<scp>Ultra</scp>‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus:<scp>II.</scp>Spin‐singlet (excited) and spin‐triplet (lowest) states of helium sequence

Turbiner, A. V.; Vieyra, J. C. López; Valle, Juan Carlos del; Nader, D. J.

doi:10.1002/qua.26879

Cited by 7 publications

(2 citation statements)

References 38 publications

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“…From there, nuclear charges can be estimated following analytic continuation of the square normalizability constraints. 32,33 The estimate of critical charges in small atomic systems and their behavior close to the threshold is an active area of research. 44?…”

Section: Discussionmentioning

confidence: 99%

“…Motivated by Equation (1), we follow a recipe for designing compact wave functions described in our previous work. [31][32][33] The total wave function, Ψ, is the antisymetrized product of the spatial wave function, ψ, and the spin function, χ, Ψ = A (ψ χ). The antisymmetrization operator is defined as…”

Section: Wave Function Describing the LI Isoelectronic Series 1s2s2p ...mentioning

confidence: 99%

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Vmc Optimization of Ultra-Compact, Explicitly-Correlated Wave

Julian Nader,

Rubenstein

2023

Preprint

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Section: Discussionmentioning

confidence: 99%

Section: Wave Function Describing the LI Isoelectronic Series 1s2s2p ...mentioning

confidence: 99%

Vmc Optimization of Ultra-Compact, Explicitly-Correlated Wave

Julian Nader,

Rubenstein

2023

Preprint

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Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus: III. Spin‐quartet state (1s2s3s) of the lithium sequence

Nader

Valle

Vieyra

et al. 2022

Int J of Quantum Chemistry

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As a continuation of Part I, dedicated to the ground state of He‐like and Li‐like isoelectronic sequences for nuclear charges Z≤20, and Part II, dedicated to two excited states of He‐like sequence, two ultra‐compact wave functions in the form of generalized Guevara–Harris–Turbiner functions are constructed for Li‐like sequence. They describe accurately the domain of applicability of the non‐relativistic Quantum Mechanics of Coulomb Charges (QMCC) for energies (2–3 significant digits [s.d.]) of the spin‐quartet state 140+ of Li‐like ions (in static approximation with point‐like, infinitely heavy nuclei). Variational parameters are fitted in Z by 2nd degree polynomials. The most accurate ultra‐compact function leads to the absolute accuracy ∼10−3 a.u. for energy, and ∼10−4 for the normalized electron‐nuclear cusp parameter for Z≤20. Critical charge Z=ZB, where the ultra‐compact trial function for the 140+ state loses its square‐integrability, is estimated, ZB()140.1em0+∼1.26−1.30. As a complement to Part I, square integrability for the compact functions constructed for the ground, spin‐doublet state 120.1em0+ of the Li‐like sequence is discussed. The critical charge, for which these functions stop to be normalizable, is estimated as ZB()120.1em0+=1.62−1.65. It implies that at Z=2—the negative helium ion He−—both states, 120.1em0+ and 140.1em0+, exist as states embedded in the continuum.

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The weakly bound states in Gaussian wells: From the binding energy of deuteron to the electronic structure of quantum dots

Rodriguez‐Espejo,

Nader,

Segura‐Landa

et al. 2024

Int J of Quantum Chemistry

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Gaussian potentials serve as a valuable tool for the comprehensive modeling of short‐range interactions, spanning applications from Nuclear Physics to the artificial confinement of electrons within quantum dots. This study focuses on examining the lowest states within Gaussian wells, with particular emphasis on the weakly bound regime. The analysis delves into the asymptotic behavior of the exact wave function at both small and large distances, motivating the development of a few parametric Ansatz which is locally accurate and yields to a fast convergent basis set. To validate its efficacy, we assess its convergence rate using a toy model of Nuclear Physics, specifically for Deuteron. Furthermore, we employ the expansion of the energy close to the threshold to derive an analytical formula for the binding energy of the Deuteron whose accuracy improves as the effective parameter approaches the critical. To conclude our study, we test the ability of our Ansatz to describe relativistic corrections into a quantum dot and its performance as an orbital in the exploration of the electronic structure of a two‐electron quantum dot.

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Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus:II.Spin‐singlet (excited) and spin‐triplet (lowest) states of helium sequence

Cited by 7 publications

References 38 publications

Vmc Optimization of Ultra-Compact, Explicitly-Correlated Wave

Vmc Optimization of Ultra-Compact, Explicitly-Correlated Wave

Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus: III. Spin‐quartet state (1s2s3s) of the lithium sequence

The weakly bound states in Gaussian wells: From the binding energy of deuteron to the electronic structure of quantum dots

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