What is the Relationship Between Atomic Orbitals in Polyelectronic Atoms?

[LogicX]

So we've all seen the pictures of orbitals in chemistry textbooks. You know, the sphere for an s orbital, the two balloons for a p orbital, etc. But they always present these models as independent systems. No one has ever told me what the orbitals look like (and yes I know that an orbital is just a an area probabilistic chance of finding an electron) when you have an s and a p orbital. Because from what I can remember, in a p orbital you don't get a node until the nucleus. So does it penetrate into the sphere of the s shell?

What about when you have multiple p orbitals in elements with higher principle quantum numbers? Do all the s orbitals stack on top of each other like concurrent spheres?

Or maybe the hydrogen atom model is not what is actually happening in polyelectronic atoms? But we still use these shapes to describe their orbitals so it must have some relation to how the electrons exist in these atoms.

I'm just a little puzzled and curious as to why no one ever taught me this, for all the time that we have spent on orbitals.

 

[Borek]

does it penetrate into the sphere of the s shell?

Yes, they coexist in the same space.

There is a little bit more to it. When there are more electrons, they repulse each other, so shapes shown for hydrogen atoms become just an approximation, but a good one. We don't know exact solutions of the Shroedinger equation for other atoms, only for hydrogen like ions.

 

[ZealScience]

In what I've learnt, the areas have some intersections, that's why there are lots of mutual shielding effect.

 

[That Neuron]

I was taught that orbitals were (like bohr's model) defined at certain inflexible points, but really that doesn't make sense, because if orbitals were not at least affected by electronegativity, water wouldn't be polar.

So are s, p d f orbitals shapes given primarily by electromagnetism or by the predisposed orbital shapes?

 

[Borek]

No idea what the question is. Orbital shapes are given by the solution of Schroedinger's equation.

 

[That Neuron]

No idea what the question is. Orbital shapes are given by the solution of Schroedinger's equation.

Ok, but to what extent does electric charge play a role in it?

 

[Borek]

Decide if you are asking about electronegativity, electromagnetism or electric charge - you mentioned all three in two posts.

Schroedinger equation takes only electrostatic interactions into account.

 

[That Neuron]

Sorry, I simply used (stupidly) electronegativity and electromagnetism as a substitute for electrostatic behaviors. I understand that electronegativity at least is simply an upgraded form of electrostatic behaviors... I just confused them in my mind for some reason.

"Schroedinger equation takes only electrostatic interactions into account."

How? just curious.

 

[Borek]

Shroedinger equation is used to calculate total energy of the system. Total energy is sum of kinetic energy and potential energy. Schroedinger equation contains two sections - one for the kinetic part and one for potential part. Kinetic energy is that of moving electrons and nuclei, potential energy is that of coulombic forces between charged particles (all electrons and all nuclei in the system). Nothing else is taken into account (which is an approximation, but in most cases good enough to yield correct results).

System can be anything from an atom with a single electron to a large molecule like protein, or even system of many molecules.

This is so oversimplified, I should ban myself for this post.

 

[kjohnson]

This is so oversimplified, I should ban myself for this post.

haha this cracked me up

 

[juanrga]

So we've all seen the pictures of orbitals in chemistry textbooks. You know, the sphere for an s orbital, the two balloons for a p orbital, etc. But they always present these models as independent systems. No one has ever told me what the orbitals look like (and yes I know that an orbital is just a an area probabilistic chance of finding an electron) when you have an s and a p orbital. Because from what I can remember, in a p orbital you don't get a node until the nucleus. So does it penetrate into the sphere of the s shell?

What about when you have multiple p orbitals in elements with higher principle quantum numbers? Do all the s orbitals stack on top of each other like concurrent spheres?

Or maybe the hydrogen atom model is not what is actually happening in polyelectronic atoms? But we still use these shapes to describe their orbitals so it must have some relation to how the electrons exist in these atoms.

I'm just a little puzzled and curious as to why no one ever taught me this, for all the time that we have spent on orbitals.

An atomic orbital (AO) is obtained from the one-electron Hidrogen-like wavefunction. In a crude approximation electrons can be taken to be non-interacting in a poli-electronic atom and then the AO describing each electron just coexist (electrons are independent in this model).

In a more realistic model, electrons in a poli-electronic atom are not described by atomic orbitals but by the poli-electronic wavefunctions. Those wavefunctions are routinely obtained using the methods of computational quantum chemistry, but are not 3-dimensional functions and, therefore, cannot be represented by 3-dimensional shapes as the AOs. For Carbon its electronic wavefunctions are 18-dimensional function (ignoring spin), if I am not wrong.