A quasilinear RISM approach for the computation of solvation free energy of ionic species G.N. Chuev a, * , S. Chiodo b , S.E. Erofeeva a , M.V. Fedorov a,c , N. Russo b , E. Sicilia b a Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, ul. Institutskaya 3, Pushchino, Moscow Region 142290, Russia b Dipartimento di Chimica and Centro di Calcolo ad Alte Prestazioni per Elaborazioni Parallele e Distribuite-Centro dÕEccellenza MURST, Universita ´ della Calabria, I-87030 Arcavacata di Rende (CS), Italy c Theory and Computation Group, Centre for Synthesis and Chemical Biology, Conway Institute of Biomolecular and Biomedical Research, Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland Received 10 October 2005; in final form 25 October 2005 Available online 28 November 2005 Abstract A linearized RISM technique is developed to treat free energies of hydrated ions. The solvent response on the solute is calculated with the introduction of an empirical repulsive bridge function. The solvent electrostatic potential is approximated by a linear dependence on the solute charge. The approximating coefficients are derived by fitting the electrostatic energy of solvent, that is in turns computed by the charging procedure. For a series of monovalent polyatomic cations and anions the method provides free energies deviating by few per- cent from the experimental data. Ó 2005 Elsevier B.V. All rights reserved. 1. Introduction Many efforts have been devoted to study experimentally and theoretically the properties of the ion hydration [1–4]. These studies have revealed that accurate simulations of ion solvation are needed to treat carefully short-range nonpolar and long-range electrostatic interactions. The short-range contribution is significantly nonlinear, whereas earlier phenomenological theories as well as numerous sim- ulations suggest that electrostatic solvation effects can be understood within the linear response theory (LRT) [4]. The linearized approach based on molecular dynamics (MD) with the Gaussian fluctuations [5,6] has been proved to give rather satisfactory results in several test computa- tions [7–9]. Unfortunately, this linearized behavior is not an universal truth, and previous calculations have shown when this linear dependence can be expected to fail [9– 12]. The objective of the present work is to develop a new quasilinear technique and apply it to calculate the ion hydration. There is a number of theoretical methods to study solvation effects. The dielectric continuum model treats solvent molecules in an implicit way, while quantum mechanical/molecular mechanics (QM/MM) and methods based on the integral equation theory are regarded as expli- cit solvation models. The reference interaction site model (RISM) [13–15] is representative of the methods based on the integral equation theory. In the RISM approach, the solvation free energy can be expressed as a function of the radial distribution functions (RDF) and the direct cor- relation ones. This model provides detailed information about solute–solvent interactions in terms of statistically averaged site–site distribution functions. A new combined scheme has been recently proposed, which is based on the RISM coupled with self-consistent-field (SCF) procedure [16,17]. This method determines the electronic structure as well as the solvent distribution around the solute in a consistent manner, i.e., a set of partial charges for the sol- ute atoms is determined from the SCF step and then plugged into a RISM calculation to obtain a solvent distri- bution around the solute. Subsequently, the electrostatic potential produced by the solvent charge distribution at 0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.10.117 * Corresponding author. Fax: +7 0967 330553. E-mail address: genchuev@rambler.ru (G.N. Chuev). www.elsevier.com/locate/cplett Chemical Physics Letters 418 (2006) 485–489