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