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.
Highlights
Anisotropic displacement parameters (ADPs) based on first-principles calculations have been successfully benchmarked for several test cases [1,2,3]
The fit obtained can be compared to the results shown in Figure 6: the suggested in the computationally economic harmonic approximation underestimates the experi‐
We suggest replacing dubious “refined” parameters with ADPs based on the harmonic approximation, which will become affordable even for medium-sized structures in the near future
Summary
Anisotropic displacement parameters (ADPs) based on first-principles calculations have been successfully benchmarked for several test cases [1,2,3]. When experiments can only provide limited information, e.g., as the result of contrast problems, low resolution, or extensive disorder, theoretical ADPs may prevent over-refinement and provide an alternative answer to describe motion in a target solid. The standard approach of the harmonic approximation, while being quite successful overall, has been consistently shown to produce ADPs that are systematically smaller than their experimental counterparts due to anharmonic effects being neglected. The step, the so-called quasi-harmonic approximation, generally improves the results of the harmonic approximation by including a temperature-induced volume increase but is extremely time-consuming and demands high computational resources that may prove unaffordable. Can the harmonic approximation with its a priori known underestimation of ADPs be empirically corrected to give results close to the quasi-harmonic approximation at a lower computational cost? Crystals 2022, 12, 283 to give results close to the quasi‐harmonic approximation at a lower computational cost? Can the harmonic approximation with its a priori known underestimation of ADPs be empirically corrected to give results close to the quasi-harmonic approximation at a lower computational cost? Here, we discuss 4.0/).
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