Bead-Fourier path integral Monte Carlo method applied to systems of identical particles Original Research Article

To make the PIMC method more effective a combined, bead-Fourier (BF), PIMC simulation scheme was introduced with its extreme cases corresponding to the ordinary “bead” and Fourier PIMC methods. Optimal choice of the number of beads and of Fourier harmonics made it possible to reproduce well the ground state energy and electron density in the H-atom. While applying the BF method to systems of identical particles a procedure of simultaneous account for all classes of permutations suggested earlier was used with subsequent symmetrization of the exchange factor in the weight function. A procedure of random walk in the spin space allows to calculate also spin dependent averages. The exact expressions obtained for the partition function and canonical averages of a D-dimensional system of N noninteracting identical particles in a harmonic field gave a reliable test of the developed MC procedures performed for N=2,3,5 in a wide temperature range. We compared the analytically available exact result for the average of sign, 〈Sgn〉, dependence versus temperature with that from our simulations and introduced the modification of the weight function (a kind of “umbrella sampling”) to increase 〈Sgn〉 and stabilize the results at low temperatures. Few electron systems (i.e. H2-molecule, Li-atom, CH4-molecule) were simulated with the aid of the suggested BF-PIMC method.