  Separating the Coulomb potential into short-range and long-range components
enables the use of different electron repulsion integral algorithms for each
component. The short-range part can be efficiently computed using the
analytical algorithm due to the locality in both Gaussian-type orbital basis
and the short-range Coulomb potentials. The integrals for the long-range
Coulomb potential can be approximated with the density fitting method. A very
small auxiliary basis is sufficient for the density fitting method to
accurately approximate the long-range integrals. This feature significantly
reduces the computational efforts associated with the $N^4$ scaling in density
fitting algorithms. For large molecules, the range separation and long-range
density fitting method outperforms the conventional analytical integral
evaluation scheme employed in Hartree-Fock calculations and provides more than
twice the overall performance. Additionally, this method yields higher accuracy
compared to regular density fitting methods. The error in the Hartree-Fock
energy can be easily reduced to 0.1 $\mu E_h$ per atom, which is significantly
more accurate than the typical error of 10 $\mu E_h$ per atom observed in
regular density fitting methods.
