Probing the (empirical) quantum structure embedded in the periodic table with an effective Bohr model

Favaro, Wellington Nardin; López‐Castillo, Alejandro

doi:10.1590/s0100-40422013000200022

Cited by 4 publications

(4 citation statements)

References 8 publications

(14 reference statements)

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“…where n(Z) is the main quantum number as a function of Z and µ(Z) ≈ Z 2/5 − 1 [26]. The IP(Z) approximately coincides with the experimental IP for Z ≤ 92.…”

Section: Effective Modelssupporting

confidence: 68%

“…The independent particle model configuration is maintained even for many-electron systems since some symmetries, such as hydrogen-like configuration and electron pair, are preserved. The most remarkable example could be the Aufbau Principle application to obtain the electron distribution for all chemical elements (see periodic table) [26,58], which is an impressive qualitative approximation for the ground state of many-electron atoms based on a hydrogen-like configuration. The zero-order atom models can be described by non-interacting electrons that move in an effective potential.…”

Section: Effective Models and Aufbau Principlementioning

confidence: 99%

“…Atoms can be described through effective potential models [26], possibly due to the Pauli Principle, avoiding collapse. Charges with the same signs, which repel each other, may benefit the separability of electrons (negative charge) and nuclei (positive charge) [12,33,59].…”

Section: Pauli Principle and Coulomb Repulsionmentioning

confidence: 99%

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Searching for distinct classes of atomic and molecular states using convergence and separability criteria

López‐Castillo

2020

Theor Chem Acc

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We demonstrated that the solution ψ to the Schrodinger equation (SE) Ĥψ = εψ converges logarithmically in the classically forbidden region, i.e., as ε′ approaches to the correct eigenvalue ε, the approximate solution ψ′ logarithmically converges to ψ. Knowing that this approximate eigenvalue procedure generates a straightforward but inefficient method to solve a general problem of n-bodies, we thereby discuss the main characteristic of the usual methods to obtain a better convergence for atoms and molecules. Such usual methods consider that the solution of SE can be approached through a linear combination of solutions of systems with analytical solutions. Hydrogen-like atom solutions are used to describe atoms and molecules. This solution avoids the convergence problem of ψ′ even for approximate eigenvalues ε′ since all the terms of the linear combination decay asymptotically to zero. We argue that this type of solution works very well for a large class of almost separable atomic and molecular states in which the separation of electronic (and nucleus) movements occurs. We also establish a comparison of this separability and other systems, like gravitational, in which separability is only possible in particular classes of restricted systems. Finally, we consider the existence of distinct atomic and molecular states that may not be described using usual methods that apply this type of solution, which implies the separability of restricted problems. Therefore, usual methods to describe atoms and molecules may be insufficient to reach solutions with different or more general electronic correlations, as discussed in the text. Strategies to achieve general or distinctive solutions, although approximated, should be further studied and developed.

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“…where n(Z) is the main quantum number as a function of Z and µ(Z) ≈ Z 2/5 − 1 [26]. The IP(Z) approximately coincides with the experimental IP for Z ≤ 92.…”

Section: Effective Modelssupporting

confidence: 68%

Section: Effective Models and Aufbau Principlementioning

confidence: 99%

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Searching for distinct classes of atomic and molecular states using convergence and separability criteria

López‐Castillo

2020

Theor Chem Acc

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“…Remark 1.3. There are indications [11] that spectral structures similar to the one presented in the H-atom occur for all atoms in the Periodic Table ; if this is actually the case, then alike conclusions of Theorem 1.1 could be drawn for other atoms as well.…”

Section: Fractal Dimensions and Main Resultsmentioning

confidence: 82%