GaAs surface

 

Similarly we used unit cells of 6,10, and 20 layers of GaAs and 6,10, and 20 layers of vacuum creating surfaces in the (110) direction. The same k-point sampling is used.

 

 

 

Again for the small system all methods handle it pretty well. The “tf.mg” setting shows a slight instability at the end.

 

 

 

 

At this point we really see a large benefit of the Thomas-Fermi mixing. The “tf.gcg” and the “dir.gcg” perform almost exactly the same.  We can see an instability in the “tf.mg” method. At the point this method strays from the “tf.gcg” method, the “tf.mg” has a dip to a unphysical lower energy before settling into the higher proper value. The absolute value of the energy difference is plotted for this set of data. The dip may be because in the total energy expression we use the band energy obtained from the input potential and not of the output potential. We do include a correction, but it is only a first-order correction. The Pulay_kerker method begins to show weakened convergence. The Broyden method performed very poorly for this system.

 

 

 

Now the instability is in the “tf.gcg” alorithm. It has a dip in energy as the”tf.mg” did in the 10-layer system. Not a substantial difference between al three, but “tf.mg” does the best. The Pulay-Kerker and the Broyden method were dismissed for this system due to their poor performance in the 10 layer system.