In molecular dynamics (MD) calculations of the free energies of ions and ionic molecules, we often encounter net charged molecular systems where the electrical neutrality condition is broken. This charge causes a problem in the evaluation of long-range Coulombic interactions under periodic boundary conditions. A standard remedy for this problem is to consider a hypothetical homogeneous background charge density to neutralize the total system. Here, we present a new expression for the evaluation of Coulombic interactions for such systems including background charge using the fast multipole method (FMM). Furthermore, an efficient scheme is developed to evaluate solute-solvent interaction energies using the FMM, reducing the computational burden for the far-field part. We calculate the hydration free energies of Mg2+, Na+, and Cl- ions dissolved in a neutral solvent using the new expression. The calculated free energies show good agreement with the results obtained using the well-established particle mesh Ewald method. This demonstrates the validity of the proposed expression. This work should make a contribution to highly parallelized MD calculations for large-scale charged systems (particularly, those with over million particles).
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry