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PHY.K02UF Molecular and Solid State Physics

## Overlap matrix S

This page calculates the elements of the overlap matrix $S_{ij}=\langle \phi_i|\phi_j\rangle$ where $\phi_i$ and $\phi_j$ are atomic orbitals.

Choose the atomic orbitals

$\phi_i$
$\phi_j$

$\phi_i =$ $\phi_{1\text{s}}$, $\phi_j =$ $\phi_{1\text{s}}$

Set the positions and the effective nuclear charges.
$x_i=$ m, $y_i=$ m, $z_i=$ m, $Z_i=$,
$x_j=$ m, $y_j=$ m, $z_j=$ m, $Z_j=$.

The script that is generated uses Monte Carlo integration to perform the integration. This is not a particularly numerically efficient method but it is easy to program. If the 'Execute' button is pressed several times, the calculated overlap integral will be slightly different every time due to the random numbers used in Monte Carlo integration. More accuracy can be obtained by increasing the number of random points N. Press the 'Execute' button after modifying the code in the left text box.