What 'wills' certain atoms to covalently form?

DrDu

Good!
Looks as if you could squeeze your argument into a hard inequality!

DrDu

[tex]\langle 1| V_2|1 \rangle =-\frac{e^2}{4\pi \epsilon_0 R}[/tex]
[tex] \langle 1| V_2|2\rangle=E_\mathrm{H}S-\langle 1|T|2\rangle [/tex]
[tex] E_\mathrm{binding}=E-E_\mathrm{H}=\frac{-\langle 1|T|2\rangle}{1+S}+S \frac{e^2}{4\pi \epsilon_0 R(1+S)}[/tex]

chemisttree

You guys have completely gone off the rails.

DrDu

Too true!
Basically I only wanted to recommend the article by Kutzelnigg to the OP as it is certainly the clearest account on how bonding works.

JohnRC

You are quite right chemisttree. I should not have got sucked in and embroiled in the detail.

All that I really had to do to point out the validity of my original model based on potential energy was to quote the virial theorem.

Because the molecular systems involve a potential function made up only of interparticle interactions arising from an inverse square law,

<V> = 2 E ; <T> = –E.

Any behaviour of the total energy of the molecular system must therefore reflect exactly a similar behaviour in the average potential energy.

The Kutzelnigg article does not seem to me to provide the "clearest explanation" for a lay person, as opposed to an expert like DrDu, and is certainly being misunderstood just a little by the latter if he thinks it invalidates my original description of how chemical bonding arises.

chemisttree

Well I had to chuckle when the bra and ket notation arrived on the scene!
Good discussion but I think we scared off the OP...

chill_factor

lol I guess I was so wrong it wasn't worth refuting.

DrDu

Kutzelnigg also discusses the implications of the virial theorem. I would like to know at what point you don't agree with his analysis.

AGNuke

Somethings are better left unknown... (Scared after reading all these)

DrDu

I did some reading and found something interesting, namely a dimensional scaling approach to H2+. That means that one does not treat the isolated three dimensional problem but looks at it in other dimensions too. Especially in one dimension, the Coulomb potentials of the two nuclei are being replaced by two attractive delta functions. This one-dimensional problem can be explicitly solved. It also obeys the virial theorem. However, as the delta functions are local, one can look at the kinetic and potential energy density at every place. Away from the delta functions, the hamiltonian is that of a free particle whence the energy density is of purely kinetic origin. The mean kinetic and potential energy in a very small region [itex] -\epsilon[/itex] to [itex]+\epsilon[/itex] around a delta function are finite (namely equal to the binding energy) but of opposite sign whence the delta functions themselves don't contribute to the total energy, the total energy can be obtained as the sum over the kinetic energy density over all space excluding the immediate surrounding of the deltas.

PS: The hamiltonian with the double delta potential is discussed and solved on wikipedia:
http://en.wikipedia.org/wiki/Delta_p...elta_Potential

Woopydalan

Just when I thought chemistry was a math-relaxed science...

DrDu

It is, but the "dangerous/illegal activities" sticky thread does not allow us to discuss anything what would be more funny.

Borek

This is a common, and serious, mistake.