The presence of an axis of symmetry determines molecular chirality
The claim that an axis of symmetry determines molecular chirality is incorrect; rather, the presence of certain symmetry elements (such as improper axes) dictates chirality, and molecules possessing standard axes of symmetry are frequently achiral.
In stereochemistry, molecular chirality is defined by the absence of certain symmetry elements—specifically, a plane of symmetry (sigma) or a center of inversion (i), which correspond to the absence of improper rotation axes (Sn). The presence of a proper axis of symmetry (Cn) does not inherently make a molecule chiral; many chiral molecules have no symmetry axes at all (C1 point group), while many molecules with symmetry axes are achiral. Therefore, the claim is chemically false.
Ogden J.S. Symmetry elements, symmetry operations and point groups. 2001. https://doi.org/10.1093/hesc/9780198559108.003.0001
Symmetry elements such as an axis of symmetry describe symmetrical (achiral) shapes rather than causing chirality [8].
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Tadashi Okusecyama, Howard Maskill. Stereochemistry and Molecular Chirality. 2013. https://doi.org/10.1093/hesc/9780199693276.003.0011
Chirality in molecules is defined by the absence of improper axes of rotation (specifically planes or centers of inversion), and the presence of certain symmetry axes actually characterizes achiral or symmetric objects [10].
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