Table 4. Nuclear Spin Eigenfunctions |X,m⟩ of the CH₃ Moiety Grouped by Their Symmetry, where X Is the Symmetry of the State and m Is the Angular Momentum Quantum Number; c = e^2πi/3a.

|A, 3/2⟩ = |ααα⟩

|A, 1/2⟩ = 1/3(|ααβ⟩ + |αβα⟩ + |βαα⟩)

|A, 1/2⟩ = 1/3(|ββα⟩ + |βαβ⟩ + |αββ⟩)

|A, −3/2⟩ = |βββ⟩

|Ea, 1/2⟩ = 1/3(|ααβ⟩ + c|αβα⟩ + c*|βαα⟩)

|Ea, −1/2 = 1/3(|ββα⟩ + c|βαβ⟩ + c*|αββ⟩)

|Eb, 1/2⟩ = 1/3(|ααβ⟩ + c*|αβα⟩ + c|βαα⟩)

|Eb, −1/2⟩ = 1/3(|ββα⟩ + c*|βαβ⟩ + c|αββ⟩)

^aCyclic permutation of the spins leaves the A states unchanged, and the E states acquire a phase.