LREAL
LREAL = .TRUE. | .FALSE. | On (or O) | Auto (or A)
Default: LREAL = .FALSE.
Description: LREAL determines whether the projection operators are evaluated in real-space or in reciprocal space.
| LREAL=.FALSE. | projection done in reciprocal space |
| LREAL=.TRUE. | projection done in real space, (old, superseded by LREAL=O) |
| LREAL=On or O | projection done in real space, projection operators are re-optimized |
| LREAL=Auto or A | projection done in real space, fully automatic optimization of projection operators (no user interference required) |
The non local part of the pseudopotential requires the evaluation of an expression:
- [math]\displaystyle{ \sum_{ij}D_{ij}|\beta_j\rangle\langle\beta_i|\psi_{n\mathbf{k}}\rangle }[/math].
where the "projected wavefunction character" is defined as:
- [math]\displaystyle{ \begin{align}C_{in\mathbf{k}}=\langle\beta_i|\psi_{n\mathbf{k}}\rangle &=\frac{\Omega}{N_{\rm FFT}}\sum_{\mathbf{r}}\langle\beta_i|\mathbf{r}\rangle\langle\mathbf{r}|\phi_{n\mathbf{k}}\rangle=\frac{\Omega}{N_{\rm FFT}}\sum_{\mathbf{r}}\beta(\mathbf{r})\phi_{n\mathbf{k}}(\mathbf{r}) \\ &=\sum_{\mathbf{G}}\langle\beta_i|\mathbf{k}+\mathbf{G}\rangle\langle\mathbf{k}+\mathbf{G}|\phi_{n\mathbf{k}}\rangle=\sum_\mathbf{G}\bar\beta(\mathbf{k}+\mathbf{G}) C_{\mathbf{G}n\mathbf{k}}\end{align} }[/math]
This expression can be evaluated in reciprocal or real space: