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| {\tt IALGO} = 38 | 48 \qquad {\tt LDIAG} = .TRUE. | .FALSE. | | {{TAGDEF|LDIAG|[logical]|.TRUE.}} |
|
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|
| \begin{tabular} {lll}
| | Description: This tag determines whether a subspace diagonalization is performed or not within the main algorithm selected by {{TAG|ALGO}} or {{TAG|IALGO}}. |
| Default \\
| | ---- |
| {\tt IALGO} & = & 8 for VASP.4.4 and older \\ | | For {{TAG|ALGO}} = <tt>Normal</tt>, <tt>Fast</tt>, and <tt>VeryFast</tt>, VASP performs a diagonalization in the subspace spanned by all orbitals. This is often referred to as the [https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Ritz_method Rayleigh–Ritz method]. |
| & = & 38 for VASP.4.5, VASP.4.6 and VASP.5.2 (if {\tt ALGO} is not set)\\
| | This step increases the convergence rate and thus is expedient in most cases. |
| {\tt LDIAG} & = & .TRUE. \\
| | Furthermore, the subspace diagonalization sorts the orbital/eigenvalues in ascending order. |
| \end{tabular}\vspace{5mm}
| |
| \begin{verbatim}
| |
| IALGO = integer selecting algorithm
| |
| \end{verbatim}
| |
| \begin{verbatim}
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| LDIAG = perform sub space rotation
| |
| \end{verbatim}
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|
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|
| Please mind, that the VASP.4.5 default is {\tt IALGO} = 38
| | For the direct optimization algorithms (for instance {{TAG|ALGO}} = <tt>All</tt> or <tt>Damped</tt>), |
| (a Davidson block iteration scheme). {\tt IALGO} = 8 is not supported for
| | a subspace diagonalization is usually not performed, but in order to improve the accuracy of the calculated forces, |
| copyright reasons in VASP.4.5, but
| | after convergence has been reached one single diagonalization in the subspace spanned by all orbitals is performed. |
| {\tt IALGO} = 38 is roughly 2 times faster for large systems than
| |
| {\tt IALGO} = 8 and at least as stable. You can select the algorithm also
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| by setting {\tt ALGO}= Normal | Fast | Very$\_$Fast in the INCAR file
| |
| (see Sec. \ref{incar-algo}).
| |
|
| |
|
| \noindent
| | For {{TAG|ALGO}} = <tt>VeryFast</tt> and <tt>Damped</tt> it is possible to switch off the subspace diagonalization by specifying {{TAG|LDIAG}} = <tt>.FALSE.</tt> in the {{FILE|INCAR}} file. |
| {\tt IALGO} selects the main algorithm, and {\tt LDIAG} determines | | Specifically, for {{TAG|ALGO}} = <tt>VeryFast</tt>, {{TAG|LDIAG}} = <tt>.FALSE.</tt> changes from an exact Rayleigh–Ritz diagonalization to Loewdin perturbation theory. |
| whether a subspace--diagonalization is performed, or not.
| |
| {\em | |
| We strongly urge the users to set the algorithms via {\tt ALGO}. Algorithms other
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| than those available via {\tt ALGO } are subject to instabilities.}
| |
|
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|
| Generally the first digit of {\tt IALGO} specifies the main algorithm,
| | Note, Loewdin perturbation theory strictly conserves the orbital order, ''i.e.'', the ''n''-th orbital will remain stored in the ''n''-th storage slot and only small rotations into that orbital can occur. |
| the second digit | | For {{TAG|ALGO}} = <tt>Damped</tt> and <tt>All</tt>, the final subspace diagonalization is simply skipped if {{TAG|LDIAG}} = <tt>.FALSE.</tt> is set. |
| controls the actual settings within the algorithm.
| | Generally using {{TAG|LDIAG}} = <tt>.FALSE.</tt> is only advised, if one wants to maintain a certain orbital order, for instance, when reading the orbitals from an existing {{FILE|WAVECAR}} file. |
| For instance 4X will always call the same routine for the | |
| electronic minimization the second digit X controls the details
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| of the electronic minimization (preconditioning etc.).
