Approximate quantum chemical methods NDO and EHT

In 1960 the calculation of the integrals involved in a MO calculation was still a prohibitive task. Even a single overlap integral required a substantial amount of time. 

1926 Schrbdinger equation 1931 Htickel method 1951 Roothaan equations 

1953 Semiempirical ir-orbitals methods (Pariser-Pople-Parr PPP) 

1970 Complete ab initio calculations for organic molecules (Pople) 

A first approximation was to use valence orbitals only, in the assumption that core atomic and molecular orbitals would contribute very little to the properties and the reactivity of organic molecules. This assumption is, in general, a valid one. A further very popular approximation was the neglect of differential overlap (NDO), developed by the Dewar school [12]. The integrals of the type pq rs are small ifp q and r s, and one assumes also that the corresponding overlap integrals are small. The NDO conditions were then written as  

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