Hirshfeld atom refinement (HAR) is a novel X-ray structure refinement technique that employs aspherical atomic scattering factors obtained from stockholder partitioning of a theoretically determined tailor-made static electron density. HAR overcomes many of the known limitations of independent atom modelling (IAM), such as too short element-hydrogen distances, r(X-H), or too large atomic displacement parameters (ADPs). This study probes the accuracy and precision of anisotropic hydrogen and nonhydrogen ADPs and of r(X-H) values obtained from HAR. These quantities are compared and found to agree with those obtained from (i) accurate neutron diffraction data measured at the same temperatures as the X-ray data and (ii) multipole modelling (MM), an established alternative method for interpreting X-ray diffraction data with the help of aspherical atomic scattering factors. Results are presented for three chemically different systems: the aromatic hydrocarbon rubrene (orthorhombic 5,6,11,12-tetraphenyltetracene), a cocrystal of zwitterionic betaine, imidazolium cations and picrate anions (BIPa), and the salt potassium hydrogen oxalate (KHOx). The non-hydrogen HARADPs are as accurate and precise as the MM-ADPs. Both show excellent agreement with the neutron-based values and are superior to IAM-ADPs. The anisotropic hydrogen HAR-ADPs show a somewhat larger deviation from neutron-based values than the hydrogen SHADE-ADPs used in MM. Elementhydrogen bond lengths from HAR are in excellent agreement with those obtained from neutron diffraction experiments, although they are somewhat less precise. The residual density contour maps after HAR show fewer features than those after MM. Calculating the static electron density with the def2-TZVP basis set instead of the simpler def2-SVP one does not improve the refinement results significantly. All HARs were performed within the recently introduced HARt option implemented in the Olex2 program. They are easily launched inside its graphical user interface following a conventional IAM.
Articles you may be interested inVibronic structure in the lowlying singlet-triplet transitions of benzene and toluene Electronic energies, geometries, and vibrational frequencies of the ground and lowlying excited states of the boron trimerThe minimum energy structure of the cyclic water trimer, its stationary points, and rearrangement processes at energies < 1 kcallmol above the global minimum are examined by ab initio molecular orbital theory. Structures corresponding to stationary points are fully optimized at the Hartree-Fock and second-order M0ller-Plesset levels, using the 6-311 + + G( d,p) basis; each stationary point is characterized by harmonic vibrational analyses.The lowest energy conformation has two free O-H bonds on one and the third O-H bond on the other side of an approximately equilateral hydrogen-bonded 0" '0"'0 (0 3 ) triangle. The lowest energy rearrangement pathway corresponds to the flipping of one of the two free O-H bonds which are on the same side of the plane across this plane via a transition structure with this O-H bond almost within the 0 3 plane. Six distinguishable, but isometric transition structures of this type connect six isometric minimum energy structures along a cyclic vibrationaltunneling path; neighboring minima correspond to enantiomers. The potential energy along this path has C 6 symmetry and a very low barrier V6=0.1±0:1 kcallmol. This implies nearly free pseudorotational interconversion of the six equilibrium structures. The corresponding anharmonic level structure was modeled using an internal rotation Hamiltonian. Two further lowenergy saddle points on the surface are of second and third order; they correspond to crown-type and planar geometries with C 3 and C 3h symmetries, respectively. Interconversion tunneling vibrations via these stationary points are also important for the water trimer dynamics. A unified and symmetry-adapted description of the intermolecular potential energy surface is given in terms of the three flipping coordinates of the O-H bonds. Implications of these results for the interpretation of spectroscopic data are discussed.(C 2 tunneling), giving 2· 2 . 2 = 8 sets of six isomers. Fi-5228
The crystal structure of C7,.6(Ss) at 100 K shows C70 to be ordered dnd the S , molecules to be partially disordered The symmetry of C,, is D,, to within experimental accuracy Crystal structures of several phases containing unsubstituted C,, have been determined by single(or twinned)-crystal X-ray diffraction: the cubic low-temperature phase of C,, (at 11 0, 153, and 200 K) [ 11, the cubic room-temperature phase of C,, (at 173 [7] and 104 K [S]). In all of these structures, C,, is disordered or shows very large amplitudes of motion. Here, we describe a structure determination of the phase C7,.6(S,) at 100 K with ordered C,, molecules.The results of a previous study of this compound at room temperature [9] were unsatisfactory for several reasons: I ) Some chemically equiuafent C-C bond lengths, with e.s.d.'s quoted as 0.03 A, differed by more than 0.2 A which is chemically very unlikely. The differences between chemically inequivalent distances expected on the basis of quantum chemical calculations is only -0.12 A [lo]. Hence, the experiment [9] cannot distinguish reliably between inequivalent C-C bonds. 2 ) If the refined distagces of chemically equivalent bonds are averaged they agree well with theory [9] [lo]. It has not been tested, however, whether a model consisting of C,, molecules with averaged bond lengths accounts for the diffraction data as well as the one which is not averaged.3) The resolution of the diffraction data was limited to -1 A and the R values seemed rather high for an ordered structure ( R ( ( F ( ) = 6.5%, wR(IF21 = 7.1 %). Thin platelets of C7,.6 (S,) with well developed (100) faces were obtained, as described in 191, by slow evaporation of a CS, solution of C,, and S, in relative amounts of 1 :6').') Crystal Data. Dark platelets of C70.6(S,), orthorhombic, space group Amm2 with a = 37.953, 6 = 20.241, c = 10.226 8, at 100 K, 2 = 4, graphite monochromatized MoK, radiation (A = 0.71069 A). Scan angle and counter aperture for the diffraction experiment were carefully chosen in order to minimize possible measurement errors resulting from partially overlapping reflection scans, the unit cell distance a being exceptionally long for a small molecule structure. Least-squares refinement of 4363 reflections with F > 60 (F), 409 parameters, R = 3.73%, W R = 3.82% for the constrained and restrained model described in the text. Atomic coordinates, bond lengths and angles, and thermal parameters have been deposited at the Cumbridge Crvstailogruphic Data Center.
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