Electron density generator from complex structure factors
These animations generate electron-density maps, starting with the lowest (hkl) complex-structure factor components (i.e., those with the longest wavelength and poorest resolution) and successively adding to these to produce the final electron-density distribution from the available information. The input data of unit-cell size, atomic positions, and atomic form-factor parameters are used to calculate the complex structure factor. In other words, I knew what I wanted to generate and didn’t need to go through the hassle of finding the phases of each structure factor. There are two molecules - a planar chloro-fluoro-benzene, with a fictitious (but easy to simulate) hexagonal unit cell; and the 3D model of benzylpenicillin, the structure of which was famously solved using x-ray crystallography by Dorothy Crowfoot-Hodgkin. The coordinates are from PNN.cif, found also in the PDB file 3kp2.
In the program generating the electron-density map for chloro-fluoro-benzene, one can render this as a heat map in 2D, or as a 3D peak version. A second option is to make the movie `fast’ or `slow’ - the slow version inserts duplicate frames in the early stage of the ED-map reconstruction, better to appreciate the addition of sinusoidal waves. For each ED map reconstruction, a parallel mapping out of the used structure factors in reciprocal space as a function of increasing Q-vector magnitude can also be generated. If both real- and reciprocal-space movies are started simultaneously, they will flow in step.
The 3D ED map of penicillin is rendered as an isosurface. It concludes with a fading in of a sphere-model of penicillin overlaid on the ED map.
One last sobering thought. All this was worked out using data gleaned from photographic plates, no phase information, and rudimentary computers, by Dorothy Crowfoot-Hodgkin by 1945. Truly a scientific hero!
The necessary data files can be downloaded at the bottom of this page.