(233d) Accelerated Kinetic Monte Carlo (kMC) Simulation and Density Functional Theory (DFT) to Predict Turn-over Frequencies in Heterogeneous Complex Catalytic Reactions

Density functional theory (DFT) involves the solution of the Schrodinger equation for the interacting electrons of a molecular structure. This method has extensively been explored to design novel catalysts. Additionally, this method has the capability to explore the electronic structure of system without introducing a large number of physical parameters. Therefore, many recent studies have investigated the catalytic performances of diverse materials using this method by considering the thermodynamics of the catalytic materials [1]. Using DFT analysis important structural features of the catalyst and electronic properties can be are derived. Therefore, these calculations help us obtain the energies associated with individual reaction pathways in heterogeneous catalysis [1,2]. However, ab-initio calculations performed with DFT fail to address issues related to the kinetics of the catalysts and therefore fail to provide us with insights into important catalyst properties such as adsorbent localization, surface coverage, and reaction turn-over frequencies (TOF) with varying pressure and temperature [2]. To this end, methods like kinetic Monte Carlo (kMC) simulation can be utilized [3,4]. However, the majority of complex heterogeneous catalysis reactions have pathways that involve elementary reactions occurring at disparate rates [5,6,7]. Since in the kMC algorithm, processes are selected based on their relative rates, it is much more likely that a faster process will occur at each step, with a very infrequent sampling of the slower processes [8]. The infrequent sampling of slower reaction steps significantly undermines the use of computational resources implemented to study the effect of slow but crucial reaction steps on the final catalytic activities [7]. Additionally, owing to a continuous sampling of fast processes, the kMC algorithm allocates most of its time in exploring kinetically trapped configurations of the system that provide no significant information regarding the evolution of the catalytic surface and makes it computationally intractable to reach properties like the TOF values or catalytic selectivity over longer time-scales [7,8]. Hence, in its conventional form, the kMC algorithm and DFT cannot be combined to complement each other in predicting important catalytic activities. Specifically, conventional kMC methods fails in cases where the DFT calculations yield elementary reaction steps with significantly different reaction rates.

Therefore, to apply the kMC algorithms alongside DFT calculations for a more general class of catalytic reactions it becomes important that efficient strategies be developed that allow us to effectively sample slow and fast catalytic reaction steps in a computationally tractable fashion [9]. To this end, we propose a novel method of combining DFT calculations with kMC simulations. Specifically, this begins by identifying the distinct reaction channels present in the reaction mechanism. In the proposed methods based on the products formed in the reactions the intermediates related to individual reaction channels are identified and segregated. Then by analyzing the activation energies obtained from DFT calculations for both the forward and reverse reactions a reaction channel is either denoted as reversible or irreversible. All the fast reactions in the catalytic surface are assumed to be reversible and accordingly the free energy of the reverse reactions is also obtained for individual reaction steps via DFT calculations. After the activation energies are obtained the rate expression using the Arrhenius law is derived for the individual reactions. Reaction rates in each of the reaction channels are adaptively coarse-grained by using a scaling factor which essentially increases the energy barriers of the fast reaction channels to bring the reactions rates of the fast reactions within a few orders of magnitude of the slow reactions. The reaction channels are coarse-grained when a channel is quasiequilbrated. The degree of quasiequilibration is determined by a threshold value which acts as a tuning parameter of the algorithm. As predicted by DFT calculations when the reaction channel with the highest energy barrier is executed the kMC method stops exploring a kinetic basin and hops to the adjacent kinetic basin and the scaling factors of all the reaction channels are reinitialized. This algorithm minimizes the re-sampling of similar system configurations and allows us to sample the slower reactions in a computationally efficient manner. As a case study, the accelerated kMC and DFT algorithm is implemented to study the complex nitrogen reduction reaction (NRR) reaction on heterogenous catalyst and obtain the TOF values.

References.

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