[movies]

I have had a number of discussions with people where I have tried to explain the octet rule.  The same question always comes up: what causes there to be an octet rule.  The best answer that I have ever been able to give is that there is no particular reason for the octet rule, but the rule does seem to apply, based on empirical observations.  My question is, does anyone have a real explanation for why there are the number of atomic orbitals that there are (the octet rule arises from the number of orbitals)?

I was thinking about this question this morning and it seems that it might be logical that the orbitals described by the Schroedinger equation account for exact solutions for energy levels with certain numbers of nodal surfaces in three dimensions.  If this is the case, an s-orbital would account for all three dimensions in one orbital because it can occupy 3 dimensions equally.  When you add a node, however, you require multiple orbitals to occupy three dimensional space, and so on for higher order orbitals.  This seems logical, but is the Schroedinger equation something that can be derived from scratch and proven to be true, or is it an equation that has been created to model what has been observed?  Furthermore, how do you account for the lack of 1-p orbitals and 2-d orbitals?  Shouldn't the same symmetry rules apply to all energy levels?

Sorry for the long treatise, but this is something that has bothered me for a long time now.

[jdurg]

I think the reason why there is no 1-p orbital has something to do with the solution to the Schroedinger equation for the first level of energy.  I'll check up on this in my P-Chem book when I get home from work.

[Demotivator]

The schroedinger equation is derived from the physics of electron matter waves and proven to be true with chemical observations.
The number of nodes in a stationary wave is related to it's energy. Also, There is only a limited number of stationary wave patterns that can be created depending on the number of nodes. The quantum number n actually defines the number of nodes as n - 1. For n =2 (one node) there can be no d orbital (d needs a minimum of 2 nodes).
This is interesting (scroll down for Stationary States in a Pool of Water)
http://www.av8n.com/physics/octet.htm

[Mitch]

The octet rule, if I remember correctly, doesn't fall out of the Schroedinger equation, but the p-orbitals and the s-orbitals do. I believe that each atom will have these orbitals at different energies and their importance in bonding depends on the nature of the atom.

Scroedinger equation can not be derived. Neither can F=ma, although there was this one day in Physics lecture where I could of sworn...

[movies]

Thanks for your explanations guys.

Demotivator, I have one specific question: can empirical observations really prove the Schroedinger equation?  It seems to me that there are way too many approximations to say it is a proof.

Okay, next question: what is the origin for the special stabilization of a filled subshell?  How does that overide the electron-electron repulsions that you incur when filling the subshell?

[Mitch]

Good question. I'm not sure either, the idea of noble configurations being the most "stable" has been hammered into me for so long, I take it for granted.


I wonder if the "stability" of having the noble configuration isn't an electronic stability but probably chemical inertness that we prescribe stability too.

[movies]

Yeah, I was thinking that too, but isn't it an exothermic reaction to go from O to O^2-?  Maybe it's not, but I guess I would be suprised if it wasn't.

[Mitch]

I think what we are really discussing now is electron affinity. It involves 2 opposing forces: 1) The electron repulsion of adding an other electron(which we've discussed). 2) The energy gained from having an electron seeing a nuclear charge. I remember from Inorganic, that there are no exothermic 2-order electron affinities, but there are quite a number 1st-order ones.

[Demotivator]

Thanks for your explanations guys.

Demotivator, I have one specific question: can empirical observations really prove the Schroedinger equation?  It seems to me that there are way too many approximations to say it is a proof.

I don't recall approximations being made for The wavefunction solutions for the schroedinger equation for an atom. Observed electronic behavior/spectra agree very well with the theory.
In the case of molecules, there are approximations (MO theory based on combining AOs from schroedinger) because the schroedinger equation for molecules gets too complex to solve. But at least MO theory uses a "sound" basis set as a starting point.

2) Like Mitch noted,
The stability of filled shells is often explained as due to the increasing coulombic attraction (remember that protons are being added) of the positively charged nucleus on the electrons which lowers the energy of the system. This is sufficient to overcome the e - e repulsions.

