"The treatment of errors in the isomporphous replacement method"

Date:
[1958]
Reference:
PP/CRI/H/2/28
Catalogue details

Licence: In copyright

Credit: "The treatment of errors in the isomporphous replacement method". Source: Wellcome Collection.

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    If, for instance, the amplitude |p| had been measured with perfect accuracy but there was nofy information about the phase, the diagram would in the non -centro symmetric case consist of a circle, radius jP|^, centred on the origin, if In the centrosymmetric case it would consist of two equal points of probability density, f » + jpj and - ¡Fl . In practice, neither amplitude nor phase is known with perfect accuracy, and the probability will be a smgjothly varying function, representing all available information about F (kW^ . We will call this function P^ L and it will be normalised so that (9) -Cci In order to portray this information in structural terms, it is necessary to make a Fourier transformation. » The most general way to do this would be to work out the transforms for all possible values of A and 13 for each hJcL . The probability of a transform being the correct one would be TT (*.«0. e») ¿de-t In this way one can imagine obtaining a continuum of structures, each with an assigned probability. The structures whose probability fell below a certain value might be rejected, and the remainder examined to see what characteristics they had in common. Such an idealised procedure could not be undertaken in practice. However, these considerations enable us to define two transforms which can - ms.'y easily be calculated» The most obvious is the most probable Fourier. This may be calculated by choosing the value of F(w)for each reflexion corresponding to the highest value of p^(A t S). This corresponds to using (1) and neglecting all errors. This Fourier will clearly have the maximum value of Ì i P (A, ßjand is the ULI WJ- 7 most likely to be correct.