[Ryuk18]

Hi everybody!

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!