Note on critical cage size for ionization of confined two-electron systems

Díaz-García, C.; Cruz, S. A.

doi:10.1016/j.physleta.2005.12.091

Cited by 14 publications

(29 citation statements)

References 17 publications

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“…This is useful for quantitative reference, since they were not reported numerically in Ref. 57 and constitute a significant improvement to the values reported in Ref. 36.…”

Section: Resultssupporting

confidence: 83%

“…We begin our discussion by considering the simplest confined many‐electron atom: helium, for which recent variational calculations have been reported when submitted to a soft‐wall confining cage with V 0 =5 57 and where the idea of electron escape is put forward. In that article, we claim that electron escape takes place for cage‐sizes where the ionization potential per electron reaches the barrier height, i.e., the point where He cannot be longer neutral.…”

Section: Resultssupporting

confidence: 71%

“…The variational energies together with the variational parameters (μ,ν)‐not explicitly reported in Ref. 57 are also shown. All values in atomic units.…”

Section: Resultsmentioning

confidence: 99%

“…Dotted lines: variational calculations using the method of Ref. 57. Symbols correspond to calculations by other authors as follows.…”

Section: Resultsmentioning

confidence: 99%

“…Here we have extended the calculations reported in Ref. 57, finding that the critical radius for electron escape does not change appreciably by using either scheme, as shown by Figure 4. In this figure, E I and E II represent the first and second ionization potentials, respectively, calculated within the partition scheme, and He + (1s) corresponds to the second ionization potential used in the superposition method.…”

Section: Resultsmentioning

confidence: 99%

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Many‐electron atom confinement by a penetrable spherical box

Díaz-García¹,

Cruz²

2008

Int J of Quantum Chemistry

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A confinement model for many-electron atoms enclosed by a spherical boundary with finite-barrier potential height is presented. The model is based on the Thomas-Fermi-Dirac-Weizsäcker (TFDW) functional formalism using known properties of the orbital electron densities and constitutes a natural extension of a previously published report for the case of infinitely hard walls [Cruz et al., Int J Quantum Chem, 2005, 102, 897]. The confining barrier potential is considered as a step-like function of finite height V 0 . This assumption demands of the appropriate description of the TFDW energy functional for both the interior and exterior regions together with corresponding ansatz orbital density representations, subject to continuity boundary conditions at the wall. For a given cage radius R and confining barrier height V 0 , the total ground-state energy is variationally optimized with respect to the characteristic parameters defining the interior and exterior orbital densities. The total ground-state energy and corresponding electronic density are obtained as function of barrier height and cage radius for many-electron atoms and ions. The model is explicitly applied to He, Li, C, and Ne and various ionic species for barrier heights (atomic units) V 0 ϭ 0, 5, and ϱ. Given a barrier height V 0 , the results are presented for the critical cage size to produce one or more unbound electrons-yet, confined by the box-until reaching threshold size values for which electron escape from the confinement region take place.

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“…This is useful for quantitative reference, since they were not reported numerically in Ref. 57 and constitute a significant improvement to the values reported in Ref. 36.…”

Section: Resultssupporting

confidence: 83%

Section: Resultssupporting

confidence: 71%

“…The variational energies together with the variational parameters (μ,ν)‐not explicitly reported in Ref. 57 are also shown. All values in atomic units.…”

Section: Resultsmentioning

confidence: 99%

“…Dotted lines: variational calculations using the method of Ref. 57. Symbols correspond to calculations by other authors as follows.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 3 more Smart Citations

Many‐electron atom confinement by a penetrable spherical box

Díaz-García¹,

Cruz²

2008

Int J of Quantum Chemistry

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On the wavefunction cutoff factors of atomic hydrogen confined by an impenetrable spherical cavity

Reyes‐García,

Cruz,

Cabrera‐Trujillo

2024

Int J of Quantum Chemistry

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The Schrödinger equation for the hydrogen atom enclosed by an impenetrable spherical cavity is solved through a Finite‐Differences approach to gain an insight on the actual nature and structure of the ansatz wavefunction cutoff factor widely used in an ad hoc manner in corresponding variational calculations to comply with the Dirichlet boundary conditions. The results of this work provide a theoretical foundation for the choice of the appropriate analytical cutoff functions that fulfill the boundary conditions. We find three different regions for the behavior of the cutoff functions. Small cavity radius where the cutoff function has a parabolic behavior, an intermediate region where the cutoff function is quasi‐linear, and a large cavity region where the cutoff function is a step‐like function. We deduce the traditional linear and quadratic cutoff functions used in the literature as well as its validity region for the confining radius. Finally, we provide a mathematical deduction of the exact cutoff function in terms of the nodal structure of the free hydrogenic wavefunctions and a relation to the Laguerre polynomials for some cavity radii where the free atomic energy level coincides with a confined energy level. We find that the cutoff function transit over several unconfined solutions in terms of its nodal structure as the system is compressed.

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Density Functional Theory Applied on Confined Many-Electron Atoms

Garza

Vargas

2014

Electronic Structure of Quantum Confined Atoms and Molecules

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Note on critical cage size for ionization of confined two-electron systems

Cited by 14 publications

References 17 publications

Many‐electron atom confinement by a penetrable spherical box

Many‐electron atom confinement by a penetrable spherical box

On the wavefunction cutoff factors of atomic hydrogen confined by an impenetrable spherical cavity

Density Functional Theory Applied on Confined Many-Electron Atoms

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