The negative-quartet relation from electron-density considerations

Abstract

On the basis of electron-density considerations, graphic explanations are given of triplets and positive and negative quartets. It is shown that the number of useful negative relations will always be much smaller than the number of useful positive relations.

Maximum entropy and the foundations of direct methods

“…We may therefore conclude that the construction of conditional probability distributions of structure factors envisaged by Hauptman & Karle amounts precisely to a reciprocal-space evaluation of the entropy functional ~eqME(p) (Bricogne, 1982). Entropy calculations thus afford a quantitative formulation of the qualitative geometric considerations put forward by Schenk (1981) to illustrate the intuitive basis of direct methods, since they provide an exact numerical estimate of how 'likely' various configurations of atoms are when some structure factors assume known values.…”

On a physical interpretation of direct-methods relationships

“…Up to now the interpretation of phase relations has been limited to a graphical explanation by the consideration of electron density waves in a crystal (Golovastikov & Belov, 1955;Stothard, 1978;Schenk, 1979Schenk, , 1981. Such a geometrical approach gives a visible result but in no way represents the real process of X-ray diffraction in a crystal.…”

Roentgenstrukturuntersuchungen an Glycopeptid-Antibiotika und ihren Komplexen mit Zellwandpeptiden Gram-positiver Bakterien

“…Ab initio-Strukturlösung [28][29][30][31] (Direkte Methoden) , der Tangensformel [35,36] und der negativen Quartettbeziehungen [37][38][39] . In dem Programm SHELXS [40]…”