# Visualising MO theory

I'm good at visual thinking so I find VSEPR theory and valence bond theory easy to understand but I'm having trouble with MO theory. 2D diagrams like this:

confuse me. I know that they represent energy levels but they don't help me visualise the concept at all. I've seen pictures of bonding and antibonding MOs like this:

but how do these look when they are actually between 2 atoms?

SpectraCat
I'm good at visual thinking so I find VSEPR theory and valence bond theory easy to understand but I'm having trouble with MO theory. 2D diagrams like this:

confuse me. I know that they represent energy levels but they don't help me visualise the concept at all. I've seen pictures of bonding and antibonding MOs like this:

but how do these look when they are actually between 2 atoms?

Well, those are all artists representations, but the ones in your second figure are a pretty good representation of how we normally draw the sigma orbitals between two atoms. You can choose to draw them a little larger, so that the overlap is more obvious, but that is basically correct.

Before I launch into an explanation of MO theory ... do you understand the shapes of atomic orbitals, including the concept of phase?

Before I launch into an explanation of MO theory ... do you understand the shapes of atomic orbitals, including the concept of phase?

Yeah I understand the shapes of atomic orbitals but this is the first time I've come across the concept of phase. I just looked it up and am confused because this contradicts what I had previously learned about atomic orbitals. I thought that the only difference between the 1s and 2s orbital was that the 2s orbital was larger but thats not the explanation this page gives:
http://www.orbitals.com/orb/
I know what the 4 quantum numbers represent but I didn't think the magnetic quantum number even applies to s orbitals. The 2s orbital in that series:

is smaller than the 1s orbital:

I'm fairly lost. Thanks for informing me that the bonding orbital in the 2nd diagram I posted is what should be seen between the 2 atoms though, at least now I can start visualising molecular orbitals. Antibonding orbitals have me baffled but I'm gonna learn this phase concept before I proceed with MO theory.

EDIT: In this picture:
[PLAIN]http://www.d.umn.edu/~pkiprof/ChemWebV2/AOs/images/p-orb.jpg [Broken]
I'm guessing the blue and red colours represent the 2 phases. Does the electron with the +1/2 spin occupy one phase while the electron with the -1/2 spin occupy the other?

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I could be wrong, but i think the guy was wrong to draw the 2s orbital smaller than the 1s orbital. See for 1s1 and 1s2 orbitals, if you draw the visual representation, you need to distinguish between the two and its difficult cos they both look the same really. So the guy drawing the picture might personally choose to make his picture of the 1s2 orbital a bit bigger. That could cause confusion.

2s orbitals should show one circle inside the other, and different colours would help the visual image. The overall size you draw the circles is kind of irrelevant.

John.

What are 1s1 and 1s2 orbitals? All I know of are "1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s etc." Is there a topic I'm missing or something?

What are 1s1 and 1s2 orbitals? All I know of are "1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s etc." Is there a topic I'm missing or something?
When talking about atomic orbitals, we are really only discussing the number of electrons. So in the periodic table, hydrogen has 1 electron, helium has 2 electrons, lithium has 3 electrons and beryllium has 4 electrons, and so on.

So.... Hydrogen atomic orbital is 1s1
helium is 1s2
lithium is 2s1
beryllium is 2s2

Hydrogen has 1 electron, but helium has 2 electrons. In the case of helium, the 2 electrons are in the exact same shell. When you draw the helium orbitals, you are still just drawing 1 shell. So from a drawing point of view, the hydrogen and helium drawings would look the very same. To counteract this confusing scenario, some artists might distinguish between the hydrogen and helium maybe by shading the two pictures differently. In reality, i think, the distinction is a different wave pattern.

Here is a list of all the orbitals for all the elements;
http://en.wikipedia.org/wiki/Electron_configurations_of_the_elements_(data_page [Broken])

Have a look at the hand-drawn atoms on the bottom of the following page, they are accurate and very good drawings;
http://dl.clackamas.cc.or.us/ch104bk/lesson7/electron.htm [Broken]

John.

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SpectraCat
When talking about atomic orbitals, we are really only discussing the number of electrons. So in the periodic table, hydrogen has 1 electron, helium has 2 electrons, lithium has 3 electrons and beryllium has 4 electrons, and so on.

So.... Hydrogen atomic orbital is 1s1
helium is 1s2
lithium is 2s1
beryllium is 2s2

Hydrogen has 1 electron, but helium has 2 electrons. In the case of helium, the 2 electrons are in the exact same shell. When you draw the helium orbitals, you are still just drawing 1 shell. So from a drawing point of view, the hydrogen and helium drawings would look the very same. To counteract this confusing scenario, some artists might distinguish between the hydrogen and helium maybe by shading the two pictures differently. In reality, i think, the distinction is a different wave pattern.

Here is a list of all the orbitals for all the elements;
http://en.wikipedia.org/wiki/Electron_configurations_of_the_elements_(data_page [Broken])

Have a look at the hand-drawn atoms on the bottom of the following page, they are accurate and very good drawings;
http://dl.clackamas.cc.or.us/ch104bk/lesson7/electron.htm [Broken]

John.

You seem to be confusing electron configurations with orbitals. Every atom of every element has a full set of orbitals (1s, 2s, 2p, etc.) .. the difference is which orbitals are populated by electrons. The electron configuration tells you which shells and shells are populated, and with how many electrons: i.e. Lithium is 1s22s1.

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SpectraCat
Yeah I understand the shapes of atomic orbitals but this is the first time I've come across the concept of phase. I just looked it up and am confused because this contradicts what I had previously learned about atomic orbitals. I thought that the only difference between the 1s and 2s orbital was that the 2s orbital was larger but thats not the explanation this page gives:
http://www.orbitals.com/orb/

I know what the 4 quantum numbers represent but I didn't think the magnetic quantum number even applies to s orbitals. The 2s orbital in that series:

is smaller than the 1s orbital:

That site is correct, except that I don't think that you are supposed to compare the relative sizes of the orbitals. Those shapes represent isodensity surfaces .. that is, surfaces created by plotting all the points which have a particular value of electron density. You are correct that for a given element and density value, the isodensity surface for the 1s orbital should appear smaller than for the 2s orbital.

I'm fairly lost. Thanks for informing me that the bonding orbital in the 2nd diagram I posted is what should be seen between the 2 atoms though, at least now I can start visualising molecular orbitals. Antibonding orbitals have me baffled but I'm gonna learn this phase concept before I proceed with MO theory.

EDIT: In this picture:
[PLAIN]http://www.d.umn.edu/~pkiprof/ChemWebV2/AOs/images/p-orb.jpg [Broken]
I'm guessing the blue and red colours represent the 2 phases. Does the electron with the +1/2 spin occupy one phase while the electron with the -1/2 spin occupy the other?

You are correct about the color coding representing the two phases. However, the phases are not associated with particular spin values ... the isodensity surface is the same for both the +1/2 and -1/2 spins. What the phases tell you about is how the orbitals add up when they overlap ... when two regions of the same phase (i.e same color) overlap, they add up (since these are really wave-functions, you should say they experience constructive interference) .. this produces bonding interactions. When the phases are different, they cancel out (i.e. they experience destructive interference) .. this produces anti-bonding interactions. This is how the MO shapes in the diagram you originally posted were generated.

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