Default | ||

LREAL | = | .FALSE. |

.FALSE. | projection done in reciprocal space |

.TRUE. | projection done in real space, (old, superseded by LREAL=O) |

On or O | projection done in real space, |

projection operators are re-optimized | |

Auto or A | projection done in real space, |

fully automatic optimization of projection operators | |

no user interference required |

Determines whether the projection operators are evaluated in
real-space or in reciprocal space:
The non local part of the pseudopotential requires the
evaluation of an expression
.
The ``projected wavefunction character'' is defined as:

This expression can be evaluated in reciprocal or real space: In reciprocal space (second line) the number of operations scales with the size of the basis set (i.e. number of plane-waves). In real space (first line) the projection-operators are confined to spheres around each atom. Therefore the number of operations necessary to evaluate one does not increase with the system size (usually the number of grid points within the cut-off-sphere is between 500 and 2000). One of the major obstacles of the method working in real space is that the projection operators must be optimized, i.e. all high frequency components must be removed from the projection operators. If this is not done 'aliasing' can happen (i.e. the high frequency components of the projection operators are aliased to low frequency components and a random noise is introduced).

Currently VASP supports three different schemes to
remove the high frequency components from the projectors.
`LREAL` = .TRUE. is the simplest one. If `LREAL` = .TRUE. is selected,
the real space projectors which have been generated by the pseudopotential generation
code are used. This requires no user interference.
For `LREAL` = On the real space projectors are optimized by VASP using an
algorithm proposed by King-Smith et al.[47]. For
`LREAL` = Auto a new scheme [48] is used which is
considerably better (resulting in more localized) projector functions
than the King-Smith et al. method. To fine-tune the optimization
procedure the flag `ROPT` can be used
if `LREAL` = Auto or `LREAL` = On is used.

We recommend to use the real-space projection scheme for systems containing
more than 20 atoms. We also recommend to use only
`LREAL` = Auto (for version VASP.4.4 and newer releases) and
`LREAL` = On (for all other versions).
Version 4.4 also supports the old mode `LREAL`= O to
allow calculations that are fully compatible to VASP.4.3 (and VASP.3.2).
The best performance is generally achieved with `LREAL`= Auto, but
if performance is not that important you can also use `LREAL`=.TRUE. which
generally requires less user interference. You can skip the
rest of the paragraph, if you use only `LREAL`=.TRUE..

For `LREAL` = O and `LREAL` = A
the projection operators are optimized by VASP
on the fly (i.e. on startup). Several flags influence the optimization

`ENCUT`(i.e. the energy cutoff), components beyond the energy cutoff are 'removed' from the projection operators.`PREC`tag specifies how precise the real space projectors should be, and sets the variables`ROPT`accordingly to the following values:For

`LREAL`= On`PREC`= Low700 points in the real space sphere ( `ROPT`=0.67)`PREC`= Med1000 points in the real space sphere ( `ROPT`=1.0)`PREC`= High1500 points in the real space sphere ( `ROPT`=1.5)

For

`LREAL`= Auto`PREC`= Lowaccuracy ( `ROPT`=0.01)`PREC`= Medaccuracy 2 ( `ROPT`=0.002)`PREC`= Highaccuracy 2 ( `ROPT`=2E-4)

These defaults can be superseded by the line

ROPT = one_number_for_each_species

in the INCAR file. For instanceROPT = 0.7 1.5

will set the number of real space points within the cutoff sphere for the first species to approximately 700, and that for the second species to 1500. In VASP.4.4 alternatively the ``precision'' of the operators can be specified writing i.e.ROPT = 1E-3 1E-3

