Dielectric relaxation dynamics of water and methanol solutions associated with the ionization ofN,N‐dimethylaniline: Theoretical analyses

Amino acid deprotonation rates from classical force fields

Acid ionization constants (pKa's) of titratable amino acid side chains have received a large amount of experimental and theoretical attention. In many situations, however, the rates of protonation and deprotonation, kon & koff, may also be important, for example in understanding the mechanism of action of proton channels or membrane proteins that couple proton transport to other processes. Protonation and deprotonation involve making and breaking of covalent bonds, which cannot be studied by classical force fields. However, environment effects on the rates should be captured by such methods. Here we present an approach for estimating deprotonation rates based on Warshel's extension of Marcus's theory of electron transfer, with input from molecular simulations. The missing bond dissociation energy is represented by a constant term determined by fitting the pKa value in solution. The statistics of the energy gap between protonated and deprotonated states is used to compute free energy curves of the two states and thus free energy barriers, from which the rate can be deduced. The method is applied to Glu, Asp, and His in bulk solution and select membrane proteins: the M2 proton channel, bacteriorhodopsin, and cytochrome c oxidase.

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.

Solvation dynamics and energetics of intramolecular hydride transfer reactions in biomass conversion

Solvent dynamics and non-equilibrium solvation alter the energetics of the hydride transfer step and thus, can significantly affect reaction kinetics.

TIME DEPENDENT DENSITY FUNCTIONAL METHODS AND THEIR APPLICATION TO CHEMICAL PHYSICS

This article reviews microscopic development of time dependent functional method and its application to chemical physics. It begins with the formulation of density functional theory. The time dependent extension is discussed after the equilibrium formulation. Its application is explained by solvation dynamics. In addition, it reviews studies of nonlinear effects on polar liquids and simple mixtures.

Protein collective motions coupled to ligand migration in myoglobin

Ligand migration processes inside myoglobin and protein dynamics coupled to the migration were theoretically investigated with molecular dynamics simulations. Based on a linear response theory, we identified protein motions coupled to the transient migration of ligand, carbon monoxide (CO), through channels. The result indicates that the coupled protein motions involve collective motions extended over the entire protein correlated with local gating motions at the channels. Protein motions, coupled to opening of a channel from the distal pocket to a neighboring xenon site, were found to share the collective motion with experimentally observed protein motions coupled to a doming motion of the heme Fe atom upon photodissociation of the ligand. Analysis based on generalized Langevin dynamics elucidated slow and diffusive features of the protein response motions. Remarkably small transmission coefficients for rates of the CO migrations through myoglobin were found, suggesting that the CO migration dynamics are characterized as motions governed by the protein dynamics involving the collective motions, rather than as thermally activated transitions across energy barriers of well-structured channels.

Exploring a free energy landscape by means of multidimensional infrared and terahertz spectroscopies

A model for the dipolar crystal system is employed to explore a role of free energy landscape (FEL), in which dipolar molecules are posted on two-dimensional lattice sites with two-state libratinal dynamics. All dipole-dipole interactions are included to have frustrated interactions among the dipoles. For the regular and distorted lattice cases, the FEL is calculated from the interaction energies and the total polarizations for all possible dipolar states at various temperatures. At high temperatures, the shape of the calculated FEL is smooth and parabolic, while it becomes bumpy at low temperatures exhibiting multiple local minima. To study dynamical aspects of the system, the single flip dynamics and the single-double mixed flips dynamics of dipoles are examined from a master equation approach. As the observables of linear absorption and two-dimensional (2D) infrared, far infrared, and terahertz spectroscopies, the first- and third-order response functions of polarization are calculated for different physical conditions characterized by the FEL. While the linear absorption signals decay in time in a similar manner regardless of the FEL profiles, the 2D signals exhibit prominent differences for those profiles. This indicates that we may differentiate the FEL profiles by changing two-time valuables in 2D spectroscopy. As illustrated in the single-double flips case, the FEL study by means of 2D spectroscopy, however, relies on the dynamics which is set independently from the FEL. The Smoluchowski equation is applied to examine the description of the collective dynamics on the microscopically calculated FEL. We found that the one-dimensional and 2D signals calculated from the Smoluchowski equation agree with those from master equation only at temperatures where the FEL becomes parabolic shape.

