# How can absolute binding free energies be calculated?

In the calculation of binding free energies, such as between a protein and a ligand, I learned that absolute values cannot be obtained from simulation (such as taught in this lecture, slide 2). Rather, with the appropriate reference state, only relative free energies can be calculated. However, there are a number of papers that discuss calculations of absolute free energies (ex. recent JACS paper). What does this mean? Are the absolute values--even among different papers--using some kind of general reference state?

• These are two very different things - binding energy isn't energy of compound but of reaction. – Mithoron Jan 18 '17 at 22:28

Free energies are computed by transforming one state into another, e.g. by transforming ligand A into a ligand B (inside a protein in our case). This transformation yields the difference in binding free energies between ligands A and B: $\Delta \Delta G^{bind}_{A \rightarrow B}$. This is a relative binding free energy.
On the other hand, if ligand A is transformed into nothing, it's absolute binding free energy is calculated: $\Delta G^{bind}_A$.
In both cases ($\Delta G$ and $\Delta \Delta G$), we are calculating differences between two states, and never calculating the absolute free energy $G$ of a single state. This is probably what you meant by: "only relative free energies can be calculated."
PS: since binding occurs in a solvent, it would be necessary to take ligand solvation and protein solvation into account, in order to properly describe the unbound state. For example, in the calculation of $\Delta G^{bind}_A$ described above, ligand A should appear in bulk water instead of disappearing completely.