Shells xxvii

Five-electron three-centre bonding units involve the distribution of five electrons amongst three overlapping AOs that are located on three atomic centres. The 7t-electrons of triatomic systems with 19 valence-shell electrons provide examples of these types of bonding units when only valence-shell pjt AOs are used to accommodate the electrons. Another example is provided by the indirect interactions of two nitrogen atoms via a hydrogen atom in medium-ring bicyclic compounds [23]. We consider here symmetrical systems, for which there are three canonical Lewis structures, XXVII-XXIX,... 

The assumed wave function and Eq. (1) are equivalent to assiuning the desired result, i.e. the separability of groups, at the outset. Also, correlations between groups, e.g. Van der Waals attractions, are not included extensions to include them do not seem possible (see Section XXVIII). Even for mshell effects the formalism provides no advantages such as the use of the Its limitations have been discussed else-where " (see also Section XXVII),... 

For convenience we continue the development on closed shell systems. Other systems are discussed in Sections XX and XXI. The theory is still based on non-localized H.F. orbitals and SCF MO s which satisfy Eqs. (12). The results are transformed into the localized description in Sections XXVII and XXVIII. 

The H2 example indicates that in intermediate cases, the /< may be examined and the starting <(> decided upon. Fortunately, thk problem does not come up in obtaining most binding energies (r = Tg) and in non-bonded interactions. For example, the composite system of two Ne atoms (starting with MO s) remains a single determinant at all r owing to exclusion efEects . The raany-electron theory for closed shells can also be applied to this system as well as to non-bonded interactions between the bonds of say a saturated hydrocarbon (see Sections XXVII and XXVIII). 

The procedures outlined above for atoms also apply to small molecules, e.g. LiH, Lig, Ng, HF, Fj, etc. For these, the theory starts with H.F. SCF MO s the l /s refer to MO pairs. The inner shells, however, can be taken directly from free atoms after an equivalent orbital transformation has been performed on say the (l(r,) (lmedium effects on the innermost shells... 

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