Canonical molecular orbitals and localized functions

As we have seen previously (Chapter 5), the eigenfunction for a polyelec-tronic atom is antisymmetric with respect to the exchange of the coordinates of any two electrons, and can be expressed as a Slater determinant whose elements are the various occupied spin-orbitals (or a linear combination of Slater determinants, in the case of open-shell atoms). The same appfies to polyelectronic molecules, the atomic orbitals being replaced by the various occupied molecular orbitals associated with the a and /3 spin-functions spin molecular orbitals. Thus, for the molecules H2O, NH3 or CH4 having five doubly occupied m.o.s (one core s orbital and four valence m.o.s), we have 

The four valence m.o.s for H2O are schematically shown in Fig. 8.7 (see also Chapter 7) and are related to the energy diagram of Fig. 7.7 and to the photoelectronic spectrum of Fig. 7.8. The various orbitals can be named ai, bi and b2 according to how they behave under each synunetry operation involving the twofold z rotation axis and the nuclear yz symmetry plane  

Orbital lai is almost entirely associated with the oxygen 2s orbital, hence it is practically a non-bonding m.o. There is another non-bonding m.o. of 7T symmetry (Ibi) and two bonding m.o.s (lb2 and 2ai). 

The existence of two non-bonding electron pairs and two bonding electron pairs is in accordance with the classical structure 

The lack of correspondence between formal bonds and bonding molecular orbitals is a general feature for polyatomic molecules, but this should not be considered as a problem, because, strictly speaking, each m.o. has no 

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