Methods based on the second order Møller–Plesset perturbation theory (MP2) and the Random Phase Approximation (RPA) have emerged as practicable and reliable approaches to improve the accuracy of density functional approximations for first principle atomistic simulations. Such approaches are in fact capable to account ab-initio for non-local dynamical electron correlation effects, which play a fundamental role, for example, in the description of non-bonded interactions. To assess the performance of MP2 and RPA for real applications, isobaric-isothermal Monte Carlo simulations have been performed to study the structural properties of bulk liquid water under ambient conditions. The choice of bulk liquid water as benchmark system is motivated by the complicated nature of the intermolecular interactions, where repulsion, polarization, hydrogen bonding and van der Waals forces play an important role and are particularly difficult to reproduce accurately in atomistic models. The results demonstrate the feasibility of such approaches which open the way for further applications.