Hirshfeld Atom Refinement of Metal–Organic Complexes: Treatment of Hydrogen Atoms Bonded to Transition Metals

Abstract

Hydrogen positions in hydrides play a key role in hydrogen storage materials and high-temperature superconductors.Our recently published study of five crystal structures of transitionmetal-bound hydride complexes showed that using aspherical atomic scattering factors for Hirshfeld atom refinement (HAR) resulted in a systematic elongation of metal−hydrogen bonds compared to using spherical scattering factors with the Independent Atom Model (IAM). Even though only standardresolution X-ray data was used, for the highest-quality data, we obtained excellent agreement between the X-ray and the neutronderived bond lengths. We present an extended version of this study including 10 crystal structures of metal−organic complexes containing hydrogen atoms bonded to transition-metal atoms for which both X-ray and neutron data are available. The neutron structures were used as a benchmark, and the X-ray structures were refined by applying Hirshfeld atom refinement using various basis sets and DFT functionals in order to investigate the influence of the technical aspects on the length of metal−hydrogen bonds. The result of including relativistic effects in the Hamiltonian and using a cluster of multipoles simulating interactions with a crystal environment during wave function calculations was examined. The effect of the data quality on the final result was also evaluated. The study confirms that a high quality of experimental data is the key factor allowing us to obtain significant improvement in transition metal (TM)−hydrogen bond lengths from HAR in comparison with the IAM. Individual adjustments and better choices of the basis set can improve hydrogen positions. Average differences between TM− H bond lengths obtained with various DFT functionals upon including relativistic effects or between double-ζ and triple-ζ basis sets were not statistically significant. However, if all bonds formed by H atoms were considered, significant differences caused by different refinement strategies were observed. Finally, we examined the refinement of atomic thermal motions. Anisotropic refinement of hydrogen thermal motions with HAR was feasible only in some cases, and isotropically refined hydrogen thermal motions were in similar agreement with neutron values whether obtained with HAR or with the IAM.

Synthesis, Structure, and Reactivity of Molybdenum– and Tungsten–Indane Complexes with Tris(pyrazolyl)borate Ligand

“…Here, we selected Mo and W complexes with a Tp or Tp* ligand and examined their reaction with InBr3. Although there are no examples of structural analyses of complexes with clear W→In dative bonds, several examples of structural analyses of complexes with TM→In dative bonds have been reported for other transition metal complexes: one example for Pt [15], Pd [22], and Ru [23]; two examples for Co [24,25]; and three examples for Ni [26][27][28] and Rh [29][30][31].…”

Locating Interstitial Hydrides in MH2@Cu14 (M = Cu, Ag) Clusters by Single-Crystal X-ray Diffraction

“…However, accurately determining the position of hydrogen atoms and the length of C–H bonds in a molecule using XRD methods can be challenging, as these methods are known to underestimate the C–H bond lengths . To supplement XRD analysis, computational methods such as Hirshfeld atomic refinement (HAR) have been developed, enabling anisotropic refinements for hydrogen atoms, although the accuracy is somewhat lower compared to atomic displacement parameters (ADPs) obtained from neutron diffraction. , It is important to consider the quality of the diffraction data, as insufficient data may limit the refinement to isotropic parameters. In contrast to theoretical calculations, a machine learning-based approach has also been employed to predict the possibility of hydride positions in copper hydride compounds. , The algorithm utilized in this method is trained with a limited data set of previously solved neutron crystal structures. − One of the key benefits of employing machine learning in this context is its potential to accelerate the analysis process and decrease the reliance on costly and time-consuming experimental techniques.…”

“… 15 To supplement XRD analysis, computational methods such as Hirshfeld atomic refinement (HAR) have been developed, 16 enabling anisotropic refinements for hydrogen atoms, although the accuracy is somewhat lower compared to atomic displacement parameters (ADPs) obtained from neutron diffraction. 17 , 18 It is important to consider the quality of the diffraction data, as insufficient data may limit the refinement to isotropic parameters. In contrast to theoretical calculations, a machine learning-based approach has also been employed to predict the possibility of hydride positions in copper hydride compounds.…”