X–N study of the electron density in (ND4)2Cu(SO4)2.6D2O at 9 K: flexible radial functions are vital

Figgis, B. N.; Iversen, Bo B.; Larson, F. K.; Reynolds, P. A.

doi:10.1107/s0108768193002812

Cited by 59 publications

(82 citation statements)

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“…Also, anharmonic motion experimentally seems to become negligible at 10 K (Figgis et al, 1993;Iversen, Nielsen et al, 1995), as is theoretically expected. Also, anharmonic motion experimentally seems to become negligible at 10 K (Figgis et al, 1993;Iversen, Nielsen et al, 1995), as is theoretically expected.…”

Section: Introductionsupporting

confidence: 54%

“…Another consideration is the sample temperature. With regard to the asphericity of the electron densities for X-ray data, it is necessary to use very flexible electronic models in order to accurately determine the atomic displacement parameters [ADP's (Figgis, Iversen, Larsen & Reynolds, 1993)]. This can be achieved with modem well regulated cooling devices (Henriksen, Larsen & Rasmussen, 1986;Larsen, 1991Larsen, , 1995.…”

Section: Introductionmentioning

confidence: 99%

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Atomic displacement parameters for Ni(ND₃)₄(NO₂)₂ from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Iversen

Larsen²,

Figgis³

et al. 1996

Acta Crystallogr Sect B

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Structural parameters derived from 9(1)K X-ray diffraction data and 13(1)K time-of-flight neutron diffraction data on perdeuterated tetraamminedinitronickel(II), Ni(ND3)4(NO2)2, are compared. It is shown that excellent agreement can be obtained for both positional and thermal parameters derived separately from the two experiments, provided that great care is taken in all steps of the process, including data collection, data reduction, and nuclear and electronic structure refinement. The mean difference in the thermal parameters, , is as low as 0.00034/~ 2 and <(AUij/cr)2> I/2 = 1.92, showing that, even without any form of scaling between the parameters, the same values can be obtained. This, compared with other such studies, indicates that time-of-flight neutron diffraction data can give structural information of a quality comparable to monochromatic neutron diffraction. The excellent correspondence between the thermal parameters derived separately from X-ray and neutron diffraction data gives confidence in the deconvolution of the thermal motion from the X-ray diffraction data, which is necessary for any study of a static electron density distribution.

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Section: Introductionsupporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Atomic displacement parameters for Ni(ND₃)₄(NO₂)₂ from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Iversen

Larsen²,

Figgis³

et al. 1996

Acta Crystallogr Sect B

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“…A great amount of work has been devoted to finding out what type of functions give the physically most sensible EDD's after a least-squares refinement. In recent years it has become evident that also the shape of the radial functions used in the least-squares procedure can have a great influence on the final result (Figgis, Iversen, Larsen & Reynolds, 1993). Even though such bias is unsatisfactory, a great virtue of the method is that the electron density is parametrized into analytical functions.…”

Section: The Multipole Refinement Methodsmentioning

confidence: 99%

“…Results from the least-squares refinement of model 1 are given in Table 3. Figgis, Iversen, Larsen & Reynolds (1993) found in their study of copper Tutton's salt, that unbiased neutron parameters can be vital in electron-density modelling using the multipole technique. In order to extract the optimum amount of electronic information about the system, presumably unbiased thermal parameters were therefore first obtained by least-squares refinement of the neutron diffraction data of Larsen, Brown, Lehman & Merisalo (11982) (see Appendix).…”

Section: Tharmonic(h ) = E Xp(-pij Hihj )mentioning

confidence: 99%

Experimental evidence for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method

