  We present a systematic investigation of the special twist method introduced
by Rajagopal $\textit{et al.}$ [ Phys. Rev. B 51, 10591 (1995) ] for reducing
finite-size effects in correlated calculations of periodic extended systems
with Coulomb interactions and Fermi statistics. We propose a procedure for
finding special twist values which, at variance with previous applications of
this method, reproduce the energy of the mean-field infinite-size limit
solution within an adjustable (arbitrarily small) numerical error. This choice
of the special twist is shown to be the most accurate single-twist solution for
curing one-body finite-size effects in correlated calculations. For these
reasons we dubbed our procedure "exact special twist" (EST). EST only needs a
fully converged independent-particles or mean-field calculation within the
primitive cell and a simple fit to find the special twist along a specific
direction in the Brillouin zone. We first assess the performances of EST in a
simple correlated model such as the 3D electron gas. Afterwards, we test its
efficiency within $\textit{ab initio}$ quantum Monte Carlo simulations of
metallic elements of increasing complexity. We show that EST displays an
overall good performance in reducing finite-size errors comparable to the
widely used twist average technique but at a much lower computational cost,
since it involves the evaluation of just one wavefunction. We also demonstrate
that the EST method shows similar performances in the calculation of
correlation functions, such as the ionic forces for structural relaxation and
the pair radial distribution function in liquid hydrogen. Our conclusions point
to the usefulness of EST for correlated supercell calculations, our method will
be particularly relevant when the physical problem under consideration requires
large periodic cells.
