  It was shown that the conventional Fock matrix calculation, which using
stored non-zero two-electron integrals, density prescreening, and data
compression methods possesses the linear scaling property with respect to the
problem size. This result follows from the proven theorem, which reads that the
total number of non-zero two-electron integrals scales asymptotically linearly
with respect to the number of basis functions for large molecular systems. An
analysis of the Fock matrix calculation with density and density difference
prescreening shows that its linear scaling property arises due to the
asymptotically linear scaling properties of the number of non-zero two-electron
integrals and the linear scaling property of the number of leading matrix
elements of the density matrix. The use of the density and the density
difference prescreening in the Fock matrix calculation consequently improves
this property. The conventional Fock matrix calculation with the stored
non-zero two-electron integrals has been reformulated to the Fock matrix
calculation with density or density difference prescreening by using the data
compression technique to store the non-zero two-electron integrals and their
indices. The numerical calculations with this method show that its linear
scaling property begins from 2500 to 4000 basis functions in dependence on the
basis function type in molecular calculations.
