Potential functions for alkali halide molecules

Repulsion and dispersion parameters for alkali–metal halide diatomic molecules were computed by ionic Rittner and truncated Rittner models with radial dependent repulsion terms. Experimental data on the bond energies, the equilibrium interionic distances, and the spectroscopic frequencies were employed for the purpose. The polarizabilities used were also computed from the experimental dipole moments of alkali–metal halides. The potential parameters obtained were compared with parameters from other sources and checked for consistency. The computed potential parameters of alkali–metal halide monomer molecules were used to predict the energetics and geometries for alkali–metal halide dimer molecules. The predicted values are in good agreement with experiment and other calculations indicating the consistency and reliability of the potential employed. Although the magnitude of repulsive and dispersive energy terms varies with potential functions employed, the difference between the two for a molecule is constant. The repulsive term is more sensitive than the attractive term. The uncertainty in the exponential repulsion results in an inaccurate representation of the attractive contribution. Introduction of the radial-dependent repulsion term changes the relative magnitudes of repulsive and dispersive parameters and hence the relative contribution to the total potential with monomers. But this has no significant effect on the energetics and geometries of the dimers.     

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.     

A microsolvation approach to the prediction of the relative enthalpies and free energies of hydration for ammonium ions

Hartree–Fock (HF) and second-order Møller–Plesset (MP2) calculations were used to investigate the structures and thermochemistry of methylammonium–water clusters (Me_4-m NH _m ⁺ (H₂O) _n , m=1–4, n=1–4). Water molecules were treated ab initio and with effective fragment potentials (EFP). In addition to a thorough phase-space search, the importance of basis set, electron correlation, and thermodynamic effects was systematically examined. Cluster structures resulted from hydrogen bond formation between the ammonium group and water molecules; upon saturation of the hydrogen bonding sites of the ammonium group, water molecules entered the second hydration shell. With only four water molecules, the experimental relative enthalpies of hydration were well reproduced at the HF level, while the MP2 relative free energies were in best agreement with experiment. Absolute energies of hydration were calculated using an empirical correction. These results strongly suggest that a HF-based microsolvation approach employing a small number of water molecules can be used to compute relative enthalpies of hydration.     

Convergence radii of the perturbation expansions for the ground-state energies of finite Hubbard models

The ground state energies of finite Hubbard molecules are calculated by numerically solving the Lieb–Wu equations for a complex Hubbard repulsion parameter U. From the positions of the singular points located in the complex plane, the radii of convergence of the perturbation expansions for the ground state energies are determined.     

A Monte Carlo simulation of Fe2+ aqueous solvation

A Monte Carlo simulation of Fe²⁺ aqueous solvation, at 298 K, including 100 water molecules, has been done using periodic boundary conditions under the minimum image conversion. The energy has been calculated in the pair-potential approach, employing the MCY potential for the H₂OH₂O interaction and an ab initio analytical potential generated by us for the Fe²⁺H₂O interaction. The examination of interaction energies and of the radial distribution functions clearly show that the first hydration shell is formed by eight water molecules. By classifying the generated configurations into different significant structures of the solvent, it has been found that the eight water molecules of the first hydration shell are situated in a lightly distorted D_4d structure which maximizes the water—solute stabilization and minimizes the water—water repulsion. Finally, the validity of our theoretical predictions is discussed.     

Estimating the Gibbs Hydration Energies of Actinium and Trans-Plutonium Actinides

The use of actinides for medical, scientific and technological purposes has gained momentum in the recent years. This creates a need to understand their interactions with biomolecules, both at the interface and as they become complexed. Calculation of the Gibbs binding energies of the ions to biomolecules, i. e., the Gibbs energy change associated with a transfer of an ion from the water phase to its binding site, could help to understand the actinides’ toxicities and to design agents that bind them with high affinities. To this end, there is a need to obtain accurate reference values for actinide hydration, that for most actinides are not available from experiment. In this study, a set of ionic radii is developed that enables future calculations of binding energies for Pu³⁺ and five actinides with renewed scientific and technological interest: Ac³⁺, Am³⁺, Cm³⁺, Bk³⁺ and Cf³⁺. Reference hydration energies were calculated using quantum chemistry and ion solvation theory and agree well for all ions except Ac³⁺, where ion solvation theory seems to underestimate the magnitude of the Gibbs hydration energy. The set of radii and reference energies that are presented here provide means to calculate binding energies for actinides and biomolecules.     

