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	projection done in real space, (old, superseded by LREAL=O)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

${\begin{aligned}C_{in\mathbf {k} }=\langle \beta _{i}|\psi _{n\mathbf {k} }\rangle &={\frac {\Omega }{N_{\rm {FFT}}}}\sum _{\mathbf {r} }\langle \beta _{i}|\mathbf {r} \rangle \langle \mathbf {r} |\phi _{n\mathbf {k} }\rangle ={\frac {\Omega }{N_{\rm {FFT}}}}\sum _{\mathbf {r} }\beta (\mathbf {r} )\phi _{n\mathbf {k} }(\mathbf {r} )\\&=\sum _{\mathbf {G} }\langle \beta _{i}|\mathbf {k} +\mathbf {G} \rangle \langle \mathbf {k} +\mathbf {G} |\phi _{n\mathbf {k} }\rangle =\sum _{\mathbf {G} }{\bar {\beta }}(\mathbf {k} +\mathbf {G} )C_{\mathbf {G} n\mathbf {k} }\end{aligned}}$

This expression can be evaluated in reciprocal or real space:

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