Can X-ray data distinguish bonding effects from vibrational smearing?

Abstract

The frequent practice of combining X-ray and neutron diffraction for distinguishing vibrational smearing from charge deformation due to chemical bonding is neither necessary nor completely satisfactory. The two effects occur principally in distinct regions of real and reciprocal space. They can be distinguished by X-ray data alone provided these extend to reciprocal radii d* > 2 A-1 and provided the refinement program allows explicitly for the bonding deformation. The success of this separation can be tested by comparison of the vibration ellipsoids of bonded atom pairs, which should have equal amplitudes in the bond direction. Application of this 'rigid-bond' test to four recent refinements using the charge deformation model shows the vibration parameters to be largely unbiased, as those from parallel spherical-atom refinements are not. Hydrogen vibration parameters cannot be derived from X-ray data because of large deformation densities at the nuclei; nor do they satisfy the rigid-bond postulate.

Dynamics and Thermodynamics of Crystalline Polymorphs. 3. γ-Glycine, Analysis of Variable-Temperature Atomic Displacement Parameters, and Comparison of Polymorph Stabilities

“…2). The differences of mean square displacements along interatomic vectors of bonded non-H atoms are <1.0×10 -3 Å 2 for all temperatures, thus satisfying the Hirshfeld's rigid-bond test 32 and warranting the quality of the ADPs obtained. Table 1.…”

Experimental studies of charge density distribution in the crystals of cytisine and N-methylcytisine. Inside the Fake Tobacco

“…Initially, only the scale factor was refined, followed by non-hydrogen, the atomic positions and atomic displacement parameters (ADPs) against all reflections. Subsequently, a high-order (sinθ/λ>0.7 Å −1 ) refinement for non-H atoms was performed, aiming at the deconvolution of the ADP's and bonding deformation effects [20]. The ADPs for H atoms were estimated using SHADE server [21].…”

“…The Hirshfeld rigid bond test [20] was applied to the nonhydrogen atoms joined by the covalent bonds after the final multipolar refinement. For each pair of non-hydrogen atoms, the values of ΔZ AB 2 (differences between the components of the U ij tensor along the bond) do not exceed the acceptable value of 10 −3 Å 2 .…”

Experimental versus theoretical charge densities: a hydrogen-bonded derivative of bicyclobutane at 85 K

“…Before the introduction of a charge deformation model it was necessary to constrain the vibration parameters of the H atoms (Hirshfeld, 1976). To this end the molecular skeleton (see Fig.…”

“…promolecule plus deformation density, was scanned throughout the asymmetric unit for possible negative values and none at all were found. Finally, the refined vibration parameters were tested against the rigid-bond postulate (Hirshfeld, 1976). The r.m.s, difference z z -z 2 (Table 2) (Table lb).…”