Tables for
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F, ch. 16.1, pp. 335-336   | 1 | 2 |

Section Parameter shift

G. M. Sheldrick,c H. A. Hauptman,b C. M. Weeks,b* R. Millerb and I. Usóna

aInstitut für Anorganisch Chemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany,bHauptman–Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, NY 14203-1196, USA, and cLehrstuhl für Strukturchemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany
Correspondence e-mail: Parameter shift

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In principle, any minimization technique could be used to minimize [R(\Phi)] by varying the phases. So far, a seemingly simple algorithm, known as parameter shift (Bhuiya & Stanley, 1963[link]), has proven to be quite powerful and efficient as an optimization method when used within the Shake-and-Bake context to reduce the value of the minimal function. For example, a typical phase-refinement stage consists of three iterations or scans through the reflection list, with each phase being shifted a maximum of two times by 90° in either the positive or negative direction during each iteration. The refined value for each phase is selected, in turn, through a process which involves evaluating the minimal function using the original phase and each of its shifted values (Weeks, DeTitta et al., 1994[link]). The phase value that results in the lowest minimal-function value is chosen at each step. Refined phases are used immediately in the subsequent refinement of other phases. It should be noted that the parameter-shift routine is similar to that used in ψ-map refinement (White & Woolfson, 1975[link]) and XMY (Debaerdemaeker & Woolfson, 1989[link]).


Bhuiya, A. K. & Stanley, E. (1963). The refinement of atomic parameters by direct calculation of the minimum residual. Acta Cryst. 16, 981–984.
Debaerdemaeker, T. & Woolfson, M. M. (1989). On the application of phase relationships to complex structures. XXVIII. XMY as a random approach to the phase problem. Acta Cryst. A45, 349–353.
Weeks, C. M., DeTitta, G. T., Hauptman, H. A., Thuman, P. & Miller, R. (1994). Structure solution by minimal-function phase refinement and Fourier filtering. II. Implementation and applications. Acta Cryst. A50, 210–220.
White, P. S. & Woolfson, M. M. (1975). The application of phase relationships to complex structures. VII. Magic integers. Acta Cryst. A31, 53–56.

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