Kohn-Sham analytic energy second derivatives with the Gaussian very fast multipole method (GvFMM)

The first application of the Gaussian very fast multipole method (GvFMM) to the calculation of molecular energy second derivatives of Kohn-Sham (KS) density functional theory (DFT) is reported. The GvFMM is used both in the solution of the coupled-perturbed KS (CPKS) equations and in the calculation of electron-electron repulsion integral second derivatives. We present benchmark tests on C24H12 and C54H18 using 3-21G and 6-31G∗ basis sets that show modest improvements of speed for the formation of J(x) (the Coulomb matrix formed from derivatives of the basis functions) and the integral second derivatives.