Table 2.

HSMC results for 125 argon molecules^a

$\stackrel{‒}{M_{\text{tot}}}$	− FA	σ A	− FB	$-F_{\mathrm{G}}^{\mathrm{B}}$	− FM	$-F_{\mathrm{G}}^{\mathrm{M}}$	− FD	n
1,000,000	4.139 (1)	0.0246 (5)	4.08 (2)	4.045 (4)	4.11 (2)	4.092 (2)	4.10 (1)	362
2,000,000	4.124 (1)	0.0175 (6)	4.06 (2)	4.077 (4)	4.09 (2)	4.100 (2)	4.09 (1)	179
4,000,000	4.116 (1)	0.0110 (9)	4.10 (1)	4.097 (3)	4.11 (1)	4.107 (2)	4.108(7)	125
10,000,000	4.1124 (6)	0.0083 (5)	4.10 (1)	4.102 (1)	4.10 (1)	4.1070 (9)	4.105 (6)	170
20,000,000	4.1102 (6)	0.0060 (5)	4.10 (1)	4.105 (1)	4.11 (1)	4.1074 (8)	4.107 (4)	99
TI	4.108 (1)		4.108 (1)	4.108 (1)	4.108 (1)	4.108 (1)	4.108 (1)

^aFree energy values are given as A_c/εN where A_c is the configurational freeenergy (equation (40)), ε is the standard Lennard-Jones energy parameter (see text) and N is the number of atoms F^A (equation (21)) is a lower bound of the free energy and σ_A (equation (23)) is its fluctuation. F^B (equations (25) and (26)) is an upper bound and $F_{\mathrm{G}}^{\mathrm{B}}$ (equation (30)) is its corresponding Gaussian approximation. F^M (equation (27)) and $F_{\mathrm{G}}^{\mathrm{M}}$ (equation (31)) are the averages of F^A with F^B and $F_{\mathrm{G}}^{\mathrm{B}}$, respectively. F^D (equation (33)) is the direct estimate for the free energy. ${\stackrel{‒}{M}}_{\text{to}\text{t}}$ is the average number of MC steps per cell, and n is the number of configurations analyzed (the sample size), where a single HSMC reconstruction was performed on each configuration. Results obtained by thermodynamic integration are denoted as TI. The statistical error appears in parenthesis; for example, 4.108(1) = 4.108±0.001.