APPARENT LOCAL DIELECTRIC RESPONSE AROUND IONS IN WATER - A METHOD FOR ITS DETERMINATION AND ITS APPLICATIONS

The solvation properties of ions in aqueous solution are determined by the unique structure of water and its dielectric properties. The orie ntational structure of the water molecules is governed in part by the dipolar nature of water but displays a much richer behavior due to hyd rogen bonding. Here, properties of the orientation angle theta of a wa ter dipole as a function of distance r from the ion, namely, the mean value [cos theta](r) and the distribution P(cos theta;r), are calculat ed from molecular dynamics simulations of Cl- in water. The orientatio nal behavior is compared to that of a point charge and a point dipole in a dielectric continuum, which can be solved analytically. More spec ifically, the microscopic field due to a point charge experienced by t he dipole is different than the macroscopic field due to a point charg e so that the problem must be viewed as a dipole in a cavity immersed in a dielectric continuum, using arguments similar to those of Kirkwoo d in relating the dielectric constant epsilon of a fluid to the dipole moment mu of molecules in the fluid. By comparing (cos theta)(r) calc ulated from simulation with the analytic expressions, an apparent ''lo cal'' dielectric response epsilon(r) dependent on r is calculated; eps ilon(r) is termed apparent because it is not a position-dependent diel ectric constant to be used in the Poisson or Poisson-Boltzmann equatio ns but rather reflects the cumulative effects of such a position-depen dent dielectric constant. The variation of epsilon(r) from the bulk di electric constant allows one to quantitate the deviations from continu um behavior. In the first two shells, epsilon(r) varies significantly with r, and a reduction in epsilon(r) in the first shell is clearly se en. Furthermore, epsilon(r) appears to appl:oach continuum bulk behavi or by about 8 Angstrom despite the considerable orientation even at r = 10 Angstrom. In addition, the simple expression for P(cos theta;r) i n the continuum approximation using epsilon(r) is used to calculate so lvation properties of ions. It is also demonstrated that, in the limit where epsilon(r) is assumed constant (i.e., that of bulk) and the den sity is assumed constant (i.e., a continuum), the Born solvation energ y expression is a limiting case of our expression for the solvation en ergy.