The quality of the Hartree−Fock and the density functional methods for the description of hydrogen bonds
is judged by comparing quantitatively the outcome of calculations on the hydrogen bonds in ammonium
(bi)fluorides with the results of accurate electron density studies by X-ray diffraction. X-ray data and analysis
for NH4F were taken from the literature; those for NH4HF2 were collected in a single-crystal diffraction
experiment. A total of 8522 reflections was measured, yielding the structure factors of 2333 independent
reflections. Rint (F2) = 0.03. A multipole refinement converged to R
w (F2) = 0.034. Quantum chemical
calculations were carried out with the CRYSTAL package, using the Hartree−Fock and the density functional
methods and a 6-311G** basis set. Both the local density and the generalized gradient(GGA) version of the
latter were applied. To make a comparison with experiment valid, the theoretical densities were converted to
structure factors that then were subjected to the same multipole refinement as the experimental ones. The
differences between the theoretical and the experimental results are shown by comparing in direct space the
electron density in the bonding regions in the crystals and the topological characteristics at the bond critical
points, in reciprocal space the structure factors as functions of the scattering angle. The GGA results showed
the best agreement with experiment, with excellent agreement both in the very short and the longer hydrogen
bonds. The curvatures of the electron density distributions along the hydrogen bonds and perpendicular to it
reveal the character of these bonds.
Films of BaTiO3 ranging from 20 nm to 300 nm in thickness were grown with pulsed laser deposition on Nb:SrTiO3. The quality of the layers was investigated using atomic force microscopy, X‐ray reflectivity and X‐ray diffraction. Both the micrographs and the X‐ray reflectivity spectra indicate a smooth surface of the layers. The X‐ray diffraction profiles measured using synchrotron radiation show features characteristic for highly crystalline thin films. The application of an external electric field parallel to the c axis changes an hkl reflection of BaTiO3 to an hk reflection. Due to the anomalous dispersion, the intensities of these two reflections are not equal and the atomic displacements can be determined from the intensity differences. The electric field‐induced intensity changes can be as large as a few percent, which makes data collection from a 100 nm film using Cu Kα radiation from an X‐ray tube feasible. The ΔI/I values of a number of reflections from the 20 and 50 nm films were measured using synchrotron radiation. The observed ΔI/I values were in good agreement with the intensity changes expected for polarization switching in the bulk.
The conventional method to measure small induced changes in integrated intensity utilizes a zero‐dimensional detector, which greatly limits the data collection speed. This paper shows that the use of an area detector in combination with an X‐ray chopper decreases the data collection time significantly. A monochromatic diffraction setup using a charge‐coupled device (CCD) detector coupled to an X‐ray image intensifier was constructed and tested. The setup proved to be sufficiently stable to measure changes in integrated intensity well below 0.1%. Subsequently, a data set of a piezoelectric KD2PO4 crystal in an external electric field was collected. The data were merged to yield 77 unique reflections. The induced structural changes were determined by a least‐squares refinement. The results agree very well with experiments in which a zero‐dimensional detector was used. The major improvement is the decrease in data collection time by one order of magnitude, without any degradation of the data quality, offering new possibilities for this type of perturbation study.
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