Electron Density Distributions in Molecules

Abstract

The electron density that is observed by X-ray diffraction differs from the theoretical static density defined via the Born Oppenheimer approximation because of intermolecular interactions in the crystal and vibrational smearing. Also, the experimental deformation density as mapped by difference Fourier synthesis is often biased by the promolecule model used in the derivation of the nuclear parameters. Better models account for the deformation density in parametric form. With the convolution approximation for vibrational smearing, such models permit the mapping of a static deformation density, provided good high-resolution data are used. Results are usually more accurate in a centrosymmetric space group but the center of inversion itself is assumed without direct experimental evidence.

The standard deformation density, relative to spherical ground-state atoms, may be decomposed into components corresponding to hypothetical stages in molecule formation, e.g. atomic orientation and hybridization or formation of submolecular fragments. Derivation of the molecular Coulomb potential requires partitioning the crystal density into molecules. Division into atoms is also arbitrary; model densities built of neutral atoms or of ions are nearly indistinguishable, especially in a small unit cell. H₂ is a poor prototype of covalent bonding; in other molecules the exclusion principle works against charge accumulation on the bond axis.

Key Words:

• Atomic charge
• centrosymmetry
• convolution
• Coulomb potential
• covalent bond
• deformation density
• multipole moments
• promolecule