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Lawrence R. Pratt

Publications and source records attributed to Lawrence R. Pratt.

At least 37 records · Page 2Linked to original sources
arXiv2003

Absolute Hydration Free Energies of Ions, Ion-Water Clusters, and Quasi-chemical Theory

Experimental studies on 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 on 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 large cluster sizes. We conclude that naive calculations on ion-water clusters ought to agree with results obtained from experimental studies of ion-water clusters because both values include the contribution, somewhat extraneous to the local environment of the ion, from the potential of the phase.

physics.chem-ph↗
arXiv2003

Quasi-chemical study of Be$^{2+}$(aq) speciation

Be$^{2+}$(aq) hydrolysis can to lead to the formation of multi-beryllium clusters, but the thermodynamics of this process has not been resolved theoretically. We study the hydration state of an isolated Be$^{2+}$ ion using both the quasi-chemical theory of solutions and ab initio molecular dynamics. These studies confirm that Be$^{2+}$(aq) is tetra-hydrated. The quasi-chemical approach is then applied to then the deprotonation of $Be(H_2O)_4^{2+}}$ to give $BeOH(H_2O)_3{}^{+}}$. The calculated pK$_a$ of 3.8 is in good agreement with the experimentally suggested value around 3.5. The calculated energetics for the formation of BeOHBe$^{3+}$ are then obtained in fair agreement with experiments.

physics.chem-ph↗
arXiv2002

Hydration of Krypton and Consideration of Clathrate Models of Hydrophobic Effects from the Perspective of Quasi-Chemical Theory

AIMD results on a liquid krypton-water system are compared to recent XAFS results for the radial hydration structure for a Kr atom in liquid water solution. The comparisons with the liquid solution results are satisfactory and significantly different from the radial distributions extracted from the data on the solid clathrate hydrate phase. The calculations also produce the coordination number distribution that can be examined for metastable coordination structures suggesting possibilities for clathrate-like organization; none are seen in these results. Clathrate pictures of hydrophobic hydration are discussed, as is the quasi-chemical theory that should provide a basis for clathrate pictures. Outer shell contributions are discussed and accurately estimated; they are positive and larger than the positive experimental hydration free energy of Kr(aq), implying that inner shell contributions must be negative. Clathrate-like inner shell coordination structures extracted from the simulation of the liquid, and then subjected to quantum chemical optimization, always decomposed. Interactions with the outer shell material are decisive in stabilizing coordination structures observed in liquid solution and in clathrate phases. The ``what are we to tell students'' question about hydrophobic hydration, often answered with structural models such as clathrate pictures, is then considered; we propose an alternative answer that is consistent with successful molecular theories of hydrophobic effects and based upon distinctive observable properties of liquid water. Considerations of parsimony, for instance Ockham's razor, then suggest that additional structural hypotheses in response to ``what are we to tell students'' aren't required at this stage

physics.bio-ph↗
arXiv2001

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

physics.chem-ph↗
arXiv2001

Quasi-chemical Theory for the Statistical Thermodynamics of the Hard Sphere Fluid

We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situation of hard-core interactions is addressed by considering the binding of solvent molecules to a precisely defined `cavity' in order to assess the probability that the `cavity' is entirely evacuated. The primitive quasi-chemical approximation corresponds to a extension of the Poisson distribution used as a default model in an information theory approach. This primitive quasi-chemical theory is in good qualitative agreement with the observations for the hard sphere fluid of occupancy distributions that are central to quasi-chemical theories but begins to be quantitatively erroneous for the equation of state in the dense liquid regime of $ρd^3>$0.6. How the quasi-chemical approach can be iterated to treat correlation effects is addressed. Consideration of neglected correlation effects leads to a simple model for the form of those contributions neglected by the primitive quasi-chemical approximation. These considerations, supported by simulation observations, identify a `break away' phenomena that requires special thermodynamic consideration for the zero (0) occupancy case as distinct from the rest of the distribution. A empirical treatment leads to a one parameter model occupancy distribution that accurately fits the hard sphere equation of state and observed distributions.

physics.chem-ph↗
arXiv2000

The hydration number of Na+ in liquid water

An `ab initio' molecular dynamics simulation of a Na+ ion in aqueous solution is presented and discussed. The calculation treats a Na+ ion and 32 water molecules with periodic boundary conditions on a cubic volume determined by an estimate of zero partial molar volume for this solute in water at normal density and at a temperature of 344+/-24 K. Analysis of the last half of the 12 ps trajectory shows 4.6 water molecules occupying the inner hydration shell of the Na+ ion on average, with 5 being the most probable occupancy. The self-diffusion coefficient observed for the Na+ is 1.0 x 10$^{-5}$ cm$^2$/s. The quasi-chemical theory of solutions provides the framework for two more calculations. First a complementary calculation, based on electronic structure results for ion-water clusters and a dielectric continuum model of outer sphere hydration contributions, predicts an average hydration shell occupancy of 4.0. This underestimate is attributed to the harmonic approximation for the clusters in conjunction with the approximate dielectric continuum model treatment of outer sphere contributions. Finally, a maximum entropy fitting of inner sphere occupancies that leads to insensitive composite free energy approximations suggests a value in the neighborhood of -68 kcal/mol for the hydration free energy of Na+ (aq) under these conditions with no contribution supplied for packing or van der Waals interactions.

