Chemical Physics 141 (1990) 379-392 North-Holland THE ROLE OF MANY-BODY INTERACTIONS IN THE STABILITY OF HYDRATED Cu2+ CLUSTERS M. Natalia zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA D.S. CORDEIRO, Jo& A.N.F. GOMES zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML Departamento de Quimica, Faculdade de Ci6ncins. Universidade do Porto, 4000 Porto, Portugal Angels GONZALEZ-LAFONT, Jose Maria LLUCH and Juan BERTRAN Department de Quimica, Facultat de CiPncies, Universitat Autbnoma de Barcelona, 08193 Bellaterra (Barcelona), Spain Received 24 January 1989; in final form 30 October 1989 The effects of three-body and, in a few cases, four-body and higher-order terms were studied for several Cu*+-( H,O), (n up to 8) clusters proposed as models of the first hydration shell of the Cu *+ ion. This is based on ab initio SCF calculations performed for the n=6 cluster and for all the required tetramer, trimer and dimer subunits of this cluster and of the n=8 cluster. The computed many-body results show that the three-body terms are non-negligible and lead to strong repulsive contributions to the total pairwise additive interaction energy of the Cu*+-( zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE HrO ),, systems. Pronounced changes on the hydration number (n) and on the optimal Cu-0 distances (r) of this ion’s first shell are obtained when two-body terms (n = 8, r= 2.09 A) alone are consid- ered or three-body terms (n = 6, r=2.15 A ) are included. The four-body terms are found to be quite small in comparison with the three-body terms. The remaining higher-order terms are shown to be even much smaller than the four-body terms, thus indicating a rapid convergence of the many-body expansion of the interaction energy for this hydrated ion. This work suggests that, when a simple model is required for the interaction potential of metal ions with water, as it is the case in Monte Carlo or molecular dynamics simulations, a good degree of accuracy depends on supplementing the usual pairwise additive type of potential by three- body terms, and modelling of these depends on detailed studies of the type presented here. 1. Introduction Ion-water interactions have long been the subject of experimental and theoretical studies due to their well known relevance in many chemical and biophys- ical phenomena. Experimentally, X-ray and neutron diffraction techniques have provided useful infor- mation about the structure of hydrated ions [ l-31. Among the theoretical methods, we single out the sta- tistical simulations which provide not only detailed information on the structural properties but also on the dynamic and thermodynamic properties of ionic aqueous solutions [ 4,5 1. Another important aspect of simulations is their ability to predict the effects of temperature and pressure in the shape of the ion’s hy- dration shells [ 6 1. Most of the simulation work has been based on the use of pair interaction potentials, a simplification primarily adopted to facilitate computational effi- ciency in such large calculations. However, non-pair- 0039-6028/90/$03.50 0 Elsevier Science Publishers B.V. (North-Holland) wise-additive interactions appear to be quite impor- tant and make significant contributions to the potential energy of ion-water systems. For instance, in studies of monovalent ions in water, such as Li+ [7,8], Na+ [9] and K+ [9], consideration of the three-body interactions was found to improve mark- edly the agreement with experimental data. Even more dominant three-body effects have been re- ported for divalent metal ions in water [ 9-121. For Mg2+ [ 9,111 and Ca2+ [ 111, it has been shown that the three-body effects are crucial to obtain reliable hydration numbers and equilibrium distances for the first hydration shells. Similar conclusions have been reached for transition metal ions. For example, sim- ulation studies of Fe2+ [ 13- 15 ] and Ni2+ [ 6 ] based on ab initio pair potentials, gave larger coordination numbers than the ones observed experimentally [ 11. In the case of Fe2+, it has been shown that this prob- lem is most likely due to the neglect of three-body forces [ 151. In what concerns the prediction of struc-