Elongation Hartree-Fock (ELG-HF) achieves linear scaling for large systems when coupled with quantum fast multipole method. However

it is a simpler method to form the Fock matrix directly from localized molecular orbitals

which requires transforming the two electron integrals from an atomic orbital basis to a localized molecular orbital basis. For each elongation step

almost constant scaling is achieved when cutoff is used to exclude atomic orbital two electron integrals that are not required in the transformation. The Schwarz inequality

molecular orbital prescreening and using a set of hybridized molecular orbitals reduce the time required to complete the transformation and eliminate additional atomic orbital two electron integrals. The results for water molecule chain verify that linear scaling for ELG-HF methods is achieved. This new method is more effective than forming the Fock matrix from atomic orbital two electron integrals when the size of the interactive region contains fewer than 120 well localized molecular orbitals.