Part 5: Activation energies

Next, let us discuss how the formation energies of transition states are mapped into activation energies. Let us focus on the H2O dissociation reaction. The formation energy of the corresponding transition state (TS1) was calculated to be 0.416 eV. The initial state of this reaction is adsorbed H2O, with a formation energy of -0.362 eV. The activation energy for this reaction is simply the formation energy of the transition state minus the energy of the initial state:

Ea,fwd,1 = AE[H2O*→OH*+H*] = FE[TS1] – FE[H2O*]

This gives a value of 0.777 eV. It can be easily verified that:

Ea,fwd,1 = E[TS1] – E[H2O*]

Note that we only care about the forward activation energy. If the event is reversible, Zacros will be able to calculate the reverse activation energy, Ea,rev,1, as the forward one minus the delta-energy of the reaction, ΔE1. The latter can be easily calculated since the formation energies of initial and final state species are known (as well as the pertinent interaction energies if applicable).

The case just noted was easy, as we only had one reactant molecule in the initial state. Let us examine a case with two molecules, namely CO*+OH* reacting towards COOH*. The activation energy is calculated as:

Ea,fwd,3 = AE[CO*+OH*→COOH*] = FE[TS3] – FE[CO*+OH*]

The resulting value is 0.405 eV. Notice that from the formation energy of TS3 we subtract the formation energy of the co-adsorbed CO*+OH* configuration, which includes the pairwise interaction energy between CO* and OH*, rather than the sum of the formation energies of CO* and OH*. This is physically meaningful as CO* and OH* have to be in close proximity in order to react. This is how Zacros understands the activation energy as well; if the COOH* formation reaction happens on an empty surface, Zacros will use the value of 0.405 eV (activation energy at the zero-coverage limit), and will not add the interaction energy between the reactive of CO*-OH* on top of that value. However, if spectator species (not participating in the reaction) exist in the neighbourhood and exert attractive or repulsive interactions, then the activation energy will be different than 0.405 eV (this is modelled by Brønsted-Evans-Polanyi relations, which are out of the scope of this tutorial).

In the following table we present the activation energies of the four reactions of interest:

Transition States DFT Energy (eV) Form. Energy (eV) Activ. Energy (eV)
TS1: H2O*→OH*+H* -11915.265 0.416 0.777
TS2: OH*→O*+H* -11898.209 1.770 0.940
TS3: CO*+OH*→COOH* -12489.544 -0.776 0.405
TS4: COOH*→CO2+H* -12489.404 -0.635 0.852
TS5: CO*+O*→CO2 -12472.435 0.632 0.988

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