  State-of-the-art methods for calculating neutral excitation energies are
typically demanding and limited to single electron-hole pairs and their
composite plasmons. Here we introduce excitonic density-functional theory
(XDFT) a computationally light, generally applicable, first-principles
technique for calculating neutral excitations based on generalized constrained
DFT. In order to simulate an M-particle excited state of an N-electron system,
XDFT automatically optimizes a constraining potential to confine N-M electrons
within the ground-state Kohn-Sham valence subspace. We demonstrate the efficacy
of XDFT by calculating the lowest single-particle singlet and triplet
excitation energies of the well-known Thiel molecular test set, with results
which are in excellent agreement with time-dependent DFT. Furthermore, going
beyond the capability of adiabatic time-dependent DFT, we show that XDFT can
successfully capture double excitations. Overall our method makes optical gaps,
excition bindings and oscillator strengths readily accessible at a
computational cost comparable to that of standard DFT. As such, XDFT appears as
an ideal candidate to work within high-throughput discovery frameworks and
within linear-scaling methods for large systems.
