Ethane to Methanol in Water

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

Ethane and methanol 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 ethane and methanol 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 free-energy perturbation (FEP), thermodynamic integration (TI/FDTI) and Bennet's acceptance ratio methods:

• mols -- Molcule description files and force field database used to create the initial configurations for the simulations data.0.lmp and data.1.lmp

• fep01 -- Calculation using FEP, multi-stage transformation of an ethane molecule into methanol. Results in fep01.lmp

• fep10 -- Calculation using FEP, multi-stage transformation of a methanol molecule into ethane. Results in fep10.lmp

• fdti01 -- Calculation using FDTI, transformation of an ethane molecule into methanol. Results in fdti01.lmp

• fdti10 -- Calculation using FDTI, transformation of a methanol molecule into ethane. Results in fdti10.lmp

• bar01 -- Calculation using BAR, 1-step transformation of an ethane molecule into methanol. Results in bar01.lmp

• bar10 -- Calculation using BAR, 1-step transformation of a methanol molecule into ethane. Results in bar10.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, fdti.py, and bar.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

bar.py 300 bar01.lmp bar10.lmp

The outputs are in kcal/mol and can be compared with the experimental value of -6.93 kcal/mol and with simulation value from the literature: -6.7 kcal/mol [Jorgensen, Ravimohan, J Chem Phys 83 (1985) 3050], -6.8 kcal/mol [Goette, Grubmüller, J Comp Chem 30 (2007) 447].

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.)