Year: 2026
Type: preprint
Abstract: A stationary scalar correlation energy admits an exact one-mode terminal representation even when the microscopic correlated return is strongly multimode. We test predictive realizations built from specified stationary information carriers in two complementary two-electron systems with the same Coulomb repulsion but different confinement: He-like ions and harmonium (Hooke's atom). For the Coulomb sequence, canonical RHF supplies the symmetry-faithful information carrier. The repeated same-mode return gives a He correlation error of $+0.1164$ m$E_{\mathrm h}$ and no more than $0.0157$ m$E_{\mathrm h}$ for Li$^+$--Ar$^{16+}$; H$^-$ is nevertheless bound and $93.3\%$ of its conventional correlation energy is recovered even though the RHF carrier is qualitatively strained. The dimensionless confinement factor $R_{CC}=D_{CC}/Z$ tends to $1.092394$. For harmonic confinement, an independently constructed response-compressed one-mode return gives $R_H=D_H/\sqrtω$; for $ω\ge0.1$ it agrees with reference-inferred values within $0.21\%$ and tends to the literature high-density limit $1.309283$. Cioslowski and Pernal locate the qualitative crossover to the radially localized strongly correlated harmonium regime at $ω_{\rm crit}\simeq0.04012$, below the quantitative domain used here. The H$^-$ endpoint and $ω_{\rm crit}$ are therefore complementary carrier-validity boundaries: they limit the predictive realization, not exact terminal one-mode representability. A broad helium Bethe--Goldstone spectrum confirms that this terminal statement is not microscopic one-pole dynamics.
Source: arXiv (Cornell University)
Author: Panas, Itai
Institution: Chalmers University of Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216318858