Nuclear magnetic resonance study of exchanging systems : The line shape analysis of the inversion of 9,10-dihydro-4,5-dimethylphenanthrene by the density matrix method

9,10-Dihydro-4,5-dimethylphenanthrene has two rotational isomers around the pivot bond. This compound shows a complex signal pattern of an AA′BB′ type for the four methylene protons in the NMR spectrum. The inversion process is analysed using the density matrix method, and at various temperatures the calculated line shapes are fitted to the observed spectra to obtain the life-time τ of the inversion. From the logarithmic plot of the life time versus 1/T, the kinetic parameters of this intramolecular inversion process are obtained as follows: E_a = 25·3 ± 1·0 Kcal/mole ΔG3 = 24°1 ± 1·0 Kcal/mole at 25·0° ΔH3 = 24·7 ± 1·0 Kcal/mole ΔS3 = 2·1 ± 0·8 e.u.