DFT for Solar System

[twynter94]

In order to apply the Kohn-Sham formalism of DFT to the solar system I would do the following:

Firstly, in that system, I would treat the sun as the nucleus and the planets as the non-interacting quasi-particles. Therefore there would be 8 such particles or 9 if we count Pluto. As a result, we would end up with 8 or 9 single particle wave functions which we would then use to construct the ground state density of the system.

In terms of setting up the Kohn-Sham Hamiltonian, for our system, most of the terms would still hold. That is, the planets are moving so they have kinetic energy, each planet would be interacting with the average density created by the quasi-particles, this would be the gravitational equivalent of the Hartree potential. Therefore, instead of the classical electrostatic Coulomb interaction, we’d use the classical Newtonian Gravitation interaction (Gravitational potential energy instead of electrostatic potential energy). The external potential would be the gravitational potential felt by each planet created by the Sun. Finally, for the Exchange-Correlation energy, perhaps we don’t need Exchange energy correction for this system because the planets are not losing or gaining energy due to exchange of coordinates, however, we may still need correlation correction because the motion of one planet is influenced by the other planets and we ignored that when we assumed non-interacting particles.

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