2d Chemistry

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

2d Chemistry

Postby anderscolingustafson » Wed Jun 25, 2014 1:23 am

How would chemistry work in 2d? I mean how would atoms be arranged and what would the periodic table look like in 2d? How would chemicals interact in 2d?
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Re: 2d Chemistry

Postby ICN5D » Wed Jun 25, 2014 5:01 pm

Well, in general, there would probably be some relation to sphere packing, for 2D. The complexity of a nucleus and molecule would be held back by the limitation, leading to simpler periodic tables, and simpler chemistry. If I recall, some atoms arrange outer electrons into the vertices of a tetrahedron, so a 2D equivalent could be something like a 2D simplex, a triangle.
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Re: 2d Chemistry

Postby Teragon » Mon Dec 28, 2015 7:06 pm

Actually we are able to build objects behaving like 2D atoms.

Image

http://www.tnw.tudelft.nl/index.php?id=33982
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Re: 2d Chemistry

Postby PatrickPowers » Tue Dec 29, 2015 5:26 pm

Teragon wrote:Actually we are able to build objects behaving like 2D atoms.

http://www.tnw.tudelft.nl/index.php?id=33982


Fascinating! I am amazed.
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Re: 2d Chemistry

Postby uky » Tue May 03, 2016 7:51 am

Sadly the link is dead
Did anyone save the content or remember how they carried out the calculations?
I'll give it a shot
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Re: 2d Chemistry

Postby Keiji » Sat May 07, 2016 12:00 pm

I did a reverse google image search on Teragon's image (which I have also mirrored here in case that disappears, too) and it seems to be about something called "quantum dots". There's a brief mention of it on page 16 of this pdf, but I wasn't able to locate any information on the enumeration in the diagram or why they behave like 2D atoms.
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Re: 2d Chemistry

Postby quickfur » Sat May 07, 2016 4:23 pm

It's very simple. Quantum dots are just devices that confine electrons (or other subatomic particles) to an energy well, so that they form 2D standing waves around the point of confinement. This is analogous to electron standing waves in an atom, where they form 3D standing waves, hence they could be interpreted as virtual 2D atoms.
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Re: 2d Chemistry

Postby Teragon » Sat May 07, 2016 8:04 pm

Quickfur is right. And they're not exactly the same as real 2D-atoms. Quantum dots are much larger than atoms. Moreover in a quantum dot there is no Coulomb potential of the nucleus, but that doesn't really matter as essentially it's the geometric shape the electrons are confined to that determines the possible states (wave functions) with their quantum numbers. In 2D the Coulomb potential of the nucleus would decay more slowly with the distance, so in detail that might make a difference. Maby I'll try and solve the Schroedinger equation for 2D hydrogen and plot the orbitals... should be easier than the known 3D case. The wave functions will be similar to sections through certain 3D orbitals:

Image

Here is something that might be interesting for you:
https://zumbuhllab.unibas.ch/pdf/refs/reviews/FewEDots_KouwenhovenRPP64_701.pdf
Last edited by Teragon on Sun May 08, 2016 3:15 pm, edited 1 time in total.
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Re: 2d Chemistry

Postby Teragon » Sun May 08, 2016 2:43 pm

As I understand it, in 2D the polar part of the Schroedinger equation will just become a constant and the azimuthal part will be the same as in 3D, with only the case |m| = l left. For a given principal quantum number n, the angular quantum number l can assume integer values from -n to n and the magnetic quantum number m, describing the projection of l onto the z-axis, doesn't make sense anymore. Therefore every subshell (set of quantum numbers n, |l|) just corresponds to one (for l = 0) or two (for |l| > 0) wave functions, not to 2l+1 different ones as in 3D. That would be slightly different from what you see in the periodic table for 2D atoms above. Not sure about the Pauli principle in 2D. If we had a 1/r-potential in 2D, the orbitals would just be crosssections of the 3D orbitals with |m| = l in the polar plane. As the potential goes like log(r), however, the radial part will be much different considering energy spacing and order, spacial extension of orbitals and stability of states. And it's going to be quite tricky to solve this part of the equation.

If you know the shape of an orbital you can immediatly tell its quantum numbers:

3D
n = 0,1,2,3,... - principal quantum number: Total number of nodes in the wave function (spherical, planar or conical)
l = 0,... n - angular quantum number: Number of nodes going through the center (= number of planar or conical nodes)
m = -l,... 0,... l - magnetic quantum number: Number of nodal planes perpendicular to the xy-plane
s = -1/2, 1/2

2D
n = 0,1,2,3,... - principal quantum number: Number of nodes in the radial direction (spheres or lines)
l = -n,... 0,... n - angular quantum number: Number of nodal lines through the center (= number of linear nodes)
s ?

