Methane to Tetrafluoromethane in Water

Example calculation of the difference in free energy of hydration upon transforming methane into tetrafluoromethane with LAMMPS using *compute fep* and *fix adapt*.

Methane and tetrafluoromethane are represented by the OPLS-AA force field (1 molecule). Water is represented by the 3-site SPC/E model (360 molecules).

The strategy used to perform the alchemical transformation is the following:

• The dual topology approach is used, therefore all the atoms of methane and perfluorommethane are present throughout the simulation, only some of them are dummy sites at the endpoints of the transformation. Masses and intramolecular terms (bond lengths, angles, dihedrals) are not changed.

• Interactions of sites that are being created (from dummy sites) or deleted (to become dummy sites) 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 exponent of the coupling parameter lambda in the soft-core pair potentials was in this example n = 1.

• Eletrostatic charges that are modified are varied linearly from the initial to the final values. This keeps the overall charge of the molecule constant, which is good for the long range electrostatics (the coupling parameter lambda has no effect on the kspace terms).

The following directories contain input files and results for calculations using Bennet's acceptance ratio (BAR) method:

• bar01 -- Calculation using BAR, 1-step transformation of a CH4 molecule into CF4. Results in bar01.lmp

• bar10 -- Calculation using BAR, 1-step transformation of a CF4 molecule into CH4. Results in bar10.lmp

The Python script bar.py found in the tools directory can be used to calculate the free-energy difference corresponding to the transformation:

bar.py 300 bar01.lmp bar10.lmp

The outputs are in kcal/mol and can be compared with the experimental value of 1.2 kcal/mol and with a simulation value from the literature (using a different force field): 0.8 kcal/mol [Gough, Pearlman, Kolmann, J Chem Phys 99 (1993) 9103]. This small free energy difference is difficult to predict.

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.)