Concluding Remarks

This chapter has presented an efficient way to calculate the short-range Coulomb energy. This is the first O(N) implementation of the CASE approximation, allowing very fast computation of CASE energies for large systems. This has been achieved through the introduction of boxing code, similar to that of the CFMM. A further speed-up has been achieved by introducing a screening for significant integrals. The increase in speed is heavily dependent on the shape of the system. For modest $\omega$ values, CASE represents a useful increase in speed even for moderately-sized systems (eg: C₅₀H₁₀₂).

The efficient implementation of the short-range integral code is crucial for the success of KWIK and other methods which can be viewed as providing corrections for the neglected part of CASE theory. These corrections will allow much larger values for $\omega$ thus enabling the CASE code to run even faster.