Breakdown and Classification of Adiabatic-Connection Convexity in Coulomb Systems
- 1College of Materials Science and Engineering
- 2Hohai University
Abstract
Convexity of the density-fixed adiabatic-connection integrand is widely observed but is not fixed by the variational structure of density-functional theory. We show that it is not universal for ordinary three-dimensional electrons with the bare Coulomb interaction. Equal-step third differences of the Levy functional give a derivative-free classification into convex, affine, concave, and mixed classes, while an exact response identity determines the local sign at regular fixed-density points. Opposite exactly solvable seeds—a closed-shell Hubbard ring and two-electron spherium—are transferred to smooth confining potentials in ordinary space. The resulting full-interval positive, negative, and mixed densities have N = 2, 6, and 8, respectively. For two distinct densities with the same particle number N = 6, one fixed four-point certificate is obtained with either sign. These deliberately engineered existence constructions do not imply that violations are common in molecular densities. Thus convexity is a property of density-preserving many-body response, not a universal exact condition.
Related
- Breakdown of Adiabatic Scaling and Noise-induced Functional Synchronization in Deeply Quiescent Excitable Systems
- Transition-state lattice modes and the breakdown of adiabatic tunneling for hydrogen and deuterium in bcc Nb
- Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation
- Breakdown of the Plane-Wave Trojan Horse Analysis of the 12C+12C Fusion Reaction: Critical Role of Coulomb Distortions
- Finite-temperature adiabatic-connection reduced density-matrix functional theory: a unified framework for i-DMFT and TAO-DFT
BibTeX
@misc{wu2026breakdown,
title = {{Breakdown and Classification of Adiabatic-Connection Convexity in Coulomb Systems}},
author = {Jian Wu},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15008317/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008317/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Breakdown and Classification of Adiabatic-Connection Convexity in Coulomb Systems
AU - Jian Wu
PY - 2026
DA - 2026/09/04
PB - ChemRxiv
DO - 10.26434/chemrxiv.15008317/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008317/v1
AB - Convexity of the density-fixed adiabatic-connection integrand is widely observed but is not fixed by the variational structure of density-functional theory. We show that it is not universal for ordinary three-dimensional electrons with the bare Coulomb interaction. Equal-step third differences of the Levy functional give a derivative-free classification into convex, affine, concave, and mixed classes, while an exact response identity determines the local sign at regular fixed-density points. Opposite exactly solvable seeds—a closed-shell Hubbard ring and two-electron spherium—are transferred to smooth confining potentials in ordinary space. The resulting full-interval positive, negative, and mixed densities have N = 2, 6, and 8, respectively. For two distinct densities with the same particle number N = 6, one fixed four-point certificate is obtained with either sign. These deliberately engineered existence constructions do not imply that violations are common in molecular densities. Thus convexity is a property of density-preserving many-body response, not a universal exact condition.
ER -