Comparison of the Maximum Entropy and Additive Potential Methods for Obtaining Rotational Potentials from the NMR Spectra of Samples Dissolved in Liquid Crystalline Solvents. The Case of 4-Nitro-1-(β,β,β-trifluoroethoxy)benzene

Article abstract of DOI:10.1021/j100126a030

The maximum entropy (ME) and additive potential (AP) methods of determining the angular distribution functions, p(ω,χ), from the partially-averaged dipolar couplings obtained from the NMR spectra of liquid crystalline samples are compared.Here ω represents the orientation of the mesophase dircetor in a molecular frame, and χ represents bond rotational motion.It is emphasized that these two methods are fundamentally different.Thus, the model-independent ME analysis can determine only p_LC(ω,χ) and p_LC(χ), which are dependent on the potential of mean torque, U_ext(ω,χ), and the subscript LC denotes that these distributions are for the liquid-crystalline phase.The AP method, which is model-dependent, can also determine p_LC(ω,χ) and p_LC(χ) but in addition yields p_iso(χ), the distribution of the internal angular coordinate in an isotropic phase, which depends on U_int(χ), an effective, mean conformational energy.The advantages of applying both the ME and AP methods to analyzing the same set of dipolar couplings is illustrated by the case of 4-nitro-1-(β,β,β- trifluoroethoxy)benzene dissolved in two nematic solvents.The ME analysis reveals that motion about the ring-O and O-C(H2) bonds is cooperative, which was then used to guide the choice for the form of U_int(χ) in the treatment of the same data by the AP method.