Classical/empirical potential for electron-ion interactions

[feynman1]

LJ potential is an empirical potential function used between 2 neutral atoms. Is there any classical/empirical potential for electron-ion interactions as well? Different from Coulomb potential, this one if any should be able to capture the mechanism of a valence electron leaving an atom and of preventing a valence electron from hitting a nucleus.

 

[mfb]

This should simply be the shielded potential of the nucleus, as the electron is unbound and the direct potential term will dominate.

 

[feynman1]

Thanks. How is shielded potential of the nucleus expressed?

 

[nasu]

Thanks. How is shielded potential of the nucleus expressed?

Why should the electron be prevented from "hitting" the nucleus?

 

[feynman1]

Why should the electron be prevented from "hitting" the nucleus?

A valence one can at most stay on the outermost layer let alone hitting the centre.

 

[mfb]

Thanks. How is shielded potential of the nucleus expressed?

Here are some references

 

[nasu]

A valence one can at most stay on the outermost layer let alone hitting the centre.

Have you ever seen an image of probability distribution for s-type orbitals? Electrons in atoms are described by quantum mechanics. They don't sit on layers like books in the library.

 

[feynman1]

Have you ever seen an image of probability distribution for s-type orbitals? Electrons in atoms are described by quantum mechanics. They don't sit on layers like books in the library.

Yes. Any emperical potential (well) able to describe such s type 'bonding' between an electron and ion?

 

[feynman1]

Here are some references

Thanks but I didn't find any help from there talking about any potential function

 

[nasu]

Yes. Any emperical potential (well) able to describe such s type 'bonding' between an electron and ion?

These are obtained by solving Schroedinger equation with Coulomb potential. Is done (for hydrogen atom) in introductory QM courses.

 

[feynman1]

These are obtained by solving Schroedinger equation with Coulomb potential. Is done (for hydrogen atom) in introductory QM courses.

OK, I actually was looking for a potential that works in classical mechanics, namely some potential+'F=ma'

 

[hutchphd]

You do understand that it wasa atomic OK, I actually was looking for a potential that works in classical mechanics, namely some potential+'F=ma'

God luck with that...
You do understand that it was problems with atomic physics that precipitated the invention of Quantum Mechanics? The best you can do is some sort of mean firld theory (which is Hartree-Fock as I recall)

 

[feynman1]

God luck with that...
You do understand that it was problems with atomic physics that precipitated the invention of Quantum Mechanics? The best you can do is some sort of mean firld theory (which is Hartree-Fock as I recall)

Yes I knew thanks. Wasn't looking for any precise QM theory.

 

[hutchphd]

More than you want to know !:
https://en.wikipedia.org/wiki/Density_functional_theory

 

[feynman1]

More than you want to know !:
https://en.wikipedia.org/wiki/Density_functional_theory

Thanks, though indeed more than I want to know.