~albertog/siesta/merge-OSSO : revision 692

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calculations by means of the inclusion in the total Hamiltonian not

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only the Darwin and velocity correction terms~(Scalar--Relativistic

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calculations), but also the spin--orbit~(SO) contribution. There are

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two approximations regarding the SO formalism: on--site and off--site.

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Within the on--site only the intra--atomic SO contribution is taken

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into account whilst when using the off--site additional neigboring

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two approaches regarding the SO formalism: on--site and off--site.

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Within the on--site approximation only the intra--atomic SO contribution is taken

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into account. In the off--site scheme additional neighboring

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interactions are also included in the SO term. By default, the off--site SO

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formalism is switched on, being necessary to change the \fdf{Spin} flag

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in the input file if the on--site approximation wants to be used. See

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\fdf{Spin} on how to handle the spin--orbit coupling.

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The on--site implementation in \siesta\ has been performed by

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The on--site spin-orbit scheme in this version of \siesta\ has been implemented by

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Dr. Ram\'on Cuadrado based on the original on--site SO formalism and

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implementation developed by Prof. Jaime Ferrer, \textit{et al}~(L

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implementation developed by Prof. Jaime Ferrer and his collaborators \textit{et al}~(L

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Fern\'andez--Seivane, M Oliveira, S Sanvito, and J Ferrer, Journal of

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Physics: Condensed Matter, {\bf 18}, 7999 (2006); L Fern\'andez--Seivane

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and Jaime Ferrer, Phys. Rev. Lett. {\bf 99}, 183401 (2007)).

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The off--site implementation in \siesta\ has been performed by

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The off--site scheme has been implemented by

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Dr. Ram\'on Cuadrado and Dr. Jorge I. Cerd\'a based on their initial

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work~(R. Cuadrado and J. I. Cerd\'a ``Fully relativistic pseudopotential

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formalism under an atomic orbital basis: spin-orbit splittings and

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J. Klemmer and R. W. Chantrell, Applied Physics Letters, {\bf 108},

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123102 (2016)).

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The inclusion of the SO term in the Hamiltonian~(and in the Density

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Matrix) will involve the increase of non--zero elements in their

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The inclusion of the SO term in the Hamiltonian (and in the Density

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Matrix) causes an increase in the number of non--zero elements in their

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off--diagonal parts, i.e., for some $(\mu,\nu)$ pair of basis

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orbitals, H$^{\sigma\sigma'}_{\mu\nu}$~(DM$^{\sigma\sigma'}_{\mu\nu}$)

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[$\sigma,\sigma'$=$\uparrow,\downarrow$] will be $\neq$0. This is

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In addition, these H$^{\sigma\sigma'}_{\mu\nu}$~(and

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DM$^{\sigma\sigma'}_{\mu\nu}$) elements will be complex, in contrast

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with typical polarized/non--polarized calculations where these

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matrices are purely real. Due to this, we encourage that previously to

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start with a full spin-orbit calculation it has to take special

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attention to the memory needed to perform it, based mainly in the size

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of the physical system and hence in the number of orbital

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involved. Note that for a non--SO calculation the memory will be

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around thirty percent lower than with SO.

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matrices are purely real. Since the spin-up and spin-down manifolds

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are essentially mixed, the solver has to deal with matrices whose

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dimensions are twice as large as for the collinear (unmixed) spin

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problem. Due to this, we advise to take special

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attention to the memory needed to perform a spin-orbit calculation.

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Unless explicitly advised the following type of calculation can be carried out

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regardless of whether on--site or off--site approximation is employed:

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\item Selfconsistent calculations for gamma point as well as for

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bulks.

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%

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\item Structure optimizations (only supported by the off--site SO

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formalism).

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\item Structure optimizations %% only supported by the off--site SO

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%% formalism *** Why ?

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%

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\item LDA+U calculations~(See Sect.\ref{sec:lda+u} for further info).

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%%% *** Incompatible... \item LDA+U calculations~(See Sect.\ref{sec:lda+u} for further info).

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%

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\item Magnetic Anisotropy Energy~(MAE) can be easily

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calculated. From first principles it is obtained after subtract

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calculated. From first principles it is obtained after subtracting

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the total selfconsistent energy calculated for two different

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magnetic orientations. In \siesta\ it is possible to perform

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calculations when different initial magnetic ordering is necessary

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calculations with different initial magnetic orderings

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by means of the use of the block \fdf{DM.InitSpin} in the fdf

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file. In doing so one will be able to include the initial

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orientation angles of the magnetization for each atom, as well as

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%

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\end{itemize}

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Note: Due to the small SO energy value contribution to the total

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Note: Due to the small SO contribution to the total

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energy, the level of precision required to perform a proper fully

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relativistic calculation during the selfconsistent process is quite

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demanding. The following values must be carefully converged and

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accurate enough: \fdf{SCF.H!Tolerance} during the

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selfconsistency~(typically between 10$^{-3}$eV -- 10$^{-4}$eV),

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\fdf{ElectronicTemperature},

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\textbf{k--point} sampling and high values of

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\textbf{k}--point sampling and high values of

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\fdf{MeshCutoff}~(specifically for extended solids). In general, one

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can say that a good calculation will have high number of \textbf{k--points},

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can say that a good calculation will have high number of \textbf{k}--points,

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low \fdf{ElectronicTemperature}, extremely small \fdf{SCF.H!Tolerance}

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and high values of \fdf{MeshCutoff}. We encourage the user to test

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carefully these options for each system. An additional point to take

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into account is the mixing scheme employed. You are encouraged to use

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\fdf{SCF.Mix} \fdf*{hamiltonian} (currently is set up by default)

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instead of the density matrix, since it speeds up the convergence.

