A new model to study proteinic systems including a many-body polarization and a hydrogen bond energy contribution is presented. This model represents an extension of an earlier water many-body model [M. Masella and J.-P. Flament, J. Chem. Phys. 107 9105 (1997)]. As in this earlier model, the new model is developed to reproduce quantum computations on small molecular aggregates, and, in this first paper, we focus our efforts in developing an accurate potential to describe interactions among all nonbonded atoms occurring in proteins, and among those atoms and six cations of biological interest: Li+, Na+, K+, Mg2+, Ca2+, and Zn2+. Intramolecular degrees of freedom are described as in classical two-body force fields. In the present paper, the new model is applied to investigate the properties of small ion-neutral [M,L-n](m+) complexes and of small hydrogen-bonded systems. The results showed that this model is able to reproduce most of the theoretical quantum predictions and experimental data published until now regarding those systems. (C) 2003 American Institute of Physics.