Experimentally consistent ion association predicted for metal solutions from free energy simulations

The calculation of association constants from computer simulations has historically been complicated because of difficulties in validating metal ion force fields for solution simulations. Here we develop a method that produces a force field for divalent metal ions in metal sulfate solutions (i.e., Mg(2+)SO(4)(2-), Ca(2+)SO(4)(2-), Mn(2+)SO(4)(2-), Fe(2+)SO(4)(2-), Co(2+)SO(4)(2-), Ni(2+)SO(4)(2-), Cu(2+)SO(4)(2-), and Zn(2+)SO(4)(2-)). Using free energy of perturbation calculations, we are able to calibrate the potential of mean force W(r) for these metal sulfate solutions. The calibrated free energy profiles then allow us to produce association constants for contact, solvent-shared, and solvent-separated ion pairs that are in excellent agreement with available ultrasonic and dielectric spectroscopic data. This metal solution force field is accurate for the calculation of relative free energies from physical and biophysical computer simulations.