pythtb.WFArray.Mmn

property WFArray.Mmn

The overlap matrix of the wavefunctions.

The overlap matrix is defined as

\[M_{mn}^{(\mathbf{b})}(\mathbf{k}) = \langle u_{m,\mathbf{k}} | u_{n,\mathbf{k}+\mathbf{b}} \rangle\]

where \(\mathbf{b}\) is a vector connecting nearest neighbor k-points in the mesh. Here, the neighboring k-points are computed in Cartesian space.

Returns:

np.ndarray

The overlap matrix of the wavefunctions. Shape is (*shape_mesh, nnbrs, nstates, nstates).

Raises:

ValueError

If the wavefunctions are not initialized or if the mesh is not a regular grid.

Notes

• The overlap matrix is only defined for regular grids in k-space.

• The overlap matrix is computed using the Cartesian metric by default. To compute the overlap matrix using reduced neighbors, use overlap_matrix() with use_k_metric=False.