Part 4: Pairwise interaction energies

Let us now focus our attention on one of the co-adsorbed configurations, in particular CO*-CO*. This configuration contains two CO adsorbates as 1st nearest-neighbours. The formation energy of this configuration was calculated as:

FE[CO*+CO*] = E[CO*+CO*] – { E[Pt(111)] + 2 E[CO] }

If these CO* molecules were placed on the surface far away from each other, the formation energy would be equal to twice the formation energy of CO*, namely -4.155 eV. However, because of the pairwise repulsive interaction that these molecules “feel” when in close proximity, the energy of the co-adsorbed configuration is higher (-3.595 eV). The difference of 0.560 is called the “interaction energy” between the CO*-CO* pair. Note that we have assumed that the DFT calculation cell is large, so that the only adsorbate-adsorbate lateral interaction is between these two CO* molecules (no interactions with periodic images). The magnitude of this pairwise interaction energy is therefore:

IE[CO*+CO*] = FE[CO*+CO*] – 2 FE[CO*]

where IE[A+B] stands for the interaction energy between A and B. It can easily be verified that:

IE[CO*+CO*] = E[CO*+CO*] – 2 E[CO*] + E[Pt(111)]

Similarly, the interaction between different species, for instance CO*+OH* is calculated as:

IE[CO*+OH*] = FE[CO*+OH*] – { FE[CO*] + FE[OH*] }

Note that 1st nearest-neighbour pairwise additive interactions are not enough to accurately capture the energetics of the adsorbate layer: longer-range pairwise interactions as well as many-body contributions may be significant (see tutorial Cluster Expansion for Oxygen on Pt(111)). Pairwise interactions are a good start, however, and it is useful to be able to compute a first estimate thereof with the approach just discussed. In the following table, we present the interaction energies for our co-adsorbed configurations:

Co-Adsorbed Species (1NN) DFT Energy (eV) Form. Energy (eV) Inter. Energy (eV)
CO*+CO* -12629.394 -3.595 0.560
OH*+H* -11915.448 0.233 0.021
O*+H* -11899.102 0.877 0.198
CO*+OH* -12489.950 -1.181 0.066
CO*+O* -12473.424 -0.357 0.423

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