| |
|
| |
|
| {\em Mind:} All implemented algorithms will result in the | | For the algorithms {{TAG|ALGO}} = <tt>Normal</tt> or <tt>Fast</tt>, by construction it is not possible to switch off subspace diagonalization, as these algorithms require subspace diagonalizations during the iterative refinement of the orbitals. |
| same result, i.e. they will correctly calculate the KS groundstate,
| | Furthermore, algorithms that minimize the total energy ({{TAG|ALGO}} = <tt>All</tt>) are often too "greedy" and tend to alternate the orbital order in the course of the SCF cycle and energy optimization. |
| {\em if they converge}. This is guaranteed because
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| all minimization routines use the same set of subroutines to calculate
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| the residual (correction) vector | |
| (${\bf H} - \epsilon {\bf S}) \vert \phi \rangle$ for the current orbitals
| |
| $\phi$ and they are considered to be converged if this correction vector becomes smaller than
| |
| some specified threshold. The only difference between the algorithms is the
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| way this correction vector is added to the trial orbital and therefore
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| the performance of the routines might be quite different. | |
|
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|
| \noindent The most extensive tests has been done for {\tt IALGO} = 38
| | In summary, the following combinations are potentially useful: |
| ({\tt IALGO} = 8 before VASP.4.5).
| |
| {\em If random vectors ({\tt INIWAV} = 1) are used for the
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| initialization of the orbitals,
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| this algorithm always gives the correct
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| KS groundstate. Therefore, if you have problems with {\tt IALGO} = 48
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| ({\tt ALGO} = Fast)
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| switch to {\tt IALGO} = 38.}
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|
| |
|
| \noindent List of possible settings for {\tt IALGO}.
| | ALGO = VeryFast ; LDIAG = .FALSE. |
| \begin{itemize}
| |
| \item[-1]
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| Performance test.
| |
|
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|
| VASP does not perform an actual calculations
| | ALGO = Damped ; LDIAG = .FALSE. |
| --- only some important parts of the
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| program will be executed and the timing for each part is printed out at the end.
| |
|
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|
| \item[5-8] Conjugate gradient algorithm (section \ref{min-en4})
| | Other combinations using {{TAG|LDIAG}} = <tt>.FALSE.</tt> are likely to yield undesirable results. |
| | {{NB|warning| {{TAG|ALGO}} {{=}} <tt>VeryFast</tt> is not supported for hybrid functionals. }} |
|
| |
|
| Optimize each band iteratively using a conjugate gradient algorithm.
| | == Related tags and articles == |
| | {{TAG|IALGO}}, |
| | {{TAG|ALGO}} |
|
| |
|
| Subspace-diagonalization before conjugate gradient algorithm.
| | {{sc|LDIAG|Examples|Examples that use this tag}} |
| The conjugate gradient algorithm is used to optimize the eigenvalue
| | ---- |
| of each band.
| |
|
| |
|
| Sub-switches:
| | [[Category:INCAR tag]][[Category:Electronic minimization]] |
| | |
| \begin{tabular} {ll}
| |
| 5 & steepest descent \\
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| 6 & conjugated gradient \\
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| 7 & preconditioned steepest descent \\
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| 8 & preconditioned conjugated gradient\\
| |
| \end{tabular}\vspace{5mm}
| |
| | |
| \noindent
| |
| {\tt IALGO} = 8 (VASP-releases older than VASP.4.5) is always fastest, {\tt IALGO} = 5-7 are only implemented for test purpose.
| |
| | |
| Please mind, that {\tt IALGO} =8 is not supported by VASP.4.5,
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| since M. Teter, Corning and M. Payne hold a patent on this algorithm.
| |
| | |
| \item[38] ({\tt ALGO} =N) Kosugi algorithm (special Davidson block iteration scheme) (see section \ref{min-david})
| |
| | |
| This algorithm is the default in VASP.4.6 and VASP.5.X. It optimizes a subset
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| of {\tt NSIM} \index{INCAR!N!NSIM|textit} bands simultaneously (Sec. \ref{incar-nsim}).
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| The optimized bands are kept orthogonal to all other bands.
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| If problems are encountered with the algorithm, try to decrease {\tt NSIM}.
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| Such problems are encountered, if linear dependencies develop in the
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| search space. By reducing {\tt NSIM} the rank of the search space is decreased.
| |
| | |
| | |
| \item[44-48] ({\tt ALGO} = F) Residual minimization method
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| direct inversion in the iterative subspace (RMM-DIIS see section \ref{min-en3} and \ref{min-en5})
| |
| | |
| The RMM-DIIS algorithm reduces the number of orthonormalization steps
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| (o($N^3$)) considerably
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| and is therefore much faster than {\tt IALGO} = 8 and {\tt IALGO} = 38,
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| at least for large systems and for
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| workstations with a small memory band width.
