  The Hartree-Fock (HF) approximation with the charge-density-wave (CDW)
instability is used to study the ground-state phase diagram of the spinless
Falicov-Kimball model (FKM) extended by $f$-$f$ hopping in two and three
dimensions. It is shown that the HF solutions with the CDW instability
reproduce perfectly the two-dimensional intermediate coupling phase diagram of
the FKM model with $f$-$f$ hopping calculated recently by constrained path
Monte Carlo (CPMC) method. Using this fact we have extended our HF study on
cases that have been not described by CPMC, and namely, (i) the case of small
values of $f$-electron hopping integrals, (ii) the case of weak Coulomb
interactions and (iii) the three-dimensional case. We have found that
ferroelectricity remains robust with respect to the reducing strength of
coupling ($f$-electron hopping) as well as with respect to the increasing
dimension of the system.
