Geometry Optimisation with CASTEP

Figure 3:Convergence of the bulk Si calculation with respect to the
basis set
We can see that gamma point sampling with a single k-point produces a structure with a much higher
energy than sampling with other k-point densities. Figure 4 below shows a plot of figure 3 with the 1 k-
point data removed for greater clarity.
Figure 4:Convergence of the basis set showing only the higher k-
point densities
The cutoff energy is a variational parameter and as it is increased the energy will converge
asymptotically on the ground state from above. However, it is important to remember that the sampling
set size is not a variational parameter. It entirely possible to increase the total final energy of the system
by increasing the density of the sampling grid. If we know more information about the wavefunction it
does not mean that this information will provide us with a lower energy structure. The key point about
convergence with respect to the sampling grid density is that the difference in energy from one grid
density to the next should be minimised. We can see from figure 4 that increasing the MP grid density
from 28 to 60 k-points has a negligible effect on the total final energy. Indeed, the two curves lie on top
of one another and cannot be separately resolved. Also, the total energy is converged with respect to the
cutoff energy when this is above about 280eV.
In summary, our fully converged basis set parameters are; 28 k-points in the reciprocal space sampling
grid and a cutoff energy of 280eV or higher. Has the reduction of systematic error helped? The bond
length for the calculation with the optimal set of parameters for both accurate wavefunction modelling
and conservation of computational resources is 2.28753 Å. This is only 1.9% away from the acepted
value of 2.332 Å. Convergence has resulted in an improvement of 6% on the answer obtained using an