List of Tables

1. Total energies in variational ($E_{VMC}$ ) and diffusion ($E_{DMC}$ ) Monte Carlo calculations; the percentages of correlation energy recovered in VMC ( $E^{VMC}_c(\%)$ ) and DMC ( $E^{DMC}_c(\%)$ ) have been evaluated using the ``exact'' ($E_0$ ) and Hartree-Fock ($E_{HF}$ ) energies from the references (1). Here ``exact'' means the ground state energy of the non relativistic infinite nuclear mass Hamiltonian. The energies are in Hartree.
2. Bond lengths ($R$ ) in atomic units; the subscript 0 refers to the ``exact'' results. For the water molecule $R$ is the distance between O and H and $\theta$ is the angle HOH (in deg), for $CH_4$ $R$ is the distance between C and H and $\theta$ is the HCH angle.
3. Binding energies in $eV$ obtained by variational ( $\Delta _{VMC}$ ) and diffusion ( $\Delta _{DMC}$ ) Monte Carlo calculations; $\Delta _0$ is the ``exact'' result for the non-relativistic infinite nuclear mass Hamiltonian. Also the percentages ( $\Delta _{VMC}(\%)$ and $\Delta _{DMC}(\%)$ ) of the total binding energies are reported.
4. Binding energies in $eV$ obtained by variational ( $\Delta _{VMC}$ ) and diffusion ( $\Delta _{DMC}$ ) Monte Carlo calculations with different trial wave functions for benzene. In order to calculate the binding energies yielded by the 2-body Jastrow we used the atomic energies reported in Ref. (2). The percentages ( $\Delta _{VMC}(\%)$ and $\Delta _{DMC}(\%)$ ) of the total binding energies are also reported.
5. Bond lengths ($r$ ) for the two lowest $^2 B_{2g}$ and $^2 B_{3g}$ states of the benzene radical cation. The angles $\alpha$ are expressed in degrees, the lengths in $a_0$ . The carbon sites are numerated from 1 to 6.
6. Total energies for the $^2 B_{2g}$ and $^2 B_{3g}$ states of the benzene radical cation after the geometry relaxation. A comparison with a BLYP/6-31G* and SVWN/6-31G* all-electron calculation (Ref. (3)) is reported.
7. Adiabatic ionization potential of the benzene molecule; our estimate is done for the $^2 B_{3g}$ relaxed geometries of the benzene radical cation, with an inclusion of the zero point motion correction between the $^2 B_{3g}$ state and the $^1 A_{1g}$ neutral molecule ground state, calculated in Ref. (4) at the B3LYP/6-31G* level.
8. Total energies in variational ($E_{VMC}$ ) and diffusion ($E_{DMC}$ ) Monte Carlo calculations for 16 hydrogen atoms in a BCC lattice at Rs=1.31 and T=0 (i.e. frozen ion positions). The energies are in Hartree for atom.
9. Pressure at different temperatures and densities. We report also the pressure obtained with Gasgun experiment (5), with Silvera-Goldman empirical potential model (6) and CEICM method (7) at $\Gamma$ point. The pressure are in GPa.