

Figure 6 shows the comparison between calculations on a 4 atom unit cell aluminium bulk using Fermi and MethfesselPaxton smearing methods. We only did nonselfconsistency calculations. We can see that Fermi smearing leads to different energy results as we increase smearing factor . We can see that the difference between Free energy and the calculated groundstate energy (we called it Harris energy) also increased dramatically for Fermi smearing. This is expected as the smearing does correspond to the physical temperature and as increases we depart from the zerotemperature regime. On the other hand, the smearing in MethfesselPaxton method is just a parameter used in the approximation. And we can see that increasing has small effect on the energies calculated using MethfesselPaxton smearing and results also improve as the order of Hermite polynomials used increases. This means a relatively large smearing factor can be used under MethfesselPaxton approximation, which allows fewer points. To be more specific, figure 7 shows that for smearing factor , (corresponding to smearing temperature of about 31565.51 K), we reach point convergence at about 10 Bloch space () points per each reciprocal lattice direction, while the total energy will be within Ha of the ground state energies calculated using low smearing and large number of points. This is compared with the requirement of 25 points for convergence with a small smearing factor, see figure 8.



Lianheng Tong 20110302