Overlap integral

In quantum chemistry , the overlap integral denotes the scalar product of the square-integrable functions in the Hilbert space . It is a measure of the overlap between two wave functions ( orbitals , "electron clouds").

${\displaystyle S_{\mu \nu }=\int \phi _{\mu }^{*}({\vec {r}})\;\phi _{\nu }({\vec {r}})\;\mathrm {d} {\vec {r}}}$

The elements behave like the elements of a Hermitian matrix S . ${\displaystyle S_{\mu \nu }}$