Overlap integrals: What are they and how do we arrive at the formula?

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Discussion Overview

The discussion revolves around the concept of overlap integrals, specifically what they represent and how the formula for calculating them is derived. The scope includes theoretical aspects and conceptual clarification related to atomic orbitals and molecular orbitals.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant seeks a clear understanding of what the overlap integral of two functions signifies and the reasoning behind it.
  • Another participant suggests that the concept relates to a "change of basis," though this is not elaborated upon.
  • A later reply clarifies that the basis refers to atomic orbitals used to construct molecular orbitals and explains that overlap integrals measure the interaction between a nucleus and electron density centered on another nucleus.
  • The same reply proposes that the formula for overlap integrals can be derived by considering the linear combination of atomic orbitals.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express varying levels of understanding and knowledge about the concept of overlap integrals and related terms.

Contextual Notes

Some assumptions about the definitions of terms like "basis" and "atomic orbitals" are not fully explored, which may limit understanding. The discussion also reflects varying familiarity with the mathematical framework involved.

Mazzur
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Hey I've been looking all over the web and I can't find any comprehensible information on overlap integrals. What does the overlap integral of two functions give us? And why?

Thanks in advance!
 
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hint: change of basis
 
ansgar said:
hint: change of basis

lol sorry - I don't have a clue what the basis even refers to...
 
Mazzur said:
lol sorry - I don't have a clue what the basis even refers to...

Basis(basis set) = atomic orbitals from which the MO is built.
So overlap integrals is a measure of the interracton between a nucleus and electron density centred on the other nucleus . Note that this is just partial example of what overlap integral is.
I guess we arrive at the formula by considering the fact that atomic orbitals can be combined linearly.
 

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