We have proposed the Gaussian and Fourier transform (GFT) method as an efficient calculation technique for the Hartree term under the periodic boundary condition (PBC), and discuss its analytical energy-gradient formalism in this Letter. We also discuss a Fourier transform technique to estimate the matrix element of the density functional theory (DFT) exchange correlation term. A first-principles molecular dynamics (MD) simulation of water at ambient conditions is executed using those methodologies. (C) 2011 Elsevier B. V. All rights reserved.