Introduction

With the realization that CASE may be a useful theory the next task is to improve the speed of CASE integral calculations. As mentioned in the previous chapter, by attenuation of the Coulomb operator to $\erfc(\omega r)/r$, the number of significant Coulomb interactions grows as only O(N) (compared with the previous O(N²)) for a large enough system. The task of finding which of the O(N⁴) integrals are significant still needs to be accomplished with an algorithm that is itself, at most, O(N).

Before that is achieved the calculation of each single integral must be optimized. This reduces to finding the most efficient way to build the (0)^(m)s, as the various recurrence relations described in Chapter 5 are the same for all two-electron integrals, regardless of the operator used (to change an operator all that is required is to change the generation of (0)^(m)s).

This chapter presents how to calculate the short-range energy as efficiently as possible. It should also be pointed out that the work described in this chapter is not only useful for CASE, but is essential for all calculations using the KWIK family of methods, as each one requires the computation of some short-range elements.