Centring of the atomic orbital

Different centring of the atomic orbitals is used in practice, although if the complete set of the orbitals were at our disposal, then it might be centred in a single point. 

Acta 2 (1964) 406 E Politzer,/. Chem. Phys. 64 (1916) 4239 K. Ruedenberg, J. Chem. Phys. 66 (1977) 375. 

It is more economic, however, to allow using the incomplete set and the possibility of AO centred in various points of space. 

We could construct a molecular orbital of any complexity exdusivefy using the orbitals g r) = exp(- r — Aj ), i.e. the f(x,y, z) = const, colloquial known as the l5 orbitals. It is clear that we could do it in any hole-repairing (plasteringlike) procedure. But why do we not do it like this The reason is simple the number of such atomic orbitals that we would have to include in the calculations would be too large. Instead, chemists allow for higher-order polynomials f(x, y, z). This makes for more efficient plastering , because, instead of spherically symmetric objects (Is), we can use orbitals g(r) of virtually any shape (via an admixture 

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