Discontinuous Behavior of the Pauli Potential in Density Functional Theory as a Function of the Electron Number

Abstract

<div>The Pauli potential is an essential quantity in orbital-free density-functional theory (DFT) and in the exact electron factorization (EEF) method for many-electron systems. Knowledge of the Pauli potential allows the description of a system relying on the density alone, without the need to calculate the orbitals.</div><div>In this work we explore the behavior of the exact Pauli potential in finite systems as a function of the number of electrons, employing the ensemble approach in DFT. Assuming the system is in contact with an electron reservoir, we allow the number of electrons to vary continuously and to obtain fractional as well as integer values. We derive an expression for the Pauli potential for a spin-polarized system with a fractional number of electrons and find that when the electron number surpasses an integer, the Pauli potential jumps by a spatially uniform constant, similarly to the Kohn-Sham potential. The magnitude of the jump equals the Kohn-Sham gap. We illustrate our analytical findings by calculating the exact and approximate Pauli potentials for Li and Na atoms with fractional numbers of electrons.</div>

N‐centered ensemble density‐functional theory for open systems

“…Note that these relations enable to understand why, in the α = 1 limit of left and right N-centered ensembles, the sum of the LZ-shifted occupied KS orbital energies matches the physical (N − 1)-and (N + 1)-electron energies, respectively (see Equations 38,40,46, and 47).…”

“…In a previous work, 14 we introduced the concept of N ‐centered ensemble for the purpose of calculating fundamental gaps, in principle exactly, within DFT. In standard approaches, the number of electrons is considered to vary continuously between two integers, thus allowing for the description of ionization or affinity processes 13–40 . The situation is completely different in an N ‐centered ensemble where, by construction, the number of electrons (which is obtained by integration of the N ‐centered ensemble density) is not affected by the charged excitation.…”

Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory

“…To date, expansion techniques remain the most common research line in the field of OF-DFT [ 3 , 12 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ]. Surely, one of the highly celebrated benefits of OF-DFT is its enormous gain in computational speed-up, as shown by Carter et al [ 44 , 45 , 46 , 47 ] and related groups [ 48 , 49 ], but also the interest in conceptual insights has recently been renewed [ 50 , 51 ].…”