Research Article: On the temperature dependence of H-Uiso in the riding hydrogen model

Date Published: July 01, 2014

Publisher: International Union of Crystallography

Author(s): Jens Lübben, Christian Volkmann, Simon Grabowsky, Alison Edwards, Wolfgang Morgenroth, Francesca P. A. Fabbiani, George M. Sheldrick, Birger Dittrich.


The temperature dependence of hydrogen Uiso and parent Ueq in the riding hydrogen model is investigated by neutron diffraction, aspherical-atom refinements and QM/MM and MO/MO cluster calculations. Fixed values of 1.2 or 1.5 appear to be underestimated, especially at temperatures below 100 K.

Partial Text

The riding hydrogen model is widely used in refining small-molecule X-ray diffraction data. Three positional and one isotropic displacement parameter can be constrained to a ‘parent atom’ that the H atom is ‘riding’ on, improving the data-to-parameter ratio and ensuring a chemically meaningful geometry. Alternatively, a single isotropic displacement parameter per riding H atom can be included in the least-squares refinement model while still constraining hydrogen positional parameters.

Single crystals of the compound N-acetyl-l-4-hydroxyproline monohydrate (NACH2O) were grown by slow evaporation of saturated solutions prepared in hot acetone. Crystals grow to sizes suitable for neutron diffraction. A series of multi-temperature X-ray diffraction data collections3 at 9, 30, 50 and 75 K on the same specimen with dimensions of 0.34 × 0.28 × 0.28 mm (0.5 mm pinhole) were collected at the DORIS beamline D3 at the HASYLAB/DESY synchrotron in Hamburg. The experimental setup consisted of an Oxford Diffraction open-flow helium gas-stream cooling device, a Huber type 512 four-circle diffractometer and a 165 mm MAR CCD detector. A wavelength of 0.5166 Å and a detector distance of 40.3 mm were chosen, allowing a high resolution of  Å or of 1.0 Å−1 to be reached with a single detector setting. The XDS program (Kabsch, 2010 ▶) was used for data integration and scaling. Standard deviations of the unit-cell parameters (Fig. 1 ▶) were obtained by calculating the variance of intermediate cells during integration.

H-/X- ratios reported here were derived from four independent methods. Benchmark results for NACH2O were obtained from multi-temperature neutron diffraction. Values for the hydrogen ADPs from multi-temperature single-crystal X-ray diffraction evaluated with the independent-atom model (IAM) cannot reach the accuracy achievable by neutron diffraction. To improve the physical significance of ADPs and their accuracy from X-ray diffraction (Jelsch et al., 1998 ▶; Dittrich et al., 2008 ▶), we therefore performed aspherical-atom refinements [either Hirshfeld-atom (Jayatilaka & Dittrich, 2008 ▶) or invariom refinement (Dittrich et al., 2004 ▶), see below]. QM/MM and MO/MO quantum mechanical cluster calculations (for details of how to run such computations see Dittrich et al., 2012 ▶) yield normal modes within the ‘molecular Einstein approximation’. These were combined with a TLS fit in the TLS+ONIOM approach (Whitten & Spackman, 2006 ▶) and were subsequently converted to give anisotropic ADPs for H atoms. Such computations were performed to complement the experimental results (see §3.3).

Four different methods providing the temperature-dependent ratio of H- to X- in the riding hydrogen treatment have been evaluated and compared. Neutron diffraction experiments provide benchmark values. ‘Invariom’ and ‘Hirshfeld-atom’ aspherical-atom refinements with high-resolution X-ray diffraction data yield very similar results, with the invariom model using constrained hydrogen positions giving a more consistent result, but the Hirshfeld-atom model being closer to neutron diffraction at higher temperatures. Implementing restraints in the TONTO program would therefore be useful. Furthermore, experimental findings can be well reproduced by the TLS+ONIOM approach. Here a single quantum chemical MO/MO cluster calculation is combined with a temperature-dependent rigid-body fit of the non-hydrogen ADPs from aspherical-atom X-ray refinements. All methods show that the ratio of H-/X-, which is usually assumed to be 1.2 or 1.5 independent of temperature, is frequently more than twice as high at lower temperatures. Fixed values of 1.2 or 1.5, as usually used in conventional spherical-atom ‘IAM’ refinements, are therefore underestimating the relative displacement of H atoms at cryogenic temperatures. Since all methods used here consistently show or reproduce that the H-/X- ratio is temperature dependent, the effect should be taken into account in low-temperature structure determinations, especially around 100 K and below. We will provide relevant functionality (program APD-TOOLKIT) in subsequent work.