Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 8.3, pp. 694-701

Chapter 8.3. Constraints and restraints in refinement

E. Prince,a L. W. Fingerb and J. H. Konnertc

aNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA,bGeophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road NW, Washington, DC 20015-1305, USA, and cLaboratory for the Structure of Matter, Code 6030, Naval Research Laboratory, Washington, DC 20375-5000, USA


Cruickshank, D. W. J. (1961). Coordinate errors due to rotational oscillations of molecules. Acta Cryst. 14, 896–897.
Finger, L. W. (1969). The crystal structure and cation distribution of a grunerite. Mineral. Soc. Am. Spec. Pap. 2, 95–100.
Gill, P. E., Murray, W. & Wright, M. M. (1981). Practical optimization. New York: Academic Press.
Hamilton, W. C. (1964). Statistics in physical science: estimation, hypothesis testing and least squares. New York: Ronald Press.
Hendrickson, W. A. (1985). Stereochemically restrained refinement of macromolecular structures. Methods in enzymology, Vol. 115. Diffraction methods for biological macromolecules, Part B, edited by H. W. Wyckoff, C. H. W. Hirs & S. N. Timasheff, pp. 252–270. New York: Academic Press.
Hendrickson, W. A. & Konnert, J. H. (1980). Incorporation of stereochemical information into crystallographic refinement. Computing in crystallography, edited by R. Diamond, S. Ramaseshan & D. Venkatesan, pp. 13.01–13.26. Bangalore: Indian Academy of Sciences.
Hestenes, M. & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems. J. Res. Natl Bur. Stand. 49, 409–436.
Jack, A. & Levitt, M. (1978). Refinement of large structures by simultaneous minimization of energy and R factor. Acta Cryst. A34, 931–935.
Johnson, C. K. (1970). Generalized treatments for thermal motion. Thermal neutron diffraction, edited by B. T. M. Willis, pp. 132–160. Oxford University Press.
Konnert, J. H. (1976). A restrained-parameter structure-factor least-squares refinement procedure for large asymmetric units. Acta Cryst. A32, 614–617.
Konnert, J. H. & Hendrickson, W. A. (1980). A restrained parameter thermal-factor refinement procedure. Acta Cryst. A36, 344–350.
Levy, H. A. (1956). Symmetry relations among coefficients of anisotropic temperature factors. Acta Cryst. 9, 679.
Prince, E. (1994). Mathematical techniques in crystallography and materials science, 2nd ed. Berlin/Heidelberg/New York/London/Paris/Tokyo/Hong Kong/Barcelona/Budapest: Spring-Verlag.
Prince, E., Dickens, B. & Rush, J. J. (1974). A study of one-dimensional hindered rotation in NH3OHClO4. Acta Cryst. B30, 1167–1172.
Prince, E. & Finger, L. W. (1973). Use of constraints on thermal motion in structure refinement of molecules with librating side groups. Acta Cryst. B29, 179–183.
Rae, A. D. (1978). An optimized conjugate gradient solution for least-squares equations. Acta Cryst. A34, 578–582.
Ralph, R. L. & Finger, L. W. (1982). A computer program for refinement of crystal orientation matrix and lattice constants from diffractometer data with lattice symmetry constraints. J. Appl. Cryst. 15, 537–539.
Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2, 65–71.
Schomaker, V. & Trueblood, K. N. (1968). On the rigid-body motion of molecules in crystals. Acta Cryst. B24, 63–76.
Schomaker, V., Waser, J., Marsh, R. E. & Bergman, G. (1959). To fit a plane or a line to a set of points by least squares. Acta Cryst. 12, 600–604.
Sygusch, J. (1976). Constrained thermal motion refinement for a rigid molecule with librating side groups. Acta Cryst. B32, 3295–3298.
Waser, J. (1963). Least-squares refinement with subsidiary conditions. Acta Cryst. 16, 1091–1094.