Chemistry Reference
In-Depth Information
New Directions in Pseudoatom-Based X-Ray
Charge Density Analysis
Tibor Koritsanszky, Anatoliy Volkov, and Michal Chodkiewicz
Abstract This chapter revisits critical aspects of pseudoatom interpretation of X-ray
Bragg diffraction data to derive the crystalline electron density experimentally. The
main focus is on the radial basis functions in the nucleus-centered multipole expan-
sion of the model density. Based on the direct-space projection of the stockholder-
partitioned quantum-chemical molecular density onto nucleus-centered spherical
harmonics, “bonded-atom” radial functions are derived, in terms of which the original
density can be reconstructed. The method allows for a quantitative access of errors
introduced by restrictions on the pseudoatom radial functions and for designing more
adequate basis sets than those routinely used in the standard model. The applicability
of the upgraded multipole formalism to X-ray charge density analysis is demonstrated
through pseudoatom fitting of simulated and experimental data. The chemical trans-
ferability of stockholder pseudoatoms is analyzed through small-molecule model
studies. A protocol to build a stockholder-atom library and the feasibility of simple
data-refinement strategies using the databank radial functions is also discussed.
Keywords Electron density
Pseudoatom model
Radial functions
Stockholder
partitioning
X-ray diffraction
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Static Electron Density from X-Ray Structure Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Multipole Expansion of the Electron Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4 The Standard Pseudoatom Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Pseudoatom RDFs from Molecular Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
6 Absolute Error of the Pseudoatom Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7 X-Ray Data Analysis with Theoretical Stockholder Pseudoatoms . . . . . . . . . . . . . . . . . . . . . . . . 11
