Monte Carlo data energy

Bennett C H 1976 Efficient estimation of free energy differences from Monte Carlo data J. Comput. Phys. 22 245-68... 

FiG. 10 Normalized density profiles p z)/for the associating fluid at a hard wall. The association energy is jk T — 7 and the bulk density is p = 0.2098 (a), e ykgT = 5 and the bulk density equals 0.9038 (b). The solid and dashed lines denote the results of the modified Meister-Kroll theory and the theory of Segura et al., respectively. The Monte Carlo data in (a) are marked as points. (From Ref. 145.)... 

The correlation energy is known analytically in the high-and low-density limits. For typical valence electron densities (1 < r, < 10) and lower densities (r, > 10), it is known numerically from release-node Diffusion Monte Carlo studies [33]. Various parametrizations have been developed to interpolate between the known limits while fitting the Monte Carlo data. The first, simplest and most transparent is that of Perdew and Zunger (PZ) [34] ... 

For the total correlation energy (r Q, so much is known about the r, — 0 and r, — 00 no limits that accurate values for all r, and can be found by interpolation [58], without ever using the Monte Carlo or other data. For the spin resolution e r, Q/e (r, Q, however, so little is known about these limits that we must and do rely on the Monte Carlo data. The spin resolution of Eq. (24) has recently been generalized to all [59]. 

For high density system, the enhancement factor becomes unity, and exchange effects dominate over the correlation effects. When the density becomes lower, the enhancement factor kicks in and includes correlation effects into the exchange energies. The enhancement factor is not unique, but can be derived differently in different approximations. The most reliable ones are parameterizations of molecular Monte-Carlo data. Some well known, and regularly used, parameterizations have been made by Hedin and Lundqvist [29], von Barth and Hedin [22], Gun-narsson and Lundqvist [30], Ceperly and Adler [31], Vosko, Wilk, and Nusair [32], and Perdew and Zunger [27]. 

H. Bennett, Efficient Estimation of Free Energy Differences from Monte Carlo Data, ... 

Figure 33. The change with polymer density of the mean-square end-to-end distance of hard-core chains of length (a) N =20 and (b) /V = 100. The data points are exact many-chain simulation results and the solid (dash-dot) lines are the self-consistent PRISM/Monte Carlo (free energy generating fuiKtional) predictions using the two solvation potentials." The dashed horizontal line is the value of / for an ideal freely joined chain with a minimum next nearest neighbor bending angle of 60°, which mimics the local hard-core repulsion.

---