# Calculating binding energy between two systems

Regarding the calculation of binding energy of molecular absorption on graphene, for which this has been discussed before, the process of calculating $$E_{AB}$$ is fairly straight forward, i.e., it is the single point energy of the relaxed complex AB. However, the calculation of $$E_A$$ and $$E_B$$ can be done in two ways:

• Just extract A and B structures from the optimized structure of AB complex and calculate the single point energy of them.

• Relax the extracted A and B structures (from the optimized AB complex) again and then calculate the single point energy of them.

Among these two methods, which method is more recommendable to use and why?

• +1. I suppose the answer depends on what binding energy you're calculating. If you're calculating the binding energy between a relaxed system and its relaxed fragments, you'd use 2, and if you're calculating the binding energy between a relaxed system and the fragments you'd get if you broke the system while it was relaxed, then you'd want to go with 1. Perhaps option 1 is more realistic to what might happen in real life? What is the purpose of your calculation? Maybe knowing that will help decide which binding energy is better for your purposes! – Nike Dattani Jun 17 at 23:17

Mathematically $$E_{\rm bind} = E(A)+E(B)-E(AB)$$ where $$E(A)$$ and $$E(B)$$ are the energies of subsystems $$A$$ and $$B$$, and $$E(AB)$$ is the energy of the compound system.
Relaxing the structures of $$A$$ and $$B$$ minimizes $$E_{\rm bind}$$.
As Susi notes, the rearrangements of the $$\ce{A}$$ and $$\ce{B}$$ fragments are a part of the binding process, and so it is natural to include this "rearrangement energy" into the overall binding energy. Starting with the fragments in the complex geometry would artificially increase the binding energy, as it would destabilize the initial fragments. So your second process is only one that gives the true binding energy.
However, if you were interested in determining the "strength" of the binding site between $$\ce{A}$$ and $$\ce{B}$$ rather than the energy of the overall binding process, you could use your first procedure. This quantity would be more useful if your goal was to determine how large a perturbation (e.g. temperature, energy of a photon) would be needed to cause dissociation. Regardless of the overall favorability of the unbinding process, the complex will need sufficient energy to overcome this barrier.