How are chemical bonds described by quantum mechanics?

[quantumcat]

I'm currently doing my Bachelor's in Physics(1st year). My textbooks aren't too clear on quantum mechanical concepts. "Bonds are formed by overlapping orbitals". I have several questions.
I've seen the graph of potential energy versus distance. For some pairs of atoms like hydrogen it dips at a certain distance and increases, whereas for others, like two Helium atoms it keeps going up. Why is this? I'm assuming the repulsion arises out of the Pauli exclusion principle, but why do some pairs of atoms have a lower potential state while others don't? We've dabbled a bit into molecular orbitals but its rather confusing. Is it that quantum math(Schroedinger's equation) allows such states only for certain pairs of atoms? We've not done a detailed section on Schroedinger"s equation yet, just the basics.
Next up, because all orbitals(except for s) are directional, does a bond form only when the atoms approach at a certain angle?

I look forward to a great time at Physics Forums!

 

[Simon Bridge]

Welcome to PF;
The quantum mechanics of atomic bonds is usually a senior or postgrad study.
It is possible you don;t have the tools to understand it beyond "overlapping orbitals".
Is this a chemistry course you are doing?

I'm currently doing my Bachelor's in Physics(1st year). My textbooks aren't too clear on quantum mechanical concepts. "Bonds are formed by overlapping orbitals". I have several questions.

I've seen the graph of potential energy versus distance. For some pairs of atoms like hydrogen it dips at a certain distance and increases, whereas for others, like two Helium atoms it keeps going up. Why is this?

Because that is what you get when you do the maths.

It sounds like you are talking about a graph of the work needed to get two nuclei a particular distance apart. The dip is because the electrons are able to partly counteract the repulsion of the nuclei.

I'm assuming the repulsion arises out of the Pauli exclusion principle,

... that would be a poor assumption. Nuclei have the same charge, so they repel each other.

.. but why do some pairs of atoms have a lower potential state while others don't? We've dabbled a bit into molecular orbitals but its rather confusing. Is it that quantum math(Schroedinger's equation) allows such states only for certain pairs of atoms?

It is because there are different configurations of energy states for different atoms.
This is something you'll get in more detail later.

Oversimplifying: as two atoms get closer together the potential wells of the nuclei add together - this has the effect of lowering the potential barrier between them. If the barrier is lower than the higher occupied energy levels, then a bond can form.

However, due to the repulsion of the nuclei, it may not be possible for the atoms to get close enough for that to happen. The details is in the exact pattern of energy levels in each atom.

You end up with rules about filling shells.

Next up, because all orbitals(except for s) are directional, does a bond form only when the atoms approach at a certain angle?

Kind of but not relevant since atoms are constantly rotating and jostling each other about so there is no need to be exact. Magnets are directional too, but you can get them to join up by putting them in a box and shaking it.

The directional nature of the states gives some molecules their characteristic shapes.

 

[HeavyMetal]

Next up, because all orbitals(except for s) are directional, does a bond form only when the atoms approach at a certain angle?

There is something in quantum chemistry called the linear combination of atomic orbitals (LCAO) method. It involves both the constructive (bonding) and destructive (antibonding) interference of atomic orbitals when they overlap. This is how we construct a wavefunction for the molecule. Another way we model molecules involves the symmetry species; this is called the symmetry-adapted LCAO method. It runs much deeper than is possible to explain at this point because you must learn group theory first. Fortunately, this is a very rudimentary concept and you might be taught soon. Ask your instructor if this is something you will end up covering. If not, and this is an area of study that you are interested in, you should consider taking a physical chemistry class.

Welcome to the forums!

 

[DrDu]

Next up, because all orbitals(except for s) are directional, does a bond form only when the atoms approach at a certain angle?

That's the case with molecular fragments and radicals but not with atoms. In atoms, although individual orbitals have directional character, like e.g. p orbitals, there are several of them and you can form superpositions of them pointing in any direction, especially along the bond axis.

 

[quantumcat]

Thanks for all the replies. I'm afraid I'll have to wait for some time to fully understand the topic. It is going over my head right now.

 

[DrDu]

Alternatively, you could get hold of some decent book on quantum chemistry and do some reading.
I recommend e.g. Ira Levine, Quantum Chemistry.

 

[Simon Bridge]

I remember it took me a lot of playing about with plots to get it.

 

[quantumcat]

I'll take a look definitely. Thanks.