Ensuring that the HF Energy is a Minimum

Another aspect of wave function instability concerns symmetry breaking, i.e. the wave function has a lower symmetry than the nuclear framework. It occurs for example for the allyl radical with an ROHF type wave function. The nuclear geometry has C21, symmetry, but the Cay symmetric wave function corresponds to a (first-order) saddle point. The lowest energy ROHF solution has only Cj symmetry, and corresponds to a localized double bond and a localized electron (radical). Relaxing the double occupancy constraint, and allowing the wave function to become UHF, re-establish the correct Cay symmetry. Such symmetry breaking phenomena usually indicate that the type of wave function used is not flexible enough for even a qualitatively correct description. 

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The main difference between HF and DFT is that in the HF approach the objective is the determination of the wave function of the system while in DFT the quantity of interest is the charge density p in fact, the Hohenberg-Kohn theorem [65] ensures that the energy E of a system is a functional of p which takes its minimum value Eo for the ground state density po. Despite this profound conceptual difference, the two methods, HF-ncorrelation and DFT, provide in ultimate analysis very similar results and the choice of one approach or the other is largely matter of convenience. 

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