Reaction between iron(II) sulphate, sulphuric acid

[Borek]

I lknow what you are aiming at - bands are constructed from molecular orbitals, so there is an analogy. But it doesn't mean there are LUMO and HOMO in metal crystal - there are overlapping bands and they are responsible for observable metal properties.

 

[Gokul43201]

Actually, the bands are not even constructed from molecular orbitals. There is absolutely no remanence of a molecular orbital in the free electron band description of a metal. You will have molecular orbitals only if there is binding to the nucleus. Conduction electrons in a metal are the valence electrons of the atoms, and they fill a band of free electron states.

 

[Borek]

IIRC you are wrong (but my English is an obstacle to precisely explain what I know - I will do my best). When you have two copper atoms their orbitals mix together (not that they create a particle) and you have LUMO and HOMO. Each added atom adds additional orbitals. When there is enough atoms the orbitals energy levels are so close that they are effectively not separated - that's when they create a band. Band behaves absolutely differently than molecular orbitals, and here you are right - but if you look at the process of creation of metal crystal there are intermediate states when there are only several atoms, that are not a standard molecule nor a metal crystal - and I believe that's the thing DrMark referred to in his questions.

SOme more thinking on my side and I realized that you wrote:

the bands are not even constructed from molecular orbitals

which contradicts what I wrote. Can you elaborate - how are the bonds constructed?

Chemical calculators for labs and education

BATE - pH calculations, titration curves
CASC - concentration conversions, solution preparation

 

[Gokul43201]

Here's one big difference : electrons in a molecular orbital are bound electrons while electrons in a Fermi sea are free electrons (they are not localized to certain orbitals or regions of space).

Yes, you are correct that if you put together 2 or 3 or 4 copper atoms, you will see some kind of molecular orbital structure. But there's a vital difference between having a cluster (some small number) of atoms and having a macroscopic crystal. In the first case, you do not have invariance over translation by a fixed length. In the latter case, you do. This results in the physics of the crystal being completely different from that of a cluster. The wavefunction (and hence all properties, such as the energy levels) of an electron in a conducting crystal is completely different from one in a cluster.

So, in short, the physics describing the behavior of valence electrons changes completely between cases where you have a small number of atoms to cases where you have a large number. You can not construct a crystal by simply making a cluster larger and larger. At some point there will be a transition to a periodic lattice, and at that point the physics of the cluster must be abandoned.

 

[Borek]

Do you mean the transition will be not continuous?

I was taught (well, it was 20 years ago, I can be missing something) that as the cluster grows number of molecular orbitals grows and the energy gaps between them get smaller and smaller, once they are small enough they form a bond. Well, perhaps that's oversimplification.

And I have doubt if you are right stating that electrons on the molecular orbitals are bound - ie they are bound to the orbital, but the orbital can spread over whole molecule (or whole cluster) - in such situation there will be no difference between free electron in the valence bond and the localized electron on the molecular orbital. The again it can be oversimplification.

Chemical calculators for labs and education

BATE - pH calculations, titration curves
CASC - concentration conversions, solution preparation

 

[GCT]

But GCT : metals do not have molecular orbitals. So there is no question of HOMOs or LUMOs in a metal.

that's quite a statement. However, it is in direct contradiction to textbook definitions, so rather than argue endlessly about it here it is:

Band theory: ...delocalized electrons move freely through "bands" formed by overlapping molecular orbitals."

...since the number of atoms in even a small piece of magnesium is enormously large, the number of molecular orbitals they form is also very large

the band is a result of closely spaced molecular orbitals

The formation of these bands or as my text calls it molecular orbitals is from the individual atomic orbitals contributed by each metal. The same rule applies, the number of MOs must equal the number of AOs combined, this many MOs must be so close on an energy level diagram that they form a continuous band of energies. The point is that the molecular orbitals do exist within metals. In all contexts, it is appropriate to say that metals do have molecular orbitals, perhaps not so assertively, and it does not deserve emphasis...however it makes no sense to say that there are no molecular orbitals. The band theory is nothing too far out special and magical from the ordinary formation of molecular orbitals from atomic orbitals, it is merely a special case.

 

[DrMark]

More fuel to the fire ;)

How is a metal particle properly described if it's dimensions are smaller then the de Broglie wavelength of its electrons ?

 

[Gokul43201]

Band theory: ...delocalized electrons move freely through "bands" formed by overlapping molecular orbitals."

Tell me this is from a graduate level condensed matter physics text, and I'll take back my previous statements.

Band structure is calculated starting from the free electron model; not starting from a molecular orbital description.

