  The Hubbard Hamiltonian is investigated by means of a variational trial wave
function of Gutzwiller's type. The wave function includes nearest - neighbor
correlations in an explicit form. To calculate density matrices the method of
Kikuchi's pseudoensemble is used. The case of half-filled fermionic band
carefully investigated in the limit of a large number of lattice sites. The
ground state energy and correlation functions are determined for lattices with
z=2,4 and 6 nearest neighbors.
