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I'd found the image attached on a website explaining the molecular orbital theory. enter image description here

My question is, shouldn't the graph have a maximum at the middle of the two hydrogen atoms? since my intuition tells me that the electrons have a great chance of being in the middle rather than anywhere else. hmm, this train of thought has led me to another question, what exactly does this graph even represent? I mean, which electrons probababilty does it even show? or does it show us the probability of finding any electron participating in the constructive bonding.

another question that I have is this, if say, we were to excite one of the electrons into the higher antibonding orbital, what would exactly happen to this orbital, the shape I mean, would it simply cease to exist? since we're literally making the bond cease to exist (bond order=0) or would it assume the shape of this?

enter image description here

I still haven't completely grasped the true nature of such orbitals, I think it's evident from all these questions.

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Bonds are in general not maxima of the electron probability distribution. Local maxima are typically centered at the nuclei. This is due to the Coloumb potential. The electron can lower its potential energy by getting closer to the nuclei so they will always try to maximize their probability around the nuclei, where all the positively charged protons are bundled. This is a bit oversimplified but in essence the reason why you see the maxima at the H position or in general at the position of nuclei.

To see bonds, you should look at the difference of the probability density of two lonely hydrogens and a H2 molecule. I.e. calculate the electronic wavefunction for a single Hydrogen Atom and then add the plots of two such single hydrogen calculations placed at the positions as in H2. Compare this with the plot coming from the H2 calculation and you should see that the H2 distribution has a higher density in between than the two unbonded hydrogens simply taken together.

Bonds as we draw them in simple chemistry are not rigorously defined mathematically and more or less a useful approximation to rationalize reactions without doing difficult calculations. There are ways to obtain a mathematical definition of bonds but these definitions are not neccessarily agreeing with the way that we draw bonds in general chemistry. One such model is Atoms in Molecules which evaluates the electron density and its topology to define bonds. But there are other models, for example Electron localization functions and i am sure that there are more, unknown to me.

Overall it is important to realize that bonds are a useful concept but they have no unambiguous clear cut underlying physical definition. Physics/Quantum mechanics yields no equation that unambiguously defines a chemical bond.

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  • $\begingroup$ thanks for the answer! But I also want to ask, where exactly did the idea for an antibonding orbital come from? was it to explain the fact that if we excite the an electron in the bond with energy, the bond will sometimes dissapear? or is there a mathematical intuition behind it as well? I am aware of the LCAO, but I have the same question for this as well, is it a mathematical consequence? or to explain observational phenomena? $\endgroup$
    – Victor Bernoulli
    Commented Jan 10, 2021 at 19:56
  • $\begingroup$ When you determine the bonding orbital, you also obtain the antibonding orbital. Both orbitals are obtained when you search for the best possible orbitals for your molecule. You start with atomic orbitals centered on each nucleus. Then you use a method to obtain better molecular orbitals, typically the Hartree-Fock method. This calculation tells you how to build better molecular orbitals from the original set of atomic orbitals. In H2 you start with 2 x S1 orbitals. You obtain 1 x bonding sigma orbital and 1 x antibonding orbital. This procedure is well defined. $\endgroup$
    – Hans Wurst
    Commented Jan 10, 2021 at 20:36
  • $\begingroup$ In H2 it appears obvious to identify the bonding sigma orbital with the single bond that we also draw in the structure H-H. But in larger molecules your orbitals often look nothing like a single bond between two nuclei. Instead the orbitals are spread out over the whole molecule. And this is the point where it gets tricky to identify a single orbital with a bond. We can still call them bonding and anti bonding by looking at their energy relative to the energy of the original atomic orbitals. I'd recommend not to overthink orbitals before you had an exposure to the mathematical background. $\endgroup$
    – Hans Wurst
    Commented Jan 10, 2021 at 20:45

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