Linear scaling conventional Fock matrix calculation with stored non-zero two-electron integrals

Abstract

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.