The influence of molecular shape on chemical reaction thermodynamics

Connecting Non-Gaussian Water Density Fluctuations to the Lengthscale Dependent Crossover in Hydrophobic Hydration

We connect density fluctuations in liquid water to lengthscale dependent crossover in hydrophobic hydration. Specifically, we employ indirect umbrella sampling (INDUS) simulations to characterize density fluctuations in observation volumes of various sizes and shapes in water and as a function of temperature and salt concentration. Consistent with previous observations, density fluctuations are Gaussian in small molecular scale volumes, but they display non-Gaussian "low-density fat tails" in larger volumes. These non-Gaussian tails are indicative of the proximity of water to its liquid to vapor phase transition and have implications on biomolecular interactions and function. We show that the onset of non-Gaussian fluctuations in large volumes is accompanied by the formation of a cavity in the observation volume. We develop a model that uses the physics of cavity-water interface formation as a key ingredient and show that it captures the nature of non-Gaussian density fluctuations over a broad region in water and in salt solutions. We discuss the limitations of this model in the very low density region of the distribution. Our calculations provide new insights into the origins of non-Gaussian density fluctuations in water and their connections to lengthscale dependent crossover in hydrophobic hydration.

Unraveling water's entropic mysteries: a unified view of nonpolar, polar, and ionic hydration

[Figure: see text]. Most chemical processes on earth are intimately linked to the unique properties of water, relying on the versatility with which water interacts with molecules of varying sizes and polarities. These interactions determine everything from the structure and activity of proteins and living cells to the geological partitioning of water, oil, and minerals in the Earth's crust. The role of hydrophobic hydration in the formation of biological membranes and in protein folding, as well as the importance of electrostatic interactions in the hydration of polar and ionic species, are all well known. However, the underlying molecular mechanisms of hydration are often not as well understood. This Account summarizes and extends emerging understandings of these mechanisms to reveal a newly unified view of hydration and explain previously mystifying observations. For example, rare gas atoms (e.g., Ar) and alkali-halide ions (e.g., K+ and Cl-) have nearly identical experimental hydration entropies, despite the significant charge-induced reorganization of water molecules. Here, we explain how such previously mysterious observations may be understood as arising from Gibbs inequalities, which impose rigorous energetic upper and lower bounds on both hydration free energies and entropies. These fundamental Gibbs bounds depend only on the average interaction energy of a solute with water, thus providing a deep link between solute-water interaction energies and entropies. One of the surprising consequences of the emerging picture is the understanding that the hydration of an ion produces two large but nearly perfectly cancelling, entropic contributions: a negative ion-water interaction entropy and a positive water reorganization entropy. Recent work has also clarified the relationship between the strong cohesive energy of water and the free energy required to form an empty hole (cavity) in water. Here, we explain how linear response theory (whose roots may also be traced to Gibbs inequalities) can provide remarkably accurate descriptions of the process of filling aqueous cavities with nonpolar, polar, or charged molecules. The hydration of nonpolar molecules is well-described by first-order perturbation theory, which implies that turning on solute-water van der Waals interactions does not induce a significant change in water structure. The larger changes in water structure that are induced by polar and ionic solutes are well-described by second-order perturbation theory, which is equivalent to linear response theory. Comparisons of the free energies of nonpolar and polar or ionic solutes may be used to experimentally determine electrostatic contributions to water reorganization energies and entropies. The success of this approach implies that water's ability to respond to solutes of various polarities is far from saturated, as illustrated by simulations of acetonitrile (CH 3CN) in water, which reveal that even such a strongly dipolar solute only produces subtle changes in the structure of water.

Equilibrium solvation in quadrupolar solvents

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and nonzero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-bridge-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from molecular-dynamics simulations.

Solvation Thermodynamics: Theory and Applications

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.

Solvent reorganization energy of electron-transfer reactions in polar solvents

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.