Introduction to Linear Methods

As mentioned in the previous chapter, the calculation of the ERIs is the bottleneck for modern day SCF calculations. The central problem is that, no matter how fast these interactions are computed, there are still O(N²) Coulomb and Exchange interactions, which grows just too fast for large molecules to be studied. It was shown in Chapter 2 that the DFT exchange (and correlation) terms can be computed in O(N) work. Therefore O(N) DFT calculations are possible if the Coulomb problem (to determine the Coulomb energy of a system of N localized distributions of charge in O(N) work) can be solved.