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Symmetry in Double Space A useful property of the double space is that it clarifies the treatment of symmetry [28]. In the single space, the symmetry of ÉG can appear confusing, because it depends on the position of the cut line. One way to avoid this confusion is to consider the symmetry of the total (electronic þ nuclear) wave function ÉÈ, which is of course independent of the position of the cut line [6, 7]. Another way is to map ÉG onto the double space. In Section II, we explained that ÉN and ÉG are respectively symmetric and ^ 2p in the double space.