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| For optimal performance, we recommend to use this switch together
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| with {\tt LREAL} = Auto (Section \ref{incar-real}).
| |
| The algorithm works in a blocked mode
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| in which several bands are optimized at the same time. This can
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| improve the performance even further on systems with a low memory
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| band width (see \ref{incar-nsim}, default is presently {\tt NSIM} = 4).
| |
| | |
| The following sub-switches exist:
| |
| | |
| \begin{tabular} {ll}
| |
| 44 & steepest descent eigenvalue minimization\\
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| 46 & residuum-minimization + preconditioning\\
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| 48 & preconditioned residuum-minimization ({\tt ALGO} = F)\\
| |
| \end{tabular}\vspace{5mm}
| |
| | |
| \noindent {\tt IALGO} = 48 is usually most reliable
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| ({\tt IALGO} = 44 and 46 are mainly for test purposes).
| |
| | |
| For {\tt IALGO} =4X, a subspace-diagonalization is performed before the
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| residual vector minimization,
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| and a Gram-Schmidt orthogonalization is employed after the RMM-DIIS step.
| |
| In the RMM-DIIS step, each band is optimized individually (without the orthogonality
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| constraint); a maximum of {\tt NDAV}\index{INCAR!N!NDAV|textbf}
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| iterative steps per band
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| are performed for each band. The default for {\tt NDAV} is {\tt NDAV=4}, and we
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| we recommend to leave this value unchanged.
| |
| | |
| Please mind, that the RMM-DIIS algorithm can fail in rare cases,
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| whereas {\tt IALGO} = 38 did not fail for any system tested up to date.
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| Therefore, if you have problems with {\tt IALGO} = 48 try first to
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| switch to {\tt IALGO} = 38
| |
| | |
| However, in some cases the performance gains due to {\tt IALGO} = 48 are
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| so significant that {\tt IALGO} = 38 might not be a feasible option.
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| In the following we try to explain what to do if {\tt IALGO} = 48 does
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| not work reliably:
| |
| | |
| In general two major problems can be encountered when using {\tt IALGO} = 48:
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| First, the optimization of unoccupied bands might fail
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| for molecular dynamics and relaxations. This is because
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| our implementation of the RMM-DIIS algorithm treats unoccupied bands
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| more ``sloppy'' then occupied bands (see section \ref{incar-wei})
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| during MD's. The problem can be solved
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| rather easily by specifying {\tt WEIMIN} = 0\index{INCAR!W!WEIMIN|textit} in the INCAR file. In that
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| case all bands are treated accurately.
| |
| | |
| | |
| The other major problem -- which occurs also for static
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| calculations -- is the initialization of the orbitals.
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| Because the RMM-DIIS algorithm tends to find eigenvectors which
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| are close to the initial set of trial vectors
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| there is no guarantee to converge to the correct ground state!
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| This situation is usually very easy to recognize; whenever
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| one eigenvector is missing in the final solution, the convergence
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| becomes slow at the end (mind, that it is possible that
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| one state with a small fractional occupancy above the
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| Fermi-level is missing).
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| If you suspect that this is the case switch to {\tt ICHARG} =
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| 12\index{INCAR!I!ICHARG|textit}
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| (i.e. no update of charge and
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| Hamiltonian) and try to calculate the orbitals with high
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| accuracy ($10^{-6}$). If the convergence is fairly slow or
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| stucks at some precision,
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| the RMM-DIIS algorithm
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| has problems with the initial set of orbitals (as a rule
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| of thumb not more than 12 electronic iterations should be required
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| to determine the orbital for the default precision for {\tt ICHARG} = 12).
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| The first thing to do in that case is to increase the number of bands
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| ({\tt NBANDS}\index{INCAR!N!NBANDS|textit})
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| in the INCAR file.
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| This is usually the simplest and most efficient fix, but it does not
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| work in all cases. This solution is also undesirable for MD's and long
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| relaxations because it increases the computational demand somewhat.
