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An approximate solution scheme, similar to the Gutzwiller approximation, ispresented for the Baeriswyl and the Baeriswyl-Gutzwiller variationalwavefunctions. The phase diagram of the one-dimensional Hubbard model as afunction of interaction strength and particle density is determined. For theBaeriswyl 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 boundexcitons. This transition can be viewed as the "inverse" of the Brinkman-Ricetransition. Close to but away from half filling, the $U>U_c$ phase displays afinite Fermi step, as well as double occupations originating from boundexcitons. As the filling is changed away from half-filling bound excitons aresupressed. For the Baeriswyl-Gutzwiller wavefunction at half-filling ametal-insulator transition between the correlated metallic and excitonicinsulating state is found. Away from half-filling bound excitons are suppressedquicker than for the Baeriswyl wavefunction.

Approximate solution of variational wave functions for strongly correlated systems: Description of bound excitons in metals and insulators