# Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: Fractional electron approach

**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.

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**ABSTRACT:**Combined quantum mechanics/molecular mechanics (QM/MM) methods have been widely used in multi-scale modelling and simulations of physical, chemical and biological processes in complex environments. In this review, we provide an overview of the recently developed QM/MM algorithms, with emphasis on our works, towards the ultimate goal of establishing an open boundary between the QM and MM subsystems. The open boundary is characterised by on-the-fly exchanges of partial charges and atoms between the QM and MM subsystems, allowing us to focus on the small QM subsystem of primary interest in dynamics simulations. An open-boundary scheme has the promise to the utilisations of small QM subsystems, high-levels of QM theory and long simulation times, which can potentially lead to new insights.Molecular Simulation 05/2014; 41:1-22. DOI:10.1080/08927022.2014.911870 · 1.12 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**THE RELIABILITY OF FREE ENERGY SIMULATIONS (FES) IS LIMITED BY TWO FACTORS: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.Journal of Chemical Theory and Computation 04/2014; 10(4):1406-1419. DOI:10.1021/ct401118k · 5.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Open-shell singlet diradicals are difficult to model accurately within conventional Kohn-Sham (KS) density-functional theory (DFT). These methods are hampered by spin contamination because the KS determinant wave function is neither a pure spin state nor an eigenfunction of the S(2) operator. Here we present a theoretical foray for using single-reference closed-shell ground states to describe diradicals by fractional-spin DFT (FS-DFT). This approach allows direct, self-consistent calculation of electronic properties using the electron density corresponding to the proper spin eigenfunction. The resulting FS-DFT approach is benchmarked against diradical singlet-triplet gaps for atoms and small molecules. We have also applied FS-DFT to the singlet-triplet gaps of hydrocarbon polyacenes.The Journal of Physical Chemistry A 01/2011; 115(1):76-83. DOI:10.1021/jp109280y · 2.78 Impact Factor