Two-dimensional molecular para-hydrogen and ortho-deuterium at zero temperature

We study molecular para-hydrogen (p-H(2)) and ortho-deuterium (o-D(2)) in two dimensions and in the limit of zero temperature by means of the diffusion Monte Carlo method. We report energetic and structural properties of both systems such as the total and kinetic energy per particle, radial pair distribution function, and Lindemann's ratio in the low-pressure regime. By comparing the total energy per particle as a function of the density in liquid and solid p-H(2), we show that molecular para-hydrogen, and also ortho-deuterium, remains solid at zero temperature. Interestingly, we assess the quality of three different symmetrized trial wave functions, based on the Nosanow-Jastrow model, in the p-H(2) solid film at the variational level. In particular, we analyze one type of symmetrized trial wave function which has been used very recently to describe solid (4)He and found that it also characterizes hydrogen satisfactorily. Using this trial wave function, we estimate the one-body density matrix rho(1)(r) of solid p-H(2) at several densities close to equilibrium and find off-diagonal long-range order with a condensate fraction n(0) that increases sizably in the regime of negative pressures. The extrapolated estimation of n(0) is observed to depend on the form of the symmetrized trial wave function used for importance sampling however the corresponding order of magnitude remains the same in all the cases. We have also computed the superfluid fraction rho(s)/rho of two-dimensional solid p-H(2) at zero temperature in an unbiased way and found that it is nonzero at negative pressures.