Research ArticleMOLECULAR STRUCTURE

Hydrogen atoms can be located accurately and precisely by x-ray crystallography

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Science Advances  27 May 2016:
Vol. 2, no. 5, e1600192
DOI: 10.1126/sciadv.1600192
  • Fig. 1 Visualization of Hirshfeld atoms and deformation Hirshfeld densities.

    (A) For diborane B2H6 (25), isosurfaces (ρ = 0.08 e/Å3) of the boron electron density used to calculate the atomic scattering factors in the IAM (left, spherical, gray) and in HAR (right, aspherical, gray) are shown. The latter is a representation of the Hirshfeld atom. Bonding effects are neglected in the IAM by using a sphere but are accounted for in HAR by using Hirshfeld’s stockholder partitioning (22). The deformation Hirshfeld density (difference between the Hirshfeld density and the spherical density) is depicted for one of the bridging H atoms (ρ = 0.006 e/Å3). Blue represents positive deformation Hirshfeld density (that is, regions that gain electron density upon the transition from a spherical to an aspherical atom representation); red represents negative deformation Hirshfeld density (that is, regions that lose electron density upon the transition). (B) The resulting HAR-based molecular structure of diborane with ADPs for all atoms, including hydrogen atoms, is shown at a 50% probability level. (C) In (tetrahydroborato)bis(triphenylphosphine)copper(I) (26), deformation Hirshfeld densities (ρ = 0.006 e/Å3) are shown for copper and boron atoms. For color code, see (A). Both atoms gain electron density in the bonding regions. The extent of this effect is an indicator for the degree of covalent bonding, and it is the reason for the improved A–H bond description. (D) The resulting HAR-based molecular structure of the compound in (C) with ADPs for all atoms, including hydrogen atoms, is shown at a 50% probability level.

  • Fig. 2 Analysis of A–H bond lengths.

    Averaged A–H bond lengths with sample standard deviations (SDs) obtained from neutron diffraction versus those obtained from x-ray diffraction (HAR and IAM models) at restricted resolution (d = 0.8 Å) and with no restriction (d = max). Twenty-four bond classes Zn–A–H are taken from Allen and Bruno (24) and indicate the atom A bonded to the H atom, and in the case of A═C, the hybridization and the number of atoms Z of any kind with n = 1, 2, 3 bonded to the C atom. For cocrystallized water, we averaged O–H bond lengths obtained from neutron diffraction using entries in the Cambridge Structural Database (CSD). The numbers of observations for all bond types for each refinement method are given in the same color code in the right-hand column. For more details on the statistical analyses, see Materials and Methods. For more analyses and representations, see the Supplementary Materials.

  • Table 1 A–H bond lengths in inorganic compounds (terminal and bridging).

    Bond lengths in (Å) stem from both IAM and HAR treatments. Reference values given in brackets are not from neutron diffraction experiments on the same compound. *All IAM values are based on our own refinements using the published structure factors and isotropic hydrogen displacements, whereas the HAR results are based on fully anisotropic refinements, including the H atoms (except for METRAF and AGOZEC, for which isotropic hydrogen displacements were used). In the literature, there is a surprising lack of neutron diffraction studies for inorganic molecular compounds. Theoretical calculations cannot serve as references because even MP4 or CCSD(T) are never more precise than 0.01 Å in terms of bond length determination (29). From electron diffraction in the gas phase, compare Hübschle et al. (25). §New crystal structure determination for this study; see Materials and Methods for more details. ||Neutron diffraction of different compounds with terminal Si-H bonds (REFCODES: UJABOX01 and COQYUC01). Here, only the Cambridge Crystallographic Data Centre (CCDC) REFCODE of the original crystal structure is given; see Materials and Methods for more details on the compound and the original publication. #Averaged over seven structures from neutron diffraction (REFCODES: HINBOV01, HIPBAL01, MIGKIY01, NEBNEO, OGEFIR01, UJABOX01, and ZEGYUF01) with a total of 12 terminal Ru-H bonds; the value in brackets is the sample SD—in all other cases, it is the least-squares estimated standard uncertainty. **Neutron diffraction of a different compound with a terminal Pt-H bond (REFCODE: CAKNEH01). No standard uncertainties on the coordinates were given. N/A, not available.

    IAM*HAR*Reference
    Diborane (25)
    (see Fig. 1)
    B–H bridging1.229(5) and
    1.248(5)
    1.296(6) and
    1.296(6)
    [1.339(6) and
    1.339(6)]
    B–H terminal1.052(6) and
    1.053(6)
    1.170(7) and
    1.168(6)
    [1.196(8) and
    1.196(8)]
    BHTPCU12 (26)
    (see Fig. 1)
    B–H bridging1.186(18)1.264(7)N/A
    B–H terminal1.093(17)1.209(7)N/A
    Cu–H bridging1.802(18)1.809(7)N/A
    Pentaphenyldisiloxane§Si–H1.391(12)1.482(9)[1.481(5), 1.506(2)]||
    QOSZONFe–H1.421(21)1.414(8)1.521(2)
    Fe–H1.442(22)1.531(9)1.529(2)
    AGOZECRu–H1.589(15)1.707(18)[1.694(71)]#
    METRAFPt–H1.601(43)1.686(4)[1.610]**

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Averaged A–H bond lengths and mean x-ray–neutron bond length differences.
    • table S1. Information on the compounds used for HAR.

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    Other Supplementary Material for this manuscript includes the following:

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