Step One: Theory
This tutorial will assume you have a reasonable understanding of what free energy calculations are, the different types that exist, and the underlying theory of the technique. It is neither practical nor possible to provide a complete education here. Instead, I will focus this tutorial on practical aspects of running free energy calculations in GROMACS, highlighting relevant theoretical points as necessary throughout the tutorial. I will provide here a list of useful papers for those who are new to free energy calculations. Do not consider this list exhaustive. It should also not supplant proper study of statistical mechanics and the many books and papers that have been written on related topics.
The objective of this tutorial is to reproduce the results of a very simple system for which an accurate free energy estimate exists. The system of choice (methane in water) is one dealt with by Shirts et al. in a systematic study of force fields and the free energies of hydration of amino acid side chain analogs. The complete publication can be found here. This tutorial will assume you have read and understood the broader points of this paper. Rather than use the thermodynamic integration approach for evaluating free energy differences, the data analysis conducted here will utilize the GROMACS "bar" module, which was introduced in GROMACS version 4.5 (and previously called g_bar). It uses the Bennett Acceptance Ratio (BAR, hence the name of the module) method for calculating free energy differences. The corresponding paper for BAR can be found here. Knowledge of this method is also assumed and will not be discussed in great detail here. Free energy calculations have a number of practical applications, of which some of the more common ones include free energies of solvation/hydration and free energy of binding for a small molecule to some larger receptor biomolecule (usually a protein). Both of these procedures involve the need to either add (introduce/couple) or remove (decouple/annihilate) the small molecule of interest from the system and calculate the resulting free energy change. There are two types of nonbonded interactions that can be transformed during free energy calculations, Coulombic and van der Waals interactions. Bonded interactions can also be manipulated, but for simplicity, will not be addressed here. For this tutorial, we will calculate the free energy of a very simple process: turning off the LennardJones interactions between the atomic sites of a molecule of interest (in this case, methane) in water. This quantity was calculated very precisely by Shirts et al. and thus it is the quantity we seek to reproduce here.

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