[msk034]

With all due apology...

If two filled orbitals (say, 2 helium atoms), are getting close - how do the orbitals behave? Ultimately, upon formation of Beryllium, they will transform into 1S and 2S, but, from the other side, the orbitals cannot start to mix right away, when they only start to feel each other - simply because of e-e coupling inside each orbital (about 0.7 eV in H-).

So, will it be right to say that the orbitals - like water drops - first deform and repel each other, and when pressure becomes high enough - or when nuclei come close enough - they collapse - again like drops - to  form 2 new prototypic 1S and 2S orbitals?

To put it differently:     
Is there any closeness region where orbitals do not mix, but instead try to avoid each other and do not penetrate into each other (region of 0 penetration )? Any reference to reseach /experiment done on this, please?

[Corribus]

Let's start with: Orbitals aren't real. They are mathematical constructs used to predict/describe characteristics of electrons. The general first approximation approach is usually to build one electron molecular orbitals from linear combinations of (one electron) atomic orbitals, as a function of a separately determined nuclear potential, and then fill in additional electrons. Important electron-electron interaction terms are then added on after the fact.

So, the answer is that orbitals aren't things that actively respond to external stimuli. This kind of language is frequently used in casual conversation but it's an inaccurate representation of what orbitals actually are and what they're used for. (I.e., the orbitals themselves don't mix. We mix them to obtain new orbitals that give a better representation, or prediction, of experimental data.)

[msk034]

That's a valuable point, thank you. Still, the  He + He model is itself oversimplification, so whatever we call the space occupied by the 2 electrons on each atom...

Will they form and maintain a zero-density area (rather layer or surface) upon pressing against each other?

[Irlanur]

any situation where nuclei come close enough together that interactions other than electromagnetic ones become important are not treated in quantum chemistry. Ask that question in a nuclear physics forum.

[Enthalpy]

What is "real" is more a philosophical question... But I'd say at least that orbitals are concrete, and we have clear pictures of them that help our representation a lot. The tunnel and atomic force microscopes have made tangible what was very abstract for the founders of QM:
http://www.zurich.ibm.com/st/atomic_manipulation/pentacene.html
http://en.wikipedia.org/wiki/Olympicene
and the same set of electrons at the microscope's tip and the pictured molecule interact over their whole extension simultaneously (...but with all their charge, mass etc concentrated at each possible location, complicated world).

A location between two helium atoms with zero electron density? I'd rather say no. The orbitals mix as the atoms get close, making a bonding one and an antibonding one. What's special here is that the number of electrons fills them all, so the favourable energy of the bonding molecular orbital is compensated by the unfavourable energy of the antibonding orbital. But the bonding molecular orbital must bring electron density between the atoms.

Well, antibonding compensating bonding would be if they simply added and subtracted as the simplified representation would like them to do. Electrons respond more finely: for instance, if you find one electron in a smaller volume (that is, destroy the orbital) by some other means, then you unlikely find an other electron in that smaller volume because they repel an other; this arrangement lets the set of electrons adopt a more favourable configuration globally, and pemits helium atoms to attract an other at some distances (van der Waals) and make a liquid.