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Total Energy Minimization Schemes

In an electronic structure calculation using a plane-wave basis, the Hilbert space is typically spanned by a huge number of basis functions (up to 105 plane waves). Therefore it would be unwise to attempt to diagonalize the Hamiltonian operator in this high-dimensional space directly. Instead, one uses algorithms which only imply vector operations on the wave function vector (in Hilbert space), rather than matrix operations. The wave functions are gradually improved in an iterative process, until they eventually converge towards the eigenvectors.

Parameter Type/Value  
delt real > 1 Step length of electronic iteration
gamma $0<\mbox{ real }<1$ If $i\_edyn=$ 2 (see below), damping parameter
delt2 see delt c.f. $eps\_chg\_dlt$
gamma2 see gamma c.f. $eps\_chg\_dlt$
$eps\_chg\_dlt$ real >0 If the total energy varies less than $eps\_chg\_dlt$, delt2 and gamma2 replace delt and gamma

Parameter Value  
$i\_edyn$   Schemes to iterate the wave functions
  0 steepest descent
  1 Williams-Soler
  2 damped Joannopoulos


 
Table 3.1: Electronic time step delt, damping parameter gamma and minimization schemes used for some bulk and slab (with and without adsorbates) calculations. The labels J, WS and SD mean that either the damped Joannopoulos or Williams-Soler or Steepest Descent minimization scheme was employed. The dimension along the z direction is given by dim(z). 
\begin{table}
\begin{center}
\begin{tabular*}{12cm}{@{\extracolsep{\fill}}lccccc...
... CO, O & 54 & J & 2 & 0.2 \\
\hline\hline
\end{tabular*}\end{center}\end{table}


next up previous contents index
Next: How to set up Up: Step-by-step description of calculational Previous: Choice of the k-point
Matthias Wittenberg
1999-08-06