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We present a first-principles study of the energy and elastic properties of solid helium at pressures below the range in which it is energetically stable. We find that the limit of mechanical stability in hcp \(^{4}\)He is \(P_{s} = -33.8(1)\) bar, which lies significantly below the spinodal pressure found in the liquid phase (i.e., \(-9.6\) bar). Furthermore, we show that the pressure variation of the transverse and longitudinal sound velocities close to \(P_{s}\) does not follow a power law of the form \(\propto \left( P - P_{s} \right) ^{\gamma }\), in contrast to what is observed in the fluid.

The behavior of pairs and clusters of vacancies in solid 4He crystals is studied with diffusion Monte Carlo method. We use a trial function suitable for describing solid 4He with long range order, arbitrary number of unoccupied sites and explicit Bose symmetry. It is found that vacancy clusters are unstable and collapse in all considered systems. We find no signature of stability of bound vacancy clusters of any size. Vacancies are found to exhibit weak attraction and a rough estimation of the binding energy is reported.

The ground state of the ionic solids LiD and LiH is theoretically studied using the Variational Monte Carlo (VMC) method. Our main focus has been the calculation of relevant properties of the H− and D− ions using a fully quantum approach. In particular, we report results on their kinetic energies, mean-squared displacements, Einstein frequencies, radial distribution functions, and density profiles around the sites. The microscopic results obtained for both isotopes show corrections beyond trivial isotopic effects due to their quantum behavior. Finally, the VMC results are compared with predictions from self consistent average phonon (SCAP) theory at T = 0 K.

A quantum Monte Carlo study at zero temperature of twodimensional H2 on top of a solid Rb surface is presented. The lattice constituted by the alkali atoms frustrates the formation of solid H2, which is the natural phase of pure two-dimensional H2. Therefore, H2 with the Rb atoms acting like fixed impurities remains in a liquid phase even at zero temperature. We present resugts for the H2 equation of state, structural properties, superfluid density and condensate fraction for a fixed Rb lattice.