[Schrödinger]

I read that "if an atom has a formal positive charge, then the electrons will be pulled closer to the nucleus, thereby reducing the size of that orbital. This effect is greater for the outer electrons."

Why should the outer electrons be contracted more than the inner electrons?

[MrTeo]

This sounds really strange to me... I thought that formal charge was only a conventional way to express the atom's "behaviour" in the molecule (just like the oxidation number)... The only explanation is that we're talking of a cation, so the formal charge is the same of the real charge of our atom...

Anyway I think that the only reason is that valence electrons are bonded with less strength to the nucleus. This means that their "potential energy hole" (think at the tunnel effect) which keeps the whole system stable and causes the existance of ionization energy (the energy needed to "pull out" the electron from its stable configuration) is not so "deep" so that they can be easily influenced by electric attractions both from the nucleus and from the nearby atoms. On the other hand the inner electrons are really stable in their configuration and they oppose natural resistance to any kind of transfer (potential energy increases if they're taken away from their position and also if you try to decrease their distance from the nucleus).

I don't think if my answer was very understandable... if you need any more clarification please ask 

By the way... where did you read that? I'd like to check the whole passage out...

[Schrödinger]

Anyway I think that the only reason is that valence electrons are bonded with less strength to the nucleus. This means that their "potential energy hole" (think at the tunnel effect) which keeps the whole system stable and causes the existance of ionization energy (the energy needed to "pull out" the electron from its stable configuration) is not so "deep" so that they can be easily influenced by electric attractions both from the nucleus and from the nearby atoms.

But then , if the valence electrons are bonded with less strength to the nucleus, then it simply contradicts the statement in the book. Even if there is a charge on the atom, why should the outer electrons be affected the most? Should they not be screened by the inner electrons?


P.S : I read that in JD Lee's "Concise inorganic chemistry". Chapter : Covalent Bond, Topic : d-orbital participation in hybridization.

[MrTeo]

Well... the valence electrons are bonded with less stength, and I don't think that even Mr. Lee could confute this... 
That's why they form bonds with other atoms (as you know you'll never see an inner electron of Na given to Cl...).

Talking of the question you asked, the outer electrons are obviously screened by the effect of the inner ones but that's why they're also easier to move from their original position... being less affected by the nucleus charge they don't have strong attraction or repulsion forces that would react against any kind of movement caused by the change of the atom's charge (think that even if the inner electrons are affected by this charge they don't move very closer as there are other stronger forces that prevent them from doing so). As I said their "potential energy hole" is not so deep and a new charge can cause them to move to another less energetic (in terms of potential energy) configuration. Maybe there's even a physical way to explain this... if i find it out i'll try to post it 

Obviously I'm not absolutely sure about what I'm saying so I'd like some other opinions from experienced chemists from the forum...
Perhaps I'm not expressing very well but the "core" of the matter should be the one I've told you...

[Schrödinger]

Talking of the question you asked, the outer electrons are obviously screened by the effect of the inner ones but that's why they're also easier to move from their original position... being less affected by the nucleus charge they don't have strong attraction or repulsion forces that would react against any kind of movement caused by the change of the atom's charge (think that even if the inner electrons are affected by this charge they don't move very closer as there are other stronger forces that prevent them from doing so). As I said their "potential energy hole" is not so deep and a new charge can cause them to move to another less energetic (in terms of potential energy) configuration.

Consider some atom with a d-orbital. Say P. Now, let's bond it to an atom that has greater electronegativity, say Cl. Consider PCl₅. Since there are Cl atoms attached to P, there is a slight positive charge accumulation on P, as Cl atoms attract the bond pair towards themselves. Thus, there is a size contraction in the 3s, 3p and 3d orbitals of P. But, this effect is greatest for 3d orbital(the outer orbital) according to Lee. Since energy of an orbital is directly proportional to the distance from the nucleus, the 3d orbital's energy can now become compatible(after contraction) with that of 3s and 3p in order to undergo hybridization.

This is what i don't get. Why should the effect be so pronounced on the 3d orbital, which is after all, diffused???

[MrTeo]

Oh right... so this is the situation, now it all seems more clear (to me at least  )

Anyway I don't think Lee's explanation of the phenomenon is very clear as we should consider just one small thing before talking of hybridization: it's a mathematical way to explain atomic phenomena and moreover it's not even the clearest way or the one which accords better to reality. Today chemists work mainly using MO theory that, while being less accessible that VB for the students it describes better the extremely difficult behaviour of the electrons in the atom, especially in the form of a strong ionic bond like the one you talk about.

In fact PCl₅ is one of the molecules that show the limits of this sort of description: as you pointed out you can't understand why these orbitals contract more than the others. This is an explanation found out to justify the fact that, with their original energies the orbitals wouldn't hybridize so the largest orbital needs to decrease its size (and energy) to get in touch with the others. I know i may sound a bit boring repeating again this but the fact that P is bonded to 5 Cl atoms and that the whole molecule has a bipyramidal structure makes us think that the only way (according to VB) to realize that geometry is to have a sp³d hybridization. We could say (obviously I'm only trying to explain this fact better) that this is a sort of "stratagem" to interpretate reality (which is as usual our touchstone of theoretical approach). Don't be disappointed but you seem to stumble always upon this sort of matters  () and this is quite interesting because remembers me my way to study chemistry, trying to understand deeply the phenomenon, independently from what the book wants to prove, trying to understand "why that happens" and not only to convince me "that happens".

If you need any more help feel free to ask again... but let me tell you just another example of how VB fails to describe even the most common properties of molecules. Take O₂: to explain its paramagnetic properties scientists hypothesized a 3-electron bond (and this is really strange for O) which was only a way to fit a property which didn't accord to the theory introducting a new kind of bond (a stratagem, as I said). MO theory doesn't need to do this: its Aufbau of the O₂ molecule shows that there are two unpaired electrons (disposed according to Hund principle which is still applied) in the external orbitals which give O₂ its characteristics.

My only advice is that you try to read something (and if you've already studied it try to deepen your knowledge of this field) about MO, I found it just great and even it is quite different in its approach you'll find it's just great the way how the molecules are described: organic and comprehensive (obviously it isn't perfect, new kinds of bonds need to be found out to justify some structures such as the diborane of the HF₂^- which I already cited but it's the best we have for now  )

[Schrödinger]

Yeah you're right. Probably this is a fact scientists would have stumbled upon while thinking of PCl₅'s structure. We should indeed try to explain why a certain event occurs and not reason out for those that don't occur . Thanks again mate!!