Microkinetic Modeling

Microkinetic modeling is a technique that is used to extend both experimental and theoretical observations to predict the results of complex chemical reactions under various conditions. In our group, we use microkinetic modeling in conjunction with density functional theory to investigate heterogeneous catalytic transformation of small molecules. For example, we are using microkinetic modeling to investigate the observed selectivity and activity of Bi- and Te-doped Pd catalysts for the dehydrogenation and esterification of primary alcohols, such as 1-propanol.

In microkinetic modeling, a set of elementary reactions that are thought to be relevant for an overall chemical transformation are specified. For each reaction, a rate constant is required for both the forward and reverse direction. These rate constants can be determined using density functional theory under transition state theory. Once the rate constants are known, a master equation for the entire reaction network can be written down. The master equation expresses the rate of change of each species in the model as a function of the instantaneous concentration of all species in the model, represented as a system of ordinary non-linear differential equations. These equations are most efficiently solved numerically, using algorithms such as BDF.

In general, microkinetic modeling returns a set of concentrations and rates as a function of time. In practice, we are most often concerned with the steady-state solution, in which the concentrations and rates have converged to some final value. The inspection of these steady-state results can tell us:

- Which species are most predominant on the surface under catalytic conditions

- What is the overall TOF (turn-over frequency, a measure of catalytic activity)

- What is the selectivity of the catalyst towards the desired product

Furthermore, it is possible to probe the sensitivity of the model to individual model parameters, such as rate constants, equilibrium coefficients, and individual adsorbate binding energies. This sensitivity analysis gives information about which steps are rate-limiting and potential descriptors for finding more active or more selective catalysts.

We have developed a Python program, Micki, which is designed to simplify the construction and solution of microkinetic models from ab initio results. It is currently designed to work generally with ab initio energies and vibrational frequencies that are stored in an ASE Atoms database (ASE is a Python library for the construction and manipulation of molecular and solid systems). Micki requires as input only the converged geometry, energy, and vibrational frequencies of each species in the model, a set of reactions to be considered in the model, and a set of reactor conditions (temperature, reactor type, etc). Additionally, Micki allows the user to probe the sensitivity of the model using a built-in sensitivity analysis module.