Introducing the mean field approximation to CDFT/MMpol method: Statistically converged equilibrium and nonequilibrium free energy calculation for electron transfer reactions in condensed phases

An energy decomposition and extrapolation scheme for evaluating electron transfer rate constants: a case study on electron self-exchange reactions of transition metal complexes

A simple approach to the analysis of electron transfer (ET) reactions based on energy decomposition and extrapolation schemes is proposed. The present energy decomposition and extrapolation-based electron localization (EDEEL) method represents the diabatic energies for the initial and final states using the adiabatic energies of the donor and acceptor species and their complex. A scheme for the efficient estimation of ET rate constants is also proposed. EDEEL is semi-quantitative by directly evaluating the seam-of-crossing region of two diabatic potentials. In a numerical test, EDEEL successfully provided ET rate constants for electron self-exchange reactions of thirteen transition metal complexes with reasonable accuracy. In addition, its energy decomposition and extrapolation schemes provide all the energy values required for activation-strain model (ASM) analysis. The ASM analysis using EDEEL provided rational interpretations of the variation of the ET rate constants as a function of the transition metal complexes. These results suggest that EDEEL is useful for efficiently evaluating ET rate constants and obtaining a rational understanding of their magnitudes.

Accelerated constant-voltage quantum mechanical/molecular mechanical method for molecular systems at electrochemical interfaces

The structure and electronic properties of a molecule at an electrochemical interface are changed by interactions with the electrode surface and the electrolyte solution, which can be significantly modulated by an applied voltage. We present an efficient self-consistent quantum mechanics/molecular mechanics (QM/MM) approach to study a physisorbed molecule at a metal electrode-electrolyte interface under the constant-voltage condition. The approach employs a classical polarizable double electrode model, which enables us to study the QM/MM system in the constant-voltage ensemble. A mean-field embedding approximation is further introduced in order to overcome the difficulties associated with statistical sampling of the electrolyte configurations. The results of applying the method to a test system indicate that the adsorbed molecule is no less or slightly more polarized at the interface than in the bulk electrolyte solution. The geometry of the horizontally adsorbed molecule is modulated by their electrostatic interactions with the polarizable electrode surfaces and also the interactions with cations attracted toward the interface when the adsorbate is reduced. We also demonstrate that the approach can be used to quantitatively evaluate the reorganization energy of a one electron reduction reaction of a molecule in an electrochemical cell.

Constrained Density Functional Theory Molecular Dynamics Simulation of Deprotonation in Aqueous Silicic Acid

The solubility of silicic acid in water is so low that the molecular mechanism behind the physical properties such as pK_a remains poorly understood, despite the importance in fields such as chemistry and geology. Theoretical calculations provide the molecular-level information on such a rare chemical species yet face difficulties in the selection of reaction coordinates and the rare-event sampling of proton transfers (PTs) in condensed phases. We propose a straightforward calculation scheme of pK_a with ab initio molecular dynamics (MD) simulation and the constrained density functional theory (CDFT), which provides structural and dynamical properties such as radial distribution functions, vibrational spectra, and reaction paths. The calculated reaction free energies of deprotonations agreed with experiments within a few kcal/mol. Analysis of the solvation structure shows that, after deprotonation, the hydronium ion D₃O⁺ repels away from the deprotonated silicic acid SiO(OD)₃^- without forming a stable contact-ion pair. The calculated vibrational spectra are consistent with the spectroscopic measurements, and the dynamical analysis of the reaction path quantifies the couplings of the OD stretch vibrations of silicic acid and water to the PT reaction in terms of the vertical energy-gap coordinate that includes both the solute and the solvent components.

A solvent–solute cooperative mechanism for symmetry-breaking charge transfer

Random rotational fluctuation of solvents generates a large transient electric field that breaks the symmetry required for symmetry breaking charge transfer.

Polarizable Embedding with a Transferable H2O Potential Function I: Formulation and Tests on Dimer

The incorporation of mutual polarization in multiscale simulations where different regions of the system are treated at different level of theory is important in studies of, for example, electronic excitations and charge transfer processes. We present here an energy functional for describing a quantum mechanics/molecular mechanics (QM/MM) scheme that includes reciprocal polarization between the two subsystems. The inclusion of polarization alleviates shortcomings inherent in electrostatic embedding QM/MM models based on point-charge force fields. A density functional theory (DFT) description of the QM subsystem is coupled to a single center multipole expansion (SCME) description of H₂O molecules in the MM subsystem that includes anisotropic dipole and quadrupole polarizability as well as static multipoles up to and including the hexadecapole. The energy functional and the coupling scheme is general and can be extended to arbitrary order in terms of both the static and induced moments. Tests of the energy surface for the H₂O dimer show that the QM/MM results lie in between the pure DFT and pure SCME values. The consistency of the many-body contributions to the energy and analytical forces is demonstrated for an H₂O pentamer.