Spurious symmetry breaking

It would seem to follow that the problem of spurious symmetry breaking can be remedied by providing sufficient electron correlation. This is indeed the case but, as we will see later, the consequences of symmetry breaking preclude using the economical MBPT methods for providing the necessary electron correlation. 

More importantly, ROHF wavefunctions are plagued by an even more severe problem—they are often unstable with respect to symmetry breaking. In cases like that of allyl, where, at the geometry of highest symmetry, two resonance structures of lower symmetry can be drawn to represent the wavefunc-tion, ROHF calculations may spuriously find that a wavefunction of lower symmetry is preferred, even at this geometry. In fact, allyl radical serves as a classic illustration of this phenomenon of symmetry breaking. 

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