Iversen¹,

Larsen²,

Souhassou³

et al. 1995

Acta Crystallogr Sect B

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The electron-density distribution (EDD) of metallic beryllium has been derived from the structure factors of Larsen & Hansen [(1984). Acta Cryst. B40, 169-179] using the maximum entropy method (MEM). Subsequent topological analysis reveals non-nuclear maxima (NNM) in the EDD. Plots of the gradient field of the electron density illustrates this finding. A possible critical-point network for the hexagonal close-packed (h.c.p.) structure of beryllium is suggested. It is thus demonstrated that it is possible to obtain detailed topological information about the electron density in metallic beryllium without the use of a structural model. In order to test the findings of the MEM, the same set of structure factors were analysed using the multipole refinement method (MRM). Use of the MRM also reveals NNM. The results of the two different approaches to electron-density analysis are contrasted and discussed. Expressed within the framework of the theory of atoms in molecules, our results suggest that the h.c.p, structure of beryllium has no Be atoms directly bonded to other Be atoms. The structure is held together through a three-dimensional network of bonds between the NNM and Be atoms as well as between different NNM. The topological analysis thus reveals that the beryllium structure has important interactions connecting Be atoms of different basal plane layers. The breaking of these interactions when forming a surface may explain the abnormally large expansion of the inter-layer distance in the beryllium surface structure.

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“…Many studies have explored detailed comparison between X-ray and theoretical EDs (Gatti et al, 1992;Schmøkel et al, 2012;Jørgensen et al, 2013) and it is widely recognized that the models used to describe the experimental ED are insufficient and therefore introduce a model bias. As an example, various studies during the past two decades have addressed the radial flexibility in the HC model (Figgis et al, 1993;Spackman et al, 1999; and currently, considerable efforts in the field are directed towards improving the description of the radial functions (Volkov & Coppens, 2001;Koritsanszky & Volkov, 2004). Only very recently has the implicit assumption about inert core electrons received attention.…”

Section: Introductionmentioning

confidence: 99%

Experimental determination of core electron deformation in diamond

Bindzus

Straasø²,

Wahlberg

et al. 2013

Acta Crystallogr A Found Adv

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Synchrotron powder X-ray diffraction data are used to determine the core electron deformation of diamond. Core shell contraction inherently linked to covalent bond formation is observed in close correspondence with theoretical predictions. Accordingly, a precise and physically sound reconstruction of the electron density in diamond necessitates the use of an extended multipolar model, which abandons the assumption of an inert core. The present investigation is facilitated by negligible model bias in the extraction of structure factors, which is accomplished by simultaneous multipolar and Rietveld refinement accurately determining an atomic displacement parameter (ADP) of 0.00181 (1) Å(2). The deconvolution of thermal motion is a critical step in experimental core electron polarization studies, and for diamond it is imperative to exploit the monatomic crystal structure by implementing Wilson plots in determination of the ADP. This empowers the electron-density analysis to precisely administer both the deconvolution of thermal motion and the employment of the extended multipolar model on an experimental basis.

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X–N study of the electron density in (ND₄)₂Cu(SO₄)₂.6D₂O at 9 K: flexible radial functions are vital

Cited by 59 publications

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Atomic displacement parameters for Ni(ND₃)₄(NO₂)₂ from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Atomic displacement parameters for Ni(ND₃)₄(NO₂)₂ from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Experimental evidence for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method

Experimental determination of core electron deformation in diamond

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X–N study of the electron density in (ND4)2Cu(SO4)2.6D2O at 9 K: flexible radial functions are vital

Cited by 59 publications

References 0 publications

Atomic displacement parameters for Ni(ND3)4(NO2)2 from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Atomic displacement parameters for Ni(ND3)4(NO2)2 from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Experimental evidence for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method

Experimental determination of core electron deformation in diamond

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X–N study of the electron density in (ND₄)₂Cu(SO₄)₂.6D₂O at 9 K: flexible radial functions are vital

Atomic displacement parameters for Ni(ND₃)₄(NO₂)₂ from 9 K X-ray and 13 K time-of-flight neutron diffraction data

Atomic displacement parameters for Ni(ND₃)₄(NO₂)₂ from 9 K X-ray and 13 K time-of-flight neutron diffraction data