Lawrence R. Pratt

Theory of the hydrophobic effect

A microscopic theory is developed which can describe many of the structural and thermodynamic properties of infinitely dilute solutions of apolar solutes in liquid water. The theory is based on an integral equation for the pair correlation functions associated with spherical apolar species dissolved in water. It requires as input the experimentally determined oxygen–oxygen correlation function for pure liquid water. The theory is tested by computing thermodynamic properties for aqueous solutions of apolar solute species. The predictions of both the Henry’s Law constant and the entropy of solution are in good agreement with experiment. The calculation of the latter quantity is essentially independent of any adjustable parameters. It is shown how the correlation functions we have calculated can be used to predict the solubility of more complicated, aspherical, and nonrigid solutes in liquid water. For the more complex molecules it is convenient to study the difference between the excess chemical potential o...

Statistical mechanics of chemical equilibria and intramolecular structures of nonrigid molecules in condensed phases

An exact classical statistical mechanical theory is developed which describes how intermolecular forces alter the average intramolecular structures of nonrigid molecules and how these forces affect the equilibrium constant of chemically reacting species. The theory lends itself to computationally convenient approximations. Three illustrative applications of the theory are given. First, the equilibrium constant for the reaction N2O2?2NO2 is studied. Second, the shift in the chemical bond lengths of N2 and O2 from their gas phase values to those in the liquid are calculated from the theory. Third, the average conformational structure of n‐butane in various dense fluid solvents is predicted. The basic methods used in the derivation of the theory are the techniques of physical cluster series (as opposed to the usual Mayer ’’mathematical’’ cluster expansions), and topological reductions. The formalism gives rise to a renormalization of chemical bonding Boltzmann factors so that the theoretical expressions are ...

MOLECULAR THEORY OF HYDROPHOBIC EFFECTS: “She is too mean to have her name repeated.”*

This paper reviews the molecular theory of hydrophobic effects relevant to biomolecular structure and assembly in aqueous solution. Recent progress has resulted in simple, validated molecular statistical thermodynamic theories and clarification of confusing theories of decades ago. Current work is resolving effects of wider variations of thermodynamic state, e.g., pressure denaturation of soluble proteins, and more exotic questions such as effects of surface chemistry in treating stability of macromolecular structures in aqueous solution.

New perspectives on hydrophobic effects

Abstract Recent breakthroughs in the theory of hydrophobic effects permit new analyses of several characteristics of hydrophobic hydration and interaction. Heat capacities of non-polar solvation, and their temperature dependences, are analyzed within an information theory approach, using experimental information available from bulk liquid water. Non-polar solvation in aqueous electrolytes is studied by computer simulations, and interpreted within the information theory. We also study the preferential solvation of small non-polar molecules in heavy water (D 2 O) relative to light water (H 2 O) and find that this revealing difference can be explained by the higher compressibility of D 2 O. We develop a quasi-chemical description of hydrophobic hydration that incorporates the hydration structure and permits quantum-mechanical treatment of the solute. Finally, these new results are discussed in the context of hydrophobic effects in protein stability and folding, and of mesoscopic hydrophobic effects such as dewetting.

A statistical method for identifying transition states in high dimensional problems

A statistical method based on Monte Carlo sampling of paths associated with Markovian stochastic processes is proposed for the location of transition states in molecularly complex reactions. It is discussed in what respects the proposed method would identify transition state regions, and an algorithm for Metropolis sampling of Metropolis paths (based on the Metropolis random walk process) is devised. Physical aspects of this new algorithm are examined, and the relation of this method to simulated annealing algorithms for physical design of circuits is noted.

Surface potential of the water liquid–vapor interface

The surface potential of the water liquid-vapor interface is studied by molecular dynamics using the TIP4P model. The surface potential predicted by this empirical model is -(130 +/- 50) mV. This value for the surface potential is of reasonable magnitude but of opposite sign to the expectations derived from laboratory experiments. The electrostatic potential displays a nonmonotonic variation with depth into the liquid. This nonmonotonic variation is explained on the basis of the nondipolar charge distribution of the H2O molecule and the observation that the more probable molecular orientations in the interfacial region place the molecular symmetry axis near the plane of the interface. It is shown that minor changes in the assumed molecular charge distribution can bring the computed surface potential into agreement with experimental expectations without qualitatively altering the nonmonotonic variation of the electrostatic potential through the interfacial region. Computed quantum mechanical descriptions of the electron distribution of the isolated H2O molecule are not compatible with the surface structure predicted by the TIP4P model and the experimental expectation that the surface potential of the water liquid-vapor interface is small, roughly of the of order of 10-100 mV. The surface potential is sensitive to details in the large distance wings of the molecular electron distribution. It is hypothesized that the surface environment qualitatively alters the wings of the distribution from the result obtained by a superposition of the isolated molecule electron densities.

