Study of confined many electron atoms by means of the POEP method

Sarsa, A.; Buendı́a, E.; Gálvez, Francisco

doi:10.1088/0953-4075/47/18/185002

Cited by 27 publications

(33 citation statements)

References 25 publications

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“…which has shown to work properly for atoms. [4,9,33] The effective potential is fixed variationally by using the POEP method. [32] A parameterization of both the radial part of the orbitals and the effective potential is employed.…”

Section: Methodsmentioning

confidence: 99%

One and two body densities for excited states of the helium confined atom

Luzón

Buendı́a

Gálvez

2019

Int J of Quantum Chemistry

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A study of the first excited states of the helium atom confined under impenetrable spherical walls is carried out. Both single particle and two body, intracule and extracule, densities are constructed. Crossing levels and Hund's rule are analyzed in terms of the contribution to the total energy from kinetic, electron-nucleus, and electron-electron energies. A study about the behavior of the single particle and two body densities is carried out. The Multiconfiguration Parameterized Optimized Effective Potential method is employed with a cut-off factor to account for Dirichlet boundary conditions. Single particle density is analytically constructed whereas the Monte Carlo algorithm is used to calculate two body densities.confined atoms, one and two-body densities | INTRODUCTIONAtoms under pressure modify considerably their properties as compared to the free species. In particular the ordering of single particle levels is different when the atoms are spatially confined, leading to a filling of the shells that differs from the well-known one of the free atoms. [1][2][3] A simple model to describe atomic confinement is to place an atom inside an impenetrable cavity of adjustable radius. In this model, the electrostatic Hamiltonian is modified by adding a confining potential of radius r c . The hard-wall confinement model is very useful to study the role of spatial limitation on the properties of atoms and molecules. [4][5][6][7][8][9] An important empirical result for atomic and molecular systems are the so-called Hund's rules. According to the first of them, for the states arising from a same configuration, the one with the highest value of the spin is the most bound, that is, it has the lowest energy. For free atoms, this result was erroneously attributed to the interelectronic energy that, for the excited states of the helium atom should be greater in the singlet than in the triplet. The first correct justification of the Hund's rule for atoms was given by Davidson [10] who showed, for the first excited states of He, that the electron-electron repulsion energy, V ee , is greater in the triplet than in the singlet and the same happens with the kinetic energy due to the virial theorem. Thus, the lower total energy of the triplet is due to a much larger decrease due to the nuclear attraction potential energy, V en , that compensates for the energy increase in both electron-electron repulsion potential and kinetic energies. Thus, the electrons in the triplet are, on average, closer to the nucleus than in the singlet, and also the average distance between the electrons is smaller in the triplet. This property, V ee greater for the triplet than for the singlet, has been observed for a great number of neutral atoms. [11,12] But the study of atomic isoelectronic sequences shows that the interelectronic repulsion reaches greater values for the singlet states than for the corresponding triplet ones as the nuclear charge of the ion increases. [13,14] This same happens when the atoms are confined, that is, the interelectronic ...

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Section: Methodsmentioning

confidence: 99%

One and two body densities for excited states of the helium confined atom

Luzón

Buendı́a

Gálvez

2019

Int J of Quantum Chemistry

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“…In early stages of the quantum mechanics, Sommerfeld proposed that positive eigenvalues found under this model indicate an electron delocalization . Naturally, it is not easy to probe such a delocalization in systems where spatial restrictions trap electrons instead of the nuclear attraction …”

Section: Introductionmentioning

confidence: 99%

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

Rodriguez‐Bautista

Vargas

Aquino

et al. 2017

Int J of Quantum Chemistry

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The electronic structure of several many-electron atoms, confined within a penetrable spherical box, was studied using the Hartree-Fock (HF) method, coupling the Roothaan's approach with a new basis set to solve the corresponding one-electron equations. The resulting HF wave-function was employed to evaluate the Shannon entropy, S q , in configuration space. Confinements imposed by impenetrable walls induce decrements on S q when the confinement radius, R c , is reduced and the electron-density is localized. For confinements commanded by penetrable walls, S q exhibits an entirely different behavior, because when an atom starts to be confined, S q delivers values less than those observed for the free system, in the same way that the results presented by impenetrable walls. However, from a confinement radius, S q shows increments, and precisely in these regions, the spatial restrictions spread to the electron density. Thus, from results presented in this work, the Shannon entropy can be used as a tool to measure the electron density delocalization for many-electron atoms, as the hydrogen atom confined in similar conditions.confined atoms, correct asymptotic behavior, Hartree-Fock, Shannon entropy, wave-function 1 | I N TR ODU C TI ON The confined atoms model is an important topic in physics and chemistry since atoms under spatial restrictions exhibit unusual characteristics, which differ to those on the same systems without such constraints. For example, effects over atoms confined by the fullerene have been analyzed using a model with a radial potential similar to a shell with width and size fitted to reproduce experimental information. [1][2][3] The simulation of the hydrogen atom submitted to high external pressures is another example of confined atoms. [4][5][6][7][8][9] In this case, the hydrogen atom was clamped at the center of one sphere, of radius R c , with impenetrable walls and consequently, wave-function or electron-density satisfy Dirichlet's boundary conditions. On this line, walls with infinite potential have been applied to study many-electron atoms, using wave-function techniques [10][11][12][13][14][15][16] or the density functional theory, [17,18] and some of these results have been contrasted with experimental values to predict sd electronic transitions observed when some metals are submitted to high pressures. [19,20] In early stages of the quantum mechanics, Sommerfeld proposed that positive eigenvalues found under this model indicate an electron delocalization. [5,21] Naturally, it is not easy to probe such a delocalization in systems where spatial restrictions trap electrons instead of the nuclear attraction. [22][23][24][25][26][27][28] The confinement by impenetrable boxes overestimates the response of physical observables, and, therefore, penetrable walls are more convenient to contrast the corresponding results with an experimental counterpart. [29][30][31][32][33] Such a model was proposed by Gorecki and Byers-Brown to reproduce the behavior of the helium atom submitted to high pressur...

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“…Here, the following form for g ( r ) is employed

g (r) = (1 - r / r_{c})

which has shown to work properly for atoms, see for example, Refs. [, , ].…”

Section: Methodsmentioning

confidence: 99%

Confinement effects on the electronic structure of M-shell atoms: A study with explicitly correlated wave functions

2017

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The ground and some excited states of Na and Mg atoms confined at the center of a spherical box with impenetrable walls are studied. Variational wave functions including dynamic correlations and configuration mixing have been obtained. Level crossings induced by confinement have been analyzed in terms of the energy of the occupied orbitals of the M shell and the weight of the different configurations. Confinement effects on the correlation energy have been studied. The parameterized optimized effective potential and the variational Monte Carlo methods have been employed. A cut off‐factor has been included to account for the hard wall confinement.

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Study of confined many electron atoms by means of the POEP method

Cited by 27 publications

References 25 publications

One and two body densities for excited states of the helium confined atom

One and two body densities for excited states of the helium confined atom

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

Confinement effects on the electronic structure of M-shell atoms: A study with explicitly correlated wave functions

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