Article
Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: Fractional electron approach
Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
The Journal of Chemical Physics (Impact Factor: 2.95). 04/2008; 128(12):124510. DOI: 10.1063/1.2832946 Source: PubMed
ABSTRACT
Electron transfer (ET) reactions are one of the most important processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, theoretical study of ET processes is challenging. To simulate ET processes at the electronic level, we have developed an efficient density functional theory (DFT) quantum mechanical (QM)/molecular mechanical (MM) approach that uses the fractional number of electrons as the order parameter to calculate the redox free energy of ET reactions in solution. We applied this method to study the ET reactions of the aqueous metal complexes Fe(H(2)O)(6)(2+/3+) and Ru(H(2)O)(6)(2+/3+). The calculated oxidation potentials, 5.82 eV for Fe(II/III) and 5.14 eV for Ru(II/III), agree well with the experimental data, 5.50 and 4.96 eV, for iron and ruthenium, respectively. Furthermore, we have constructed the diabatic free energy surfaces from histogram analysis based on the molecular dynamics trajectories. The resulting reorganization energy and the diabatic activation energy also show good agreement with experimental data. Our calculations show that using the fractional number of electrons (FNE) as the order parameter in the thermodynamic integration process leads to efficient sampling and validate the ab initio QM/MM approach in the calculation of redox free energies.

 "For calculating D r G H;c we assume unit activity coefficients. Since the metal and ligands exist at high concentrations (1–4 molal) in the simulated systems, and hence the solutions are far from the standard state, we also used the Bdot extension of the Debye–Hü ckel theory to estimate activity coefficients for the individual ions (Helgeson et al., 1981; Mambote et al., 2003; Zeng et al., 2008). "
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ABSTRACT: Chloride and bisulfide are the primary ligands believed to control the transport of copper in hydrothermal fluids. Ab initio molecular dynamics (MD) simulations based on density functional theory were conducted to predict the stoichiometries and geometries of Cu(I) complexes in mixed chloride and hydrosulfide (HS− and H2S(aq)) fluids at ambient temperature and at 327 °C and 500 bar, and to assess the relative importance of the chloride and hydrosulfide ligands for Cu transport. The simulations accurately reproduce the identity and geometries of Cu(I) chloride and bisulfide species derived from experimental solubility, UV–Vis, and in situ XAS results. The simulations indicate the following ligand preference: HS− > Cl− > H2S for Cu(I) complexes, but predict a high stability of the mixedligand complex, CuCl(HS)−, a species similar to NaClCuHS species in vapour phase suggested by Zajacz et al. (2011). The thermodynamic properties (formation constants, log Ks) of Cu(I) chloride and bisulfide complexes were investigated by distanceconstrained MD simulations using thermodynamic integration. The predicted log Ks of the following reactions are in good agreement (within 1 log unit) with the experimental values (Brugger et al., 2007 and Liu et al., 2001): 
 "In the special case of electron transfer, Yang and coworkers realized that it is possible to choose the fractional number of electrons as the parameter λ which then reduces the number of QM calculations to one at each sampling step. The simulation results have been in good agreement with experiments and other simulations [83]. When a chemical reaction is of interests, in addition to the relative free energies of the reactant and product states, one would also like to know the free energy changes along the reaction process, in particular free energy of the transition state, which often determines the reaction rate in classical transition state theory. "
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ABSTRACT: Determining the free energies and mechanisms of chemical reactions in solution and enzymes is a major challenge. For such complex reaction processes, combined quantum mechanics/molecular mechanics (QM/MM) method is the most effective simulation method to provide an accurate and efficient theoretical description of the molecular system. The computational costs of ab initio QM methods, however, have limited the application of ab initio QM/MM methods. Recent advances in ab initio QM/MM methods allowed the accurate simulation of the free energies for reactions in solution and in enzymes and thus paved the way for broader application of the ab initio QM/MM methods. We review here the theoretical developments and applications of the ab initio QM/MM methods, focusing on the determination of reaction path and the free energies of the reaction processes in solution and enzymes.  [Show abstract] [Hide abstract]
ABSTRACT: In this article we review the key modeling tools available for simulating biomolecular systems. We consider recent developments and representative applications of mixed quantum mechanics/molecular mechanics (QM/MM), elastic network models (ENMs), coarsegrained molecular dynamics, and gridbased tools for calculating interactions between essentially rigid protein assemblies. We consider how the different length scales can be coupled, both in a sequential fashion (e.g. a coarsegrained or grid model using parameterization from MD simulations), and via concurrent approaches, where the calculations are performed together and together control the progression of the simulation. We suggest how the concurrent coupling approach familiar in the context of QM/MM calculations can be generalized, and describe how this has been done in the CHARMM macromolecular simulation package.
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