physics.chem-ph↗
arXiv2000

The Hydration Number of Li+ in Liquid Water

A theoretical treatment based upon the quasi-chemical theory of solutions predicts the most probable number of water neighbors in the inner shell of a Li+ ion in liquid water to be four. The instability of a six water molecule inner sphere complex relative to four-coordinated structures is confirmed by an `ab initio' molecular dynamics calculation. A classical Monte Carlo simulation equilibrated 26 water molecules with a rigid six-coordinated Li(H2O)6+ complex with periodic boundary conditions in aqueous solution. With that initial configuration for the molecular dynamics, the six-coordinated structure relaxed into four-coordinated arrangements within 112 fs and stabilized. This conclusion differs from prior interpretations of neutron and X-ray scattering results on aqueous solutions.

physics.chem-ph↗
arXiv1999

Quasi-Chemical Theory and Implicit Solvent Models for Simulations

A statistical thermodynamic development is given of a new implicit solvent model that avoids the traditional system size limitations of computer simulation of macromolecular solutions with periodic boundary conditions. This implicit solvent model is based upon the quasi-chemical approach, distinct from the common integral equation trunk of the theory of liquid solutions. The physical content of this theory is the hypothesis that a small set of solvent molecules are decisive for these solvation problems. A detailed derivation of the quasi-chemical theory escorts the development of this proposal. The numerical application of the quasi-chemical treatment to Li$^+$ ion hydration in liquid water is used to motivate and exemplify the quasi-chemical theory. Those results underscore the fact that the quasi-chemical approach refines the path for utilization of ion-water cluster results for the statistical thermodynamics of solutions.

physics.chem-ph↗
arXiv1998

Molecular theories and simulation of ions and polar molecules in water

Recent developments in molecular theories and simulation of ions and polar molecules in water are reviewed. The hydration of imidazole and imidazolium solutes is used to exemplify the theoretical issues. The treatment of long-ranged electrostatic interactions in simulations is discussed extensively. It is argued that the Ewald approach is an easy way to get correct hydration free energies in the thermodynamic limit from molecular calculations; and that molecular simulations with Ewald interactions and periodic boundary conditions can also be more efficient than many common alternatives. The Ewald treatment permits a conclusive extrapolation to infinite system size. The picture that emerges from testing of simple models is that the most prominent failings of the simplest theories are associated with solvent proton conformations that lead to non-gaussian fluctuations of electrostatic potentials. Thus, the most favorable cases for the second-order perturbation theories are monoatomic positive ions. For polar and anionic solutes, continuum or gaussian theories are less accurate. The appreciation of the specific deficiencies of those simple models have led to new concepts, multistate gaussian and quasi-chemical theories, that address the cases for which the simpler theories fail. It is argued that, relative to direct dielectric continuum treatments, the quasi-chemical theories provide a better theoretical organization for the computational study of the electronic structure of solution species.

physics.chem-ph↗
arXiv1998

Quasi-chemical Theories of Associated Liquids

It is shown how traditional development of theories of fluids based upon the concept of physical clustering can be adapted to an alternative local clustering definition. The alternative definition can preserve a detailed valence description of the interactions between a solution species and its near-neighbors, i.e., cooperativity and saturation of coordination for strong association. These clusters remain finite even for condensed phases. The simplest theory to which these developments lead is analogous to quasi-chemical theories of cooperative phenomena. The present quasi-chemical theories require additional consideration of packing issues because they don't impose lattice discretizations on the continuous problem. These quasi-chemical theories do not require pair decomposable interaction potential energy models. Since calculations may be required only for moderately sized clusters, we suggest that these quasi-chemical theories could be implemented with computational tools of current electronic structure theory. This can avoid an intermediate step of approximate force field generation.

physics.chem-ph↗
arXiv1997

Hydrolysis of ferric ion in water and conformational equilibrium

Reported here are results of theoretical calculations on the hexaaquoferric complex and deprotonated products to investigate the molecular mechanisms of hydrolysis of ferric ion in water. The combination of density functional electronic structure techniques and a dielectric continuum model for electrostatic solvation applied to the Fe(H$_2$O)$_6$$^{3+}$ complex yields -1020~kcal/mol (experimental values -1037~kcal/mol to -1019~kcal/mol) for the absolute free energy of the aqueous ferric ion. The predicted reaction energy change for the first hydrolysis is 2 kcal/mol (compared to 3 kcal/mol experimental). For the second hydrolysis, we found an unexpected low energy isomer of Fe(H$_2$O)$_4$(OH)$_2$$^{+}$ with five ligands in the inner sphere and one water outside. The cis and trans isomers are, respectively, slightly lower and higher in energy. Extrusion of the additional water to the outer sphere is nearly thermoneutral. The reaction free energy for the second hydrolysis is predicted in the range 16-18~kcal/mol, higher than the experimental value of 5~kcal/mol. Since the theoretical predictions for the second hydrolysis are higher than experimental values and novel structures were encountered, we argue that conformational entropy is important in these reactions.

