  We report a study of the electronic dissociation energy of the water dimer
using quantum Monte Carlo (QMC) techniques. We have performed variational
quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) calculations
of the electronic ground state of the water monomer and dimer using
all-electron and pseudopotential approaches. We have used Slater-Jastrow trial
wave functions with B3LYP-like single-particle orbitals, into which we have
incorporated backflow correlations. When backflow correlations are introduced,
the total energy of the water monomer decreases by about 4-5 mHa, yielding a
DMC energy of -76.42830(5) Ha, which is only 10 mHa above the experimental
value. In our pseudopotential DMC calculations, we have compared the total
energies of the water monomer and dimer obtained using the locality
approximation with those from the variational scheme recently proposed by
Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula
scheme are larger and the extrapolation of the energy to zero time step always
lies above the result obtained with the locality approximation. However, the
errors cancel when energy differences are taken, yielding electronic
dissociation energies within error bars of each other. The dissociation
energies obtained in our various all-electron and pseudopotential calculations
range between 5.03(7) and 5.47(9) kcal/mol and are in good agreement with
experiment. Our calculations give monomer dipole moments which range between
1.897(2) and 1.909(4) Debye and dimer dipole moments which range between
2.628(6) and 2.672(5) Debye.
