A HARMONIC SUBSTITUTE MODEL SHEDS LIGHT UPON THE ROTATIONAL TUNNELING SPECTRUM OF INFINITELY MANY COUPLED METHYL-GROUPS

Orientational coupling of N methyl groups may lead to several rotational tunnelling peaks. A former calculation for a cyclic chain of up to four coupled rotors yielded the result that peaks which are separate for N = 2 quickly approach each other with increasing N at any coupling strength. Therefore, a single smooth peak was predicted for real systems. Here, we consolidate this picture by examining the quantum mechanics of a cyclic chain of up to N = 10 interacting rotors. This is feasible only after mapping the original problem to some suitable harmonic substitute. For large N and for real systems, the smooth A<->E type peak is expected to be asymmetric with its longer tail at the side of higher energy transfers; the inelasticity of the broad E<->E* type peak will hardly be visible.