Electron Distribution and Molecular Motion in Crystalline Benzene: An Accurate Experimental Study Combining CCD X-ray Data on C₆H₆ with Multitemperature Neutron-Diffraction Results on C₆D₆

Abstract

The electronic properties of the benzene molecule, for example its quadrupole moment and the electric field gradients (EFG's) at the H nuclei, are of fundamental importance in theoretical and experimental chemistry. With this in mind, single-crystal X-ray diffraction data on C₆H₆ were collected with a charge-coupled device detector at T≈110 K. As accurate modelling of the thermal motion in the crystal was regarded as vital, especially for the hydrogen atoms, anisotropic-displacement parameters (ADP's) for the C and H atoms in C₆H₆ were derived in a straightforward fashion from analysis of the temperature dependence of ADP's for the C and D atoms in C₆D₆ at 15 K and 123 K obtained by neutron diffraction. Agreement between C-atom ADP's derived from thermal-motion analysis of neutron data and those obtained from multipole refinement by using the X-ray data is extraordinarily good; this gives confidence in the modelling of vibrational motion for the H atoms. The molecular quadrupole moment derived from the total charge density of the molecule in the crystal is (-29.7±2.4)x10-40 C m², in excellent agreement with measurements made in the gas phase and in solution. The average deuterium nuclear quadrupole coupling constant (DQCC) derived from EFG tensors at H atoms is 182±17 kHz, also in excellent agreement with independent measurements. The strategy employed in this work may be of more general applicability for future accurate electron density studies