Quantum Catalysis: The Modeling of Catalytic Transition States

Abstract

We present an introduction to the computational modeling of transition states for catalytic reactions. We consider both homogeneous catalysis and heterogeneous catalysis, including organometallic catalysts, enzymes, zeolites and metal oxides, and metal surfaces. We summarize successes, promising approaches, and problems. We attempt to delineate the key issues and summarize the current status of our understanding of these issues. Topics covered include basis sets, classical trajectories, cluster calculations, combined quantum -mechanical/molecular-mechanical (QM/MM) methods, density functional theory, electrostatics, empirical valence bond theory, free energies of activation, frictional effects and nonequilibrium solvation, kinetic isotope effects, localized orbitals at surfaces, the reliability of correlated electronic structure calculations, the role of d orbitals in transition metals, transition state geometries, and tunneling.Computational chemistry has achieved great strides in recent years, and it has become a strong partner with experimental methods, displacing purely analytic theory almost completely. The essential element in computational chemistry is the use of very general theoretical frameworks that can be applied broadly across a number of fields. Examples are molecular orbital theory, molecular mechanics, transition state theory, 2

Multidimensional Tunneling, Recrossing, and the Transmission Coefficient for Enzymatic Reactions

“…KIEs are a powerful tool to elucidate reaction mechanisms, and they provide a means of characterizing the properties of the transition state of any reaction. They have been widely used to probe the degree to which quantum mechanical tunneling contributes to enzymatic reaction rates; however, uncertainties in such interpretations are often caused by the masking of intrinsic KIEs by the multiple-step nature of reaction mechanisms; this complication has been referred to as kinetic complexity. ,,,, Sophisticated methods have been developed by experimentalists for extracting the intrinsic KIEs that directly reflect the chemical step from the observed KIEs obtained from raw experimental kinetic data. ,,,, …”

Performance of Molecular Orbital Methods and Density Functional Theory in the Computation of Geometries and Energies of Metal Aqua Ions

“…For organometallic compounds, the influence of the basis set and the computational method on the structure, reaction, or activation energies was investigated in earlier studies. [1][2][3][4][5][6][7] The requirements for the basis sets of transition metals were analyzed, in particular those for the valence nd shell and the formally empty (n+1)s and (n+1)p shells, being involved in metal-ligand bonding. 1,2 In systems with static electron correlation, which may arise from the d manifold of a transition metal or from an elongated bond, in which the bonding (occupied) molecular orbital (MO) is close to its antibonding (unoccupied) counterpart, methods based on a single reference such as Hartree-Fock (HF), singlereference configuration interaction (CI), or perturbation theory are inadequate.…”

“…For organometallic compounds, the influence of the basis set and the computational method on the structure, reaction, or activation energies was investigated in earlier studies. − The requirements for the basis sets of transition metals were analyzed, in particular those for the valence n d shell and the formally empty ( n +1)s and ( n +1)p shells, being involved in metal−ligand bonding. , …”

Computational Design of Functionalized Metal–Organic Framework Nodes for Catalysis

“… 52 , 53 , 64 − 68 , 70 − 72 Similar progress has been made in homogeneous catalysis. 52 , 53 , 64 − 68 , 73 − 75 In both these instances, the chief tool is generally Kohn–Sham density functional theory 76 (KS-DFT), and by using KS-DFT each elementary step in a catalytic reaction (or in a family of reactions) can be described in a detail that is often not available from experiment alone.…”

“…In the quest for improved catalyst design, the computational modeling of nanoporous materials plays a prominent role. − Modeling catalysis on MOFs, like modeling traditional heterogeneous catalysis, − poses higher-level challenges than modeling molecular − catalysis because one must model not only the local catalytic site but also the structure of the support and its possible local and long-range influence on reactivity and selectivity. Theoretically informed surface catalysis design has made significant progress, and interaction energies of molecules and atoms with metal surfaces can now be described with sufficient accuracy to predict trends in reactivity for transition metals and alloys. ,,− ,− Similar progress has been made in homogeneous catalysis. ,,− ,− In both these instances, the chief tool is generally Kohn–Sham density functional theory (KS-DFT), and by using KS-DFT each elementary step in a catalytic reaction (or in a family of reactions) can be described in a detail that is often not available from experiment alone.…”