  We propose a simple and efficient real-space approach for the calculation of
the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be
precise, we calculate the first two terms in the asymptotic expansion of the
total energy per electron which correspond to the classical and zero-point
energies of the Wigner crystals. Our approach employs Clifford periodic
boundary conditions to simulate the infinite electron gas and a renormalized
distance to evaluate the Coulomb potential. This allows us to calculate the
energies unambiguously and with a higher precision than those reported in the
literature. Our results are in agreement with the literature values with the
exception of the zero-point energy of the 2-dimensional Wigner crystal for
which we find a significant difference. Although we focus on the ground state,
i.e., the triangular lattice and the body-centered cubic lattice, in two and
three dimensions, respectively, we also report the classical energies of
several other common lattice structures.
