A computational method for the evaluation of dispersion and repulsion contributions to the solvation energy is here presented in a formulation which makes use of a continuous distribution of the solvent, without introducing additional assumptions (e.g., local isotropy in the solvent distribution). The analysis is addressed to compare the relative importance of the various components of the dispersion energy (n = 6, 8, 10) and of the repulsion term, to compare several molecular indicators (molecular surface and volume, number of electrons) which may be put in relation to the dispersion-repulsion energy, and to define simplified computational strategies. The numerical examples refer to saturated hydrocarbons in water, treated with the homogeneous approximation of the distribution function which for this type of solution appears to be acceptable.

We present a simple computational method for the evaluation of solute-solvent dispersion energy contributions in dilute isotropic solutions, supplementing the method with an analysis of its sensitivity with respect to several parameters (or features of the solvation model) which are left free in the general formulation. The method is a natural complement of the electrostatic solvation procedure described in preceding articles.

The process of inserting cavities in water is studied with the aim of a better description of some of the terms necessary in continuum quantum mechanical models. Free-energy changes for the formation of soft and hard spherical cavities in TIP4P water have been computed by Monte Carlo (MC) simulation with statistical perturbation theory, up to a radius of 6 Angstrom. The free-energy change for the formation of a hard sphere, Delta G(cav), is obtained combining the Delta G(sol) of a soft repulsive sphere with the Delta G corresponding to the process of transforming the soft sphere into a hard one. Two definitions of hard-sphere repulsive potentials have been considered, one only based on the distance of oxygens from the center of the cavity, while the other also excludes hydrogens from the same region. Differences in free energies are significant. The cubic polynomial expression Delta G(cav), obtained by extrapolating the exact scaled particle theory (SPT) expression for very small excluding cavities, gives results in agreement with MC, with effective ''hard-sphere'' diameter for water larger than 2.77 Angstrom. The SPT prediction is compared with other treatments based on surface tension. It is shown that a properly chosen surface and an ''effective'' surface tension of water lead to a good agreement with MC Delta G(cav) without curvature or microscopic corrections. The ''effective'' surface tension of water turns out to be very close to the experimental value. Some different simple ways to extend SPT expression to nonspherical cavities have been compared, for a limited number of nonspherical convex cavities modelled as n interlocking spheres, meant to mimic n-alkanes in the all-staggered conformation. Entropy changes for soft cavities have been computed with two methods, i.e., combining free energy and enthalpy computations and by finite difference methods. Discrepancies between SPT predictions and MC results are significant. The calculated probability distributions of relevant angles of first hydration shell waters are consistent with orientations where no O-H or O-lone pair vector points towards the cavity. Their variation when the cavity size increases is mostly quantitative and only the broadening of the bands observed for the largest cavities might indicate the early stage of the transition to hydration patterns peculiar to an infinite hydrophobic surface. (C) 1997 American Institute of Physics

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Partial molar volumes for hard-sphere cavities in TIP4P water were computed running Monte Carlo simulations in the isothermal, isobaric (NPT) ensemble at 298 K and 1 atm. The explored size range goes from very small cavities up to cavities with a radius of 10 Å. The excess volumes extracted from these data show a nonideal contribution that changes sign for a radius between 8 and 10 Å. The same behavior was also found by computing the quantity directly from distribution functions by means of the Kirkwood-Buff integrals. The results are analyzed also in terms of hydration shell models which are based on the truncation of the Kirkwood-Buff integrals at the distances of the minima of the radial distribution functions. Another choice of truncation based on the oscillatory behavior of the excess volume as a function of the cutoff radius is also considered.

Infinitely dilute aqueous solutions of Nd3+, Gd3+, and Yb3+ have been studied with molecular dynamics simulations, using ab initio effective ion–water pair potentials based on the polarizable continuum model. Structural results, as first peak positions of g(r) are in good agreement with experimental data. We obtain a coordination number of 9 for all the cations. This value agrees with experimental measurements for Nd3+ and Gd3+ but overestimates them for Yb3+. Significant differences between Yb3+ and the other two ions have however been observed in a detailed analysis of the solvation shell structure, based on the diagonalization of the inertia tensor. A similarity index based on a linear combination of the inertia tensor eigenvalues is proposed. Going from Nd3+ to Yb3+, structures like a capped square antiprism (CSQA) are more favored than a tricapped trigonal prism. In contrast to the lanthanide contraction observed for the most probable ion–oxygen distances, in CSQA structures the distance from the center of mass of the polyhedron to the capped O increases from Nd3+ to Yb3+. Dynamics of internal rearrangements has been studied and residence times of waters in the first and second hydration shell have been calculated. Diffusion coefficients for the ions appear somewhat underestimated with respect to the experimental data, which agree with the value we obtain for hydration shell waters. Linear and angular velocity correlation functions and spectra of first shell waters show a large increase of intensity at high frequency compared to bulk solvent. The Yb3+ solution consistently presents these features in enhanced form.

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The Menshutkin reaction NH3 + CH3 Cl → CH3NH3 + + Cl- in aqueous solution is studied using the CASSCF method combined with the polarizable continuum model in a version that includes electrostatic, repulsion, and dispersion solute−solvent interactions. The solvent reaction field is inserted in the CASSCF Hamiltonian resorting to a mean-field approximation. The C 3 v symmetry is maintained for all the geometries considered and the active space is generated distributing four electrons in four orbitals of a1 type. The results of the present study are in excellent agreement with recent ab initio calculations, which use both continuum and discrete solvation models, and with available experimental data. The analysis of the electronic structure of the transition state by the VB method explains the mechanism of this reaction in terms of a Linnett-type nonpaired spatial orbital representation as in a four-electron, three-center bonding unit.