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.

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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	projection done in real space, (old, superseded by LREAL=O)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:

$\sum_{ij}D_{ij}|\beta_j\rangle\langle\beta_i|\psi_{n\mathbf{k}}\rangle$.

where the "projected wavefunction character" is defined as:

$\begin{align}C_{in\mathbf{k}}=\langle\beta_i|\psi_{n\mathbf{k}}\rangle &=\frac{\Omega}{N_{\rm FFT}}\sum_{\mathbf{r}}\langle\beta_i|\mathbf{r}\rangle\langle\mathbf{r}|\phi_{n\mathbf{k}}\rangle=\frac{\Omega}{N_{\rm FFT}}\sum_{\mathbf{r}}\beta(\mathbf{r})\phi_{n\mathbf{k}}(\mathbf{r}) \\ &=\sum_{\mathbf{G}}\langle\beta_i|\mathbf{k}+\mathbf{G}\rangle\langle\mathbf{k}+\mathbf{G}|\phi_{n\mathbf{k}}\rangle=\sum_\mathbf{G}\bar\beta(\mathbf{k}+\mathbf{G}) C_{\mathbf{G}n\mathbf{k}}\end{align}$

This expression can be evaluated in reciprocal or real space:

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