Derivatives of the approximated electrostatic potentials in the fragment molecular orbital method

The electrostatic potential in the Fragment Molecular Orbital (FMO) method describes the effect of the environment upon fragments, but approximations are necessary to achieve linear scaling. We have developed the derivative of the point charge approximation in this study to enable accurate and fast gradient calculations for geometry optimizations and molecular dynamics of large systems. The accuracy is tested in comparison with the numeric gradient for solvated sodium cation, water cluster, α-helix of polyalanine, and hydrated chignolin. The errors are found to be reduced by approximately one order of magnitude.