ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
The Fourier coefficients Dh of a hypersection of the double Patterson function at a fixed value of U can be written as Dh = (1/V) Σh′FhFh′F_{\overline {\bf h + h^\prime}} cos 2πh′. U/cos 2πh. (U/2). It is shown that also Dh = FhGh, where Gh is the Fourier coefficient of a reduced structure derived from the original structure by positioning an atom with form factor Σh′fi(h′)fj({\overline {\bf h + h^\prime}}) halfway in between those atoms i and j, which are a vector U apart. If U is a single vector between two atoms with form factor f(h), then the reduced structure contains only one atom, at the origin, and Gh = (1/V) Σh′f(h′)f({\overline {\bf h + h^\prime}}). We obtain the relation Σh′FhFh′F_{\overline {\bf h + h^\prime}} cos 2 πh′. U/[cos 2πh. (U/2) Σh′f(h′)f{\bf h + h^\prime;}] = Fh. Using this formula with probabilities for the signs of the triple products, the single vectors U are found by a scanning process, as we demonstrate on a heavy atom structure. The signs of the structure factors have thus been calculated directly from the triple products.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739471000810
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