Classical/empirical potential for electron-ion interactions

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Discussion Overview

The discussion revolves around the exploration of classical or empirical potentials for electron-ion interactions, particularly in contrast to the Coulomb potential. Participants are interested in understanding how such potentials might capture the dynamics of valence electrons in atoms, including their behavior in relation to the nucleus.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant inquires about the existence of a classical/empirical potential for electron-ion interactions, distinct from the Coulomb potential.
  • Another participant suggests that the shielded potential of the nucleus could serve this purpose, asserting that the direct potential term would dominate for unbound electrons.
  • Several participants express curiosity about how the shielded potential of the nucleus is mathematically expressed.
  • There is a discussion regarding the concept of electrons "hitting" the nucleus, with some participants arguing that valence electrons are constrained to the outermost layers of an atom.
  • One participant emphasizes that electrons are described by quantum mechanics and do not occupy fixed layers, referencing the probability distribution of s-type orbitals.
  • Another participant asks if there is an empirical potential that can describe the bonding between an electron and an ion, specifically in a classical context.
  • Responses indicate that solutions to the Schrödinger equation with Coulomb potential are typically used in quantum mechanics, particularly for hydrogen atoms.
  • One participant expresses a desire for a potential that operates within classical mechanics, prompting a response about the historical context of atomic physics and the development of quantum mechanics.
  • There is mention of mean field theory, specifically Hartree-Fock, as a possible approach to the problem.
  • Links to density functional theory are provided, though one participant notes that the information may be more than they were seeking.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence or formulation of a classical/empirical potential for electron-ion interactions. Multiple viewpoints are presented regarding the nature of electron behavior and the applicability of classical mechanics versus quantum mechanics.

Contextual Notes

The discussion highlights limitations in the understanding of electron behavior in classical terms, with references to quantum mechanics and the historical challenges that led to its development. There are unresolved questions regarding the mathematical expression of shielded potentials and the nature of electron bonding.

feynman1
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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.
 
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This should simply be the shielded potential of the nucleus, as the electron is unbound and the direct potential term will dominate.
 
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Thanks. How is shielded potential of the nucleus expressed?
 
feynman1 said:
Thanks. How is shielded potential of the nucleus expressed?
Why should the electron be prevented from "hitting" the nucleus?
 
nasu said:
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.
 
feynman1 said:
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.
 
nasu said:
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?
 
mfb said:
Here are some references
Thanks but I didn't find any help from there talking about any potential function
 
  • #10
feynman1 said:
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.
 
  • #11
nasu said:
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'
 
  • #12
feynman1 said:
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)
 
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  • #13
hutchphd said:
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.
 
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