physics.chem-ph↗
arXiv1997

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.

physics.chem-ph↗
arXiv1997

Molecular Modeling of Trifluoromethanesulfonic Acid for Solvation Theory

Reported here are theoretical calculations on the triflic acid and water, establishing molecular scale information necessary to modeling of the structure, thermodynamics, and ionic transport of Nafion membranes. To characterize side chain flexibility and accessibility of the acid proton, free energies for rotation of both carbon-sulfur and sulfur-oxygen (hydroxyl) bonds are presented. The energetic barrier to rotation of the acid proton away from the sulfonic acid oxygen plane is substantially flattened, with barrier less than one kcal/mol, by electrostatic solvation. The activation free energy for acid-water proton interchange is about 4.7 kcal/mol.

physics.chem-ph↗
arXiv1997

Electrostatic potentials and free energies of solvation of polar and charged molecules

Theories of solvation free energies often involve electrostatic potentials at the position of a solute charge. Simulation calculations that apply cutoffs and periodic boundary conditions based on molecular centers result in center-dependent contributions to electrostatic energies due to a systematic sorting of charges in radial shells. This sorting of charges induces a surface-charge density at the cutoff sphere or simulation-box boundary that depends on the choice of molecular centers. We identify a simple solution that gives correct, center-independent results, namely the radial integration of charge densities. Our conclusions are illustrated for a Lennard-Jones solute in water. The present results can affect the parameterization of force fields.

physics.chem-ph↗
arXiv1996

Origin of entropy convergence in hydrophobic hydration and protein folding

An information theory model is used to construct a molecular explanation why hydrophobic solvation entropies measured in calorimetry of protein unfolding converge at a common temperature. The entropy convergence follows from the weak temperature dependence of occupancy fluctuations for molecular-scale volumes in water. The macroscopic expression of the contrasting entropic behavior between water and common organic solvents is the relative temperature insensitivity of the water isothermal compressibility. The information theory model provides a quantitative description of small molecule hydration and predicts a negative entropy at convergence. Interpretations of entropic contributions to protein folding should account for this result.

physics.chem-ph↗
arXiv1995

The hydration free energy of water

We study the chemical potential of water as a function of charge based on perturbation theory. By calculating the electrostatic-energy fluctuations of two states (fully charged and uncharged) we are able to determine accurate values for the dependence of the chemical potential on charge. We find identical results for the chemical-potential difference of fully charged and uncharged water from overlapping-histogram and acceptance-ratio methods and by smoothly connecting the curves of direct exponential averages. Our results agree with those of Rick and Berne (J. Am. Chem. Soc., 1994, 116, 3949) with respect to both the chemical-potential difference and its dependence on the charge coupling parameter. We observe significant deviations from simple Gaussian-fluctuation statistics. The dependence on the coupling parameter is not quadratic, as would be inferred from linear continuum models of electrostatics.

chem-ph↗
arXiv1995

On the free energy of ionic hydration

The hydration free energies of ions exhibit an approximately quadratic dependence on the ionic charge, as predicted by the Born model. We analyze this behavior using second-order perturbation theory. This provides effective methods to calculating free energies from equilibrium computer simulations. The average and the fluctuation of the electrostatic potential at charge sites appear as the first coefficients in a Taylor expansion of the free energy of charging. Combining the data from different charge states allows calculation of free-energy profiles as a function of the ionic charge. The first two Taylor coefficients of the free-energy profiles can be computed accurately from equi- librium simulations; but they are affected by a strong system-size dependence. We apply corrections for these finite-size effects by using Ewald lattice sum- mation and adding the self-interactions consistently. Results are presented for a model ion with methane-like Lennard-Jones parameters in SPC water. We find two very closely quadratic regimes with different parameters for positive and negative ions. We also studied the hydration free energy of potassium, calcium, fluoride, chloride, and bromide ions. We find negative ions to be solvated more strongly compared to positive ions of equal size, in agreement with experimen- tal data. We ascribe this preference of negative ions to their strong interac- tions with water hydrogens, which can penetrate the ionic van der Waals shell without direct energetic penalty in the models used. We also find a positive electrostatic potential at the center of uncharged Lennard-Jones particles in water, which favors negative ions. Regarding finite-system-size effects, we show that even using only 16 water molecules it is possible to calculate accu- rately the hydration free energy of sodium if self-interactions are considered.

chem-ph↗