Publikationsdatum:
1989-02-01
Beschreibung:
It is shown that an electron density distribution of the formρk= exp [Σfj(rk)xj] has maximum entropy under the constraint that the expected values of a set of functions,fj(r), are constant. For a Fourier map the functionsfj(r) are the magnitudes of the structure factors for a set of reflectionshjincludingF(000). The values of the parametersxjfor which [(exp (2πihj. r))] = [Fobs(hj)[ for an arbitrarily large set of reflections may be found by an iterative algorithm in whichxi+ 1=xi+Hi-1Δi, where the matrixHis positive definite. Because the distributionρ(r) is everywhere positive, if non-negativity of electron density is sufficient information to determine a unique structure by direct methods, it follows that the maximum entropy procedure must lead to the same unique structure. Maximum entropy is thus an efficient way of expressing the phase implications of a large set of structure amplitudes.
Print ISSN:
0108-7673
Digitale ISSN:
2053-2733
Thema:
Chemie und Pharmazie
,
Geologie und Paläontologie
,
Physik
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