NOTE: This tutorial was intended to be used with Gromacs version 3.1.4 and may not be compatible with newer versions. The tutorial will be revised in the near future. Note, a brief tutorial on Free Energy calculation with Gromacs 3.3.x can be found at the DillGroup Wiki.
Free energy is perhaps the most important thermodynamic quantity. Many, if not almost all of the physical properties a chemist or a biochemist can be interested in depend directly or indirectly on the free energy of the system. For example, binding constants, association and dis-association constant and conformational preferences are all directly related to the difference in free energy between alternate states.
Free energy is a statistical property, it can be seen as a measure of the probability of finding a system in a given state. Furthermore, it is a global property that depends on the extent of the phase (or configuration) space accessible to the molecular system. To get a good estimate of the absolute free energy you would theoretically need to sample the whole phase space, which is not possible.
What can be calculated is the difference in free energy between two related states of a system, which corresponds to the relative probability of finding a system in one state as opposed to the other.
The free energy is usually expressed as the Helmholtz function, F, or the Gibbs function, G. The Helmholtz function is appropriate for a system with a constant number of particles, temperature and volume (constant NVT; the corresponding ensemble is also referred to as the canonical ensemble) whereas the Gibbs free energy is appropriate for constant number of particles, pressure and temperature (NPT ensemble).