Rotational tunneling of orientationally coupled methyl groups: Molecular field approximation versus numerically exact solution

The orientational coupling of methyl groups leads to a split rotational tunneling line. We study the dependence of this splitting on the type and strength of the interaction. Two types of pair potentials are considered (M1) cos 3φi cos 3φj and (M2) cos 3(φi+φj). The tunneling spectra are calculated numerically exact for N=2 and N=3 rotors by using a sparse matrix method (SMM). For model M1 we also probe the molecular field approximation (MFA). For both, N=2 and N=3, not even qualitative agreement is found between MFA and SMM. But a trend can be seen towards MFA-like behavior; with increasing N, the dependence of the splitting on the coupling strength qualitatively resembles the MFA prediction. However, by our SMM results, we are led to the conjecture, that for moderate coordination numbers a considerable splitting should occur within a much broader range of coupling strengths than predicted by MFA.