Analytical energy gradient of Gaussian and Fourier transform (GFT) method for periodic condensed systems

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.