Modes

In the PAW approximation, we need to describe smooth valence states:

gpaw/wavefunctions/pw.py

\[\tilde\psi(\mathbf{r}) = \sum_{G^2/2<E_c} c_\mathbf{G} e^{i\mathbf{G}\cdot\mathbf{r}}\]

gpaw/wavefunctions/lcao.py

\[\tilde\psi(\mathbf{r}) = \sum_{a\mu} c_{a\mu} \Phi_{a\mu}(\mathbf r - \mathbf R_a)\]

gpaw/wavefunctions/fd.py

\(N_1 \times N_2 \times N_3\) grid-points:

\[\tilde\psi(\mathbf{r}_{ijk}) = \tilde\psi_{ijk},\]
\[\mathbf{r}_{ijk} = \frac{i}{N_1}\mathbf{a}_1 + \frac{j}{N_2}\mathbf{a}_2 + \frac{k}{N_3}\mathbf{a}_3\]