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Communication: Determination of relativistic effects from X-ray structure factors
2.A. Fischer, D. Tiana, W. Scherer, K. Batke, G. Eickerling, H. Svendsen, N. Bindzus, and B. B. Iversen, J. Phys. Chem. A 115, 13061 (2011).
3.W. Scherer, A. Fischer, and G. Eickerling, “The experimental density perspective of chemical bonding,” in The Chemical Bond, edited by G. Frenking and S. Shaik (Wiley-VCH, 2014), pp. 309–344.
and G. Eickerling
, e-print arXiv:1512.07440
6.M. Reiher and A. Wolf, Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science (Wiley, 2009), p. 555.
8.See, e.g., C. Gatti and P. Macchi, Modern Charge-Density Analysis (Springer, Dordrecht; New York, 2012), and references therein.
9.A. Volkov, P. Macchi, L. J. Farrugia, C. Gatti, P. Mallinson, T. Richter, and T. Koritsanszky, Xd2006 — a computer program for multipole refinement, topological analysis of charge densities and evaluation of intermolecular interaction energies from experimental or theoretical structure factors (2006).
See supplementary material at http://dx.doi.org/10.1063/1.4942244
for full computational details employing different (quasi-relativistic) model Hamiltonians, details on the EHCM refinements, and a comparison to theoretical reference data obtained from Ref. 15
12.G. Eickerling, C. Hauf, E.-W. Scheidt, L. Reichardt, C. Schneider, A. Muñoz, S. Lopez-Moreno, A. Humberto Romero, F. Porcher, G. André, R. Pöttgen, and W. Scherer, Z. Anorg. Allg. Chem. 639, 1985 (2013).
14.C. Gold, “Über die Natur konkurrierender Wechselwirkungen in Cer-basierten 1-9-4 Verbindungen,” Ph.D. thesis, Universität Augsburg, 2013.
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In this communication, a procedure is presented which allows for the determination of the scalar-relativistic contraction of individual electronic shells of transition metal atoms from X-ray structure factor data. The procedure is verified and benchmarked employing theoretical and experimental F(hkl) data, revealing an overall good agreement between the experimentally determined results and the theoretical reference values. From the experimental data, the relativistic contraction of the n = 2 shell of a cerium atom is, for example, determined as 0.097 pm, compared to a theoretical reference value of 0.116 pm. It is further demonstrated that the reproducibility of the results is excellent when comparing different experimental data sets. Finally, the dependency of the according results on the data resolution of the structure factor data is investigated.
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