My recent studies of para-benzyne radical anion has shown that relative energy difference between C2v and D2h structures calculated at DFT level of theory are proportional to the electron self-interaction error included in DFT potential. The more HF exchange DFT potential has the smaller is the electron self-interaction error. Thus the most common B3LYP potential places D2h structure lower in energy mostly because of the electron self-interaction error.
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Self-interaction error is a serious drawback of the DFT. It's leads to many artifacts when DFT is applied to distonic ions: charge distribution, dipole moment, etc...