Conclusions

The effect of CASE on a variety of molecular properties has been examined in this chapter. Not surprisingly, with all properties investigated, there is an increase in error with increasing $\omega$. Wavefunctions are perhaps the best property for CASE to reproduce. With $\omega=0.15\:a_{0}^{-1}$ a wavefunction which reproduces the energy to within a microhartree can be generated. This is significant as it means CASE can be used for the first few cycles of the SCF, allowing fast generation of the wavefunction, and then a final traditional (or KWIK-type) iteration to produce an accurate energy.

To investigate chemical energetics, a more conservative $\omega$ value is required. Ionization potentials are the hardest property studied for CASE to reproduce. This is because, as mentioned in Chapter 6, ionization potentials involve removing an electron from a charged system, and thus there is an uncancelled interaction. For small $\omega$ values the addition of a constant to the operator is very worthwhile for properties involving an uncancelled interaction, but the usefulness of this additional term decays with increasing $\omega$ until, eventually, it becomes disadvantageous.

The error introduced by CASE seems to be practically independent of the basis set used. Bond lengths, at least initially, usually increase with increasing small $\omega$. The decline in accuracy is slower than the energetic properties, and $\omega$ values of $0.2 \:a_{0}^{-1}$, or even a little higher, can be used to generate reasonable geometries.