Andrew Burgess^1*, Edward Linscott^2,3*, David O'Regan^1*

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

* Corresponding authors emails: burgesan@tcd.ie, edward.linscott@psi.ch, david.o.regan@tcd.ie

DOI10.24435/materialscloud:zn-y8 [version v1]

Publication date: Jan 16, 2025

How to cite this record

Andrew Burgess, Edward Linscott, David O'Regan, Tilted-plane structure of the energy of finite quantum systems, Materials Cloud Archive 2025.13 (2025), https://doi.org/10.24435/materialscloud:zn-y8

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.

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Keywords

density-functional theory static correlation error MARVEL/P4