Ion Pair Potentials-of-Mean-Force in Water

Recent molecular simulation and integral equation results alkali-halide ion pair potentials-of-mean-force in water are discussed. Dielectric model calculations are implemented to check that these models produce that characteristic structure of contact and solvent-separated minima for oppositely charged ions in water under physiological thermodynamic conditions. Comparison of the dielectric model results with the most current molecular level information indicates that the dielectric model does not, however, provide an accurate description of these potentials-of-mean-force. We note that linear dielectric models correspond to modelistic implementations of second-order thermodynamic perturbation theory for the excess chemical potential of a distinguished solute molecule. Therefore, the molecular theory corresponding to the dielectric models is second-order thermodynamic perturbation theory for that excess chemical potential. The second-order, or fluctuation, term raises a technical computational issue of treatment of long-ranged interactions similar to the one which arises in calculation of the dielectric constant of the solvent. It is contended that the most important step for further development of dielectric models would be a separate assessment of the first-order perturbative term (equivalently the {\it potential at zero charge} ) which vanishes in the dielectric models but is generally nonzero. Parameterization of radii and molecular volumes should then be based of the second-order perturbative term alone. Illustrative initial calculations are presented and discussed.Comment: 37 pages and 8 figures. LA-UR-93-420

Revised self-consistent continuum solvation in electronic-structure calculations

The solvation model proposed by Fattebert and Gygi [Journal of Computational Chemistry 23, 662 (2002)] and Scherlis et al. [Journal of Chemical Physics 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multi-grid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [Physical Review Letters 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation (SCCS) model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the PCM model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond forming compounds.Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at http://link.aip.org/link/?jcp

Molecular theory of solvation: Methodology summary and illustrations

Integral equation theory of molecular liquids based on statistical mechanics is quite promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. Beginning with a molecular interaction potential force field, it uses diagrammatic analysis of the solvation free energy to derive integral equations for correlation functions between molecules in solution in the statistical-mechanical ensemble. The infinite chain of coupled integral equations for many-body correlation functions is reduced to a tractable form for 2- or 3-body correlations by applying the so-called closure relations. Solving these equations produces the solvation structure with accuracy comparable to molecular simulations that have converged but has a critical advantage of readily treating the effects and processes spanning over a large space and slow time scales, by far not feasible for explicit solvent molecular simulations. One of the versions of this formalism, the three-dimensional reference interaction site model (3D-RISM) integral equation complemented with the Kovalenko-Hirata (KH) closure approximation, yields the solvation structure in terms of 3D maps of correlation functions, including density distributions, of solvent interaction sites around a solute (supra)molecule with full consistent account for the effects of chemical functionalities of all species in the solution. The solvation free energy and the subsequent thermodynamics are then obtained at once as a simple integral of the 3D correlation functions by performing thermodynamic integration analytically.Comment: 24 pages, 10 figures, Revie