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Phase determination and extension using X-ray multiple diffraction and the maximum-entropy method.

C M Wang¹, C H Chao, S L Chang

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan.

Acta Crystallographica. Section A, Foundations of Crystallography

|June 22, 2001

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Researchers extended crystal structure phases using the maximum-entropy method, determining over 100 phases and a detailed electron-density map for C(25)H(25)NO(2). This advances crystallographic phase determination techniques.

Area of Science:

Crystallography
Materials Science
Computational Chemistry

Background:

Accurate crystal structure determination relies on phase information, which is experimentally challenging to obtain.
The maximum-entropy method (MEM) is a powerful computational technique for phase extension in crystallography.

Purpose of the Study:

To extend the phases of structure factors for the organic crystal C(25)H(25)NO(2).
To deduce an electron-density map using an iterative phase extension procedure.

Main Methods:

Utilized 77 initial phases derived from experimental triplet phases obtained via psi-scan three- and four-beam diffraction.
Applied the maximum-entropy method (MEM) with space group symmetry as constraints to 2040 measured two-beam Bragg diffraction intensities.
Employed minimum chi(2) criteria for phase set selection in iterative extrapolation.

Related Experiment Videos

Main Results:

Successfully extended the phases of structure factors for C(25)H(25)NO(2).
Determined over 100 additional phases through the iterative MEM procedure.
Deduced an electron-density map at a resolution of 1.97 Å.

Conclusions:

The maximum-entropy method is effective for phase extension in complex organic crystals.
The developed phase extension strategy enabled the deduction of a high-resolution electron-density map.
This work demonstrates a robust approach for solving crystal structures where direct phase determination is difficult.