  An approximate solution scheme, similar to the Gutzwiller approximation, is
presented for the Baeriswyl and the Baeriswyl-Gutzwiller variational
wavefunctions. The phase diagram of the one-dimensional Hubbard model as a
function of interaction strength and particle density is determined. For the
Baeriswyl wavefunction a metal-insulator transition is found at half-filling,
where the metallic phase ($U<U_c$) corresponds to the Hartree-Fock solution,
the insulating phase is one with finite double occupations arising from bound
excitons. This transition can be viewed as the "inverse" of the Brinkman-Rice
transition. Close to but away from half filling, the $U>U_c$ phase displays a
finite Fermi step, as well as double occupations originating from bound
excitons. As the filling is changed away from half-filling bound excitons are
supressed. For the Baeriswyl-Gutzwiller wavefunction at half-filling a
metal-insulator transition between the correlated metallic and excitonic
insulating state is found. Away from half-filling bound excitons are suppressed
quicker than for the Baeriswyl wavefunction.