Free energy landscapes of electron transfer system in dipolar environment below and above the rotational freezing temperature

Electron transfer reaction in a polar solvent is modeled by a solute dipole surrounded by dipolar molecules with simple rotational dynamics posted on the three-dimensional distorted lattice sites. The interaction energy between the solute and solvent dipoles as a reaction coordinate is adopted and free energy landscapes are calculated by generating all possible states for a 26 dipolar system and by employing Wang-Landau sampling algorithm for a 92 dipolar system. For temperatures higher than the energy scale of dipole-dipole interactions, the free energy landscapes for the small reaction coordinate region have quadratic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] whereas for the large reaction coordinate region, the landscapes exhibit a nonquadratic shape. When the temperature drops, small notched structures appear on the free energy profiles because of the frustrated interactions among dipoles. The formation of notched structure is analyzed with statistical approach and it is shown that the amplitude of notched structure depend upon the segment size of the reaction coordinate and is characterized by the interaction energy among the dipoles. Using simulated free energy landscapes, the authors calculate the reaction rates as a function of the energy gap for various temperatures. At high temperature, the reactions rates follow a bell shaped (inverted parabolic) energy gap law in the small energy gap regions, while it becomes steeper than the parabolic shape in a large energy gap regions due to the nonquadratic shape of the free energy landscape. The peak position of parabola also changes as the function of temperature. At low temperature, the profile of the reaction rates is no longer smooth because of the many local minima of the free energy landscape.

Free energy landscape analysis of two-dimensional dipolar solvent model at temperatures below and above the rotational freezing point

Ionic solvation in a polar solvent is modeled by a central charge surrounded by dipolar molecules posted on two-dimensional distorted lattice sites with simple rotational dynamics. Density of states is calculated by applying the Wang-Landau algorithm to both the energy and polarization states. The free energy landscapes of solvent molecules as a function of polarization are depicted to explore the competition between the thermal fluctuation and solvation energy. Without a central charge, for temperatures higher than the energy scale of the dipole-dipole interactions, the energy landscape for the small polarization region exhibits a parabolic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] for electron transfer reaction, while there is an additional quartic contribution to the landscape for the large polarization region. When the temperature drops, the simulated free energy landscapes are no longer smooth due to the presence of multiple local minima arising from the frustrated interaction among the dipoles. The parabolic contribution becomes negligible and the energy landscape becomes quartic in shape. For a strong central charge, the energy landscape exhibits an asymmetric profile due to the contributions of linear and cubic terms that arise from the charge-dipole interactions.

Theoretical Study on Electronic and Spin Structures of [Fe2S2]2+,+ Cluster: Reference Interaction Site Model Self-Consistent Field (RISM-SCF) and Multireference Second-Order Møller−Plesset Perturbation Theory (MRMP) Approach

Electronic structures of [Fe(2)S(2)(SCH(3))(4)](2-,3-) in DMSO solution are calculated using reference interaction site model complete active space self-consistent field (RISM-CASSCF)/multireference second-order Møller-Plesset perturbation theory (MRMP) method. For the reduced state, we obtain both the low-spin Fe(3+)Fe(2+) localized and high-spin Fe(2.5+)Fe(2.5+) delocalized forms, which are very close in energy. The spin interaction constants obtained from the energies of states with various spin multiplicities are in good agreement with the available experimental estimates both for the oxidized and for the reduced states. The dynamic electron correlation effect is found to be important in estimating the spin interaction between the Fe ions. The redox potentials are calculated to be 2.87 and 2.78 eV for the localized and delocalized reduced states, respectively, which are close to the experimental values. We devise a simple model for calculating the free energy curves of the reduction process based on the RISM-SCF theory. The activation barrier height is calculated to be 7.4 kcal/mol at the equilibrium geometry of oxidized state, indicating that the reduction reaction will occur efficiently in DMSO solvent. The effect of solvent fluctuation on the free energy profiles is discussed on the basis of the present calculations.

