My Chemistry textbook says that on approaching each other, atomic orbitals of atoms interact. This interaction, it says, can be additive and subtractive, and lead to formation of bonding and anti-bonding orbitals. I have a question. Since regular orbital boundaries only represent a 90% probability boundary, overlap should take place at quite large distances, and therefore, bonding orbitals should be formed, and electrons should occupy them. But I'm quite certain this is not the case. Why is this so? What really is the nature of addition between atomic orbitals? Is there a minimum distance they must be at before addition can take place? If so, why?
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$\begingroup$ Crossposted to chemistry.stackexchange.com/q/22390 $\endgroup$– Qmechanic ♦Commented Jan 5, 2015 at 1:17
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$\begingroup$ You cannot say there is a "boundary" of an orbital. I think this is really a flaw in how orbitals are visualized. Instead, think of electron probability "clouds." There can be interactions at all distances. $\endgroup$– Geoff HutchisonCommented Jan 5, 2015 at 16:31
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2 Answers
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You can look at it from a couple of angles. For one thing it's a tunneling problem: for an electron to go from one molecule to another that is several orbital diameters away is a long "jump", which will suppresses the probability of finding a charged ionic bond state of the form $M^---M^+$greatly over the neutral $M--M$ state. The ionic bond is also energetically greatly suppressed for molecules that don't have strong electronegativity differences, the resulting probability for that outcome will be low. The splitting of energy levels happens anyway, of course, which means that the far more likely process is that the "local electron" will move into the lower energy state (if it can). If the system is symmetric and has similar energy levels, there will be a possibility of resonant energy exchange. This is very important for e.g. the chemistry of dye molecules. Getting them too close actually quenches the optical emission.
answered Jan 4, 2015 at 23:56
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$\begingroup$ Okay, so the electron, most of the time, does move into the lower energy level? If this happens, will the attraction to form a bond continue properly? $\endgroup$ Commented Jan 4, 2015 at 23:59
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$\begingroup$ Also, why doesn't this happen at very large distances? I suspect that at this stage orbitals are small, so electron-electron repulsion is high, even if one remains in the "antibonding" part of the orbital combination. Thus, the electron doesn't fall, and overlap continues. Is this the case? $\endgroup$ Commented Jan 5, 2015 at 0:04
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$\begingroup$ The system moves into the lowest possible energy level, if it can. I can't tell you what the selection rules are and on what time scales this can happen, that's what the molecular dynamics people are dealing with. Interactions at long distances are just a tunneling problem: the probability of finding an electron on the other molecule drops exponentially with distance. So as you bring the two molecules closer, the interaction will become stronger very quickly. $\endgroup$ Commented Jan 5, 2015 at 0:05
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Let's take the very simple case of H + H $\rightarrow$ H2.
At infinite separation, you have two isolated 1s orbitals for each electron.
If there is any interaction between the two H atoms, you will see one orbital become more stable and one become less stable. Now, the question will become whether you can detect this shift at say 0.4 nm separation, but certainly we can calculate using simple quantum mechanics the difference in energy between the two molecular orbitals.
So the true answer to your question is that it's a gradient.
At very large separations, the two atoms function independently. As they get closer together, there are small differences in energy between bonding and anti-bonding orbitals, but less than $kT$ and eventually you'll form a weakly-bound bonding molecule.
