Abstract
SOME of the electron repulsion integrals [ϕaχb|θcψd]=∫ϕa*(1)χb(1)r−112θ*cψd(2) d(1)d(2) which arise in the molecular orbital theory based on linear combinations of atomic orbitals are sufficiently difficult that reasonably accurate approximate formulae would have real value. If such an integral is regarded as involving two charge distributions ϕ*aχb and θc*ψd, the integrals causing difficulty are those in which one or both charge distributions involve a pair of atomic orbitals not both on the same atomic centre. As many workers have noticed1–8, tractable approximations for these integrals are obtained if the product of two orbitals on different centres is replaced by linear combinations of one-centre orbital products. This causes the general electron repulsion integral to be reduced to a linear combination of Coulomb-type integrals. The methods so far proposed, however, have not been entirely satisfactory for all the integrals for which they are needed.
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HARRIS, F., REIN, R. Approximation of Molecular Integrals. Nature 212, 1232 (1966). https://doi.org/10.1038/2121232a0
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DOI: https://doi.org/10.1038/2121232a0
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