The HD and HD̄ Methods for Accelerating the Convergence of Three-Center Nuclear Attraction and Four-Center Two-Electron Coulomb Integrals over B Functions and Their Convergence Properties

Abstract

Three-center nuclear attraction and four-center two-electron Coulomb integrals over Slater-type orbitals are required for ab initio and density functional theory (DFT) molecular structure calculations. They occur in many millions of terms, even for small molecules and require rapid and accurate evaluation. The B functions are used as a basis set of atomic orbitals. These functions are well adapted to the Fourier transform method that allowed analytical expressions for the integrals of interest to be developed. Rapid and accurate evaluation of these analytical expressions is now made possible by applying the HD and HD̄ methods for accelerating the convergence of the semi-infinite oscillatory integrals. The convergence properties of the new methods are analysed. The numerical results section shows the high predetermined accuracy and the substantial gain in the calculation times obtained using the new methods.