Borek : No, the transition from a cluster to a crystal is not abrupt. Periodicity first nucleates within the bulk of the cluster and grows outwards with increasing number of atoms, N. As N increases, the fraction of atoms that belong in a crytalline grain(N_x/N) increases, but never reaches 1. Even in large, pure crystals, the surface atoms have distorted, cluster-like structure, but this number is negligible compared to N.

 

[Gokul43201]

And I have doubt if you are right stating that electrons on the molecular orbitals are bound - ie they are bound to the orbital, but the orbital can spread over whole molecule (or whole cluster) - in such situation there will be no difference between free electron in the valence bond and the localized electron on the molecular orbital.

Yes you are correct. The difference between conductors and insulators comes from the relative position of the Fermi energy with respect to the band edges.

 

[GCT]

Tell me this is from a graduate level condensed matter physics text, and I'll take back my previous statements.

Band structure is calculated starting from the free electron model; not starting from a molecular orbital description.

alright, I'm just not going to go on with this discussion of whether metals have molecular orbitals or not, obviously you are aware of a different mechanism starting from two atomic orbitals (or not) to bands; where according to you, these bands are do not consist of closely spaced molecular orbitals, but that of something completely different. I'm not completely disagreeing with you as I'm no expert on this subject and have yet to learn further about it.

On to a more interesting proposal for you Gokul, can you give us an explanation of how a metal, such as magnesium, would react with aqueous hydrochloric acid, in relevance to orbital dynamics? I'm not trying to cause you to trip here, I just think that the answer would be quite interesting (such cases, in conforming to your standards, are explained thorugh LUMO and HOMO interactions with organic molecules).

Mg_{(s)}+HCl_{(aq)} \rightarrow MgCl_2_{(aq)} + 2H^{+}_{(aq)}

 

[GCT]

How is a metal particle properly described if it's dimensions are smaller then the de Broglie wavelength of its electrons ?

don't know off the top of my head, Gokul might be able to answer this question more throughly in the meanwhile...more research for me. Also you might get better answers posting in one of the physics subforums, e.g. "atoms, particles etc.."

 

[DrMark]

don't know off the top of my head, Gokul might be able to answer this question more throughly in the meanwhile...more research for me. Also you might get better answers posting in one of the physics subforums, e.g. "atoms, particles etc.."

This is not a question for me just a challenge for you and anybody living in a quantum well will surely know the answer ;)

 

[Gokul43201]

alright, I'm just not going to go on with this discussion of whether metals have molecular orbitals or not, obviously you are aware of a different mechanism starting from two atomic orbitals (or not) to bands; where according to you, these bands are do not consist of closely spaced molecular orbitals, but that of something completely different.

I did not say anything about them being completely different. The origin of the energy bands of a crystalline solid is in the single atom states, but the bands are not constructed the way molecular orbitals are. Crystal symmetry imposes additional conditions on them; so when you go from a cluster to a crytal, you change the energy dispersion of the system. Hence you can not say that metals have molecular orbitals. However, this does not mean that you can not use some form of molecular orbital theory to understand reactions with bulk metals.

In a metal, the equivalent of the LUMO and the HOMO is the same thing, known as the Fermi energy. When an electrophile or nucleophile binds to the surface of a metal, it raises or lowers the Fermi energy locally (it also affects the HOMO of the binding ion). The relative position of the Fermi level with respect to the HOMO of the adsorbed ion is what seems to be important to determining the mechanism. In addition, the binding ions form a cluster at the surface whose energetics may now be roughly described in terms of LUMOs and HOMOs (since the crystalline symmetry has been destroyed locally) for the cluster. Current theoretical understanding involves semi-empirical approximations based on the Extended Huckel Model.

To summarize :

1. You can not speak of LUMOs and HOMOs of a metal, unless you are talking about nanoparticles/clusters

2. You can not provide a simple Molecular Orbital description of reactions with bulk metals (short of doing a Hartree-Fock simulation or somesuch)

http://www.qtp.ufl.edu/~roitberg/pdf/1999_01.pdf
http://www.iupac.org/publications/pac/2000/7201/7201pdf/3_rao.pdf
http://www.cartage.org.lb/en/themes/Sciences/Chemistry/Electrochemis/Electrochemical/ElectrodeKinetics/ElectrodeKinetics.htm

 

[Gokul43201]

More fuel to the fire ;)

How is a metal particle properly described if it's dimensions are smaller then the de Broglie wavelength of its electrons ?

You are now talking about nanoparticles/clusters. To the crudest approximation you may treat this as a particle in a box problem and get a rough idea for the dispersion spectrum. But really good calculations have been done using DFT (and a host of other techniques that I know little about) for such particles.