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9. Results and discussion

In this chapter we present results obtained using the penalty functional method applied to bulk crystalline silicon. We show how the energy converges as the two spatial cut-offs; the support region radius and density-kernel cut-off, are increased and in particular that the estimate of the energy is variational with respect to these parameters. We also consider the difference in convergence of absolute energies and energy differences by calculating the energy-volume curve and comparing with the results obtained from the CASTEP plane-wave code [82] and from experiment. Finally we consider the scaling of the method with system-size (confirming that it is indeed linear) and the scaling with support region radius and density-kernel cut-off.


Peter Haynes