Molecular modeling in heterogeneous catalysis

Heterogeneous catalytic cycles are complex process involving diffusion, adsorption, surface reaction and desorption. Further catalytic reactions involves individual phenomenon occurring on catalytic sites to overall reactions occurring in reactors which can be up to the size of 1 m diameter. Hence reactions can range in wide length scales. Relevant time scales can also span from femtoseconds (10^-15) up to hours. This makes modeling of catalytic reactions challenging. Heterogeneous catalysis is traditionally considered as an experimental field and molecular modeling is emerging as complementary to experimental studies. Different computational methods at different time and length scales are co-linked to explain phenomenon from atomic to the macroscopic level. Computer modeling can provide new insights into reaction pathways and predict properties of catalysts. Modeling can be used to explain experimental results, suggest new experiments and substitute experiments in the screening of different catalysts or reaction conditions. Initially the modeling techniques need to be validated against experimental studies.

Different levels of molecular modeling

Molecular modeling needs to be carried out at different levels using different computational techniques. These models can then be correlated to obtain an overall view from atomic to macroscopic level. The different methods of molecular modeling include :

1. Quantum chemical calculations
2. Atomistic simulations
3. Microkinetic modeling

1. Quantum chemical calculations

Quantum chemical calculation method provides information about the smallest details in heterogeneous catalytic processes. Most detailed chemical informations are used to predict the energies, electronic structures, spectroscopic properties of small arrangements of atoms and catalytic chemistry. For example, activation energy barriers for individual elementary steps on surfaces can be calculated which is difficult to predict by experiments. Detailed information about presumed active sites for catalysis may be obtained because the explicit chemical details of system are considered. The method is based on solution of Schrödinger equation. Various methods have been advanced to solve the Schrödinger equation such as semi-empirical methods and ab-initio techniques.

Semi-empirical methods

Semi-empirical methods are significantly less computationally demanding. This method introduces approximations to facilitate evaluation of terms introduced by electron – electron interactions. Method that has been most widely used for catalytic systems containing transition metals is ZINDO ( Zerner's Intermediate Neglect of Differential Overlap). This semi-empirical method is extensively used to describe the electronic structure and the spectroscopic features of compounds [1]. It has also been used for understanding the reaction mechanism. Ma et al. [2] reported molecular simulation of the hydrodesulfurization mechanism of thiophenic compounds over molybdenum disulfide using ZINDO.

Ab initio methods

These methods are more computational intensive. Among ab intio methods Hartree–Fock (HF) method adequately represent electron correlation such as configuration interaction and density functional theory (DFT). DFT calculations are reported more and more for various catalytic systems. Fajin et al. [3] used DFT to study the effect of doping of transition metals on gold catalyst for the reaction of oxygen dissociation. D'Amore et al. [4] investigated the adsorption of TiCl₄ on the surfaces of MgCl₂ crystals by DFT methods to study the structure of the active species in industrial MgCl₂ -supported Ziegler–Natta catalyst used for ethene and propene polymerization.

2. Atomistic simulations

In addition to the events at the active site, physical adsorption and diffusion are important steps in a full catalytic cycle as discussed earlier. These phenomena which occur on longer time and length scales are analyzed using atomistic models. Atomistic simulations are used to predict macroscopic thermodynamic and transport properties such as adsorption isotherms, heats of sorption, diffusion coefficients and activation energies for diffusion. The method use systems of hundreds or thousands of molecules. Molecular simulation needs knowledge of the chemical composition and structure of the material. Basic structures can be determined by X-ray diffraction studies or other techniques. Simple potential functions describe the interaction energies between reactants and catalysts. Dispersion, repulsion, electrostatic forces and intramolecular forces are typically accounted. Induced dipole and other forces may also be included if they are considered to be important. Methods include Montecarlo and Molecular dynamics method.