SCF and CI Studies of Hund's rules for the effects of electronic correlation and delocalization. I

In connection with the reinterpretation of Hund's multiplicity rules for molecules, a detailed study has been made of the energy differences in the total energy and its components for the triplet and singlet Π_u states of the hydrogen molecule and the analogous states of the four- and six-membered hydrogen atom rings. For the hydrogen molecule, both SCF and CI studies indicated that the outer electron is considerably more contracted in the triplet than in the singlet state. In both approximations, the energy difference is dominated for all bond distances of chemical and physical significance by the electron-nuclear attraction component and not by the electron repulsion component as predicted by simple first-order perturbation theory. Although the correlation energy for each of the states is of the same magnitude as the energy differences considered here, the difference of the correlation energies is much smaller. It had little effect on the qualitative differences between these states of the hydrogen molecule. For the four- and six-membered rings, SCF studies were made on the lowest singlet and triplet states where one electron was promoted from the σ_g to a Π_u orbital. Even though the coupled electrons were more delocalized in these cases, the electron repulsion became relatively more important. However in all cases, the lower state had the highest electron repulsion energy and lower electron-nuclear attraction. The triplet state continued to have the more contracted outer open-shell orbital.     

The investigation on the relative stability of different clusters of thiourea dioxide in water using gas phase quantum chemical calculations

The relative stability of different clusters of thiourea dioxide (TDO) in water is examined using gas phase quantum chemical calculations at the MP2 and B3LYP level with 6‐311++G(d,p) basis set. The possible equilibrium structures and other energetic and geometrical data of the thiourea dioxide clusters, TDO‐(H₂O)_n (n is the number of water molecules), are obtained. The calculation results show that a strong interaction exists between thiourea dioxide and water molecules, as indicated by the binding energies of the TDO clusters progressively increased by adding water molecules. PCM model is used to investigate solvent effect of TDO. We obtained a negative hydration energy of ?20.6 kcal mol^?1 and free‐energy change of ?21.0 kcal mol^?1 in hydration process. On the basis of increasing binding energies with adding water molecules and a negative hydration energy by PCM calculation, we conclude thiourea dioxide can dissolve in water molecules. Furthermore, the increases of the C? S bond distance by the addition of water molecules show that the strength of the C? S bonds is attenuated. We find that when the number of water molecules was up to 5, the C? S bonds of the clusters, TDO‐(H₂O)₅ and TDO‐(H₂O)₆ were ruptured. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The hydration of anions in nonaqueous media

A very simple isopiestic method based on that of S. Christian is used for measuring the salting-in of water into nonpolar, low-volatility solvents by tetraalkylammonium salts. The quantity of excess water which is dissolved in such solvents is directly proportional to the salt concentration and is sharply dependent on the nature of the anion but is nearly insensitive to that of the R₄N⁺ cation. The hydration ratioH, which we define as the moles of excess solubilized water per mole of R₄N⁺ X^–, is directly relatable to the enthalpy of hydration of the anion X^– in several solvents and in the gas phase. The quantityH is also correlated with many free-energy terms including those for the Hofmeister lyotropic series, for the ability of the anions to salt nonelectrolytes out of water, for the free-energy terms for separation of these ions by reverse osmosis membranes, and for their nucleophilicities. A surprising (but not unprecedented) feature of the hydration ratio is that it, rather than its logarithm, behaves as a free-energy term. It is proposed that all these properties have in common the free energy of hydration of the anions, and this notion is supported by a close correspondence between the anionic hydration ratio and their hydrogen-bonding energies with proton donors in aprotic solvents. The results support scattered observations by other workers that isolated water molecules do not have an unusual inherent affinity for anions. Accordingly, large anionic hydration energies in bulk aqueous media reflect extensive cooperative interactions in the solvent. Implications for nucleophilic activity in phase transfer catalysis and enzyme activity are mentioned.     

A theoretical study of the hydration of Rb+ by Monte Carlo simulations with refined ab initio-based model potentials

