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

[Mazzur]

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!

 

[ansgar]

hint: change of basis

 

[Mazzur]

hint: change of basis

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

 

[mccoy1]

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.