Born-Oppenheimer approximation energetics

The transition from (1) and (2) to (5) is reversible each implies the other if the variations 5l> admitted are completely arbitrary. More important from the point of view of approximation methods, Eq. (1) and (2) remain valid when the variations 6 in a trial function are constrained in some systematic way whereas the solution of (5) subject to model or numerical approximations is technically much more difficult to handle. By model approximation we shall mean an approximation to the form of as opposed to numerical approximations which are made at a lower level once a model approximation has been made. That is, we assume that H, the molecular Hamiltonian is fixed (non-relativistic, Born-Oppenheimer approximation which itself is a model in a wider sense) and we make models of the large scale electronic structure by choice of the form of and then compute the detailed charge distributions, energetics etc. within that model. 

Initially the properties calculated were energetic in nature and related to IR spectroscopic measurements.64 Bishop s work was the first serious attempt to calculate the rovibronic energies of the hydrogen molecule and molecular ion without using the Born-Oppenheimer approximation (i.e., three- and four-body calculations). Many years later, this work is still cited and the relativistic... 

There has been some discussion in the literature as to whether a H-bond is stronger than a D-bond. That is, how does the isotopic substitution of a protium nucleus by a twice-as-rnassive deuterium affect the energetics of binding. Since the electronic part of the interaction energy is based upon the Born-Oppenheimer approximation which places the nuclei at rest, AE j is unaffected by any isotopic substitution, including this one. Indeed, the po-... 

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