BINODIC MADELUNG RULE 2026
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Julio gutierrez samanez
Mar 23, 2026, 2:16:58 AMMar 23
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BINODIC MADELUNG RULE 2026
Dear colleagues: Revisiting the famous Madelung rule, which, as we all know, has not been derived from quantum mechanics and perhaps never will be—in the words of Dr. Eugen Schwarz, in a communication he made to this list in 2012, and in several of his substantial works—I believe that we have no better empirical rule that, despite its many shortcomings or inaccuracies, comes closer to reality, at least if we only consider it as a sequence of atomic nuclei or protons and not as an electronic distribution. The long table I made this Sunday afternoon, taking advantage of the quiet, is an adaptation or reinterpretation of Madelung's Rule (1936) using the binodic model. This model considers the duplication of n in symmetric pairs with the same number of elements: (2, 2; 8, 8; 18, 18; 32, 32...), which comes from doubling the ratio 2n^2. That is: (2n^2, 2n^2), when the series n is 1, 1; 2, 2; 3, 3; 4, 4, ... In each binode (N), there are 4N^2 elements, and the summation (4 ≤ 4N^2) describes the entire series Z. I will complete this new table with the experimental configurations that do not coincide with the theoretical configurations, along with those that take a different position, such as (n-1)d < 4s, which produces the configuration 3d < 4s, etc. The work is still in draft form.
Hugs to all.
Julio
Dear colleagues: Revisiting the famous Madelung rule, which, as we all know, has not been derived from quantum mechanics and perhaps never will be—in the words of Dr. Eugen Schwarz, in a communication he made to this list in 2012, and in several of his substantial works—I believe that we have no better empirical rule that, despite its many shortcomings or inaccuracies, comes closer to reality, at least if we only consider it as a sequence of atomic nuclei or protons and not as an electronic distribution. The long table I made this Sunday afternoon, taking advantage of the quiet, is an adaptation or reinterpretation of Madelung's Rule (1936) using the binodic model. This model considers the duplication of n in symmetric pairs with the same number of elements: (2, 2; 8, 8; 18, 18; 32, 32...), which comes from doubling the ratio 2n^2. That is: (2n^2, 2n^2), when the series n is 1, 1; 2, 2; 3, 3; 4, 4, ... In each binode (N), there are 4N^2 elements, and the summation (4 ≤ 4N^2) describes the entire series Z. I will complete this new table with the experimental configurations that do not coincide with the theoretical configurations, along with those that take a different position, such as (n-1)d < 4s, which produces the configuration 3d < 4s, etc. The work is still in draft form.
Hugs to all.
Julio
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