Calculating binding energy between two systems

Question

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?

Answer 1

The binding energy is defined in terms of the relaxed structures: it is the minimum energy required to disassemble a system of particles into separate parts.

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 $E_{\rm bind}$.

Answer 2

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.