## Abstract

Informed by an abstraction of Kohn-Sham (KS) computation called a KS machine, a functional analytic perspective is developed on mathematical aspects of density functional theory. A natural semantics for the machine is bivariate, consisting of a sequence of potentials paired with a ground density. Although the question of when the KS machine can converge to a solution (where the potential component matches a designated target) is not resolved here, a number of related ones are. For instance: can the machine progress toward a solution? Barring presumably exceptional circumstances, yes in an energetic sense, but using a potential-mixing scheme rather than the usual density-mixing variety. Are energetic and function space distance notions of proximity-to-solution commensurate? Yes, to a significant degree. If the potential components of a sequence of ground pairs converges to a target density, do the density components cluster on ground densities thereof? Yes, barring particle number drifting to infinity.

Original language | English (US) |
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Article number | 495203 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 56 |

Issue number | 49 |

DOIs | |

State | Published - Dec 8 2023 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- General Physics and Astronomy