Internal rotation in alkyl benzene derivatives: maximum entropy and constrained maximum entropy analysis of the dipolar couplings of samples dissolved in a nematic liquid crystal solvent

Abstract

We have analysed a set of NMR dipolar couplings of ethylbenzene (Ph–CH₂–CH₃) as solute in the liquid crystalline solvent ZLI1132. The analysis has been carried out by means of the maximum entropy (ME) method in the unconstrained formulation. The unconstrained ME technique confirms recent ab initio results for ethylbenzene: besides the well established absolute maximum of the probability density in relation to the ethyl group perpendicular to the phenyl ring, we have found a relative shallow maximum when the ethyl group is in the plane of the aromatic ring. This contrasts with other previously reported studies which considered this conformation as the transition state. The similarity between ab initio and ME results has prompted the proposal of a constrained maximum entropy method as a tentative one for combining the information from the liquid crystal NMR spectroscopy (LXNMR) technique with knowledge of the conformations of the isolated molecule coming from ab initio calculations found in the literature. Due to lack of a parameterised function describing the torsional motion of the ethyl group around the phenyl ring, we have tested the method for the case of the benzyl chloride dissolved in ZLI1132. We can see that, whereas the unconstrained ME method strongly depends on the degree of the orientational order of the molecule, in agreement with the general principle of maximum entropy, the constrained ME method gives a peaked distribution function even if that order is low. Detailed theoretical calculations of the entire potential energy surface of the crucial molecule of ethylbenzene seem to be highly requested in order to be used as an input in the constrained ME method. The latter could be useful in the study of solvent effects.