calculateHamiltonianAndOverlap¶

Usage Examples¶

Evaluate a simple molecular system:

hamiltonian, overlap = calculateHamiltonianAndOverlap(molecule_configuration)

Evaluate a bulk system in a non-Gamma kpoint:

hamiltonian, overlap = calculateHamiltonianAndOverlap(bulk_configuration, kpoint=(0.1, 0.0, 0.0))

Notes¶

• Calculates Fourier transformed Hamiltonian, \(H({\bf k})\) and overlap matrix \(S({\bf k})\). The real space Hamiltonian is defined by \(H_{ij} = \langle \phi_i | \hat{H}_{1el} | \phi_j \rangle,\) and the overlap matrix \(S_{ij} = \langle \phi_i | \phi_j \rangle\), where \(\phi_i\) are the basis functions. The Fourier transform is obtained by summing over all the cells in the periodic system

  \[M({\bf k})_{\mu \nu} = \sum_{\bf R} M_{(\mu, {\bf 0}),(\nu, {\bf R})} e^{i {\bf k} \cdot {\bf R}},\]

  where \({\bf R}\) is given relative to the central cell, \({\bf R}={\bf 0}\).

• The calculator must be density matrix-based for this function to perform successfully.

• Consider Note on Spin in low level interface functions for details on how to handle the spin parameter.