We present a Quantum Monte Carlo study of the dissociation
energy and the dispersion curve of the water dimer, a prototype
of hydrogen bonded system. These calculations are based on
a wave function which is a modern and fully correlated 
implementation of the Pauling's valence bond idea: the 
Jastrow Antisymmetrised Geminal Power (JAGP). With this 
variational wave function we obtain a binding energy of 
-4.5(0.1), that is only slightly increased to -4.9(0.1) kcal/mol 
by using the Lattice Regularized Diffusion Monte Carlo (LRDMC). 
These value are in fair agreement with the value of -5.0 kcal/mol 
reported by experiments and other theoretical works.
Thanks to the simplicity and the accuracy of our variational 
approach, we are able to dissect the various contributions to 
the binding energy of the water dimer in a systematic and 
controlled way: in particular we estimated the van der Waals 
contribution, ~1.5(0.2) kcal/mol, and the intermolecular “covalent” 
contribution, ~1.1(0.2) kcal/mol, to the hydrogen bond.
The present Quantum Monte Carlo approach based on the JAGP 
wavefunction reveals as a promising tool for the interpretation 
and the quantitative description of weakly interacting systems, 
where both dispersive and covalent energy contributions play an 
important role.