Calculating t in LCAO

Physics Q&A
1

I don’t understand the derivation of t in the lecture notes of the LCAO model.
We have
t=-\langle 1|H|2\rangle = -\langle 1| K +V_1+V_2| 2\rangle = - \langle 1|V_1|2\rangle
I don’t understand how we get the last similarity. Thank you

2

To cancel the extra terms we use that

(K + V_2)|2\rangle = E_0 |2\rangle

and that \langle 1 | 2 \rangle \approx 0.

Opening the brackets then gives the desired result.