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Linear Scaling

Tails

Ignore function tails. By default no tails are ignored. Both CPU time and disk space can be saved by using the TAILS option. This option is most effective when combined with the Confine suboption, as explained in the Examples document.

TAILS {bas crbas} (core crcore) {fit crfit}

One real argument for keys basis and core, which should be a small value; default crbas=1e-6. The core criterion defaults to the bas criterion (if set). The tail criterion specifies that tails of exponentially decaying (basis) functions are ignored, in the construction of Bloch functions, beyond the point where the remaining part of the function tail (radially) integrates to less than the criterion, relative to the integral of the function from zero to infinity. Also for the fit one can specify a cutoff, but this is turned of by default: crfit=1e-15. Here we advise to use a more strict criterion than for crbas (because the fit is usually much more dependent than the basis). This option has some refinements. For example

Tails confine=1e-2 bas=1e-5 Rosa

As you see there are two new elements ('confine' and 'Rosa'). The first (confine =) specifies that all basis functions are optimized for the tails option, by multiplying the tail of the function with a rapidly decaying function. This step affects the shape of all functions outside the radius where the relative norm of the function is smaller than 1e-2. The effects on the shape of the functions are typically very small. The second new entry (Rosa) has the effect that the criterion becomes more strict for tight functions. For safer (but slower) calculations, specify smaller values for confine and bas, such as confine=1e-3 bas=1e-6.

The "Rosa" key works as follows. Determine the radius R where according to the normal criterion the function is negligible. Next substitute R -> R + 3*exp(-R/3). This means that for tight functions the tails radius is replaced by 3, and for diffuse functions this modifier has no effect.

Tentatively, based on the work by Rosa Bulo, we suggest to use

Tails bas=1e-3 Rosa

The TAILS keyword works most effectively when combined with the confinement keyword, described elsewhere in this document. The confine key described here should not be confused with the confinement option for each atom type. The confine option here affects functions in the region where they become very small, independent of the distance to the nucleus. The confinement option introduces a soft cut-off for all functions of a particular atom type, at a specific distance from the nucleus.

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