The All Valence Electron NDO models

Prior to 1965, all we had in our armoury were the a and n Hiickel theories, and a very small number of rigorous calculations designated ab initio (to be discussed later). The aims of quantum chemistry in those days were to give total energies and charge distributions for real molecules, and the seventh decimal place in the calculated properties of LiH. Practical chemists wanted things like reliable enthalpy changes for reactions, reaction paths, and so on. It should come as no surprise to learn that the practical chemists therefore treated theoreticians with scepticism. 

Theoreticians did little to improve their case by proposing yet more complicated and obviously unreliable parameter schemes. For example, it is usual to call the C2 axis of the water molecule the z-axis. The molecule doesn t care, it must have the same energy, electric dipole moment and enthalpy of formation no matter how we label the axes. I have to tell you that some of the more esoteric versions of extended Hiickel theory did not satisfy this simple criterion. It proved possible to calculate different physical properties depending on the arbitrary choice of coordinate system. 

To look ahead a little, there are properties that depend on the choice of coordinate system the electric dipole moment of a charged species is origin-dependent in a well-understood way. But not the charge density or the electronic energy Quantities that have the same value in any coordinate system are sometimes referred to as invariants, a term borrowed from the theory of relativity. 

Pople and Santry seem to have been the first authors to give a systematic treatment of this problem. They identified two important types of transformation amongst the basis functions  

I jfpr example, descriptive organic chemistry emphasizes the carbon sp3 hybrid imic orbitals at the expense of the more usual 2s, 2px, 2py and 2p, ones. 

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Aer case, the invariant physical property has to be the same before and after jl sformation. Pople and coworkers proceeded to examine the consequences jtjje context of the all valence electron NDO models. I write NDO rather than ho because the more sophisticated of these models retain many two-electron (ggrals that would be set to zero under the ZDO prescription. 

The most elementary all valence electron NDO model is that known as Ippmplete neglect of differential overlap (CNDO). Segal and Pople introduced (his in 1966. Only valence electrons are explicitly treated, the inner shells being tijicen as part of the atomic core. The ZDO approximation is applied to the WO-electron integrals, so that... 

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