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Density fitting is used to approximate all of the 4-index 2-electron integrals in the explicitly correlated MP2-R12 theory of Kutzelnigg and Klopper. The resulting method—DF-MP2-R12—requires only 2- and 3-index integrals over various 2-electron operators, and is extremely efficient. The errors arising from the fitting process can be made small by using robust fitting formulas throughout, such that the error in each fitted integral is quadratic in the error of the fitted orbital product densities. Sample calculations on glycine reveal that for large basis sets DF-MP2-R12 is faster than a standard MP2 calculation and takes only a small fraction of the time for the Hartree–Fock calculation.
Frederick R. Manby (Thu,) studied this question.