element, namely, the choice of the reaction coordinate for determining the free energy of activation to characterize the mechanism of enzymatic processes. Then, we illustrate a variety of factors that have been found to contribute to catalysis in specific enzymatic reactions by lowering the free energy of activation relative to that for the uncatalyzed process in aqueous solution. Finally, we provide a summary of the major conclusions. 2. Methods for Computational Studies of Enzymatic Reactions in Aqueous Solution In this section, we present a brief summary of the theory and key computational techniques that we use for studying chemical reactions catalyzed by enzymes and the corresponding uncatalyzed reactions, both in aqueous solution. 2.1. Generalized Transition State Theory Generalized transition state theory (TST) provides a theoretical framework for understanding chemical reactions in the gas phase, in solution, and in enzymes. Conventional 24,25 and generalized 26 transition state theory were originally developed for gas-phase reactions, but transition state theory is readily generalized to liquid-phase reactions, 27 and it has become the framework for both qualitative and quantitative studies of reactions catalyzed by enzymes. The rate constant for a reaction at temperature T can be conveniently expressed as follows: (1) where β = 1/(k B T), k B being Boltzmann's constant, h is Planck's constant, and k TST is the transition state theory rate constant. The transmission coefficient, γ(T), which has a value of unity in simple transition state theory, has three components, 7 (2) which account for, respectively, dynamical recrossing of the transition state hypersurface that separates the reactants and products, quantum mechanical tunneling in the reaction coordinate, and nonequilibrium distributions in phase space. Note that γ(T), κ(T), and Γ(T) are called, respectively, the transmission coefficient, the tunneling transmission coefficient, and the recrossing transmission coefficient. In eq 1, ΔG ‡ (T) is the molar standard-state quasithermodynamic free energy of activation, which is related to the potential of mean force, W(T,q), also called the PMF, by eq 3, 28,29 (3) where q ‡ and q R are values of the reaction coordinate, q, at the transition state and reactant state, respectively, G R (q) corresponds to the free energy of the mode in the reactant state, R, which correlates with the reaction coordinate, and C(T,q) is a correction term that is due to the Jacobian of the transformation from a locally rectilinear reaction coordinate to the Gao et al.

We present a rigorous analysis of unique, wide electrochemical window solutions for rechargeable magnesium batteries, based on aromatic ligands containing organometallic complexes. These solutions are comprised of the transmetalation reaction products of Ph(x)MgCl(2-x) and Ph(y)AlCl(3-y) in different proportions, in THF. In principle, these reactions involve the exchange of ligands between the magnesium and the aluminum based compounds, forming ionic species and neutral molecules, such as Mg(2)Cl(3)(+)·6THF, MgCl(2)·4THF, and Ph(y)AlCl(4-y)(-) (y = 0-4). The identification of the equilibrium species in the solutions is carried out by a combination of Raman spectroscopy, multinuclear NMR, and single-crystal XRD analyses. The association of the spectroscopic results with explicit identifiable species is supported by spectral analyses of specially synthesized reference compounds and DFT quantum-mechanical calculations. The correlation between the identified solution equilibrium species and the electrochemical anodic stability window is investigated. This study advances both development of new nonaqueous solution chemistry and possible development of high-energy density rechargeable Mg batteries.

The high charge-state dopant Zr4+ improves the structural stability and electrochemical behavior of the lithiated transition metal oxide LiNi0.6Co0.2Mn0.2O2.