Extrapolation of small-cluster exact-diagonalization calculations is used t
o study the ground state phase diagram of the spinless one-dimensional Fali
cov-Kimball model at half filling. Our results show that the phase diagram
has an extremely simple structure for the Coulomb interactions U greater th
an or equal to 2. Here the ground states are the most homogeneous configura
tions (mhc) with the smallest periods. Valence transitions are discontinuou
s and only of the type insulator-insulator. In this region the finite size
effects are negligible and thus the picture of valence transitions is defin
itive. For U < 2 the phase diagram exhibits a more complicated structure. H
ere we have specified a domain where the ground states are the mhc and a me
tallic domain where the ground states are mixtures of configurations with t
he empty configuration. The boundary between these two domains is the bound
ary of discontinuous insulator-metal transitions. Unlike the case U greater
than or equal to 2 the valence transitions are gradual in the weak couplin
g limit.