Antisymmetric features of atomic charge density: Their significance in studies of electron redistribution accompanying bonding, and their relevance to thegeneral problem of structure and properties of molecules

Abstract

A discussion is given of aspects of atomic charge density which possess the property of antisymmetry about the reference nuclear centre. It is shown that components of electronic charge density displaying this property must be an integral part of all bonded atoms possessing non-centric environments. The significance of such components for detailed X-ray diffraction studies of the electron redistribution which characterizes covalent bond formation is demonstrated for the case of carbon in diamond, and it is shown that the so-called "forbidden" 222 reflexion there is a natural consequence of antisymmetric features required by the non-centric (tetrahedral) disposition of bonded atoms in this lattice. Detailed X-ray studies of anthracene, salicylic acid, and cyanuric acid are cited to illustrate the importance and generality of antisymmetry concepts in accurate examinations of molecular systems; their significance in explaining long-standing discrepancies in the location of hydrogen atoms by X-ray and neutron diffraction methods is also noted. The discussion also demonstrates the relevance of antisymmetry to recent important neutron diffraction studies of fluorite structures at different elevated temperatures. Here, the accessible aspects of atomic charge density are those of nuclear charge density, i.e. nuclear vibrational behaviour, and it is shown that the presence of significant anharmonicity in the anionic vibrational pattern is responsible for the unusual diffraction effects observed. This anharmonicity has the same antisymmetry characteristics as those responsible for the 222 reflexion observed in X-ray studies of diamond. It is predicted that .future neutron studies of diamond structures (C, Si, Ge) at elevated temperatures should reveal a range of "forbidden" reflexions produced by antisymmetric components in the nuclear motions about their equilibrium positions. The discussion concludes with brief comments on the multipolar nature of bonded atoms arising from antisymmetric components in their electronic charge densities. Preliminary remarks are made on the relevance of the multipole concept to general problems of structure and properties of molecular systems.

The effect of asymmetry of the atomic charge distribution on the positions of terminal atoms as determined with X-rays

“…O'Connell, Ray & Maslen (1966) made a careful analysis of the difference density in triaminotrinitrobenzene (Cady & Larsen, 1965), and found very little bond-density in the N-O bonds. They explained this situation in terms of a shift of terminal atoms toward the bond peak, as predicted by Dawson (1965).…”

“…It has been stated by Dawson (1965) that the bond lengths to terminal atoms in a molecule, as determined by X-rays, should be smaller than those obtained by spectroscopic or neutron-and electron-diffraction methods; this is because, as a result of bonding, the centroid of the atomic density is displaced towards its bonded neighbour. This statement has been amply verified for bonds involving hydrogen atoms, of type X-H (X is C, N, O).…”

The crystal structure of 8-aza-2,6-diaminopurine sulfate monohydrate

“…The maximum shift in a parameter in the final cycle of least-squares refinement was less than 0.2 times its standard deviation. A difference Fourier calculated at the end of the refinement was practically featureless except for some residual density on the bonds, probably indicating the presence of bonding electrons (Dawson, 1965;Beagley & Small, 1963Hodgson & Ibers, 1969;O'Connell, Rae, & Maslen, 1966).…”

Pseudoatom expansions of the first-row diatomic hydride electron densities

“…The pseudoatom densities may be expressed as finite multipole expansions about the nuclei (Dawson, 1965), ' /sin m~0~ 1…”