Clamped-nuclei approach

As this citation makes clear, many aspects of chemical behaviour can be rationalized in terms of molecular electronic structure calculations made in the clamped nuclei approach. 

At the same time that Heisenberg was formulating his approach to the helium system, Born and Oppenheimer indicated how to formulate a quantum mechanical description of molecules that justified approximations already in use in treatment of band spectra. The theory was worked out while Oppenheimer was resident in Gottingen and constituted his doctoral dissertation. Born and Oppenheimer justified why molecules could be regarded as essentially fixed particles insofar as the electronic motion was concerned, and they derived the "potential" energy function for the nuclear motion. This approximation was to become the "clamped-nucleus" approximation among quantum chemists in decades to come.36... 

In the second approach, the so-called clamped-nucleus treatment, the effect of the perturbation on the electronic and nuclear motion is treated sequentially. First, the Born-Oppenheimer approximation is applied to the vibronic wavefunction of the ground state, ov ri, Rk ), which is therefore expressed as a product of an electronic wavefunction o( ri Rk ) vibrational wavefunction (. R/f )... 

A typical discrete set of chemical importance is a nuclear arrangement in the clamped nucleus version of the Bom-Opp-enheimer approximation. A single molecular isodensity contour (MIDCO) surface is a crisp continuum set. A simple generalization of the CSM approach from finite, discrete point sets to continua is provided by the crisp average of sets. 

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