In that case the real space operators will be optimized for an accuracy of approximately 1meV/atom (). The ``precision'' mode works both for LREAL=On and LREAL=Auto (but to maintain compatibility with older VASP versions it is only selected if`LREAL`= Auto is specified in the INCAR file). The precision mode is generally switched on if the value for`ROPT`is smaller than 0.1. The ``precision'' mode and the conventional mode can be intermixed, i.e. it is possible to specifyROPT = 0.7 1E-3

in that case the number of real space points within the cutoff sphere for the first species will be approximately 700, whereas the real space projector functions for the second species are optimized for an accuracy of approximately 1 meV. We recommend to use the ``precision'' mode with a target accuracy of around eV/atom if your version supports this.If you use the mode in which the number of grid points in the real space projection sphere is specified, you have to select ROPT carefully, especially if a hard species is mixed with a soft species. In that case the following lines in the OUTCAR file must be checked (here is the output for

`LREAL`= On, but that one for`LREAL`= Auto is quite similar )Optimization of the real space projectors maximal supplied Q-value = 12.85 optimization between [QCUT,QGAM] = [ 4.75, 9.51] = [ 6.33, 25.32] Ry Optimized for a Real-space Cutoff 2.30 Angstroem l X(QCUT) X(cont) X(QGAM) max X(q) W(q)/X(q) e(spline) 0 9.518 9.484 -.004 18.582 .11E-03 .16E-06 0 -2.149 -2.145 .001 3.059 .17E-03 .25E-06 1 8.957 8.942 .003 9.950 .14E-03 .34E-06 1 1.870 1.870 .001 1.837 .95E-03 .51E-06 2 3.874 3.866 .000 4.764 .15E-03 .68E-07

The meaning of`QCUT`and`QGAM`is explained in Sec. 11.5.6. The most important information is given in the column`W(q)/X(q)`(respectively the column`W(low)/X(q)`for`LREAL`= Auto). The values in these columns*must*be as small as possible. If these values are too large, increase the ROPT tag from the default value. As a rule of thumb the maximum allowed value in this column is for`PREC`= Med. (For`PREC`= Low errors might be around and for`PREC`= High errors should be smaller than ). If`W(q)/X(q)`is larger than the errors introduced by the real space projections can be substantial. In this case`ROPT`*must*be specified in the INCAR file to avoid incorrect results. If the new precision mode is used in VASP.4.4 (`ROPT`0.1) the code automatically selects the real-space cutoff so that the required precision is reached.

A few comments for non-experts and experts:
Real space optimization (`LREAL` = .TRUE., `LREAL` = On or `LREAL` = Auto)
always results in a small (not necessarily negligible)
error (the error is usually a constant energy shift for each atom).
If you are interested in energy differences of a few
meV use only calculations with the *same setup* (i.e. same `ENCUT`,
`PREC`, `LREAL` and `ROPT` setting) for
all calculations.
For example, if you want to calculate
surface energies recalculate the bulk groundstate energy with
exactly the same setting you are going to use for the surface.
Another possibility is to relax the surface
with real space projection, and to do one final
total energy calculation with `LREAL` = .FALSE. to get exact energies.
Anyway, for `PREC` = Med, the errors introduced by the real space
projection are usually of the same order magnitude as those introduced
by the wrap around errors.
For `PREC` = High errors are usually less than meV. `PREC` = Low
should be used only for high speed MD's,
if computer resources are really a problem.

A few notes for experts: There are three parameters for the
real space optimization (see Sec. 11.5.6).
First the energy-cutoff (equivalent to `QCUT` in Sec. 11.5.6)
then a value which specifies from which energy-cutoff the
projection operator should be zero
(equivalent to `QGAM` in Sec. 11.5.6)
and the maximal radial extend of the real space projection operator
(equivalent to `RMAX` in Sec. 11.5.6).
The first parameter `QCUT` is fixed by the energy cutoff, the second one
is set to `QGAM`=2*`QCUT` for `PREC` = Low and `PREC` = Med,
and to `QGAM`=3*`QCUT` for `PREC`= High.
Finally the maximal radial extend of the projector functions is determined by `ROPT` (respectively
by `PREC` if `ROPT` is not specified in the INCAR file).