Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

66 Perturbation Theories for Fluids and Solids

If all probabilities are equal, p

i

/p

j

= 1, and

ln



w

j

w

i



=−ln



Q

j

Q

i



= β



F

j

−F

i



∝ β



μ

E

j

−μ

E

i



. (3.102)

This suggests weighting factors of the form w

i

= exp(βμ

E

i

) = exp(a

i

βμ

E

), where

μ

E

is the excess chemical potential of the N-particle system and a

i

are coefficients

such that a

1

= 0, a

M

= 1 and intermediate values can be obtained from a previous

simulation.

The expanded ensemble method can also be applied to simulations in the Gibbs

and other ensembles (Escobedo and de Pablo 1996, 1997c, Chang and Sandler 2003).

REFERENCES

Agrawal, R., M. Mehta, and D. A. Kofke. 1994. Efficient evaluation of three-phase coexistence