Nonanalyticity of the optimized effective potential with finite basis sets

@article{Gidopoulos2012NonanalyticityOT,
  title={Nonanalyticity of the optimized effective potential with finite basis sets},
  author={Nikitas I. Gidopoulos and Nektarios N Lathiotakis},
  journal={Physical Review A},
  year={2012},
  volume={85},
  pages={052508}
}
We show that the finite-basis optimized effective potential (OEP) equations exhibit previously unknown singular behavior. Imposing continuity, we derive new well-behaved finite-basis-set OEP equations that determine OEP for any orbital and any large enough potential basis sets and which adopt an analytic solution via matrix inversion. 

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References

SHOWING 1-10 OF 27 REFERENCES
Numerical Recipes in C: The Art of Sci-entific Computing
TLDR
This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes, with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines.
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
43
Numerical Recipes: The Art of Scientific Computing
Rev
  • Mod. Phys. 80, 3,
  • 2008
Phys
  • 128, 104104,
  • 2008
Phys
  • Rev. 90, 317,
  • 1953
Phys
  • 127, 114104,
  • 2007
Phys
  • 126, 0841107,
  • 2007
Phys
  • Rev. Lett. 98, 256401
  • 2007
...
...