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| A simple alternative -- which worked in all tested cases -- is
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| to use {\tt IALGO} = 38 (Davidson)
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| for a few non selfconsistent iterations and to switch then to the RMM-DIIS
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| algorithm. This setup is automatically selected when
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| {\tt ALGO} = Fast is specified in the INCAR file (IALGO must not
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| specified in the INCAR file in this case).
| |
| | |
| The final option is somewhat complicated and requires an understanding of
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| how the initialization algorithm of the RMM-DIIS algorithm works:
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| after the random initialization of the orbitals,
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| the initial orbitals for the RMM-DIIS algorithm are determined during a
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| non selfconsistent steepest descent phase
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| (the number of steepest descent sweeps is given by {\tt
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| NELMDL}\index{INCAR!N!NELMDL|textit},
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| default is {\tt NELMDL}=-12 for RMM-DIIS, section \ref{incar-nelm}).
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| During this initial phase in each sweep,
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| one steepest descent step per orbital is performed between
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| each sub space rotation.
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| This "automatic" simple steepest descent approach during the delay is
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| faced with a rather ill-conditioned minimization problem and can fail
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| to produce reasonable trial orbitals for the RMM-DIIS
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| algorithm.
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| In this case the quantity in the column "rms" will not decrease during
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| the initial phase (12 steps), and
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| you must improve the conditioning of the problem
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| by setting the {\tt ENINI} parameter in the INCAR file.
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| {\tt ENINI}\index{INCAR!E!ENINI|textbf} controls the cutoff during the initial (steepest descent) phase
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| for {\tt IALGO} = 48. Default for {\tt ENINI} is {\tt ENINI} = {\tt ENCUT}.
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| If convergence problems are observed,
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| start with a slightly smaller {\tt ENINI}; reduce {\tt ENINI} in steps of $20~\%$, till
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| the norm of the residual vector (column "rms") decreases continuously
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| during the first 12 steps.
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| | |
| A final note concerns the mixing: {\tt IALGO} = 48 dislikes too
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| abrupt mixing. Since the RMM-DIIS algorithm always stays in the space
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| spanned by the initial orbitals, and too strong mixing (large
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| {\tt AMIX}\index{INCAR!A!AMIX|textit}, small {\tt
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| BMIX}\index{INCAR!B!BMIX|textit}) might require to change the Hilbert space,
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| the initial mixing
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| must not be too strong for {\tt IALGO} = 48.
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| Try to reduce {\tt AMIX} and increase {\tt BMIX} if you suspect such a situation.
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| Increasing {\tt NBANDS} also helps in this situation.
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| | |
| \item[53-58] Treat total free energy as variational quantity and minimize the
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| functional completely selfconsistently.
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| This algorithm is based on an idea first proposed in Refs. \cite{sti89,gil89,ari92}.
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| The algorithm has been carefully optimized and should be selected
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| for Hartree-Fock type calculations. The present version is rather stable and
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| robust even for metallic systems.
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| Important sub-switches:
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| | |
| \begin{tabular} {ll}
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| 53 & damped MD with damping term automatically determined by the given
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| time-step ({\tt ALGO} = D)\\
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| 54 & damped MD (velocity quench or quickmin) \\
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| 58 & preconditioned conjugated gradient ({\tt ALGO} = A)\\
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| \end{tabular}\vspace{5mm}
| |
| | |
| \noindent
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| Furthermore {\tt LDIAG} determines, whether the subspace rotation matrix (rotation
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| matrix in the space spanned by the occupied and unoccupied orbitals) is optimized.
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| The current default is {\tt LDIAG} = .TRUE. selecting the algorithm
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| presented in
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| Ref. \cite{marsalgo07}. This allows for efficient groundstate calculations
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| of metals and small gap semiconductors. {\tt LDIAG} = .FALSE.
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| selects Loewdin perturbation theory for the subspace rotation matrix\cite{kre96b}
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| which is much faster but generally significantly less stable for metallic and small gap systems.
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| | |
| \noindent
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| The preconditioned conjugate gradient ({\tt IALGO} = 58, {\tt ALGO} = A)
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| algorithm is recommended for insulators.
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| The best stability is usually obtained if the number of bands
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| equals half the number of electrons (non spin polarized case).
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| In this case, the algorithm is fairly robust and fool proof and might
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| even outperform the mixing algorithm.
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| For small gap systems and for metals, it is however usually required (metals)
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| or desirable (semiconductors) to use a larger value for {\tt NBANDS}.
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| In this case, we recommend to use the damped MD algorithm ({\tt IALGO} =
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| 53, {\tt ALGO} = Damped)
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| instead of the conjugate gradient one.
