The Maximum Entropy Method: Traditional direct methods have proved to be immensely successful when applied to single crystals where the diffraction data are complete and have atomic resolution (i.e. around 1.1Å), but this leaves whole classes of important problems which are inaccessible to such techniques i.e. electron diffraction data, powders, proteins and surfaces.

A new method, the maximum entropy (ME) formalism, has the potential to tackle these problems, and has been developed as a practical technique for solving crystal structures. Based on information theory and using Bayesian statistics, it builds electron density through constrained entropy maximisation.

Phasing tree in the maximum entropy method

References for Maximum Entropy Methods:

  1. 'A Multisolution Phase Determination Method in X-ray Crystallography', C.Bannister, G.Bricogne & C.J.Gilmore, in Bayesian Methods and Maximum Entropy, Ed. J.Skilling, Kluwer, (1989), 225-232.
  2. 'A Multisolution Method of Phase Determination by Combined Maximisation of Entropy and Likelihood. I: Theory, Algorithms and Strategy', G.Bricogne & C.J.Gilmore, Acta Cryst, (1990), A46, 284-297.'A Multisolution Method of Phase Determination by Combined Maximisation of Entropy and Likelihood. II: Applications to Small Molecules', C.J.Gilmore, G.Bricogne & C. Bannister, Acta Cryst. (1990), A46, 297-308.
  3. ‘Maximum Entropy, Likelihood and the Phase Problem in Single Crystal and Powder Diffraction' C.J. Gilmore & G.Bricogne in Crystallographic Computing 5, Ed. D.Moras Oxford University Press, (1991), 298-307.
  4. 'A Multisolution Method of Phase Determination by Combined Maximisation of Entropy and Likelihood. VI Automatic Likelihood Analysis via the Student t-test, with an application to the Powder Structure of Magnesium Boron Nitride', K.Shankland, C.J. Gilmore, G.Bricogne, & H.Hashizume, Acta Cryst. (1993), A49, 493-501.
  5. 'Applications of the Maximum Entropy Method to Powder Diffraction and Electron Crystallography', C.J.Gilmore, K.Shankland & G.Bricogne Proc. Roy. Soc. Series A, (1993), 442, 97-111.
  6. 'Maximum Entropy, Likelihood Ranking and the Phase Problem for Single Crystal, Powder Diffraction and Electron Microscopy' C.J.Gilmore in Crystallographic Computing 6: A Window on Modern Crystallography, Ed. H. Flack, Oxford University Press, (1993), 25-46.
  7. 'The MICE Computer Program, and its application to Direct Phase Determination for Powders, Electron Diffraction and Macromolecules', C.J.Gilmore & W.Nicholson Trans. Amer. Cryst. Association. (1994), 30, 15-27.
  8. 'Maximum Entropy and Bayesian Statistics in Crystallography' C.J.Gilmore, Acta Cryst. (1996), A52, 561-589
  9. 'MICE Computer Program' C.J.Gilmore & G.Bricogne Methods in Enzymology (1997), 277, 65-78.
  10. 'An Introduction to Maximum Entropy in Action' C.J.Gilmore in Electron Crystallography, Ed. S.Fortier, Kluwer (1998), 109-117.
  11. 'Structure Determination using Maximum Entropy and Likelihood' C.J.Gilmore in Electron Crystallography, Ed. D.L.Dorset, Kluwer (1997), 295-304.
  12. 'Developments in Maximum Entropy and Likelihood' C.J.Gilmore in Direct Methods in Macromolecular Crystallography, Ed. S.Fortier, Kluwer, (1998), 455-462.
  13. 'A Multisolution Method of Phase Determination by Combined Maximisation of Entropy and Likelihood. VI The Use of Error-Correcting Codes as a Source of Phase Permutation and their Application to the Phase Problem in Powder, Electron and Macromolecular Crystallography’ C.J. Gilmore, W. Dong & G.Bricogne, Acta Cryst. (1998), A55, 70-83.
  14. 'Direct Determination of the Modulated Lamellar "Ripple" Phase of Hydrated Lecithin' D.L.Dorset & C.J.Gilmore Z. Krist. (1998), 213, 432-435.