Electron behavior in covalent bonds

[Mhorton91]

So I was sitting in my very low level biology class today, and we covered some basic chemical concepts that we will need for the class, basics of atoms, the periodic table, sub atomic particles ect...

Then we got to the section on bonds, covalent bonds specifically. She showed the typical intro level pictures of how 2 (or more) atoms can share electrons (I attached one similar).

Now, given my very restricted "understanding" (non mathematical) of how electrons behave at the quantum level; it left me wondering how the actual "sharing" of electrons take place between atoms. Given that (if I understand correctly) if we don't observe the electrons, each electron is theoretically in all possible locations at every given moment, how then do 2 atoms share electrons?

I'm sure I'm missing something that most of you will find obvious, but, I'm adopting the "there is no stupid question" philosophy, and since a Google search didn't return anything as far as I could see, here I am.


Thanks for anyone who reads this. I also wasn't sure if this belonged here or in the quantum mechanics section, so I took a guess.



Thanks for any insight!
Marshall H.

 

[mfb]

each electron is theoretically in all possible locations at every given moment

You can use this as a model, but the probability to find an electron somewhere does depend on the position. The probabilities are given by the orbitals. The "shared" electrons have orbitals that are distributed over both atoms, while most other electrons are bound to one of the atoms (with a negligible probability to find it at the other atom).

 

[dextercioby]

[...] it left me wondering how the actual "sharing" of electrons take place between atoms. Given that (if I understand correctly) if we don't observe the electrons, each electron is theoretically in all possible locations at every given moment, how then do 2 atoms share electrons?[...]

That's one of the best questions one could ask: the answer has to do with the new foundations of chemistry offered by the physical theory of quantum mechanics developed after 1925. Each atom has an energetic bound spectrum as a whole which one can 'exactly' determine only for the H-atom (which is a 2-point particle). So one can formulate a coherent theory let's say for the H_2 molecule, a 4-particle system. If one makes a lot of simplifying assumptions (infinite heavy nuclei, neglecting nuclear wavefunctions and spins), one can infer that the individual electrons from each of the 2 atoms are described each by a 1s orbital (wavefunction) - which itself has indeed a probabilistic nature as your remark shows - which then overlaps one with the other giving rise to a so-called molecular orbital. Under this new concept, one then says that the electrons are shared. The bonding molecular orbital of the H_2 molecule is called 'sigma bond' and is the simplest possible covalent bond.

 

[Mhorton91]

You can use this as a model, but the probability to find an electron somewhere does depend on the position. The probabilities are given by the orbitals. The "shared" electrons have orbitals that are distributed over both atoms, while most other electrons are bound to one of the atoms (with a negligible probability to find it at the other atom).

That's one of the best questions one could ask: the answer has to do with the new foundations of chemistry offered by the physical theory of quantum mechanics developed after 1925. Each atom has an energetic bound spectrum as a whole which one can 'exactly' determine only for the H-atom (which is a 2-point particle). So one can formulate a coherent theory let's say for the H_2 molecule, a 4-particle system. If one makes a lot of simplifying assumptions (infinite heavy nuclei, neglecting nuclear wavefunctions and spins), one can infer that the individual electrons from each of the 2 atoms are described each by a 1s orbital (wavefunction) - which itself has indeed a probabilistic nature as your remark shows - which then overlaps one with the other giving rise to a so-called molecular orbital. Under this new concept, one then says that the electrons are shared. The bonding molecular orbital of the H_2 molecule is called 'sigma bond' and is the simplest possible covalent bond.

Alright thanks for the answers guys!

I hopefully understand what you're telling me:

So, if for visualization purposes we simplify it back down, a "shared" electron's orbital would be a path such that it would be circling both nucleuses in the given bond, and where the non shared would only circle it's given nucleus?

I asked my instructor (I go to a community college) about it after class, because I didn't want to throw words like: quantum, theoretically, and probabilistic around in a very intro science class, she didn't really have a good answer from a physics stand point, which I suppose is to be expected from a bio teacher


Also, I have heard of the probabilistic limitations of finding an electron in a given position, I'm guessing the fact that it is strictly calculated in probabilities is due to the uncertainty principle... which, if I understand it states that the more sure we are of the location, the less sure we are of momentum, and vice versa... or does that have nothing to do with this question?

 

[DrDu]

I tried to summarize the concept of a covalent bond in post #5 in the following thread:
https://www.physicsforums.com/showthread.php?t=724034

 

[mfb]

So, if for visualization purposes we simplify it back down, a "shared" electron's orbital would be a path such that it would be circling both nucleuses in the given bond, and where the non shared would only circle it's given nucleus?

"Circling" is way too classical here. The electrons are not zipping around in an atom.

I'm guessing the fact that it is strictly calculated in probabilities is due to the uncertainty principle

There is a relation to that.

 

[Mhorton91]

I tried to summarize the concept of a covalent bond in post #5 in the following thread:
https://www.physicsforums.com/showthread.php?t=724034

I read your post in that thread... I think it's safe to say I'm a long ways from having even a basic understanding of quantum mechanics

"Circling" is way too classical here. The electrons are not zipping around in an atom.

I understand that part, I'm just trying to get a picture in my head of what's happening... and the more I read and research ... the more I feel like maybe it isn't something I can accurately visualize.