New features relative to diatomic molecules

The existence of more than two nuclei in polyatomic molecules means that molecular orbitals are polycentric, extending, in principle, over the whole molecule. It is in this sense that molecular orbitals in polyatomic systems are said to be delocalized. Within the linear combination of atomic orbitals (l.c.a.o.) approach, valence m.o.s are approximated by linear combinations of the valence a.o.s of all the intervening atoms. Just as for diatomic molecules, this is an approximation because only a finite set of basis fimctions are being used. The eventual inclusion of virtual a.o.s of energy close to the valence orbital energies can help to improve the results. 

From a certain number, M, of a.o.s an equal number of m.o.s i ) are constructed (conservation of orbital number)  

The electronic wavefunction is a Slater determinant (or a combination of Slater determinants in the case of open-shell systems) based on the occupied m.o.s, each one taken twice (if doubly occupied) and associated either with a or P spin functions (molecular spin-orbitals) 

This can be simply represented by the product of the diagonal functions between short vertical bars i(l) M2) M ) 

The total electron density function (for real functions) is given by 

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