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Electron-Ion and Ion-Ion Interactions

For consistency, one should apply the same prescription to all the electrostatic interactions in the system, i.e. not only the electron-electron terms, but also the electron-nucleus and nucleus-nucleus interactions. These can be included by re-writing Eq. (gif) to involve all charged particles as


where tex2html_wrap_inline5833 is the many-body wavefunction for the electrons and nuclei and tex2html_wrap_inline7851 now also includes the charge density due to the nuclei. In all our calculations we have made the adiabatic approximation to separate the electronic and nuclear dynamical variables


where the tex2html_wrap_inline7853 appear only as parameters in tex2html_wrap_inline7855 . To make further progress we must assume a form for the nuclear part of the wavefunction, tex2html_wrap_inline7857 . The simplest assumption is that tex2html_wrap_inline7857 can be written as an appropriately symmetrised product of single-nucleus functions which are very strongly localised and therefore non-overlapping. The above equation then reduces to


where the tex2html_wrap_inline7861 denote the centres of the single-nucleus functions, and n is the electron density. Note that the first two terms of the above equation correspond exactly to the electron-electron interaction in Eq. (gif), and that the electron-nucleus and nucleus-nucleus terms now involve only the Ewald interaction. The above result can be understood in the following way. We are treating the ions as classical particles with well defined positions and therefore expect no exchange-correlation terms involving these particles. This leaves only the Hartree interaction which is correctly described by the Ewald interaction. One consequence of this is that as the Ewald interaction has a continuous derivative, the forces on the ions are continuous functions of the ionic positions, which means that this scheme is suitable for use in quantum molecular dynamics calculations.

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996