  We report a quantum Monte Carlo (QMC) study, on a very simple but
nevertheless very instructive model system of four hydrogen atoms, recently
proposed in Ref. 1. We find that the Jastrow correlated Antisymmetrized Geminal
Power (JAGP) is able to recover most of the correlation energy even when the
geometry is symmetric and the hydrogens lie on the edges of a perfect square.
Under such conditions the diradical character of the molecule ground state
prevents a single determinant ansatz to achieve an acceptable accuracy, whereas
the JAGP performs very well for all geometries. Remarkably, this is obtained
with a similar computational effort. Moreover we find that the Jastrow Factor
is fundamental in promoting the correct resonances among several configurations
in the JAGP, that cannot show up in the pure Antisymmetrized Geminal Power
(AGP). We also show the extremely fast convergence of this approach in the
extension of the basis set. Remarkably only the simultaneous optimization of
the Jastrow and the AGP part of our variational ansatz is able to recover an
almost perfect nodal surface, yielding therefore state of the art energies,
almost converged in the complete basis set limit (CBS), when the so called
Diffusion Monte Carlo is applied.
