Authors: Doug Collins and Jim Stewart

Contact: Jim Stewart, Department of Chemistry,

University of Maryland, College Park, MD 20742, USA

MEFFIT combines a positive definite map of constrained exponential electron density formed by MEDENS and a difference map prepared by FOURR using phases calculated by RFOURR from the MEDENS output map. The effect of this process is to produce a new map such that the maximum entropy phases and the observed structure moduli will be produced upon Fourier transformation of the new map. MERUN may be used to set up an input stream to drive all the programs needed in the refinement process.

Method

The focus of program MEFFIT is adjustment of a positive definite density map toward agreement with observed structure factor magnitudes. The designed application is sequential improvement of an imperfectly phased set of structure factors through manipulation of its corresponding noisy or low resolution density function by MEDENS, MEFFIT, and necessary Fourier routines. On a grid suitably fine for the desired final resolution, an initial electron density function is converted by MEDENS into a maximum-entropy density, which is a positive definite exponential function. This map is used as input to RFOURR to calculate structure factors (including phases), which can be subsequently used in FOURR to form a companion difference electron density map.

MEFFIT generates a new positive-definite exponential density in a maximum-entropy adjustment of the prior exponential density. The new density is computed by pointwise multiplication of the former by exp{constant*difference density}, then scaled to restore the original mean value. As a stand-alone process, this combination of a positive definite density, and the difference density which it implies, constitutes one maximum-entropy step in the adjustment of a positive definite density to match better the experimentally observed moduli.

A useful number of MEFFIT steps is likely to be in the range 4 - 10. The associated file handling of prior, difference, and updated maps, in addition to the usual bdf handling, is simple but a source of confusion. For the usual iterative application of MEFFIT, MERUN can be used to construct the Xtal input stream and run the programs. Although the criterion for completion might be a target R value which is suitably small, if the R value is changing slowly after several iterations it is unlikely that further substantive change is occurring in either the structure factor phasing or the exponential density itself. In any case, the process is exceptionally stable, and not critically dependent on the termination point.

After the desired number of iterations has been run, the last part of which is RFOURR to compute structure factors, the final Fobs Fourier map may be calculated. This gives the electron density in its standard formulation, but with structure factor phasing corresponding to the final exponential density. This whole process has the structure: FOURR; MEDENS; RFOURR; (FOURR; MEFFIT; RFOURR); FOURR; in which the parentheses show the inner loop of programs.

File Assignments

Reads maximum entropy map from file me1

Reads difference map from file me2

Writes adjusted maximum entropy map to file mem

Example

MEFFIT ac 3.99

See MERUN documentation for an example of how this input is meshed with that of MEDENS, RFOURR, and FOURR to carry out the refinement process.

References

Collins, D.M. and Mahar, M.C. 1983. Electron Density: An Exponential Model. Acta Cryst. A39, 252-256.