| Ground state properties of thin film electron systems with a uniform positive background are investigated using the variational Monte Carlo, and "fixed-node" diffusive Monte Carlo procedures. For the variational calculations correlated trial functions are used to model the ground state.;Calculations of the total ground state energy indicate, it is necessary to include the many-body correlations beyond the exchange interaction. This is made evident by the significantly higher energies of the Slater determinant wavefunctions compared to the energies of the correlated trial functions and "fixed-node" Monte Carlo procedure.;The density profiles from the functional density method and the "fixed-node" Monte Carlo method qualitatively are similar, however the functional density profile consistently shows greater penetration beyond the film surfaces compared to the profile from the "fixed-node" procedure. The agreement between the profiles increases with a decrease in r(,s) from 5 to 3.5. The finite size effects in the electronic density are significant, particularly for the systems with the lower values of r(,s), and larger film widths. The size effects are also reflected by the negative values of some of the surface dipole barriers.;The densities of the films studied, in terms of the Wigner parameter r(,s), are 2, 3.5, 5. For r(,s) = 5 the film widths, in units of the Wigner radius, are .86823, 4.51686, 7.58067. For r(,s) = 3.5 the film width is 6.452657 (= 4.51686 at r(,s) = 5), and for r(,s) = 2 the film width is 11.29215 (= 4.51686 at r(,s) = 5). The properties calculated are the ground state energy, surface energy, surface dipole barrier, electronic density, total radial distribution function, and the like and unlike spin radial distribution functions. To gauge the significance of correlation beyond the exchange interaction the ground state energy is calculated using a Slater determinant wavefunction, and compared with the energies from the variational and "fixed-node" Monte Carlo procedures. Additional calculations of the electronic density are performed using the functional density formalism with the local density approximation. A comparison is made with the electronic density of the "fixed-node" method to judge the suitability of the local density approximation. |