An infinitely diluted aqueous solution of Rb⁺ was studied using ab initio-based model potentials in classical Monte Carlo simulations to describe its structural and thermodynamic features. An existing flexible and polarizable model [Saint-Martin et al. in J Chem Phys 113(24) 10899, 2000] was used for water–water interactions, and the parameters of the Rb⁺–water potential were fitted to reproduce the polarizability of the cation and a sample of ab initio pair interaction energies. It was necessary to calibrate the basis set to be employed as a reference, which resulted in a new determination of the complete basis set (CBS) limit energy of the optimal Rb⁺–OH₂ configuration. Good agreement was found for the values produced by the model with ab initio calculations of three- and four-body nonadditive contributions to the energy, as well as with ab initio and experimental data for the energies, the enthalpies and the geometric parameters of Rb⁺(H₂O) _n clusters, with n = 1,  2,…, 8. Thus validated, the potential was used for simulations of the aqueous solution with three versions of the MCDHO water model; this allowed to assess the relative importance of including flexibility and polarizability in the molecular model. In agreement with experimental data, the Rb⁺–O radial distribution function (RDF) showed three maxima, and hence three hydration shells. The average coordination number was found to be 6.9, with a broad distribution from 4 to 12. The dipole moment of the water molecules in the first hydration shell was tilted to 55° with respect to the ion’s electric field and had a lower value than the average in bulk water; this latter value was recovered at the second shell. The use of the nonpolarizable version of the MCDHO water model resulted in an enhanced alignment to the ion’s electric field, not only in the first, but also in the second hydration shell. The hydration enthalpy was determined from the numerical simulation, taking into account corrections to the interfacial potential and to the spurious effects due to the periodicity imposed by the Ewald sums; the resulting value lied within the range of the various different experimental data. An analysis of the interaction energies between the ion and the water molecules in the different hydration shells and the bulk showed the same partition of the hydration enthalpy as for K⁺. The reason for this similarity is that at distances longer than 3 Å, the ion–water interaction is dominated by the charge-(enhanced) dipole term. Thus, it was concluded that starting at K⁺, the hydration properties of the heavier alkali metal cations should be very similar.     

An application of the reaction field theory to hydrated metal cations in the framework of the MNDO,AM1, and PM3 methods

A reaction field theory, combined with the MNDO, AM1, and PM3 molecular orbital methods, was applied to hydration phenomena of metal cationic species. The first hydration shell was treated explicitly by using a supermolecular model, [M(H₂O)_n]^m+, and its surrounding medium was described with a continuum dielectric. Hydration free energies were evaluated as a sum of the contributions from the electrostatic interaction with the bulk medium, the hydrated cluster formation, the cavity formation, and the vaporization of water molecules forming the cluster. As a whole, calculated hydration energies were in good agreement with the corresponding experimental data over various kinds of metal cationic species. © 1995 by John Wiley & Sons, Inc.     

Computation of hydration free energies using a parameterized continuum model: Study of equilibrium geometries and reactive processes in water solution

A parameterized self-consistent reaction field model allowing computation of the total free energy of hydration of organic molecules at the ab initio level is presented. The approach uses electrostatic plus polarization energies calculated with the help of a continuum model. The remaining solvation free energy terms are obtained by a simple formula based on atomic parameters and atomic accessible surface areas (ASAs), which are determined with the ASA analytical algorithm. Analytical derivatives of the atomic surfaces areas have been implemented. The atomic parameters have been obtained by a linear regression fit of the calculated and experimental free energies of solution in water for a set of 35 molecules, leading to a standard deviation of 0.75 kcal/mol. Effects of nonelectrostatic terms on solute geometries, association energies, and activation barriers are illustrated. © 1996 by John Wiley & Sons, Inc.     

Molecular Dynamics Simulation of Mg2+ and Ca2+ Ions in Water

Molecular dynamics simulations of single Mg²⁺ and Ca²⁺ ions in water have been carried out. Different ion-water potentials from the literature have been used, whereas the same water potential, a rigid simple point charged model, has been considered in all the simulations. Structural, thermodynamic, and dynamic properties have been calculated, and the results for different potentials have been compared with available experimental data. The study includes ion–water radial distribution functions, coordination numbers, solution enthalpies, hydration free energies, self-diffusion coefficients, and reorientational times of water molecules in the hydration shells.     

Theoretical studies on the conformation of saccharides. V. Hydration of the acetal segment in glycosides

Hydration sites of the acetal segment were studied in five of the most stable conformers of 2-methoxy-tetrahydropyran (MTHP) as the first step in the determination of the hydration scheme of glycosides. The intramolecular geometries of a supermolecule formed with MTHP and water were calculated by a PCILO quantum-chemical method. The hydration sites determined can be classified into two groups: (a) individual sites, in which water interacts with one oxygen only, and (b) bridging sites, in which water interacts with both oxygens. The interaction energies of the individual sites are approximately 22 kJ mol^?1, and 26 and 29 kJ mol^?1 in the bridging sites. An increase of the number of water molecules in the hydration shell of MTHP showed that monohydration of the glycosidic linkage oxygens was most advantageous. Despite of the fact that the hydration shell have various structures in the individual MTHP conformers, the obtained results indicate that the hydration does not operate against the anomeric or exoanomeric effects, i.e., it does not influence the equilibrium of the MTHP conformers in favor of the trans arrangements of a glycosidic bond. Therefore, the experimentally observed stabilization of the trans positions in aqueous solutions should be considered as a result of influence of water being a dielectric continuum.     

