We show numerically that the nature of the doping-induced metal-insulator transition in the two-dimensional Hubbard model with hopping matrix element
t and Coulomb repulsion
U is radically altered by the inclusion of a term
W that depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length ${\ensuremath{\xi}}_{l}$ in the insulating state. At
W/t=0.05 and
U/t=4, we find results consistent with ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/2}$ where ${\ensuremath{\mu}}_{c}$ is the critical chemical potential. In contrast, ${\ensuremath{\xi}}_{l}\ensuremath{\sim}|\ensuremath{\mu}\ensuremath{-}{\ensuremath{\mu}}_{c}{|}^{\ensuremath{-}1/4}$ for the Hubbard model at
U/t=4. At half-filling, we calculate the density of states $N(\ensuremath{\omega})$. The large value of $N(\ensuremath{\omega})$ in the vicinity of $\ensuremath{\omega}={\ensuremath{\mu}}_{c}$ present at
W=0 is suppressed with growing values of
W. At finite doping, the
d-wave pair-field correlations are enhanced with growing values of
W. The numerical results imply that at finite values of
W doping the antiferromagnetic Mott insulator leads to a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor.