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Convergence of the freeze-and-thaw cycles

The script FDE runs a self-consistent calculation when a convergence criterion is fulfilled. The convergence criterion is the change in the total dipole moment. This is a tight convergence criterion, as the dipole moment is highly sensitive to small changes in electron density. The convergence parameter $ \varepsilon^{j}_{}$ for the j -th step in the freeze-and-thaw procedure is computed by means the following expression

$\displaystyle \varepsilon^{j}_{}$ = $\displaystyle {\frac{{\lvert\Delta\mu^j_A\rvert+\lvert\Delta\mu^j_B\rvert}}{{2}}}$ (15.10)

where
$\displaystyle \lvert$Δμji$\displaystyle \rvert$ = $\displaystyle \lvert$μij$\displaystyle \rvert$ - $\displaystyle \lvert$μij-1$\displaystyle \rvert$        i = A, B  

is the difference between the dipole moments of two consecutive steps for the i -th subsystem. Eq. (15.10) allows to consider changes in both subsystems or one of them because of the relaxation of their electron densities. By default, FDE stops when $ \varepsilon^{j}_{}$≤0.005 a.u.. The default value for the convergence criteria can be changed using the flag --epsilon= real where real is a decimal number.

The maximum number of freeze-and-thaw cycles can be specified by --max-iter= integer, and the default value is 20.

In order to make easy the convergence of the iterative solution of the KSCED coupled equations, a damping factor η must be used for the matrix elements of the embedding potential $ \bigl($vemb$ \bigr)_{{ij}}^{}$ as perturbation to a given subsystem

d$\displaystyle \bigl($vemb$\displaystyle \bigr)_{{ik}}^{j}$ = (1 - η)$\displaystyle \bigl($vemb$\displaystyle \bigr)_{{ik}}^{j}$ + η$\displaystyle \bigl($vemb$\displaystyle \bigr)_{{ik}}^{{j-1}}$ (15.11)

for the j -th iteration. Here d$ \bigl($vemb$ \bigr)_{{ik}}^{j}$ is the matrix element effectively used in the j -th iteration after the damping. In FDE the starting value of η can be changed using --start-damp= real (default value is 0.45 ) where real is a decimal number. The damping parameter can also dynamically change at each iterative step (according to the convergence process) of a quantity set by --step-damp= real (default value is 0.10 ). The minimum value set by --max-damp= real (default value is 0.90 ).

fde.input options:
epsilon= real
max-iter= integer
start-damp= real
max-damp= real
step-damp= real


next up previous contents index
Next: Embedding energy error Up: Options Previous: Monomolecular and supermolecular basis   Contents   Index
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