Mapping DFT Energies to Zacros Input

Part 6: Zacros input

Let us take a moment to summarise what we have done so far. We started from a dataset containing the DFT-computed energies for gas and surface species participating in the water-gas shift reaction on Pt(111). The dataset also contained the energy of the clean Pt(111) surface (Part 1). We subsequently chose a reference set of species, according to the rules of Part 2, and calculated the formation energies of all our species with respect to the reference (Part 3). Using these formation energies, we were further able to compute pairwise interaction energies between co-adsorbed species, and activation energies for elementary reactions.

We will shortly discuss how these numbers are translated into Zacros input. For convenience, we have compiled all our data and calculated values into the table below. The numbers highlighted with orange will be used in the Zacros input files.

Gas species: formation energies

The formation energies of the gas species are defined in file simulation_input.dat using the keyword gas_energies. The block of instructions for defining the gas species of our example would be (for more details on each of the keywords please refer to the tutorial Ziff-Gulari-Barshad Model in Zacros):

n_gas_species             5
gas_specs_names           CO        H2O       H2        CO2      O2
gas_energies              0.000     0.000     0.000    -0.615     4.913 # in eV
gas_molec_weights        28.0102   18.0153    2.0159   44.0096   31.9988
gas_molar_fracs           1.00e-5   0.950     0.000     0.000     0.000

Surface species: formation energies and lateral interactions

The formation energies of the surface-bound species along with any pertinent lateral interactions are defined in file energetics_input.dat. Zacros uses a cluster-Hamiltonian type of approach for capturing lattice energetics (more about this on the tutorial Cluster Expansion for Oxygen on Pt(111)). This approach decomposes the total energy of the lattice into single-, two-, and many-body contributions, referred to as “figures” or “clusters”. Each such cluster is defined using blocks of instructions between keywords cluster...end_cluster. For instance, the instructions for defining the cluster representing bound H₂O in our example would be:

cluster H2O_Point
  sites 1
  lattice_state
    1 H2O*   1
  cluster_eng        -0.362
end_cluster

Similarly, the instructions for defining a cluster representing the repulsive interaction between bound CO and OH would be:

cluster CO-OH_1NN
  sites 2
  neighboring 1-2
  lattice_state
    1 CO*   1
    2 OH*   1
  cluster_eng         0.066
end_cluster

In the example above the cluster contained molecules of different species. If we wanted to define the interaction between a pair of molecules (both of the same species) we would use the same construct with the additional setting of the graph multiplicity:

cluster CO_pair_1NN
  sites 2
  neighboring 1-2
  lattice_state
    1 CO*   1
    2 CO*   1
  graph_multiplicity  2
  cluster_eng         0.560
end_cluster

The graph multiplicity of 2 specifies that whenever Zacros detects an instance of this pattern, it will add a contribution equal to 0.560/2 eV in the total energy of the lattice. Since the pattern is symmetric, it will be detected twice, resulting in the correct contribution of 0.560 eV per distinct CO*-CO* pair. If we did not specify the graph multiplicity, Zacros would have used the default value of 1, adding 0.560 eV twice to the total energy of the lattice. More information is provided in “Part 3: Input for two-body terms” of the tutorial Cluster Expansion for Oxygen on Pt(111).

Reactions: activation energies

Finally, let us discuss how the activation energies are used in the Zacros input. These parameters, along with the mechanistic information about the elementary steps are contained in file mechanism_input.dat. Each elementary steps is defined by a block of instructions enclosed within keywords step...end_step, for irreversible steps, or reversible_step...end_reversible_step, for reversible steps. It is advisable to always use reversible steps in specifying a mechanism, so that the simulation satisfies microscopic reversibility and thermodynamic consistency. In our example, if we wanted to define for instance H₂O dissociation, we would write:

reversible_step H2O_dissociation
  sites 2
  neighboring 1-2
  initial
   1 H2O*   1
   2 *      1
  final
   1 OH*    1
   2 H*     1
  pre_expon  1.042e+13
  pe_ratio   1.000e+00
  activ_eng  0.777
end_reversible_step

We will only make a few brief comments here; for more details please refer to “Part 4: Reaction mechanism” of the tutorial Ziff-Gulari-Barshad Model in Zacros. Notice that we defined this as a two-site event, since there will have to be a neighbouring empty site available for the dissociation of the H₂ molecule. To calculate the rate constant of the forward step of any reversible reaction, Zacros uses the Arrhenius equation:

where k_fwd is the rate constant, A_fwd is the pre-exponential, E_a,fwd the activation energy, k_B is Boltzmann's constant, and T is the temperature. A similar equation applies to the reverse step. As shown in the above block of instructions, Zacros allows to define the forward pre-exponential (pre_expon), the ratio between forward and reverse pre-exponentials (pe_ratio). and the forward activation energy (activ_eng). In our case we have calculated an estimated value of the pre-exponentials (same value for forward and reverse), by evaluating the expression k_BT/h_Planck at 500 K (see the supplementary materials of Refs. 2 and 3 for more information about calculating pre-exponentials). We further use the activation energy value as computed above.

As another example, let us define the COOH* decomposition into gas CO₂ and H* as an irreversible step. As noted before, it is preferable to define all steps as reversible; yet our choice to treat this decomposition step as irreversible will not create any problems if we only care about the forward water-gas shift reaction with no CO₂ in the gas phase. The instructions defining this step are:

step COOH_decomposition
  gas_reacs_prods  CO2 1
  sites 1
  initial
    1 COOH* 1
  final
    1 *     1
  pre_expon  1.042e+13
  activ_eng  0.852
end_step

Notice that for this step we did not have to define a pre-exponential ratio. On the other hand, we had to define explicitly the gas product of this reaction (CO₂) using the keyword gas_reacs_prods.

Finally, let us look into an adsorption/desorption step, for instance for H₂O:

reversible_step H2O_adsorption
  gas_reacs_prods  H2O -1
  sites 1
  initial
    1 *     1
  final
    1 H2O*  1
  pre_expon  2.776e+07
  pe_ratio   2.665e-06
  activ_eng  0.000
end_reversible_step

The adsorption step is spontaneous, so we specified an activation energy of zero. The pre-exponential was calculated by the following equation:

where A_site is the effective area of the catalytic site (taken here as 1 Ų), and m is the mass of the adsorbing molecule (also T = 500 K, as before). This expression for the pre-exponential has units of inverse pressure inverse time (bar^-1s^-1). Zacros multiplies this value with the partial pressure of the adsorbing gas species in order to calculate the rate constant of the adsorption event.

Desorption is represented in Zacros as the reverse step of the event defined above. Thus, when Zacros encounters a bound H₂O molecule on the lattice, it will add such a desorption in the queue of possible lattice processes. The activation energy of this step at the zero-coverage limit will be equal to the formation energy of H₂O gas minus that of H₂O* (the binding energy of water, 0.362 eV). In this particular example, the activation energy of water dissociation will be the same even in the presence of spectator adsorbates, since we have not defined any interactions of H₂O* with other species.

Download the four Zacros input files of this example.