How do we know what electron orbitals look like?

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SaggiSponge
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How do we know what electron orbitals look like?

Is it observational, or is it purely mathematical? I've also been learning about hybridized orbitals, and I couldn't find an explanation as to how we know what 'combined' orbitals look like. I'm assuming it's a mathematical model based on what we know about electrons, but I couldn't find anything to confirm that. Apparently scientists have actually observed electrons, but that was somewhat recently.
My understanding of quantum physics can be graphed with a sine wave.

Soupspoon
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Re: How do we know what electron orbitals look like?

The simple (and simplistic) answer is that it's a statistical distribution.

Given a certain configuration of bonds and electrons to form them, they're somewhere in that 'lobe' or whatnot, respective to their atom (or the ring of atoms, in the case of those cyclics).

But at that level of reality everything is statistical, to a significant degree, and it's not so much that it is 'somewhere' in the lobe, but everywhere. Smeared out, as a wave(-like) thing, still with charge/mass/whatever of an electron (as we know it).

(I don't pretend that I'm an expert on current thinking. This is from education 20+ years ago, possibly only even half-remembered, and even then it was with the knowledge that all this view was really just 'slightly further down the rabbit hole' of quantum physics, sufficient to tide me over until I specialised further in that direction (which I didn't do). But it might do for starters...)

PM 2Ring
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Re: How do we know what electron orbitals look like?

This article from 2005 by David Villeneuve Orbital Imaging: Laser-generated high-harmonic radiation produces tomographic images of molecular orbitals describes how to get the shape of the wave function of a molecular electron orbital.

Spoiler:
Using a computed tomography algorithm, we converted the data to a 3-D image that represents the wave function of a single electron orbital of the highest occupied state of nitrogen (bottom). Red represents positive values of the wave function, and blue represents negative values.

This article from 2015 talks about a newer technique which can image orbitals of single atoms.

Hydrogen Atoms under Magnification: Direct Observation of the Nodal Structure of Stark States
Spoiler:
A. S. Stodolna, A. Rouzée, F. Lépine, S. Cohen, F. Robicheaux, A. Gijsbertsen, J. H. Jungmann, C. Bordas, and M. J. J. Vrakking
Phys. Rev. Lett. 110, 213001 – Published 20 May 2013
[...]
In this Letter, we report photoionization microscopy experiments where this nodal structure is directly observed. The experiments provide a validation of theoretical predictions that have been made over the last three decades.

A newly-developed “quantum microscope” uses photoionization and an electrostatic magnifying lens to directly observe the electron orbitals of an excited hydrogen atom.

BeerBottle
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Re: How do we know what electron orbitals look like?

The pictures you typically see of orbitals in textbooks or online (a sphere for an s orbital, a kind of 3D figure of 8 for a p orbital etc) are representations of a mathematical function called the wavefunction. This is a 3D function that describes the wave-like properties of an electron.

Where do these wavefunctions come from? They are solutions to the Schrödinger equation, which is the central equation in quantum physics. In the case of orbitals we are thinking about electrons bound in atoms. For bound electrons only certain functions are valid solutions for the Schrödinger equation, and so only certain electron orbitals are "allowed" in atoms. You may know the names of these solutions already, the first few are commonly called 1s, 2s, 2p, 3s, 3p, 3d, 4s etc etc and so on forever.

Each of these orbital labels refers to a mathematical function (a wavefunction) which is a valid solution to the Schrödinger equation. It is then a simple matter to describe how orbitals can combine (hybridize, overlap, whatever you want to call it) - we just add the wavefunctions together. So the chemical bond in H2 can be described as a sum of the two H 1s orbital wavefunctions.

In a sense then, the answer to your question is that these are mathematical functions which come from the prevailing theory (quantum mechanics). So that's all nice and neat then.

Spoiler:
umm, except that we can't actually solve the Schrödinger equation for atoms with more than 1 electron. So for every atom except hydrogen, we just pretend that the orbitals are the same as for hydrogen. Neat eh?

doogly
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Re: How do we know what electron orbitals look like?

The things in your spoiler are not true. If you go to grad school, you can do helium. Tremendous improvement!

And then the physical chemists do some things with numbers instead of exact mathematical functions that seem to maybe be actually legit and interesting, but I wouldn't know anything about that.
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BeerBottle
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Re: How do we know what electron orbitals look like?

doogly wrote:The things in your spoiler are not true. If you go to grad school, you can do helium. Tremendous improvement!

And then the physical chemists do some things with numbers instead of exact mathematical functions that seem to maybe be actually legit and interesting, but I wouldn't know anything about that.
I disagree. To be precise, there is no analytical solution to the time dependent Schrödinger equation for an n electron system where n>1. So you cannot "do" helium. Even if you go to grad school.

http://www.nyu.edu/classes/tuckerman/ad ... node3.html

doogly
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Re: How do we know what electron orbitals look like?

Sure, we do perturbation theory. It was a little glib, "we just pretend that the orbitals are the same as for hydrogen" is absolutely false.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?

BlackSails
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Re: How do we know what electron orbitals look like?

BeerBottle wrote:
doogly wrote:The things in your spoiler are not true. If you go to grad school, you can do helium. Tremendous improvement!

And then the physical chemists do some things with numbers instead of exact mathematical functions that seem to maybe be actually legit and interesting, but I wouldn't know anything about that.
I disagree. To be precise, there is no analytical solution to the time dependent Schrödinger equation for an n electron system where n>1. So you cannot "do" helium. Even if you go to grad school.

http://www.nyu.edu/classes/tuckerman/ad ... node3.html

The best part of your post is that link you posted is from one of my classes

ijuin
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Re: How do we know what electron orbitals look like?

Of course, the very concept of visual information no longer holds valid when you get down to the size scale where any wavelength short enough to reflect/refract is by necessity energetic enough to destroy the target (i.e. ionizing radiation). Once we get down to that scale, we can only use models that say "this is what the shape is like".

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