Density Description of Molecular Vibrations

Briefly, we record here that the problem of molecular vibrations can be expressed, at least formally, in terms of the ground-state density at equilibrium, as discussed by Handler and March.54 Everything is subsumed then into an equation expressing the density change, Ap say, from its equilibrium value, when the nuclei are subjected to small displacements from equilibrium. The equation determining the density change has the form 

The change in potential energy AV is first order in the nuclear displacements, and of course, Ap is obtained correctly to the same order from equation (122). Handler and March show that the Thomas-Fermi approximation to the linear response function F has the form 

To transcend this approximation involves accurate knowledge of the Green function for bound states.55 56 

While the above affords a fundamental route for the future, a more immediately practical approach is provided by modelling the charge density according to bond charge models. One example of these will be given below, from the work of Parr and his colleagues. 

---