Chemical bonding transformation properties

M.G. Voronkov, V.P. Milesshkevich and Y.A. Yuzhelevskii, The Siloxane Bond Physical Properties and Chemical Transformations, Consultants Bureau, New York, 1978. 

From the chemical point of view, the most direct and dramatic consequence of the )3-decay is undoubtedly the sudden change of chemical identity undergone by the radioactive atom, which drastically affects all its properties, including the ability to form, or maintain, chemical bonds. If the radioactive atom is chemically combined, the change of its atomic number is often sufficient to cause the disruption of the molecule, particularly when the nuclide formed from the decay is a chemically inert, noble gas atom. Other important chemical consequences follow directly from the intrinsic physical characteristics of the nuclear transformation. 

The fundamental premise of chemistry is that all matter consists of molecules. The physical and chemical properties of matter are those of the constituent molecules, and the transformation of matter into different materials (compounds) is the result of their reactions to form new molecules. A molecule consists of two or more atoms held in a relatively fixed array via valence-electron orbital overlap (covalent bonds chemical bonds). 

Theoreticians often resort to an analysis of the molecular orbitals. However, orbitals are not observable entities, they have only a mathematical meaning. Furthermore, they can be transformed by any unitary transformation into a new set of orbitals without changing energy or other properties of the molecule. For example, they can be presented as delocalized or localized MOs. A unique definition of chemical bonding, however, should be independent of the form of the MOs. The chemical bond should preferentially be described with the help of a molecular quantity that is observable. 

The electron denstiy distribution p(r) of an atom or molecule is an observable property that can be measured by a combination of X-ray and neutron diffraction experiments [22]. Also, it is easy to calculate p(r) once the MOs and the wave function of a molecule have been determined. The distribution p(r) is invariant with regard to any unitary transformation of the MOs. It has been shown by Hohenberg and Kohn that the energy of a molecule in its (nondegenerate) ground state is a unique functional of p(r) [23]. In other words, the physical and chemical properties of a molecule can be related to p(r). Thus, p(r) represents the best starting point for an analysis of chemical bonding. 

In the early 1940s, an investigation of chemical bonding from the momentum-space viewpoint was initiated by Coulson and Duncanson (Coulson, 1941a,b Duncanson, 1941, 1943 Coulson and Duncanson, 1941,1942 Duncanson and Coulson, 1941) based on the Fourier transformation of the position wave function. [They also gave a systematic analysis of the momentum distributions and the Compton profiles of atoms (Duncanson and Coulson, 1944, 1945, 1948).] They first clarified the momentum-space properties of the fundamental two-center MO and VB wave functions, which may be outlined as follows. 

The two fundamental building blocks of Hartree-Fock theory are the molecular orbital and its occupation number. In closed-shell systems each occupied molecular orbital carries two electrons, with opposite spin. The occupied orbitals themselves are only defined as an occupied one-electron subspace of the full space spanned by the eigenfunctions of the Fock operator. Transformations between them leave the total HF wave function invariant. Normally the orbitals are obtained in a delocalized form as the solutions to the HF equations. This formulation is the most relevant one in studies of spectroscopic properties of the molecule, that is, excitation and ionization. The invariance property, however, makes a transformation to locahzed orbitals possible. Such localized orbitals can be valuable for an analysis of the chemical bonds in the system. 

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