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| | |
| The stability of the all bands simultaneously algorithms depends strongly
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| on the setting of {\tt TIME}\index{INCAR!T!TIME|textit}. For the conjugate gradient case,
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| {\tt TIME} controls the step size in the trial step, which is required
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| in order to perform a line minimization of the energy along the gradient
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| (or conjugated gradient, see section \ref{incar-ibrion}
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| for details). Too small steps make the line minimization less accurate,
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| whereas too large steps can cause instabilities. The step size
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| is usually automatically scaled by the actual step size minimizing the
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| total energy along the gradient (values can range from 1.0 for
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| insulators to 0.01 for metals with a large density of states at
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| the Fermi-level).
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| | |
| For the damped MD algorithm ({\tt IALGO} = 53, {\tt ALGO} = Damped), a sensible {\tt TIME} step is even
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| more important. In this case {\tt TIME} is not automatically adjusted,
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| and the user is entirely responsible to chose an appropriate value.
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| Too small time-steps slow the convergence
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| significantly, whereas too large values will always lead to divergence.
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| It is sensible to optimize this value, in particular, if many different
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| configurations are considered for a particular system. It is recommended
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| to start with a small step size {\tt TIME}, and to increase {\tt TIME}
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| by a factor 1.2 until the calculations diverge. The largest
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| stable step {\tt TIME} should then be used for all calculations.
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| | |
| The final algorithm {\tt IALGO} = 54 also uses a damped molecular
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| dynamics algorithm and quenches the velocities to zero if they
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| are antiparallel to the present forces (quick-min).
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| It is usually not as efficient as {\tt IALGO} = 53, but
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| it is also less sensitive to the { \tt TIME} parameter.
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| (for detail please also read section \ref{incar-ibrion}).
| |
| | |
| {\em Note: it is very important to set the {\tt TIME} tag for these algorithms (see
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| section \ref{incar-time})}.
| |
| | |
| \item[2] Orbitals and one-electron energies are kept fixed. One electron
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| occupancies and electronic density of states (DOS) are, however, recalculated.
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| This option is only useful if a pre-converged WAVECAR file is read. The option
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| allows to run selected post-processing tasks, such as local DOS, or the interface code
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| to Wannier90.
| |
| | |
| \item[3] Orbitals (one-electron wavefunctions) are kept fixed.
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| One-electron energies, one electron
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| occupancies, band structure energies, and the electronic density of states (DOS) are,
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| as well as, the total energy are recalculated for the present Hamiltonian.
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| This option is only useful if a pre-converged WAVECAR file is read. The option
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| also allows to run selected post-processing tasks, such as local DOS, or the interface code
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| to Wannier90.
| |
| | |
| \item[4] Orbitals are updated by applying a sub-space rotation, i.e.
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| the Hamiltonian is evaluated in the space spanned by the orbitals (read from WAVECAR),
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| and one diagonalization
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| in this space is performed. No optimization outside the subspace spanned by the orbitals
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| is performed.
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| {\em Note: if {\tt NBANDS} is larger or equal to the total number of plane waves, the
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| resulting one-electron orbitals are exact.}
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| \item[15-18] Conjugate gradient algorithm
| |
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| Subspace-diagonalization after iterative refinement of the eigenvectors
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| using the conjugate gradient algorithm.
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| This switch is for compatibility reasons only and should not be used any longer.
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| Generally {\tt IALGO} = 5-8 is preferable, but was not implemented previous to
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| VAMP 1.1.
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| Sub-switches as above.
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| \item[28] Conjugate gradient algorithm (section \ref{min-en4})
| |
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| Subspace-diagonalization before conjugate gradient algorithm.
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| No explicit orthonormalization of the gradients to the trial orbitals is done.
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| This setting saves time, but does fail in most cases ---
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| mainly included for test purpose. Try {\tt IALGO} = 4X instead.
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| | |
| \item[90] Exact Diagonalization.
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| This flag selects an exact diagonalization of the one-electron Hamiltonian.
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| This requires a fairly large amount of memory, and should be selected with caution.
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| Specifically, we recommend to select this algorithm for RPA or $GW$ calculations,
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| if many unoccupied orbitals are calculated (more than 30-50~\% of the states
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| spanned by the full plane wave basis). To speed up the calculations,
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| we recommend to perform a routine groundstate calculation before
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| calculating the unoccupied states.
| |
| \end{itemize}
| |