Electronic relaxation dynamics of Ni2+-ion aqueous solution: Molecular-dynamics simulation

Electronic relaxation dynamics of Ni2+-ion aqueous solution is investigated using molecular-dynamics (MD) simulations with the model-effective Hamiltonian developed previously. The nonadiabatic transition rates from the first three excited states to the ground state are evaluated by the golden rule formula with the adiabatic MD simulations. The MD simulations with the fewest-switch surface-hopping method are also carried out to obtain a more detailed description of the electronic relaxation dynamics among the excited states. We found out that the transitions among the three excited states are very fast, in the order of 10 fs, while the transition between the excited and ground states is slow, about 800 ps. These findings are consistent with the time scales of energy dissipation detected by the transient lens experiment. In both simulations, we explore the effects of the quantum decoherence, where the decoherence functions are derived by the energy-gap dynamics with the displaced harmonic-oscillator model.

Proton Transfer in Nanoconfined Polar Solvents. 1. Free Energies and Solute Position

The reaction free energy curves for a model phenol-amine proton-transfer system in a confined CH3Cl solvent have been calculated by Monte Carlo simulations. The free energy curves, as a function of a collective solvent coordinate, have been obtained for several fixed reaction complex radial positions (based on the center-of-mass). A smooth, hydrophobic spherical cavity was used to confine the solvent, and radii of 10 and 15 A have been considered. Quantum effects associated with the transferring proton have been included by adding the proton zero-point energy to the classical free energy. The results indicate the reaction complex position can be an important component of the reaction coordinate for proton-transfer reactions in nanoconfined solvents.

Solvation Dynamics in Reverse Micelles: The Role of Headgroup−Solute Interactions

We present molecular dynamics simulation results for solvation dynamics in the water pool of anionic-surfactant reverse micelles (RMs) of varying water content, w(0). The model RMs are designed to represent water/aerosol-OT/oil systems, where aerosol-OT is the common name for sodium bis(2-ethylhexyl)sulfosuccinate. To determine the effects of chromophore-headgroup interactions on solvation dynamics, we compare the results for charge localization in model ionic diatomic chromophores that differ only in charge sign. Electronic excitation in both cases is modeled as charge localization on one of the solute sites. We find dramatic differences in the solvation responses for anionic and cationic chromophores. Solvation dynamics for the cationic chromophore are considerably slower and more strongly w(0)-dependent than those for the anionic chromophore. Further analysis indicates that the difference in the responses can be ascribed in part to the different initial locations of the two chromophores relative to the surfactant interface. In addition, slow motion of the cationic chromophore relative to the interface is the main contributor to the longer-time decay of the solvation response to charge localization in this case.

Solvation Dynamics in Acetonitrile: A Study Incorporating Solute Electronic Response and Nuclear Relaxation

The solvent reorganization process after electronic excitation of a polar solute in a polar solvent such as acetonitrile is related mainly to the time evolution of the solute-solvent electrostatic interaction. Modern laser-based techniques have sufficient time resolution to follow this decay in real time, providing information to be confirmed and interpreted by theories and models. We present here a study aimed at the investigation of the different steps involved in the process taking place after a vertical S(0) --> S(1) excitation of a large size chromophore, coumarin 153 (C153), in acetonitrile, from both the solute and the solvent points of view. To do this, we use accurate quantum mechanical calculations for the solute properties within the polarizable continuum model (PCM) and classical molecular dynamics (MD) simulations, both equilibrium and nonequilibrium, for C153 in the presence of the solvent. The geometry of the solute is allowed to change in order to study the role of internal motions in the time-dependent solvation process. The solvent response function has been obtained from the simulation data and compared to experiment, while the comparison between equilibrium and nonequilibrium MD results for the solvation response confirms the validity of the linear response approximation in the C153-acetonitrile system. The MD trajectories have also been used to monitor the structure of the solvation shell and to determine its change in response to the change in the solute partial charges.

Ab Initio Molecular Dynamics Simulation of the Aqueous Ru2+/Ru3+ Redox Reaction: The Marcus Perspective

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.