Electron affinities provide an interesting clue. I've read that N-(g) is not stable while C- and O- are stable (exothermic).
The reason is that N- forces the extra electron to pair up in a p orbital (repulsion). C- allows the e to occupy an empty p orbital.
Yet, O- forces the electron to pair up, so why is it not unstable? The reason given is that the extra nuclear charge is sufficient to overcome the unfavorable repulsion. O2-(g), however, is endothermic since there is too much repulsion.

[movies]

I don't recall approximations being made for The wavefunction solutions for the schroedinger equation for an atom. Observed electronic behavior/spectra agree very well with the theory.
In the case of molecules, there are approximations (MO theory based on combining AOs from schroedinger) because the schroedinger equation for molecules gets too complex to solve. But at least MO theory uses a "sound" basis set as a starting point.

I thought the Schroedinger equation could only be solved exactly for single electron atoms.  Can it be solved exactly for multi-electron atoms?

2) Like Mitch noted,
The stability of filled shells is often explained as due to the increasing coulombic attraction (remember that protons are being added) of the positively charged nucleus on the electrons which lowers the energy of the system. This is sufficient to overcome the e - e repulsions.

Protons aren't being added, electrons are, and with each additional electron the Z[/sub]eff[/sub] will go down, right?  Are you saying that the Coulombic attraction is still enough to overcome that repulsion?  Then it stops when that energy level is full because the next available orbital is so much higher in energy, right?  So you could say the O^3- is very hard to make because there is a very "dilute" Z_eff to an approaching electron and that electron would never get close enough to the nucleus to be held tightly because the higher energy levels don't allow for sufficient penetration through the filled, lower energy shells.  Is that correct?

Electron affinities provide an interesting clue. I've read that N-(g) is not stable while C- and O- are stable (exothermic).
The reason is that N- forces the extra electron to pair up in a p orbital (repulsion). C- allows the e to occupy an empty p orbital.
Yet, O- forces the electron to pair up, so why is it not unstable? The reason given is that the extra nuclear charge is sufficient to overcome the unfavorable repulsion. O2-(g), however, is endothermic since there is too much repulsion.

I think this agrees with my reasoning above, please correct me if I am thinking about it wrong.  Can the explanation for the instability of N- be used to explain the relative stability of other atoms that have half-filled sets of orbitals, (e.g. manganese)?

[Mitch]

It's just a matter of balancing Z_eff versus electon-electron repulsion. Second order electron affinities are always endothermic. Demotivator mentioned adding a proton because he was referring to the increasing exothermic nature of first-order electon affinities accross a period(and noting the exceptions).

[Demotivator]

1) You're right, it is solved exactly for single electron atoms.
As far as the validity of the approximate solutions, I've read:

"No exact solution of the Schroedinger equation is possible for any of the atoms heavier than hydrogen, but methods of successive approximations can be used to obtain very good approximate solutions to the Schroedinger equations which describe the electrons in heavier atoms. Modern digital computers are almost mandatory in the very laborious calculations required to obtain accurate results for many-electron atoms by successive approximations."

As I understand it,  by approximations they don't mean chemical fudge factors, but numerical iterative methods.

2) As Mitch pointed out, I meant adding protons as you move across a period so Zeff is increasing. Now if you stop on an element like O and just keep adding electrons to get to O-, then Zeff decreases but is still strong enough in this case.  If gets to O2- or O3- , like you say Zeff is too diluted and so on.

3) I guess you can put it that way, unstable N- can be used to illustrate the relative stability of half filled shells.
What it boils down to with Hund's rule is that maximum multiplicity, in half filled shells, lies lowest in energy because:
" a symmetric spin state forces an antisymmetric spatial state where the electrons are on average further apart and provide less shielding for each other, yielding a lower energy. "

[movies]

Awesome.  Thanks again guys, I've learned a lot in this thread.

[AWK]

http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Langmuir-1919b.html
http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Langmuir-1919.html
http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Lewis-1916/Lewis-1916.html

[Donaldson Tan]

Awesome.  Thanks again guys, I've learned a lot in this thread.

me too