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A new arrangement of the Periodic Table of the Chemical Elements?

lpetrich

lpetrich

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Mathematicians Have Proposed a New Structure to The Periodic Table noting Formal structure of periodic system of elements | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
"We have investigated almost 5,000 substances consisting of two elements in different proportions. We then looked for similarities within this data. For example, sodium and lithium are similar because they combine with the same elements in the same proportions (e.g. with oxygen or chlorine, bromine, and iodine). We thus found patterns we can use to classify the elements."

This system, based on chemical bonds, rearranges the elements in a new way. Some elements remain grouped together, such as halogens, because they bond the same way; but others are separated, like silicon and carbon, which, when bonded, form very different compounds.
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But I cannot make any sense out of the arrangement. It looks like a big fat mess without rhyme or reason. So I'm sticking with the arrangement that is now traditional.  Alternative periodic tables shows other ones, but none of them are the sort of mess that this new one is.
 
It seems to me that the geometry of the electron energy levels of elements are the best way to organize. This is essentially a grouping based on bonding but more reliably would express the more fundamental properties of elements, such as isotopic quantum leap.
 
Gun Nut said:
It seems to me that the geometry of the electron energy levels of elements are the best way to organize. This is essentially a grouping based on bonding but more reliably would express the more fundamental properties of elements, such as isotopic quantum leap.
Click to expand...
How is that supposed to work?
 
 Electron configurations of the elements (data page)
Electron Configuration for all the elements in the Periodic Table
6.9: Electron Configurations and the Periodic Table - Chemistry LibreTexts

The Periodic Table is usually arranged with electron-configuration details, and those are related to physical and chemical properties. This arrangement is built on electron orbitals for hydrogen atoms. Since that is a two-body problem, it can be solved in closed form. One can solve it with either some complicated-looking orthogonal polynomials in spherical coordinates, or else with operator algebra, as it's called.

The electron has four quantum numbers in the solution:
  • n, the principal one: 1, 2, 3, 4, 5, ...
  • l, the orbital angular momentum: integers from 0 to (n-1)
  • m, the orbital angular momentum projection: -l, -(l-1), ..., -1, 0, 1, ..., (l-1), l (total: 2l+1)
  • s, the spin projection: -1/2, +1/2 (total: 2)
The orbital angular momentum is often denoted by letters:
  • 0: s - sharp
  • 1: p - principal
  • 2: d - diffuse
  • 3: f - fundamental
  • 4: g
  • 5: h
These names are from what some early spectroscopists called some alkali-metal spectral lines.

So the principal quantum numbers have these angular momenta:
  • 1: s
  • 2: s p
  • 3: s p d
  • 4: s p d f
  • 5: s p d f g

Electrons in atoms can be interpreted as having these quantum numbers. However, outer electrons have higher energy for higher angular momentum for the same n values because higher angular momentum means farther out than lower angular momentum.

Electrons also obey the Pauli Exclusion Principle, meaning that no two electrons can have the same state. They must always have different states. Furthermore, each electron added must be in the lowest energy state possible, and which quantum numbers it will have is given by something called Hund's rules.
 
The result is this order of energy-level shell filling. I have made a table with each (n,l) set where it is usually displayed in the Periodic table.
[TABLE="class: grid"]
[TR]
[TD]1s
[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]2s
[/TD]
[TD][/TD]
[TD][/TD]
[TD]2p
[/TD]
[/TR]
[TR]
[TD]3s
[/TD]
[TD][/TD]
[TD][/TD]
[TD]3p
[/TD]
[/TR]
[TR]
[TD]4s
[/TD]
[TD][/TD]
[TD]3d
[/TD]
[TD]4p
[/TD]
[/TR]
[TR]
[TD]5s
[/TD]
[TD][/TD]
[TD]4d
[/TD]
[TD]5p
[/TD]
[/TR]
[TR]
[TD]6s
[/TD]
[TD]4f
[/TD]
[TD]5d
[/TD]
[TD]6p
[/TD]
[/TR]
[TR]
[TD]7s
[/TD]
[TD]5f
[/TD]
[TD]6d
[/TD]
[TD]7p
[/TD]
[/TR]
[/TABLE]

1s1 is hydrogen, and 1s2 is helium. Hydrogen is usually placed atop the alkali metals, ns1, though it has some properties in common with the halogens, np5. Helium is placed atop the other noble gases, np6, and not atop the alkali earths, ns2.

The nd block is of transition metals, and the nf block is of rare earths (lanthanides and actinides). The rare earths are usually moved below the rest of the table.
 
lpetrich said:
Gun Nut said:
It seems to me that the geometry of the electron energy levels of elements are the best way to organize. This is essentially a grouping based on bonding but more reliably would express the more fundamental properties of elements, such as isotopic quantum leap.
Click to expand...
How is that supposed to work?
Click to expand...

It's my understanding (which may be flawed) that the true nature of elemental matter is defined by the geometry of the electron "orbits" (I know its not like Newtonian orbits, like they taught in elementary school). The type of stable bonds that can form is a function of how those geometries interact to form new geometries, and how those geometries are changed by isotopes to make quantum leaps to other forms of matter. I thought that it was believed that a comparison of geometry is more descriptive of nature of the element than, say, just the number of elementary particles that make up the element.
 
The Photographic Periodic Table of the Elements has lots of stuff on the elements.

The Photographic Periodic Table of the Elements - default arrangement has links to other arrangements:
  • 1: default: gap below yttrium
  • 2: first-in-row rare earths below yttrium
  • 3: last-in-row rare earths below yttrium
  • Wide: rare earths between alkali earths and transition metals
  • Scerri: hydrogen with halogens, noble gases, alkali metals, alkali earths, (est of the PT
  • Scerri 2: rest of the PT, hydrogen and halogens, noble gases, alkali metals, alkali earths
  • Scerri Wide: like Scerri 2, but with rare earths before transition metals
  • Left Step: rare earths, transition metals, post-transition elements, noble gases, hydrogen and alkali metals, helium and alkali earths
  • Right Step: hydrogen and alkali metals, helium and alkali earths, post-transition elements, noble gases, transition metals, rare earths
Right Step is hydrogenlike shell-filling order: 1s / 2s, 2p / 3s, 3p, 3d / 4s, 4p, 4d, 4f / 5s, 5p, 5d, 5f / 6s, 6p, 6d / 7s, 7p

The properties of the elements can be graphed in periodic-table form:
Covalent Radius for all the elements in the Periodic Table
Ionization Energies for all the elements in the Periodic Table
Melting Point for all the elements in the Periodic Table
Boiling Point for all the elements in the Periodic Table
Abundance in the Universe for all the elements in the Periodic Table
Abundance in Earth's Crust for all the elements in the Periodic Table
Abundance in the Ocean for all the elements in the Periodic Table
Abundance in Humans for all the elements in the Periodic Table
and numerous other properties. It's much easier to see trends in properties than with that mixed-up PT.
 
Jimmy Higgins said:
Guy must hate Helium.
skepticalbip said:
Amazing... A periodic table that only a mathematician could love.
Click to expand...
My thoughts exactly. Genius confused as to why idea they came up with isn't catching on.

Here is a less neck stinging image.

View attachment 22208
Click to expand...

That's truly ugly. What do the colours signify? What do the arrows mean (what is implied by their length, or direction, or angle)? Where are Argon, Neon and Helium? What (not to put too fine a point on it) the fuck?
 
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