Geometry Optimisation with CASTEP

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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
arbitrary set of basis set parameters. One final point on sampling grids. An important factor in dictating the required sampling grid density is the size of the supercell. A large real space supercell might require only a very sparse reciprocal space sampling grid. Our small bulk silicon unit cell requires quite a dense MP grid. In the later silicon (100) surface example the supercells contain 20 atoms but require only a 9 k-point sampling grid. Of course, the electronic complexity of the constituent atoms also plays a role in determining the required sampling grid density. Next: A Variable Cell calculation Up: Geometry Optimisation with CASTEP Previous: Other output files 2005-04-04
Page 1 and 2: Next: Recipe Geometry Optimisation
Page 3 and 4: Next: Inputs Up: Geometry Optimisat
Page 5 and 6: Next: The Size and Shape Up: Inputs
Page 7 and 8: In both cases if [units] are not sp
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Page 11 and 12: KPOINTS_MP_SPACING [units] Where is
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Page 15 and 16: Next: Atomic masses Up: The .cell f
Page 17 and 18: It is possible to fix the positions
Page 19 and 20: Next: External pressure that is Up:
Page 21 and 22: Next: General Job Parameters Up: In
Page 23 and 24: When a calculation that was stopped
Page 25 and 26: Next: Electronic Minimisation Param
Page 27 and 28: Next: Example - Bulk Silicon Up: Th
Page 29 and 30: the default value is 3 but it must
Page 31 and 32: We must now choose a supercell to e
Page 33 and 34: Next: The .castep file Up: Geometry
Page 35 and 36: 4 -2.14844155E+002 -9.84322032E-003
Page 37 and 38: BFGS: Final Configuration: ========
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Page 45 and 46: 3 -2.16474423E+002 2.10512829E-007
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Page 51 and 52: thickness We can see that the total
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Geometry Optimisation with CASTEP

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