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The ground state for the half-filled $t-t'$ Hubbard model is treated withinthe Hartree-Fock approximation and the slave boson approach includingcorrelations. The criterium for the metal-insulator transition in the Slaterscenario is formulated using an analytical free-energy expansion in thenext-nearest-neighbor transfer integral $t'$ and in direct antiferromagneticgap $\Delta$. The correlation effects are generally demonstrated to favor thefirst-order transition. For a square lattice with a strong van Hovesingularity, accidental close degeneracy of antiferromagnetic and paramagneticphases is analytically found in a wide parameter region. As a result, thereexists an interval of $t'$ values for which the metal-insulator transition isof the first order due to the existence of the van Hove singularity. Thisinterval is very sensitive to model parameters (direct exchange integral) orexternal parameters. For the simple and body-centered cubic lattices, thetransition from the insulator antiferromagnetic state with increasing $t'$occurs to the phase of an antiferromagnetic metal and is a second-ordertransition which is followed by a transition to a paramagnetic metal. Theseresults are quantitatively modified when taking into account the intersiteHeisenberg interaction, which can induce first-order transitions. A comparisonwith the Monte Carlo results is performed.

Metal-insulator transition and antiferromagnetism in the generalized Hubbard model: Treatment of correlation effects