Electrons chemical bonds

Linus Pauling, The Shared-Electron Chemical Bond, Proc. Nat. Acad. Sci. U. S.,... 

The interchange energy of electrons is in general the energy of the non-polar or shared-electron chemical bond. 

Chemically speaking there is little to say. Canonical Hartree-Fock molecular orbitals leave no place for classical chemical concepts such as bonds between atoms or groups, lone pairs, resonance hybrids, etc. However, chemists still utilize these concepts because they are extremely useful in correlating and understanding chemical facts. Even when one manages to localize the canonical molecular orbitals (which is not always straightforward) in regions such that they could be associated with lone pairs or individual chemical bonds, it is important to bear in mind that the orbitals represent localized one-electron states, and not a two-electron chemical bond between atoms or a lone pair of electrons, as will be discussed further. 

One-electron and three-electron chemical bonding, and increased-valence structures... 

Pauling L (1928) The shared-electron chemical bond. Proc Natl Acad Sci USA 14 359... 

Figure 2.3 Formation of two-center two-electron chemical bonds and role of overlap in bond strength. The stronger overlap also leads to lower energy bonding orbitals and higher energy antibonding orbitals.

Figure 5.5 Formation of a polar two-center two-electron chemical bond between different atoms A and B leads to non-symmetric distribution of electron density and adds ionic component to bonding.

Density-functional theory, even with rather crude approximations such as LDA and GGA, is often better than Hartree-Fock LDA is remarkably accurate, for instance, for geometries and frequencies, and GGA has also made bond energies quite reliable. Therefore, the aura of mystery appeared around DFT (see discussion of this by Baerends and Gritsenko [367]). The simple truth is not that LDA/GGA is particularly good, but that Hartree-Fock is rather poor in the two-electron chemical-bond description. This becomes clear when one considers the statistical two-electron distribution, which is usually cast in terms of the exchange-correlation hole the decrease in probabihty to find other electrons in the neighborhood of a reference electron, compared to the (unconditional) one-electron probabihty distribution [337]. 

Assume the existence of a local subset of basis orbitals assigned to each two-electron chemical bond of the molecule. Such basis orbitals can be constructed from local atomic hybrids or off-centered bond functions, for example. We do not discuss the actual choice of the basis set here supposing only that each basis function is uniquely assigned to one of the chemical bonds of the molecule. The term chemical bond is used here in a broad sense it refers to two-center bonds as well as other two-electron fragments (inner shells, lone pairs) of the system. 

In this section we aimed to overview a theory for the representation of local two-electron chemical bonds in a many-electron system. The above ideas became well known in the past few decades and several effective computational and interpretative schemes have been developed and applied on these grounds (see Surjan 1989). The best known achievement is that of the PCILO method (Diner et al. 1969, Malrieu 1977) which was elaborated under semiempirical schemes though some ab initio PCILO calculations were also published (Daudey et al. 1974a, Otto Ladik 1982). The basic idea of PCILO is to start from a fully localized SCF reference state and approach the exact solution by means of perturbation theory. 

Identifying the main quantum mechanical issues of electrons chemical bonding electronic vibration, electronic localization, and inter-electronic dipole interaction (van der Waals bonding) ... 

Pauling, L. [1928] The Shared-Electron Chemical Bond , Proceedings of the National Academy of Science, USA, 14, 359-362, 1928. 

The acetylene molecule with its unique six-electron chemical bond, strength, high energy, and at the same time its vulnerability to diverse transformation hardly fits the Procrustean bed of modern theories of valency and reactivity. Being a steady challenge to theorists [121,122], it stimulates the development of fundamental works in the field of structure of matter and energy transformation. 

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