Solution (source code)

= Solution

The bridged, sterically hindered <biphenyl> framework is twisted and does not rapidly interconvert the two faces of each <methylene group> on the <NMR> timescale. Label one <hydrogen> on each CH2 $H_A$ and the other $H_B$. Replacing $H_A$ versus $H_B$ by a test <substituent> gives diastereomeric environments, so these <hydrogens> are <diastereotopic> and need not have equal <chemical shifts> even in an <achiral> solvent. Molecular symmetry relates the two $H_A$ sites to each other and the two $H_B$ sites to each other.

Each methylene <hydrogen> undergoes <geminal coupling> to its partner, giving the two doublets, each accounting for two <hydrogens> overall. Their separation is $0.21$ ppm; at operating frequency $\nu_0$ in MHz it corresponds to $0.21\nu_0$ Hz. This separation is not the <geminal coupling> constant, which must be measured from the line spacing within a doublet. If the shift separation is not large compared with that coupling, an AB pattern with second-order distortion is expected rather than ideal first-order doublets. A racemic pair of twisted <conformations> still has these signals: <enantiomers> have the same spectrum in an <achiral> medium, while the two <hydrogen> environments within each <molecule> remain different.