scholarly journals Mendeleev Table: a Proof of Madelung Rule and Atomic Tietz Potential

2017 ◽  
Author(s):  
Eugene D. Belokolos ◽  
Keyword(s):  
Tietz Potential ◽  
Madelung Rule

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

2012 ◽  
Vol 137 (1) ◽  
pp. 014101 ◽  
Author(s):  
Chun-Sheng Jia ◽  
Yong-Feng Diao ◽  
Xiang-Jun Liu ◽  
Ping-Quan Wang ◽  
Jian-Yi Liu ◽  
...  
Keyword(s):  
Potential Model ◽  
Diatomic Molecules ◽  
Tietz Potential

Recent attempts to change the periodic table

2020 ◽  
Vol 378 (2180) ◽  
pp. 20190300 ◽  
Author(s):  
Eric Scerri
Keyword(s):  
Recent Work ◽  
Periodic Table ◽  
Natural Kinds ◽  
Superheavy Elements ◽  
Theme Issue ◽  
Philosophical Approach ◽  
Specific Data ◽  
Madelung Rule

The article concerns various proposals that have been made with the aim of improving the currently standard 18-column periodic table. We begin with a review of 8-, 18- and 32-column formats of the periodic table. This is followed by an examination of a possible, although rather impractical, 50-column table and how it could be used to consider the changes to the periodic table that have been predicted by Pyykkö in the domain of superheavy elements. Other topics reviewed include attempts to derive the Madelung rule as well as an analysis of what this rule actually provides. Finally, the notion of an ‘optimal’ periodic table is discussed in the context of recent work by philosophers of science who have examined the nature of classifications in general, as well as the notion of natural kinds. The article takes an unapologetically philosophical approach rather than focusing on specific data concerning the elements. Nevertheless, some pragmatic issues and educational aspects of the periodic table are also examined. This article is part of the theme issue ‘Mendeleev and the periodic table’.

Spin-orbital exclusion principle and the periodic system

2020 ◽  
Vol 92 (3) ◽  
pp. 515-525
Author(s):  
Viktor Vyatkin
Keyword(s):  
Atomic Nucleus ◽  
Quantum Number ◽  
Atomic Number ◽  
Periodic System ◽  
Value Distribution ◽  
Exclusion Principle ◽  
Real Sequence ◽  
Spin Orbital ◽  
Quantum Numbers ◽  
Madelung Rule

AbstractGroups of electrons, radial with respect to the atomic nucleus and with the same value of the orbital quantum number and the same number on the subshell, are considered. A spin-orbital exclusion principle is established, regulating the spin value distribution on the subshells with the same value of the orbital number. According to this principle, all subshells are divided into positive and negative ones, depending on the direction of the spin of their first electron. It is found that, in the real sequence of the appearance of new subshells, a spin-orbital periodicity takes place, which develops in cycles consisting of two periods that are mirror-symmetric to each other in the direction of the spin of their electrons. Moreover, atomic number of any period is equal to the sum of the principal and orbital quantum numbers of its subshells, and this can serve as an explanation for the Madelung rule. It is demonstrated that Mendeleev’s chemical periodicity lags behind the spin-orbital periodicity by two elements and repeats its structure. From these positions, the absence of a pair in the first period of Mendeleev’s table and the pairing of all its other periods are explained. Based on the obtained results, an eight-period table of elements, the prototype of which being Janet’s left-step table, is compiled and briefly described.

scholarly journals Exact and Poisson summation thermodynamic properties for diatomic molecules with shifted Tietz potential

2019 ◽  
Vol 93 (9) ◽  
pp. 1171-1179 ◽  
Author(s):  
A. N. Ikot ◽  
W. Azogor ◽  
U. S. Okorie ◽  
F. E. Bazuaye ◽  
M. C. Onjeaju ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Diatomic Molecules ◽  
Tietz Potential ◽  
Poisson Summation

Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method

2014 ◽  
Vol 92 (3) ◽  
pp. 215-220 ◽  
Author(s):  
W.A. Yahya ◽  
K. Issa ◽  
B.J. Falaye ◽  
K.J. Oyewumi
Keyword(s):  
Iteration Method ◽  
Vibrational Energy ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Quantum Numbers ◽  
Approximate Analytical Solutions ◽  
Relative Closeness ◽  
Klein Gordon ◽  
Tietz Potential ◽  
Schrödinger System

We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.

scholarly journals ROTATIONAL-VIBRATIONAL EIGEN SOLUTIONS OF THE D-DIMENSIONAL SCHRÖDINGER EQUATION FOR THE IMPROVED WEI POTENTIAL

2020 ◽  
Vol 4 (2) ◽  
pp. 269-283
Author(s):  
Edwin Samson Eyube ◽  
Yabwa Dlama ◽  
Umar Wadata
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Goodness Of Fit ◽  
Bound State ◽  
Fit Indices ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Vibrational Energies ◽  
Eigen Solutions ◽  
Tietz Potential

In this present study, we have employed the techniques of exact quantization rule and ansatz solution method to obtain closed form expressions for the rotational-vibrational eigensolutions of the D-dimensional Schrödinger equation for the improved Wei potential, for cases of h′ ≠ 0 and h′ = 0. By using our derived energy equation and choosing arbitrary values of n and ℓ, we have computed the bound state rotational-vibrational energies of CO, H2 and LiH for various quantum states. The mean absolute percentage deviation (MAPD) and the Lippincott criterion ware used as a goodness-of-fit indices to compare our result with the Rydberg-Klein-Rees (RKR) and improved Tietz potential data in the literature. MAPD of 0.2862%, 0.2896% and 0.0662% relative to the RKR data for CO ware obtained. For the improved Wei and Morse potential, our computed energy eigenvalues for CO, H2 and LiH are in excellent agreement with existing results in the literature

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