Published January 16, 2025 | Version v1
Dataset Open

Tilted-plane structure of the energy of finite quantum systems

  • 1. School of Physics, Trinity College Dublin, The University of Dublin, Ireland
  • 2. PSI Center for Scientific Computing, Theory and Data, 5232 Villigen PSI, Switzerland
  • 3. National Centre for Computational Design and Discovery of Novel Materials (MARVEL), Paul Scherrer Institute, 5352 Villigen, Switzerland

* Contact person

Description

The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory. The magnetic analog of Koopmans' theorem in density functional theory is also derived. Moving to fractional electron count, the tilted-plane condition is derived, lifting certain assumptions in previous works. This generalization of the flat-plane condition characterizes the total energy surface of a finite system for all values of electron count N and magnetization M. This result is used in combination with tabulated spectroscopic data to show the flat-plane structure of the oxygen atom, among others. We find that derivative discontinuities with respect to electron count sometimes occur at noninteger values. A diverse set of tilted-plane structures is shown to occur in d-orbital subspaces, depending on chemical coordination. General occupancy-based total-energy expressions are demonstrated thereby to be necessarily dependent on the symmetry-imposed degeneracies.

Files

File preview

files_description.md

All files

Files (422.9 KiB)

Name Size
md5:03f8f8c92eea0824186856c7e79931fd
228 Bytes Preview Download
md5:c0b53e0c985c002cc1e74b5a8472e94e
421.4 KiB Download
md5:59d67bed1fc79914ac28fbd2c44e4073
1.2 KiB Preview Download

References

Journal reference (Paper in which the data is discussed)
A. Burgess, E. Linscott, D. O'Regan, Phys. Rev. Lett. 133, 026404 (2024), doi: 10.1103/PhysRevLett.133.026404

Preprint (Preprint in which the data is discussed)
A. Burgess, E. Linscott, D. O'Regan, arXiv 2307.16003 (2024), doi: 10.48550/arXiv.2307.16003