Berechnung der elektr. Feldgradienten aus Elektronendichten

By use of the program system developed within this project it is possible to plot electron densities around a nucleus three-dimensionally for arbitrary crystallized compounds. Online-calculation of electric field gradients, an important and significant quantity in solid state physics and -chemistry, can be performed from these densities. A by-product of the project (the so-called hybrid program, http://www.users.sbg.ac.at/~moe) allows a nearly automatic refinement of spectra by using the principle of biological evolution ("genetic algorithm"). Applications: physics, chemistry, pharmacy. Despite our high level of technology and besides general problems (Heisenberg uncertainty) it is nowadays impossible to produce microscopes with inneratomic resolution i.e. to display electronic distributions around atomic nuclei. By "indirect" methods, however, such electron plots can be created: If X-rays penetrate a crystal, a distribution of differently bright reflection spots will arise on a film around the sample (similar to the more or less intense stripes occurring at optical interference). These patch-intensities can be subsequently processed by special mathematical methods in order to reconstruct the underlying electronic distributions. In former times these electron densities were displayed as two-dimensional grid peaks, similar to the lines of uniform altitude on geographic maps. We, however, modified a program from computer tomography in such a way that electron densities can now be displayed as three-dimensional bodies on a computer terminal or printer, the occurring colour saturation ("opacity") being a measure of the density. By this, we are able to display the electron distributions nearby the nucleus and those more far away which are responsible for the bonding to neighbouring ions. In a further program step we can select special densities on the computer screen and calculate the site-dependent differences of the electric field around the nucleus (i.e. the electric field gradient efg). The latter is represented by an ellipsoid in 3 dimensions and may be plotted within the same frame as the electron densities. These plots already meet the idea of an "atomic microscope" very closely. By comparison with experimental efg`s from a nuclear resonance method (Mössbauer spectroscopy), we are able to draw valuable conclusions concerning chemical and physical properties like, e.g., the electronic influence on superconducting behaviour, strength and direction of chemical bonding a.s.o.. The hybrid program mentioned above was created in order to evaluate the experimental efg`s from the observed Mössbauer spectra easier, faster and less ambiguously than before. Conventional programs very often yield the disadvantage of leaving questionable solutions for the relevant parameters or even diverging, if the initial parameters values are too far from the final solution. Our program, on the other hand, generates an "initial population" of a multitude of parameter sets, which are subsequently processed by cross-over, mutation and selection, similar to chromosomes during hereditary transmission. After some "generations" normally one set is left yielding the best refinement of the observed spectrum, analogous to Darwin`s "survival of the fittest". The study underlying the above program was awarded the "Christian-Doppler-Preis" of the state Salzburg.