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Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.

The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work, we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies, and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the statistical uncertainty of the vibrational parameters by 1 order of magnitude. Preliminary results based on variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters and harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties).

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. Our 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) [Casula et al. J. Chem. Phys. 2003, 119, 6500-6511]. With this variational wave function we obtain a binding energy of -4.5(0.1) kcal/mol that is only slightly increased to -4.9(0.1) kcal/mol by using the Lattice Regularized Diffusion Monte Carlo (LRDMC). This projection technique allows for the substantial improvement in the correlation energy of a given variational guess and indeed, when applied to the JAGP, yields a binding energy in fair agreement with the value of -5.0 kcal/mol reported by experiments and other theoretical works. The minimum position, the curvature, and the asymptotic behavior of the dispersion curve are well reproduced both at the variational and the LRDMC level. Moreover, 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. This is achieved by appropriately switching off determinantal and Jastrow variational terms in the JAGP. Within this scheme, we estimate that the dispersive van der Waals contribution to the electron correlation is substantial and amounts to 1.5(0.2) kcal/mol, this value being comparable with the intermolecular covalent energy that we find to be 1.1(0.2) kcal/mol. The present Quantum Monte Carlo approach based on the JAGP wave function is revealed 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.