Models of Electron Density in Molecules

Localized Models of Electron Density in Molecules.—Based on the linear response equation (122), applied however to periodic monatomic crystals, Jones and March57 have argued that in discussion of vibrational properties the correct tool 

It seems clear that in molecules with one type of atom only, say ozone, one should have a similar sort of decomposition. In independent work and from a different direction, Bader and his co-workers have likewise insisted on the importance of Vp in dividing a molecule into fragments which are localized and transferable. As one example, the work of Bader and Beddall58 effects such a partitioning into fragments based on the virial theorem, and the interested reader is referred to this and various other papers which throw very considerable light on electron densities in specific molecules and on partitioning the electron cloud.59-85 

Turning from these fundamental arguments, which are still difficult to implement, we shall discuss models embodying, independently, some related ideas. We refer first to the work of Anderson and Parr,88 who write for a diatomic molecule with nuclei at Ra and R  

The third term in equation (127) is the deviation from a rigid atoms in molecules model, that is, it represents a non-perfectly-following part of the density as the nuclei move. 

It has to be stressed that equation (127) has not, so far, been given a first principles basis. One could envisage, by comparing model (127) with X-ray scattering experiments, getting a useful test on a homonuclear diatomic molecule but as far as we are aware that has not been done to date. In concluding this 

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