I am trying to find the difference between density fitting (DF) and resolution of the Identity (RI) approximations. I have read the following in the article [J. Chem. Phys. 118, 8149 (2003)]:
"Density fitting mathematically resembles a resolution of the identity RI in the specific case where the fitting criterion and target integral type coincide. However, RIs in quantum mechanics usually involve a summation over states and an implied overlap metric, neither of which appear in density fitting. Furthermore RIs do not offer a framework in which to discuss fitting criteria, constraints or robust fitting."
I still do not know what this exactly means. Could anyone give me a hand?
Thank you in advance!