A theoretical study of 1-D and 2-D helium lattices

One- and two-dimensional (1-D and 2-D) helium lattices have been studied using ab initio RHF/6-31G** computations. Structural, physical and thermochemical properties have been calculated and analyzed for the 1-D and 2-D He-N lattices respectively up to N = 50 and N = 36. Asymptotic properties of the 1-D He-N lattices are obtained by extrapolating N-dependence properties to large values of N. Analysis of the results show that the bulk per-atom interaction (binding) energies increase while the optimized inter-atomic distances (bond lengths) slightly decrease with the increase in size of the 1-D HeN lattices and both reach their asymptotic values of 0.352 cm(-1) and 3.18775 angstrom, respectively. Between the square and hexagonal (packed) structures of the 2-D He-N, lattices, the latter is more favored. Extrapolated values of the calculated properties, including lattice parameter, binding and zero point energies, heat capacity, and entropy have also been calculated for both 1-D and 2-D HeN lattices. The surface densities for monolayer films of helium atoms with square and hexagonal configurations have been calculated to be respectively 9.84 x 10(18) and 1.04 x 10(19) helium atoms/cm(2) which are comparable to the experimental value of 2.4 x 10(19) helium atom/m(2) well within the typical large and directional error bars of the experiments. Surface effects have been investigated by comparing the packed HeN 2-D lattices with the same value of N but with different geometries (arrangements). This comparison showed that the HeN lattices prefer arrangements with the smallest surface area.