Helmholtz free energy

Summary

In MD simulations, the Helmholtz free energy ($F$) describes “the useful work obtainable from a closed thermodynamic system at a constant temperature.” It is a property of a macrostate of a system, and is proportional to the logarithm of its partition function. Frenkel & Smit (1) define it as a system’s total energy minus the contribution of entropy ($F=E-TS$).

Details

$$F\propto {\beta }^{-1}\ln Z_{\Sigma }\text{\hspace{1em}(1)}$$ $$F\propto -{\beta }^{-1}\ln {\int }_{\Sigma }{e}^{-\beta U(\mathbf{x})}d\mathbf{x}\text{\hspace{1em}(2)}$$

Two states $A$ and $B$ with free energies $F_A$ and $F_B$ can be compared as: $\Delta F_{A,B}={\beta }^{-1}\ln \left(\frac{P_A}{P_B}\right)$

Reduced free energy

The definition of the reduced free energy $f$ depends on whether the simulation uses a canonical ensemble ($f=\beta F$) or an isothermal-isobaric ensemble ($f=\beta G$).

Extensively cites (2)

1.

Understanding Molecular Simulation. 2002; Available from: https://doi.org/10.1016/b978-0-12-267351-1.x5000-7

2.

Hénin J, Lelièvre T, Shirts MR, Valsson O, Delemotte L. Enhanced Sampling Methods for Molecular Dynamics Simulations [Article v1.0]. Living Journal of Computational Molecular Science. 2022;4(1):1583. Available from: https://doi.org/10.33011/livecoms.4.1.1583