[Acidman]

Please view the attached image.

[Acidman]

What I'm asking is, why is the σ1s molecular orbital is just around the 2 nucleus. Why isn't also in-between them ? Like this :

[Borek]

I am not sure what your question is. If the orbital surrounds both nuclei it definitely exists between them as well.

[ATMyller]

The orbital is an abstraction. The electrons can be anywhere inside the orbital sphere, they are not limited to the outer circle.

[Acidman]

An orbital is the place where there is the highest probability of finding an electron. Molecular orbital theory says that new type of orbitals are formed when 2 nuclei come nearer. If we consider two 1s orbitals of some atom combine to form σ1s molecular orbital. Then my question is why does electrons tend to be present more around the nuclei than between the two nuclei ? For example, p-orbital is depicted to be dumbbell shaped. That is, electron tends to be present along that shape more than any other area in the atom. So its is normally depicted that σ1s molecular orbital is around the two nuclei. But the attraction force on an electron by the nuclei is strongest between the two nuclei. So why isn't the molecular orbital present there too ?

[Acidman]

Ok... I understand now. I thought that orbital meant only those boundaries. Now I understand that they can be present anywhere inside the orbital. 

Thanks, ATMyller and Borek.

[Acidman]

Next doubt is:

Molecular orbital theory says that atomic orbitals for the atoms approaching for bonding overlap to undergo constructive and destructive interference to form molecular orbitals.

Let us consider 2 Hydrogen atoms approaching each other for bonding. They have only one electron in 1s orbital. So how can they form both constructive and destructive molecular orbitals ? I think they can only form only one of those. But according to the theory it forms both. So how is this possible ?

[mjc123]

Two atomic orbitals combine to make two molecular orbitals, that's how it works. Of course, they don't have to be both occupied, and in H₂ only the bonding orbital is occupied.
Compare the H atom - it has not only the 1s orbital, but 2s, 2p, 3s etc. When the electron is in the 1s, the other orbitals don't physically exist, but they represent stable solutions of the Schrodinger equation - they are energy levels that an electron can occupy for a finite time, and can undergo transitions between them, as observed in the spectrum of atomic H. So with a molecule like H₂; the molecular orbitals are solutions of the SE for the molecule, and can be described as combinations of atomic orbitals.

[Acidman]

How can 2 atomic orbitals combine to give 2 molecular orbitals
If 2 H atoms are approaching, and if their electron's waves are in-phase then they combine constructively to form one bonding molecular orbital. Now from where can another molecular orbital be formed ?

[mjc123]

By combining constructively and destructively. σ_A+σ_B is the bonding MO and σ_A-σ_B is the antibonding orbital. You start with two orbitals, you end with two. That's the rule - n atomic orbitals combine to give n molecular orbitals. Think of the Pauli principle; an orbital can be occupied by no more than 2 electrons. Where can the (potentially) 2n electrons from the n atomic orbitals go?

[Acidman]

I think pauli's rule applies to only atomic orbitals.
Take N₂ as an example. Each N atom has 1s² 2s² 2p³ configuration. So I think their 2p orbitals combine to form a molecular orbital and share 3 electrons so that both the Nitrogen atoms achieve octet. So why is another molecular orbital required ?
 Their electrons can have only one wave, they should either be constructive or destructive and they can not be both. So then they must form only one molecular orbital, right ?

[Irlanur]

It's always the same confusion, and the confusion HAS to come up, given the way MO-theory is usually taught.

consider this.

- The atomic orbitals of the H-atom are exact analytical solutions to the Schrödinger equation (Wavefunctions).
-even for helium, such an analytical solution does not exist, because it's a many-body problem.
-orbitals in many-body systems are one-electron wavefunctions. They are only a mathematical help. The true wavefunction can never be expressed as a product of one-electron functions, nevertheless it's done.
-don't be confused by MO-theory, if you never had the math/physics for it. just learn the rules (or don't...) and don't try to interpret too much, it will most probably be wrong anyway.

[Acidman]

I have to somehow understand this. Even if I don't have the maths/physics for it some one else can have that. And that someone maybe can explain me. And in hope that someone will explain this to me, I've posted my doubt here....

[mjc123]

You can't really understand it without the maths/physics that you will learn if you study chemistry or physics at university. (If anyone can be said to understand it, as distinct from merely knowing the solutions to the equations. I don't claim to.) Any hand-waving explanation we try to give at this level (or indeed undergraduate level), some quantum physicist will pop up and say "that's not true". And it isn't really, it's just a model to try and help us understand. But lots of things in quantum mechanics have no analogue in classical physics, so any mental model we construct in terms of familiar things will necessarily be inadequate.

I think pauli's rule applies to only atomic orbitals.

No, it applies to MOs as well. Of course the "four quantum numbers" of an electron in an atom are not directly applicable to MOs, but the general principle still applies. Two electrons can have the same spatial wavefunction (i.e. "occupy the same orbital") only if their spins are opposite. So no more than two per orbital. This is a consequence of the fundamental properties of fermions (particles with half-integral spin); one of those things with no classical analogue.
Why do you think He₂ doesn't exist? If two 1s atomic orbitals, each with 2 electrons, can form one MO, to which Pauli's principle doesn't apply, why can't you get 4 electrons in a bonding MO and form a really strong bond? The answer is that Pauli does apply; the 2 AOs combine to give 2 MOs, one bonding and one antibonding, each filled with 2 electrons, so there is no overall bonding.
Another approach to the question is via symmetry. Any solution to the Schrodinger equation - any permissible electron wavefunction - must conform to the symmetry of the molecule. For H₂, for example, this means, among other things, that it must be either symmetrical or antisymmetrical with respect to interchange of the H atoms. Now the individual atomic orbitals, 1s_A and 1s_B, do not satisfy this criterion - they transform into each other, not plus or minus themselves. However, we can form molecular orbitals that satisfy the symmetry by linear combination of the atomic orbitals; in this case (1s_A + 1s_B) and (1s_A - 1s_B). The former has lower energy than the atomic orbitals, and the latter higher, so the two electrons go into the bonding MO and form a stable bond. Note that the output of this mathematical process is always the same number of orbitals as you put in; that's how it works.

Their electrons can have only one wave, they should either be constructive or destructive and they can not be both. So then they must form only one molecular orbital, right ?

Distinguish between electrons and orbitals. Electrons are real physical things [some might dispute this statement], orbitals are not; they are mathematical abstractions, possible states that an electron might occupy. So two actual electrons in an actual molecule may interfere either constructively or destructively, but not both at the same time. But both possibilities exist - that, in a sense, is what we mean by saying "the two AOs form two MOs". And spectroscopy demonstrates that electrons can and do occupy these other states (however briefly), and undergo transitions between them. So in that sense all these other orbitals are "real".
I hope all this is at least some help, not just a load of mumbo-jumbo.