Efficiency of Implementation and Use

Also as already noted above, taking advantage of molecular symmetry can provide very large savings in time. However, structures optimized under the constraints of symmetry should always be checked by computation of force constants to verify tlierr nature as stationary points on die full PES. Additionally, it is typically worthwhile to verify that open-shell wave functions obtained for symmetric molecules are stable with respect to orbital changes that would generate other electronic states. 

Finally, the use of ECP basis sets for heavy elements improves efficiency by reducing the scale of the electronic structure problem. In addition, relativistic effects can be accounted for by construction of the pseudopotential. 

One area that takes advantage of many of the above formalisms is the application of HF theory to periodic solids. Periodic HF theory has been most extensively developed within the context of the crystal code (Dovesi et al. 2000) where it is available in RHF, UHF, and ROHF forms. Such calculations can be particularly useful for elucidating band structure in solids, assessing defect effects, etc. 

With very, very large systems, fast-multipole methods analogous to those described in Section 2.4.2 can be used to reduce the scaling of Coulomb integral evaluation to linear 

Even if the number of paired electrons remains constant but the nature of the bonds is substantially changed, the HF level can show rather large errors. For instance, the atmospheric reaction converting CO and HO to H and CO2 is known to be exoergic with an energy 

Another fairly conservative reaction is the removal or attachment of a single electron from/to a molecule. As already discussed in Chapter 5, Koopmans theorem equates the energy of the HOMO with the negative of the IP. This approximation ignores the effect of electronic relaxation in the ionized product, i.e., the degree to which the remaining electrons redistribute themselves following the detachment of one from the HOMO. If we were to 

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