Free Energy of Hydration of Methane

Example calculation of the free energy of hydration of methane with LAMMPS using *compute fep* and *fix adapt/fep*.

Methane is represented by the 5-site OPLS-AA model (1 molecule). Water is represented by the 4-site TIP4P-Ew model (360 molecules). Interactions of sites that are being created or deleted are treated using soft-core verions of the Lennard-Jones and Coulomb potentials (*pair lj/cut/coul/long/soft*) in order to avoid singularities.

The following directories contain input files and results for calculations using free-energy perturbation (FEP) and finite-difference thermodynamic integration (FDTI):

• mols -- molecule description files and force field database used to create the initial configuration used for the simulations data.lmp

• fep01 -- Calculation using FEP, multi-stage creation of a methane molecule. Results in fep01.lmp

• fep10 -- Calculation using FEP, multi-stage deletion of a methane molecule. Results in fep10.lmp

• fdti01 -- Calculation using TI/FDTI, creation of a methane molecule. Results in fdti01.lmp

• fdti10 -- Calculation using TI/FDTI, deletion a methane molecule. Results in fdti10.lmp

The free-energy profiles can be observed by plotting the values in the third column of the results files. The Python scripts fep.py, nti.py and fdti.py found in the tools directory can be used to calculate the free-energy differences corresponding to the above transformations:

fep.py 300 < fep01.lmp

fep.py 300 < fep10.lmp

nti.py 300 0.002 < fdti01.lmp

nti.py 300 0.002 < fdti10.lmp

fdti.py 300 0.002 < fdti01.lmp

fdti.py 300 0.002 < fdti10.lmp

The outputs are in kcal/mol and can be compared with the experimental value of 2.0 kcal/mol, or with a simulation value from the literature obtained with the same force field models used here: 2.27 kcal/mol [MR Shirts, VS Pande, J Chem Phys 122 (2005) 134508].

These example calculations are for tutorial purposes only. The results may not be of research quality (not enough sampling, size of the step in lambda or of the delta for numerical derivative not optimized, no evaluation of ideal-gas contributions, etc.)