  The basis-set correction method based on density-functional theory consists
in correcting the energy calculated by a wave-function method with a given
basis set by a density functional. This basis-set correction density functional
incorporates the short-range electron correlation effects missing in the basis
set. This results in accelerated basis convergences of ground-state energies to
the complete-basis-set limit. In this work, we extend the basis-set correction
method to a linear-response formalism for calculating excited-state energies.
We give the general linear-response equations, as well as the more specific
equations for configuration-interaction wave functions. As a proof of concept,
we apply this approach to the calculations of excited-state energies in a
one-dimensional two-electron model system with harmonic potential and a
Dirac-delta electron-electron interaction. The results obtained with
full-configuration-interaction wave functions expanded in a basis of Hermite
functions and a local-density-approximation basis-set correction functional
show that the present approach does not help in accelerating the basis
convergence of excitation energies. However, we show that it significantly
accelerates basis convergences of excited-state total energies.
