Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study

Crystals, vol. 12, pp. 283

Abstract

Anisotropic displacement parameters (ADPs) for an organopalladium complex were obtained from synchrotron diffraction data between 100 and 250 K and compared to the results from first-principles calculations at the harmonic approximation. Calculations and experiments agree with respect to the orientation of displacement ellipsoids and hence the directionality of atomic movement, but the harmonic approximation underestimates the amplitudes of motion by about 20%. This systematic but modest underestimation can only be reliably detected with a high-quality experimental benchmark at hand. Our experiments comprised diffraction data at 20 K intervals from 130–250 K on the same crystal. An additional high-resolution data set was collected at 100 K on a second crystal and underlined the robustness of our approach with respect to the individual sample, resolution, and instrumentation. In the temperature range relevant for our study and for many diffraction experiments, the discrepancy between experimentally determined and calculated displacement appears as an almost constant temperature offset. The systematic underestimation of harmonic theory can be accounted for by calculating the ADPs for a temperature 20 K higher than that of the actual diffraction. This entirely empirical “+20 K rule” lacks physical relevance but may pave the way for application in larger systems where a more reliable quasi-harmonic approximation remains computationally demanding or even entirely unaffordable.

Authors 5

1. Damian Mroz Aachen Institute of Physical Chemistry

   RWTH Aachen University

   Affiliation as printed

   Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52056 Aachen, Germany

2. Ruimin Wang

   Shanxi University

   Affiliation as printed

   Institute of Molecular Science, Shanxi University, Taiyuan 030006, China

3. Carsten Paulmann

   Universität Hamburg

   Affiliation as printed

   Mineralogisch-Petrographisches Institut, Hamburg University, 20146 Hamburg, Germany

4. Ulli Englert corresponding Aachen Institute of Inorganic Chemistry

   Shanxi University · RWTH Aachen University

   Affiliation as printed

   Institute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1, 52056 Aachen, Germany

   Institute of Molecular Science, Shanxi University, Taiyuan 030006, China

5. Richard Dronskowski corresponding Aachen Institute of Inorganic Chemistry

   Shenzhen Polytechnic University · RWTH Aachen University

   Affiliation as printed

   Hoffmann Institute of Advanced Materials, Shenzhen Polytechnic, 7098 Liuxian Blvd, Shenzhen 518055, China

   Institute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1, 52056 Aachen, Germany