Edit: Made a mistake in the first sentence and confused azimuth and polar angle, now corrected.
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Re: 2d Chemistry

Postby Prashantkrishnan » Tue Sep 27, 2016 7:30 pm

If you know the shape of an orbital you can immediatly tell its quantum numbers:

3D
n = 0,1,2,3,... - principal quantum number: Total number of nodes in the wave function (spherical, planar or conical)
l = 0,... n - angular quantum number: Number of nodes going through the center (= number of planar or conical nodes)
m = -l,... 0,... l - magnetic quantum number: Number of nodal planes perpendicular to the xy-plane
s = -1/2, 1/2

2D
n = 0,1,2,3,... - principal quantum number: Number of nodes in the radial direction (spheres or lines)
l = -n,... 0,... n - angular quantum number: Number of nodal lines through the center (= number of linear nodes)
s ?


For 3D, l = 0, 1, 2, ... n-1.
I would expect it to be the same for 2D.

In the case of m, we know for instance that in 3D, the p orbitals are px, py and pz, corresponding to the three coordinate axes. In 2D, I would expect that there are only two p orbitals for every principal quantum number.

I am unable to understand the use of magnetic quantum number to denote the orbitals. The orbitals px, py and pz are interchangeable, while the numbers -1, 0 and 1 are not. But if this is acceptable, then I suppose for 2D, m = 0, 1, 2, ... l.

We could define molecular shapes and hybridisation using these assumptions.

3D:
sp - Linear
sp2 - Trigonal planar
sp3 - Tetrahedral
sp3d - Trigonal bipyramidal
sp3d2 - Octahedral
sp3d3 - Pentagonal bipyramidal

2D:
sp - Linear
sp2 - Trigonal
sp2d - Tetragonal
sp2d2 - Pentagonal(?)

Extending to 4D, I would assume that there are 4 p orbitals and 7 d orbitals, as I think the number of each type of orbitals would form an arithmetic progression (Not sure about this). This gives the following shapes:

4D:
sp - Linear
sp2 - Trigonal planar
sp3 - Tetrahedral realmic
sp4 - Simplex
sp4d - Tetrahedral bipyramidal
sp4d2 - Trigonal tetrapyramidal (uncertainty in nomenclature)
sp4d3 - Aerochoral
sp4d4 - Pentagonal tetrapyramidal (uncertainty in nomenclature)

In the meanwhile, magnetic quantum numbers seem more difficult to assign in 4D...
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Re: 2d Chemistry

Postby Teragon » Sun Oct 09, 2016 7:03 pm

Prashantkrishnan wrote:For 3D, l = 0, 1, 2, ... n-1.
I would expect it to be the same for 2D.


It's not the same because m is the quantum number associated with the azimuth. So l in 2D corresponds to m in 3D.
You get it if you solve Schroedinger's equation. At some point you arrive at something of the following form:
d Y(phi)²/d phi² = -Z(r)*Y(phi) and the solutions for Y are of the form e^(i*l*phi)
l can either be a positive or a negative integer with l<n.

Prashantkrishnan wrote:In the case of m, we know for instance that in 3D, the p orbitals are px, py and pz, corresponding to the three coordinate axes. In 2D, I would expect that there are only two p orbitals for every principal quantum number.


You are right and the two of them are distinguished by l being positive or negative.

Prashantkrishnan wrote:I am unable to understand the use of magnetic quantum number to denote the orbitals. The orbitals px, py and pz are interchangeable, while the numbers -1, 0 and 1 are not. But if this is acceptable, then I suppose for 2D, m = 0, 1, 2, ... l.


Orbitals may be interchangeable (= degenerated/having the same energy), but they remain different orbitals (you have to write down all three of them to obtain the full atom). In this case -1, 0 and 1 are also interchangeable. However they do not have to. For example there may be a distinguished direction given by an external magnetic field. m is the projection of the angular momentum in that direction and in this case m = 0 is different from m = +-1 in energy.

All I can say about 4D for the moment is there has to be an additional quantum number and it's gonna play the same role as m.
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Re: 2d Chemistry

Postby The Shadow » Sat Nov 05, 2016 4:46 pm

Years ago I found a paper solving the 2d Schroedinger equation with 1/r electric field. (They did it numerically as I recall, as the logarithm in the potential makes things hopeless to solve in closed form.)

The results were quite weird, looking nothing like the usual periodic table. I'd have to hunt it up again to give details, though.
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