The Hydration Number of Li+ in Liquid Water

The hydration of ions in water is not only fundamental to physical chemistry, but is also relevant to the current issue of selectivity of biological ion channels. In the context of potassium channels for example, the free energies for replacement of inner shell water ligands with peptide carbonyls donated by proteins of the channel, specifically for the preference of K{sup +} over Na{sup +}. Studies to elucidate the thermodynamic features of such inner shell exchange reactions require prior knowledge of the ion hydration structures and energetics. Simulations have produced a range of results including both four and six inner shell water neighbors with considerable statistical dispersion. Simulations are typically not designed to provide sole determinations of such properties, although they do shed light on the issues determining the hydration number of ions in water. The theoretical scheme used here to address these problems for the Li{sup +}(aq) ion is based upon the quasi-chemical organization of solution theory, which is naturally suited to these problems.

Statistical mechanics of small chain molecules in liquids. I. Effects of liquid packing on conformational structures

When a chain molecule can be viewed as a collection of overlapping spherical groups, the effect of a solvent on the conformational structure of the chain molecule is described by the distribution function for the cavity particles associated with the spherical groups. This article discusses the calculation of the cavitydistribution function for n‐butane disolved in various apolar solvents: the liquidscarbon tetrachloride, n‐butane, and n‐hexane. We consider the common picture where the CH3 and CH2 groups in n‐butane are simple spheres. For that model, the cavitydistribution function is a four‐point correlation function. We find that the superposition approximation for the four‐point function, while qualitatively correct, overestimates the effects of the solvent. An alternative scheme, which is called the two cavitymodel, yields results that agree quantitatively with a computer simulation study of liquidn‐butane. We find that a solvent medium produces significant shifts in the conformational equilibrium of n‐butane from that found in the gas phase. This phenomenon is the result of the nature of the local packing of solvent molecules neighboring the solute species under investigation. The conformational equilibrium is sensitive to this packing. The bulk packing fractions (molecular density times the volume of the molecule) of the liquids CCl4 and C4H10 are nearly identical. Even so there are noticeable differences between the intramolecular structure of n‐butane in liquidcarbon tetrachloride and in the neat liquid. Previous ideas on conformational equilibria have ignored the importance of steric (i.e., liquid packing) effects, and have assumed that solvent shifts in conformational structures can be attributed entirely to dielectric effects. Our calculations show that this assumption is wrong. The n‐butane molecule contains no significantly polar groups. yet solvent media produce substantial shifts. For example, the t r a n s–g a u c h e equilibrium constant, x g /x t , for n‐butane in the gas phase at room temperature is roughly 0.5, while we find it is about 1.0 when n‐butane is dissolved in liquid CCl4 at the same temperature and 1 atm pressure. We discuss why the phenomenon has been overlooked, and suggest experiments to document its existence.

Ion sizes and finite-size corrections for ionic-solvation free energies

Free energies of ionic solvation calculated from computer simulations exhibit a strong system size dependence. We perform a finite-size analysis based on a dielectric-continuum model with periodic boundary conditions. That analysis results in an estimate of the Born ion size. Remarkably, the finite-size correction applies to systems with only eight water molecules hydrating a sodium ion and results in an estimate of the Born radius of sodium that agrees with the experimental value.

Absolute hydration free energies of ions, ion–water clusters, and quasichemical theory

Experimental studies of ion–water clusters have provided insights into the microscopic aspects of hydration phenomena. One common view is that extending those experimental studies to larger cluster sizes would give the single-ion absolute hydration free energies not obtainable by classical thermodynamic methods. This issue is reanalyzed in the context of recent computations and molecular theories of ion hydration, particularly considering the hydration of H+, Li+, Na+, and HO− ions, and thence the hydration of neutral ion pairs. The hydration free energies of neutral pairs computed here are in good agreement with experimental results, whereas the calculated absolute hydration free energies and the excess chemical potentials deviate consistently from some recently tabulated hydration free energies based on ion–water cluster data. We show how the single-ion absolute hydration free energies are not separated from the potential of the phase in recent analyses of ion–water cluster data, even in the limit of la...