Abstract

Inequalities (Harker and Kasper, 1948) and nonnegative determinants (Karle and Hauptman, 1950) are historically the first “direct methods” for phase determination from the moduli and the a priori known information on the electron-density function ϱ(r). Although Harker and Kasper have convincingly shown that inequalities are efficient for the determination of small structures (N ~ 10), the simple low-order inequalities are not useful for more complex structures. In order to make practical use of the determinants (or the associated matrices), new work has been performed recently in the following directions: More “refined” properties of the Karle-Hauptman determinants and matrices (Sections 9.2 and 9.3)—in particular, the introduction of statistical considerations provides more restrictive relations than inequalities; construction of very-high-order determinants (for example, one of order 400 has been used for insulin; Section 9.4); new determinants, that make better use of the a priori information, or the introduction of new information (for example stereochemistry, Section 9.5).

Keywords

Hydrate Benzene Recombination Lysozyme Dinate 

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References

  1. Bertaut, E. F. (1956). Acta Crystallogr. 9, 455–460.CrossRefGoogle Scholar
  2. Braun, P. B., Hornstra, J. J., and Leenhouts, J. I. (1969). Philips Res. Rep. 24, 85.Google Scholar
  3. Brunie, S., and Tsoucaris, G. (1974). Cryst. Struct. Commun. 3, 481–484.Google Scholar
  4. Castellano, E., Podjarny, A., and Navaza, J. (1973). Acta Crystallogr. Sect. A 29, 609–615.ADSCrossRefGoogle Scholar
  5. Cochran, W. (1955). Acta Crystallogr. 8, 473–478.CrossRefGoogle Scholar
  6. Cooper, A., Norton, D. A., and Hauptman, H. (1969). Acta Crystallogr. Sect. B 25, 814–828.CrossRefGoogle Scholar
  7. Diamond, R. (1963). Acta Crystallogr. 16, 627–639.CrossRefGoogle Scholar
  8. Eller, G. von (1962). Acta Crystallogr. 15, 590–595.CrossRefGoogle Scholar
  9. Gassman, J. (1976). Acta Crystallogr. Sect. 32, 274–280.ADSGoogle Scholar
  10. Gifkins, M . (1972). Thesis, University of York, York, England.Google Scholar
  11. Goedkoop, J. A. (1950). Acta Crystallogr. 3, 374–378.MathSciNetCrossRefGoogle Scholar
  12. Harker, D., and Kasper, J. S. (1948). Acta Crystallogr. 1, 70–75.MathSciNetCrossRefGoogle Scholar
  13. Hauptman, H. (1971). Z. Kristallogr. 134, 28.CrossRefGoogle Scholar
  14. Heinerman, J. J. L., and Kroon, J. (1976). Acta Crystallogr. Sect. A 32, 115–119.ADSCrossRefGoogle Scholar
  15. Hirshfeld, F. L. (1968). Acta Crystallogr. Sect. A 24, 301–311.ADSCrossRefGoogle Scholar
  16. Hughes, E. W. (1953). Acta Crystallogr. 6, 871.CrossRefGoogle Scholar
  17. Karle, J. (1966). Acta Crystallogr. 21, 273–276.CrossRefGoogle Scholar
  18. Karle, J. (1972). Acta Crystallogr. Sect. B 28, 3362–3369.CrossRefGoogle Scholar
  19. Karle, J., and Hauptman, H. (1950). Acta Crystallogr. 3, 181–187.MathSciNetCrossRefGoogle Scholar
  20. Karle, J., and Karle, I. L. (1966). Acta Crystallogr. 21, 849–859.CrossRefGoogle Scholar
  21. Kitaigorodski, A. I. (1961). Theory of Crystal Structure Determination, Consultants Bureau, New York.Google Scholar
  22. Klug, A. (1958). Acta Crystallogr. 11, 515–543.CrossRefGoogle Scholar
  23. Knossow, M. (1975). Thèse de 3ème cycle, Université de Paris, Paris.Google Scholar
  24. Knossow, M., Rango, C. de, Mauguen, Y., Sarrazin, M. and Tsoucaris, G. (1977). Acta Crystallogr. Sect. A 33, 119–125.ADSCrossRefGoogle Scholar
  25. Lajzerowicz, J., and Lajzerowicz, J. (1966). Acta Crystallogr. 21, 8–12.CrossRefGoogle Scholar
  26. Main, P. (1974). Personal communication.Google Scholar
  27. Mauguen, Y. (1972). Unpublished.Google Scholar
  28. Mauguen, Y., Rango, C. de, and Tsoucaris, G. (1973). Acta Crystallogr. Sect. A 29, 574–578.ADSCrossRefGoogle Scholar
  29. Messager, J. C., and Tsoucaris, G. (1972). Acta Crystallogr. Sect. A 28, 482–484.ADSCrossRefGoogle Scholar
  30. Podjarny, A. D., and Yonath, A. (1977). Acta Crystallogr. Sect. A 33, 655.ADSCrossRefGoogle Scholar
  31. Podjarny, A. D., Yonath, A., and Traub, W. (1976). Acta Crystallogr. Sect. A 32, 281–292.ADSCrossRefGoogle Scholar
  32. Rango, C. de (1969). Thèse, Université de Paris, Paris.Google Scholar
  33. Rango, C. de, Tsoucaris, G., and Zelwer, C. (1974). Acta Crystallogr. Sect. A 30, 342–353.ADSCrossRefGoogle Scholar
  34. Rango, C. de, Mauguen, Y., and Tsoucaris, G. (1975a). Acta Crystallogr. Sect. A 31, 227–233.ADSCrossRefGoogle Scholar
  35. Rango, C. de, Mauguen, Y., and Tsoucaris, G. (1975b). Xth International Congress of Crystallography, Amsterdam.Google Scholar
  36. Sarrazin, M. (1970). CECAM Workshop reports, Orsay, France.Google Scholar
  37. Sarrazin, M. (1971). Personal communication.Google Scholar
  38. Sarrazin, M. (1973). Personal communication.Google Scholar
  39. Tollin, P., and Cochran, W. (1964). Acta Crystallogr. 17, 1322–1324.CrossRefGoogle Scholar
  40. Taylor, D. J., and Woolfson, M. M. (1975). Xth International Congress of Crystal lography, Amsterdam, S. 16.Google Scholar
  41. Tsoucaris, G. (1969). C. R. Acad. Sci. Ser. B 268, 875.Google Scholar
  42. Tsoucaris, G. (1970a). Acta Crystallogr. Sect. A 26, 492–499.ADSCrossRefGoogle Scholar
  43. Tsoucaris, G . (1970b). Acta Crystallogr. Sect. A 26, 499–501.ADSCrossRefGoogle Scholar
  44. Wilson, A. J. C. (1949). Acta Crystallogr. 2, 318–321.CrossRefGoogle Scholar
  45. Woolfson, M. M. (1954). Acta Crystallozr. 7. 61–64.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • G. Tsoucaris
    • 1
  1. 1.Laboratoire de PhysiqueUniversité de Paris—Sud, Centre PharmaceutiqueChatenay-MalabryFrance

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