In the first part of this thesis we study correlation and atomization energies, accompanied with the determination of the ground state optimal structure for a restricted ensemble of molecules. For each of them we performed a full all-electron SR geometry optimization, starting from the experimental molecular structure. After the energy minimization, we carried out all-electron VMC and DMC simulations at the optimal geometry within the so-called ''fixed node approximation''. The basis that we used was composed by exponential and Gaussian orbitals for both the three-body and the pairing determinant, in this way both the antisymmetric and the bosonic part are well described. However, both in the AGP and in the Jastrow part we never used a large basis set, in order to keep the wave function as simple as possible. The accuracy of our wave function can be obviously improved by an extension of the one particle basis set. Nevertheless, for most of the molecules studied with a simple JAGP wave function, a DMC calculation is able to reach the chemical accuracy in the binding energies and the SR optimization yields very precise geometries already at the VMC level.
In the first part of this section some results will be presented for a small
set of widely studied molecules and belonging to the G1 database.
In the second subsection we will treat the benzene and its radical cation 
, by taking into account its distortion due to the Jahn-Teller
effect, that is well reproduced by our SR geometry optimization.