  The Bethe-Salpeter Equation (BSE) can be applied to compute from
first-principles optical spectra that include the effects of screened
electron-hole interactions. As input, BSE calculations require single-particle
states, quasiparticle energy levels and the screened Coulomb interaction, which
are typically obtained with many-body perturbation theory, whose cost limits
the scope of possible applications. This work tries to address this practical
limitation, instead deriving spectral energies from Koopmans-compliant
functionals and introducing a new methodology for handling the screened Coulomb
interaction. The explicit calculation of the $W$ matrix is bypassed via a
direct minimization scheme applied on top of a maximally localised Wannier
function basis. We validate and benchmark this approach by computing the
low-lying excited states of the molecules in Thiel's set, and the optical
absorption spectrum of a $\text{C}_{60}$ fullerene. The results show the same
trends as quantum chemical methods and are in excellent agreement with previous
simulations carried out at the TD-DFT or $G_{0}W_{0}$-\text{BSE} level.
Conveniently, the new framework reduces the parameter space controlling the
accuracy of the calculation, thereby simplifying the simulation of
charge-neutral excitations, offering the potential to expand the applicability
of first-principles spectroscopies to larger systems of applied interest.
