Fast-growth thermodynamic integration: Results for sodium ion hydration

Slow-growth thermodynamic integration (TI) is a simple method to calculate free energy differences in fluid and macromolecular systems. A recently derived identity (Jarzynski, C. Phys. Rev. Lett. 78, 2690, 1997) permits the calculation of free energy differences from repeated TIs at arbitrary growth rates. Here, I investigate the quantitative accuracy of the resulting 'fast-growth' TI for the charging of a sodium ion in water. To estimate the corresponding free energy of hydration, I use simple expressions involving the means and variances of the non-equilibrium work.