Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study
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 orienta...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/12/2/283 |
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| author | Damian Mroz Ruimin Wang Carsten Paulmann Ulli Englert Richard Dronskowski |
| author_facet | Damian Mroz Ruimin Wang Carsten Paulmann Ulli Englert Richard Dronskowski |
| author_sort | Damian Mroz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T22:14:07Z |
| format | Article |
| id | doaj.art-3ad3d20f81bb48b2b660d04258b7e524 |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-09T22:14:07Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-3ad3d20f81bb48b2b660d04258b7e5242023-11-23T19:26:02ZengMDPI AGCrystals2073-43522022-02-0112228310.3390/cryst12020283Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case StudyDamian Mroz0Ruimin Wang1Carsten Paulmann2Ulli Englert3Richard Dronskowski4Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52056 Aachen, GermanyInstitute of Molecular Science, Shanxi University, Taiyuan 030006, ChinaMineralogisch-Petrographisches Institut, Hamburg University, 20146 Hamburg, GermanyInstitute of Molecular Science, Shanxi University, Taiyuan 030006, ChinaInstitute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1, 52056 Aachen, GermanyAnisotropic 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.https://www.mdpi.com/2073-4352/12/2/283displacement parametersharmonic approximationresolutionquasi-harmonic approximationsynchrotron radiationtemperature-resolved diffraction |
| spellingShingle | Damian Mroz Ruimin Wang Carsten Paulmann Ulli Englert Richard Dronskowski Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study Crystals displacement parameters harmonic approximation resolution quasi-harmonic approximation synchrotron radiation temperature-resolved diffraction |
| title | Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study |
| title_full | Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study |
| title_fullStr | Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study |
| title_full_unstemmed | Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study |
| title_short | Temperature-Resolved Anisotropic Displacement Parameters from Theory and Experiment: A Case Study |
| title_sort | temperature resolved anisotropic displacement parameters from theory and experiment a case study |
| topic | displacement parameters harmonic approximation resolution quasi-harmonic approximation synchrotron radiation temperature-resolved diffraction |
| url | https://www.mdpi.com/2073-4352/12/2/283 |
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