The impact of the Resolution of the Identity approximate integral method on modern ab initio algorithm development

The computation of the two-electron four-center integrals over gaussian basis functions is a significant component of the overall work of many ab initio methods used today, Improvements in the computational efficiency of the base algorithms have provided significant impact, Somewhat overlooked are methods that provide approximations to these integrals and their implementation in application software. A partial review of approximate integral techniques focused on the resolution of the identity (RI) four-center, two-electron integral approximation is given. The past and current uses of the RI algorithms are presented along with possibilities for further exploitation of the technology.