The effects of librations on the ¹³C chemical shift and ²H electric field gradient tensors in β-calcium formate

The magnitudes and orientations of the principal elements of the ¹³C chemical shift anisotropy (CSA) tensor in the molecular frame of the formate ion in β-calcium formate is determined using one-dimensional dipolar-shift spectroscopy. The magnitudes of the principal elements of the ¹³C CSA tensor are σ_11C=104 ppm, σ_22C=179 ppm, and σ_33C=233 ppm. The least shielding element of the ¹³C CSA tensor, σ_33C, is found to be collinear with the C-H bond. The temperature dependence of the ¹³C CSA and the ²H quadrupole coupling tensors in β-calcium formate are analyzed for a wide range of temperature (173-373 K). It was found that the span of the ¹³C CSA and the magnitude of the ²H quadrupole coupling interactions are averaged with the increasing temperature. The experimental results also show that the ²H quadrupole coupling tensor becomes more asymmetric with increasing temperature. A librational motion about the σ_22C axis of the ¹³C CSA tensor is used to model the temperature dependence of the ¹³C CSA tensor. The temperature dependence of the mean-square amplitude of the librational motion is found to be 〈α²〉 = 2.6× 10^-4(T) rad² K^-1. The same librational motion also accounts for the temperature-dependence of the ²H quadrupole coupling tensor after the relative orientation of the ¹³C CSA and ²H electric field gradient tensors are taken into account. Reconsideration of the results of a previous study found that the librational motion, not the vibrational motion, accounts for an asymmetry in the ¹H-¹³C dipolar coupling tensor of α-calcium formate at room temperature.