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instead of density matrix mixing, since it speeds up the convergence.

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The pseudopotentials have to be properly generated and tested for each

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specific system and they have to be in their fully relativistic form

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specific system and they have to be in their fully relativistic form,

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together with the non--linear core corrections. Finally it is worth to

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mention that the selfconsistent convergence for some non--high symmetric

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mention that the selfconsistent convergence for some non--highly symmetric

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magnetizations directions with respect to the physical symmetry axis

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could be coumbersome, however

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could still be difficult.

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\begin{fdfentry}{Spin!OrbitStrength}[real]<1.0>

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It allows to vary the strength of the

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spin--orbit interaction from zero to any positive value. It can be

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used for both the on--site and off-site SOC flavors.

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used for both the on--site and off-site SOC flavors, but only for

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debugging and testing purposes, as the only physical value is 1.0.

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\end{fdfentry}

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\end{fdflogicalF}

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For the off--site SO approximation some mandatory flags have to set

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up to \fdffalse\ in the fdf file:

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\begin{fdflogicalT}{PAO!OldStylePolOrbs}

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By default is set up to \fdftrue, however it has to set up to \fdffalse.

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\end{fdflogicalT}

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\begin{fdflogicalT}{DM.MixSCF1}

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By default is set up to \fdftrue, however it has to set up to \fdffalse.

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\end{fdflogicalT}

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\begin{fdflogicalT}{Restricted.Radial.Grid}

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By default is set up to \fdftrue, however it has to set up to \fdffalse.

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\end{fdflogicalT}

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% *** The following items should not be relevant.

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%%For the off--site SO approximation some mandatory flags have to set

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%%up to \fdffalse\ in the fdf file:

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%%\begin{fdflogicalT}{PAO!OldStylePolOrbs}

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%% By default is set up to \fdftrue, however it has to set up to \fdffalse.

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%%\end{fdflogicalT}

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%%\begin{fdflogicalT}{DM.MixSCF1}

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%% By default is set up to \fdftrue, however it has to set up to \fdffalse.

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%%\end{fdflogicalT}

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%%\begin{fdflogicalT}{Restricted.Radial.Grid}

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%% By default is set up to \fdftrue, however it has to set up to \fdffalse.

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%%\end{fdflogicalT}

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\begin{fdfentry}{OccupationFunction}[string]<FD>

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String variable to select the function that determines the

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occupation of the electronic states. Two options are available:

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occupation of the electronic states. These options are available:

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\begin{fdfoptions}

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\option[FD]%

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The usual Fermi-Dirac occupation function is used.

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The occupation function proposed by Methfessel and

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Paxton (Phys. Rev. B, \textbf{40}, 3616 (1989)), is used.

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\option[Cold]%

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The occupation function proposed by Marzari, Vanderbilt et. al

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(PRL, \textbf{82}, 16 (1999)), is used, this is commonly referred

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to as \emph{cold smearing}.

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\end{fdfoptions}

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The smearing of the electronic occupations is done, in both cases,

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The smearing of the electronic occupations is done, in all cases,

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using an energy width defined by the \fdf{ElectronicTemperature}

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variable. Note that, while in the case of Fermi-Dirac, the

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occupations correspond to the physical ones if the electronic

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integration of the physical quantities at a lower cost. In

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particular, the Methfessel-Paxton scheme has the advantage that,

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even for quite large smearing temperatures, the obtained energy is

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very close to the physical energy at $T=0$. Also, it allows a much

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very close to the physical energy at $T=0$. Also, it allows a much

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faster convergence with respect to $k$-points, specially for

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metals. Finally, the convergence to selfconsistency is very much

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improved (allowing the use of larger mixing coefficients).

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For the Methfessel-Paxton case, one can use relatively large values

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for the \fdf{ElectronicTemperature} parameter. How large depends

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on the specific system. A guide can be found in the article by

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J. Kresse and J. Furthm\"uller, Comp. Mat. Sci. \textbf{6}, 15

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(1996).

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For the Methfessel-Paxton case, and similarly for cold smearing, one

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can use relatively large values for the \fdf{ElectronicTemperature}

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parameter. How large depends on the specific system. A guide can be

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found in the article by J. Kresse and J. Furthm\"uller,

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Comp. Mat. Sci. \textbf{6}, 15 (1996).

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If Methfessel-Paxton smearing is used, the order of the

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corresponding Hermite polynomial expansion must also be chosen (see

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\begin{fdfentry}{ElectronicTemperature}[temperature/energy]<$300\,\mathrm{K}$>

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Temperature for Fermi-Dirac or Methfessel-Paxton

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distribution. Useful specially for metals, and to accelerate

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selfconsistency in some cases.

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Temperature for occupation function. Useful specially for metals,

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and to accelerate selfconsistency in some cases.

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\end{fdfentry}

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