Corpus ID: 233296362

Born-Oppenheimer potential energy surfaces for Kohn-Sham models in the local density approximation

  title={Born-Oppenheimer potential energy surfaces for Kohn-Sham models in the local density approximation},
  author={Yuki Goto},
  • Y. Goto
  • Published 2021
  • Physics, Mathematics
We show that the Born-Oppenheimer potential energy surface in KohnSham theory behaves like the corresponding one in Thomas-Fermi theory up to o(R) for small nuclear separation R. We also prove that if a minimizing configuration exists, then the minimal distance of nuclei is larger than some constant which is independent of the nuclear charges. 


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  • 1986
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