### Applications of Density Fitting in Large-scale Mean-field Theory Computations

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** Robert Parrish,
Georgia Institute of Technology **

Density fitting is a popular rank-reduction technique for simplifying manipulations of the ubiquitous electron repulsion integrals of quantum chemistry. By casting the four-index electron-repulsion integral tensor into a product of two- and three-index tensors, the number of molecular integrals and required storage are drastically reduced, while the new rate-limiting steps become efficient, easily parallelized matrix multiplication operations. We present a number of novel applications of density fitting within Hartree-Fock, configuration interaction singles, and coupled-perturbed Hartree-Fock. We also discuss extensions of these techniques to density functional theory, time-dependent density functional theory, coupled-perturbed Kohn-Sham theory, and to Hartree-Fock and density functional theory gradients. In each of these methods, our implementation of a density-fitted algorithm for the electron repulsion integrals in the open-source PSI4 package has opened the door to systems at least one order of magnitude larger. Using this code, computations with hundreds of atoms and thousands of basis functions are now routine on modest workstations.

**Abstract Author(s):** Robert M. Parrish and C. David Sherrill