Wepropose a schematic model whose analytic solutions closely reproduce ournumerical calculations. Our results are in good agreement with experimentalspectra of doped ZnO nanoparticles at a doping density of $1.4\times 10^{20}$cm$^{-3}$.

Quantum plasmons and intraband excitons in doped nanoparticles: Failure of the Tamm-Dancoff approximation and importance of electron-hole attraction