M1-site in dioctahedral micas: a novel approach from information theory to fix its content

Abstract

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 o q(r)REF, the easier one attains by MEM a correct D; (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.