Structural parameters of hydration of Be<Superscript>2+</Superscript> and Mg<Superscript>2+</Superscript> ions in aqueous solutions of their salts

Published data on structural characteristics of hydration of beryllium and magnesium ions in aqueous solutions of their salts under standard conditions, obtained by various methods, as well as authors’ X-ray data are reviewed. Structural parameters of the immediate environment of Be²⁺ and Mg²⁺, specifically coordination numbers, interparticle distances, and types of ionic association, are discussed. It is noted that Be²⁺ coordinates four water molecules at an average distance of 0.167 nm and Mg²⁺ coordinates six water molecules at an average distance of 0.210 nm. In aqueous solutions of their salts, both Be²⁺ and Mg²⁺ form the second coordination spheres.     

Accuracy of free energies of hydration for organic molecules from 6-31g*-derived partial charges

Absolute free energies of hydration have been computed for 13 diverse organic molecules using partial charges derived from ab initio 6-31G* wave functions. Both Mulliken charges and charges fit to the electrostatic potential surface (EPS) were considered in conjunction with OPLS Lennard–Jones parameters for the organic molecules and the TIP4P model of water. Monte Carlo simulations with statistical perturbation theory yielded relative free energies of hydration. These were converted to absolute quantities through perturbations to reference molecules for which absolute free energies of hydration had been obtained previously in TIP4P water. The average errors in the computed absolute free energies of hydration are 1.1 kcal/mol for the 6-31G* EPS charges and 4.0 kcal/mol for the Mulliken charges. For the EPS charges, the largest individual errors are under 2 kcal/mol except for acetamide, in which case the error is 3.7 kcal/mol. The hydrogen bonding between the organic solutes and water has also been characterized. © John Wiley & Sons, Inc.     

Isotope effect of hydrogen and lithium hydride molecules. Application of the dynamic extended molecular orbital method and energy component analysis

In order to explore the isotope effect including the nuclear–electronic coupling and nuclear quantum effects under the one-particle approximation, we apply the dynamic extended molecular orbital (DEMO) method and energy component analysis to the hydrogen and lithium hydride isotope molecules. Since the DEMO method determines both electronic and nuclear wave functions simultaneously by variationally optimizing all parameters embedded in the basis sets, the virial theorem is completely satisfied and guarantees the relation of the kinetic and potential energies. We confirm the isotope effect on internuclear distances, nuclear and electronic wave functions, dipole moment, the polarizability, and each energy component. In the case of isotopic species of the hydrogen molecule, the total energy decreases from the H₂ to the T₂ molecule due to the stabilization of the nuclear–electronic potential component, as well as the nuclear kinetic one. In the case of the lithium hydride molecule, the energy lowering by replacing ⁶Li with ⁷Li is calculated to be greater than that by replacing H with D. This is mainly caused by the small destabilization of electron–electron and nuclear–nuclear repulsion in ⁷LiH compared to ⁶LiH, while the change in the repulsive components from ⁶LiH to ⁶LiD increases. Received: 24 March 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

Free energy calculations involving NH4+ in water

The analysis of the hydration of NH₄⁺ and the estimation of relative or absolute free energies of hydration by means of Monte Carlo computer simulations using different 1-6-12 potential functions is reported. Two electrostatic representations of NH₄⁺ (used respectively by W.L. Jorgensen and P.A. Kollman) in conjunction with two common water models (TIP3P and TIP4P) are considered. A change in relative hydration free energies of 1.7 kcal/mol is found when the NH₄⁺ models are mutated into each other in either TIP3P or TIP4P. The NH₄⁺ → Na⁺ mutation in both solvent models leads to similar but overestimated relative hydration energies of about ?28.7 kcal/mol. Similarly, the NH₄⁺ annihilation significantly overestimates the absolute free energy of hydration.     

Ab initio studies of structural features not easily amenable to experiment: Part 15. The influence of solvation on molecular structure in some formic acid and carbonic acid hydrates

The completely relaxed ab initio geometries (4—21G) of a trihydrate of carbonic acid and of the monohydrates of cis and trans formic acid are compared with the corresponding unhydrated structures. The maximum structural changes caused by hydration in the free acid structures are of the order of magnitude of 0.03 Å and 3° for bond distances and bond angles, respectively. The corresponding changes in free and complexed water are 0.005 Å and 5°, respectively. The results are significant for the general problem of the transferability of gas phase molecular structures to molecules in solution and for estimates of the uncertainties in theoretical hydration energy surfaces which are generated by using fixed, monomer geometries for water and solvate molecules. Compared with the free geometries, the sum total of the structural changes in some of the systems studied corresponds to energies of several kcal mol^?1.