Position and momentum densities complementarity at work, Refining a quantum model from different data sets

J.-M. Gillet,^a S. Ragot and P.J. Becker^a

^aLaboratoire Structures, Propriétiés et Modélisation des Solides, CNRS/UMR8580, Ecole Centrale Paris, Grande Voie des Vignes 92295 Chatenay-Malabry Cedex, France (gillet@spms.ecp.fr)

Although Bragg and Compton scattering are well-established techniques, very few attempts to combine information originating from those experiments have been made so far. This remark also holds for Bragg magnetic scattering.

We propose a quite general procedure to refine a quantum model from different data sets using basic Bayesian statistics. As an illustration, different results for extracting chemical information such as charge transfer in ionic-covalent compounds will be given.

Influence of correlation in data, as introduced in momentum density reconstruction, will be explored and extension to other combinations of experiments will be suggested.

At a different level of interpretation and accuracy, a simultaneous approach of position and momentum representations of the One electron Density Matrix (1DM) requires, at least, a possibility of working beyond the straight path of “independent electrons” scheme in a perfect 3D lattice. We will describe an ab-initio computational strategy to the calculation of the 1DM that reproduces infinite lattices results with a good accuracy but that enables for the of defects in the structure as well as a fair account for electron correlation energy. This Cluster Partitioning Method (CPM) will be shown to be efficient for studies ranging from intra-atomic correlation mechanisms in ionic solid to analysis of hydrogen bond in ice and, with few compromises, an extension to more complicated structures.