MEED: a program package for electron-density-distribution calculation by the maximum-entropy method

Abstract

MEED (maximum‐entropy electron density) is a program package to calculate the electron‐density distribution from a set of structure‐factor data by the maximum‐entropy method. MEED is an upgraded version of the original maximum‐entropy program, MEMTARO, which was used in the first study to use the maximum‐entropy method (MEM) on silicon [Sakata & Sato (1990). Acta Cryst. A46, 263–270]. MEED is applicable to any space group and can cope with both single‐crystal and powder X‐ray diffraction data, whereas MEMTARO can only after modification. Another upgraded feature is the speed of calculation. By employing a new algorithm, MEED is much faster than MEMTARO for the same calculation. Computing time depends on various factors, such as the number of reflection data, accuracy of data and the number of symmetry operations. It is estimated that MEED is typically 100 times faster than MEMTARO. In an extreme case like the beryllium powder‐data case, MEED is 600 times faster than MEMTARO. MEED is coded in Fortran77 for both a scaler computer, FACOM M780, and a vector computer, FACOM VP2600, which are mainframe computers at the Computation Center of Nagoya University. MEED enables the electron‐density distribution to be calculated for any crystalline material, with a fine pixel size, e.g. with 128 × 128 × 128 pixels to a unit cell, provided that accurate diffraction data are available. MEED can overcome, to some extent, one of the biggest drawbacks of MEM analysis, the vast computing time required.

The Influence of the Completeness of the Data Set on the Charge Density Obtained with the Maximum-Entropy Method. A Re-examination of the Electron-Density Distribution in Si

“…In order to see the influence of the completeness in the data set on the MEM density, we reanalysed the complete set up to 664 as listed in Table 1 with the computer program MEED (Kumazawa, Kubota, Takata, Sakata & Ishibashi, 1993). The number of pixels used is 120 x 120 x 120.…”

Dysnomia, a computer program for maximum-entropy method (MEM) analysis and its performance in the MEM-based pattern fitting

“…However, F obs (Rietveld)'s are doubly biased toward structure factors, F(h j ), calculated from structural parameters refined in the Rietveld analysis because both phases and calculated profiles used for the intensity partitioning of overlapped reflections are derived from the structural model (McCusker et al, 1999). Though overlapped reflections may be grouped together (Kumazawa et al, 1993), MEM analysis from powder diffraction data still suffers from the partial loss of structural information because of the overlap of reflections, which is marked in compounds with lower symmetry and in powder diffraction data of relatively low resolution.…”

Thermal Motion in Sodium Nitrite: The Temperature Dependence of Debye-Waller Factors

“…We adopt another method; the maximum entropy method is superior, because no a priory assumption has been made on charge distribution. [17] The electron charge is determined by maximum entropy method at 353K, as given in Fig. 4.…”