Node 4: X-ray, electron and neutron techniques in density mapping

Electron density mapping (or imaging) includes several fields including momentum and spatial maps. Often, recently, multipole analysis is carried out upon high-resolution crystallographic data in order to interpret bonding patterns, valence and other electronic orbitals, and comparisons to isolated atomic electron densities. Usually there is little investigation of the robustness or errors of the atomic form factors used in such analyses - normally they are embedded in some useful computational package. Experimentally, the missing information from the higher order reflections limits the spatial extent needed to determine particular (higher order) multipole terms.

The problem of absolute charge density & bonding determination is a crucial one for the field of deformation or difference density studies and the corresponding interrogation of the modification of valence electronic orbitals from an atomic reference by the formation of molecules and crystals. Generic problems in achieving absolute profiles of electron densities, and problems in achieving accurate uncertainty estimates, have been known for some time. The field is flourishing and attempting to address key fundamental questions in theoretical and quantum chemistry, but the clean interpretation of results is very complex. Recent and further developments in form factor and structural computations can address part of this problem.

A major experimental difficulty in modern synchrotron approaches to structural evaluation lies in the determination of the overall experimental scale factor. Particularly for small or micro-crystallites commonly investigated with the flux of synchrotron beams, the overall scale factor is undetermined and is therefore a fitted parameter to minimize the least-squares discrepancy between the set of transformed experimental structure factors and the set of theoretically computed structure factors. Errors of individual sub-shell wavefunctions will then not agree with the overall scale, and hence some deformation mapping details (i.e. the radial redistribution of electron density) will then be anomalous. The detailed radial atomic density of a given theoretical reference or computation often has more significant errors with particular medium or high-Z systems including transition metals, lanthanides and actinides.

Where a single elemental structure is involved, current empirical fitting is an effective method and experimental errors are largely normalized so the remaining electron density variation is a good approximation to the deformation electron density due to bonding. However, in inorganic and metallo-enzymes the scale factor is not uniquely determined. There is no single theoretical scale factor correction. Typical input theories for atomic form factor components disagree by 200% for numerous elements from 1 keV to 3 keV X-ray energies, and at higher energies these discrepancies can still persist at the 10% level or more. Even in the experimental situation, extinction effects will dramatically suppress low order peaks (for example) and yet, since these are the strongest peaks, this error will lead to a scale factor correction dominated by extinction errors of low-order peaks, and hence suppressing or enhancing the contributions of higher-order peaks.

The solution of this generic problem requires major collective work of theoreticians from several different fields, together with collected efforts of several different experimental groups. Although we have here emphasized one particular major issue, there are other similar issues in momentum space which would be investigated via such a node and in this network. Spackman, Skelton, Freeman, Cookson, Vos and Barnea and many others have and can make contributions towards this area of development.