International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by E. Arnold, D. M. Himmel and M. G. Rossmann © International Union of Crystallography 2012 |
International Tables for Crystallography (2012). Vol. F, ch. 16.1, p. 418
Section 16.1.4.3. Parameter shift
G. M. Sheldrick,^{a} C. J. Gilmore,^{b} H. A. Hauptman,^{c}^{‡} C. M. Weeks,^{c}^{*} R. Miller^{c} and I. Usón^{d}
^{a}Lehrstuhl für Strukturchemie, Georg-August-Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany,^{b}Department of Chemistry, University of Glasgow, Glasgow G12 8QQ, UK,^{c}Hauptman–Woodward Medical Research Institute, Inc., 700 Ellicott Street, Buffalo, NY 14203–1102, USA, and ^{d}Institució Catalana de Recerca i Estudis Avançats at IBMB-CSIC, Barcelona Science Park. Baldiri Reixach 15, 08028 Barcelona, Spain |
In principle, any minimization technique could be used to minimize by varying the phases. So far, a seemingly simple algorithm, known as parameter shift (Bhuiya & Stanley, 1963), 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). 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) and XMY (Debaerdemaeker & Woolfson, 1989).
References
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.