  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 the statistical uncertainty of the vibrational parameters by one
order of magnitude. Preliminary results based on Variational Monte Carlo
calculations on the water molecule demonstrate the possibility to evaluate
geometrical parameters, 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).
