Calculation of bridge function coefficients via modified Mayer-samplings

Two modified Mayer-sampling methods are described based on Transition Matrix Monte Carlo (TMMC) and overlap sampling for calculating the integrated diagrams appearing in the coefficients of the bridge function; bn(r) constructed in terms of the total correlation function h(r) for a hard-sphere system. Calculations are performed using prescribed h(r) for reduced densities at 0.2, 0.5 and 0.8 up to the third-order expansion in density. The results from these methods compared with the generic Monte Carlo Mayer-sampling are analysed in detail. It was found that the TMMC Mayer-sampling approach shows better precision over core and tail regions of b2(r) and b3(r), and the overlap sampling method shows overall improvement in the precision of the bridge coefficients. Both methods can be straightforwardly applied to calculate higher order bridge function coefficients and to any model systems with relatively simple modifications.