Study of the electron density in MgO, (Mg 0.963 Fe 0.037 )O and Cu 2 O by the maximum entropy method and multipole refinements: comparison between methods

Merli, Marcello; Pavese, Alessandro; Ranzini, Mariagrazia

doi:10.1007/s00269-002-0253-7

Cited by 10 publications

(4 citation statements)

References 22 publications

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“…Such a CP is the one best defined throughout the elementary cell and least affected by bias due to interpolation over the qgrid, as observed by Merli et al (2002) who provided a detailed study of all the CPs of MgO, (Mg,Fe)O and CuO. In Table 4 we have neglected the case of the EDs reported in Table 3oa, because the large disagreements therein shown make such a model of modest interest for a further discussion.…”

Section: Topological Properties Along Mg--o Bondmentioning

confidence: 87%

“…By means of (2) one models the atomic thermal motion effects in q(r) STAT , so as to provide a q(r) REF representative of an ED at finite temperature. We have used U¼ 0.0043 A 2 , which has been obtained in the study quoted above of Merli et al (2002), and describes an atom vibrating through a volume significantly larger than that of a pixel. Structure factors have been generated as Fourier coefficients of q(r) REF , and successively used in MEM calculations in lieu of experimental diffraction intensities.…”

Section: Theoretical Simulated Ed and Structure Factorsmentioning

confidence: 99%

“…A quantum "static" ED, q(r) STAT , for MgO [SG: Fm3m; a ¼ 4.2122(4) A; Mg(0, 0, 0), O( 1 = 2 , 1 = 2 , 1 = 2 ); see Merli et al (2002) for details about crystallographic parameters] has been generated using the CRYSTAL98 code (Saunders et al, 1998), which implements the Hartree-Fock technique in the case of crystals and generates electron wave functions by linear combinations of atomic orbitals. In the present calculation we have used 8-511G and 8-411G basis sets for Mg and O, respectively.…”

Section: Theoretical Simulated Ed and Structure Factorsmentioning

confidence: 99%

“…Roversi et al (1998) thoroughly dealt with the role of prior-ED and apriori knowledge provided by structure fragments, in reconstructing EDs by MEM. Merli et al (2002) compared EDs by MEM with those determined via multi-pole analysis, using accurate experimental data. Dobrzynski & Waliszewski (2003) investigated different sources of uncertainty reflecting onto the accuracy of charge density and momentum density obtained by MEM.…”

Section: Introductionmentioning

confidence: 99%

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About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO

Merli¹,

Pavese²

2006

Zeitschrift Für Kristallographie - Crystalline Materials

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The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [q(r) REF ]. The Fourier coefficients of q(r) REF have been calculated, and used as "observed" diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [q(r) MEM ] and q(r) REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs, on the basis of a set of observed structure factors. We have carried out our study varying the number of observed structure factors [i.e. sin (q)/l cut-off], the nature of the prior-density [uniform density and procrystal-like model] and the way in which the prior-density is treated during MEM maximization [fixed or free to change]. We observe that (i) it is recommendable to use the prior-density as a start point only, and allow it to change during maximization; (ii) the closer is the prior-density to q(r) REF , the easier one attains by MEM a correct ED; (iii) if the prior-density is varied and a sufficient large number of observed structure factors used, then MEM tends to yield converging EDs, regardless of the prior-density chosen as a start point.

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Section: Topological Properties Along Mg--o Bondmentioning

confidence: 87%

Section: Theoretical Simulated Ed and Structure Factorsmentioning

confidence: 99%

Section: Theoretical Simulated Ed and Structure Factorsmentioning

confidence: 99%