  Ions are critical to the structure and stability of polyelectrolytes such as
nucleic acids. In this work, we systematically calculated the potentials of
mean force between two like-charged nanoparticles in salt solutions by Monte
Carlo simulations. The pseudo-spring method is employed to calculate the
potential of mean force and compared systematically with the inversed-Boltzmann
method. An effective attraction is predicted between two like-charged
nanoparticles in divalent/trivalent salt solution and such attraction becomes
weakened at very high salt concentration. Our analysis reveals that for the
system, the configuration of ion-bridging nanoparticles is responsible for the
attraction, and the invasion of anions into the inter-nanoparticles region at
high salt concentration would induce attraction weakening rather than the
charge inversion effect. The present method would be useful for calculating
effective interactions during nucleic acid folding.
