### Abstract

The approach used to calculate the two-electron integral by many electronic structure packages including generalized atomic and molecular electronic structure system-UK has been designed for CPU-based compute units. We redesigned the two-electron compute algorithm for acceleration on a graphical processing unit (GPU). We report the acceleration strategy and illustrate it on the (ss|ss) type integrals. This strategy is general for Fortran-based codes and uses the Accelerator compiler from Portland Group International and GPU-based accelerators from Nvidia. The evaluation of (ss|ss) type integrals within calculations using Hartree Fock ab initio methods and density functional theory are accelerated by single and quad GPU hardware systems by factors of 43 and 153, respectively. The overall speedup for a single self consistent field cycle is at least a factor of eight times faster on a single GPU compared with that of a single CPU.