New Effective Potentials Extraction Method for the Interaction between Cations and Water X. Periole, ²,‡ D. Allouche, ² A. Ramı ´rez-Solı ´s, ‡ I. Ortega-Blake, § J. P. Daudey, ² and Y. H. Sanejouand* ,² Laboratoire de Physique Quantique, UMR 5626 of C.N.R.S., I.R.S.A.M.C., UniVersite ´ Paul Sabatier, 118 Route de Narbonne, Toulouse Cedex, 31062, France; Facultad de Ciencias, UniVersidad Auto ´ noma del Estado de Morelos, CuernaVaca, Morelos, 62290, Me ´ xico; and Laboratorio de CuernaVaca del Instituto de Fı ´sica, UniVersidad Nacional Auto ´ noma de Me ´ xico, Apdo. Postal 48-3, CuernaVaca, Morelos, 62251, Me ´ xico ReceiVed: March 31, 1998; In Final Form: July 31, 1998 A very simple method for the extraction of effective interaction potentials from ab initio calculations was proposed (Periole et al. J. Phys. Chem. 1997, 101, 5018), and simple two-body cation-water interaction potentials were derived for several cations, Li + , Na + ,K + , Be 2+ , Mg 2+ , and Ca 2+ , using two facts: first, water molecules in the close vicinity of cations are strongly structured and present a constrained orientation towards the ion; second, at larger distances the ion-water interaction is mainly electrostatic. In the present work, an extension to Rb + and Sr 2+ and some refinements of this method are presented. In particular, we explore the most adequate way of including the nonadditivity and polarization effects that arise from the ion-water-water and water-water interactions. The potentials obtained with the new extraction methods are compared with the empirical potentials of Åqvist (Åqvist, J. J. Phys. Chem. 1990, 94, 8021) that were adjusted to reproduce experimental data. Those obtained with the exploration-TIE method are also tested by performing molecular dynamics simulations of the various cation-water systems and the results are found to be in good agreement with experimental data. In particular, they yield cation hydration free energy differences (ΔG values) that are, in general, in good accordance with experimental figures. This latter method is ideally suited and easy to apply to obtain effective interaction potentials for molecular systems with restricted geometric conditions that appear in numerical simulations, either Monte Carlo or molecular dynamics. Introduction The use of numerical simulations for the study of complex molecular systems, e.g. proteins and the chemical behavior of their active sites, is now a common application. One of the limiting factors in these studies is the availability of adequate potentials. On the one hand, they have to be of the simplest possible form, since they will be used in costly simulations in which a large number of atoms is involved and, on the other hand, they have to lead to a reasonable reproduction of the molecular interactions being considered. This has led to the construction of effective two-body potentials, originally for simple systems (for instance, well-known water potentials such as SPC/E, TIP4p, etc.) and now for complex cases where the reduced cost of such potentials can be used advantageously. Recently, a method for easily constructing an effective potential for the interaction of ions with water has been proposed. 1 The important feature of this method is that the ion remains all the time inside its hydration shell with very particular orientations of the water molecules in its close vicinity. There are a few models taking advantage of the constrained orientation of waters. Cordeiro et al. 2 proposed a model we shall call “breathing” and is discused below. Bleuzen et al. 3 proposed a model we shall call single-molecule detachment also discused below, and Sanchez-Marcos and coworkers 4-7 have developed a model that keeps the hydrated ion either fixed or with a restrained relaxation and construct an interaction of this cluster with water. Recently, Wasserman et al. 8 took this idea further by considering the hexahydrate as a molecule and describing the interaction energy of the first shell as intramolecular energy, in this way accounting for water relaxation. Floris et al. 9-11 have developed a method where nonadditivity is accounted for by a polarizable continuum environment where the solute-solvent interaction is computed, producing thus a corrected effective potential. We can say that the idea is quite succesful, leading to a general agreement with experiment even on the solvation energies where earlier works had failed. 2,12,13 Some of the above models are quite refined and certainly improve the system description. In our previous work, 1 we used a similar idea by trying to obtain in the most inexpensive manner a very simple potential that can be used for relative comparisons, that is, a simple potential fitted to reproduce the environment and the longer range interactions adequately reproduced by the electrostatic part. In that paper the parameters for the effective potentials describing the interaction of monovalent and divalent cations with an aqueous environment were determined. They were obtained from the results of ab initio calculations of M(H 2 O) n systems where M ) Li + , Na + ,K + , Be 2+ , Mg 2+ , and Ca 2+ and n ) 6, except for Be 2+ , where n ) 4. These potentials allow us to reproduce the water-cation interaction energy at the Hartree-Fock (HF) level through an analytical form, namely, a sum of two-body Lennard- Jones and electrostatic potentials, the water-water interactions being described using the TIP3p potential. 14 In that work different forms for the effective potentials were tested and the best fits of ab initio data were obtained with a smooth r -7 repulsive and a classical r -4 attractive term, in addition to the standard Coulombic interaction. Note that a smooth r -7 , or r -8 , * Corresponding author. ² Universite ´ Paul Sabatier. ‡ Universidad Auto ´noma del Estado de Morelos. § Universidad Nacional Auto ´noma de Me ´xico. 8579 J. Phys. Chem. B 1998, 102, 8579-8587 10.1021/jp981688t CCC: $15.00 © 1998 American Chemical Society Published on Web 10/01/1998