Aluminum in the fcc structure †In this tutorial how to perform the total energy calculation of a metallic system is described by taking Al as an example. We use von BarthCar normconserving pseudopotential as distributed in the QuantumESPRESSO web page. Optimizing the cell parameter †In this example, the cell is optimized by using 'vcrelax.' Cutoff energy of 30 Ry and nonshifted 12 x 12 x 12 are used. In the metallic systems, the smearing technique is used with the keywords "occupation='smearing'", "smearing", and "degauss" with the number of bands ("nbnd") slightly larger than the half of the number of bands to accomodate partially unoccupied bands. How to determine the parameters for the smearing technique is discussed below. &control calculation = 'vcrelax' restart_mode = 'from_scratch', pseudo_dir = '/home/ikutaro/QE/pseudo/' outdir = './tmp' prefix = 'al' tprnfor = .true. tstress = .true. / &system ibrav = 2 A = 4.020 nat = 1 ntyp = 1 ecutwfc = 30.0 ecutrho = 120.0 occupations = 'smearing' smearing = 'mp' degauss = 0.01 nbnd = 12 / &electrons diagonalization = 'cg' conv_thr = 1.0e12 mixing_beta = 0.5 / &ions ion_dynamics='bfgs' / &cell cell_dynamics='bfgs' / ATOMIC_SPECIES Al 0.0000 Al.pzvbc.UPF ATOMIC_POSITIONS (crystal) Al 0.000000000000 0.000000000000 0.00000000000 K_POINTS (automatic) 16 16 16 0 0 0 Determining the smearing width †Now let us examine the smearing function and width. We use the FermiDirac (smearing='fd'), Gaussian (smearing='gaussian'), MethfesselPaxton (smearing='mp'), and MarzariVanderbilt (smearing='mv') and vary smearing width (degauss) from 0.05 to 0.10. An example input is the following. Only difference from the previous one is "calculation='scf'" &control calculation = 'scf' restart_mode = 'from_scratch', pseudo_dir = '/home/ikutaro/QE/pseudo/' outdir = './tmp' prefix = 'al' tprnfor = .true. tstress = .true. / &system ibrav = 2 A = 4.020 nat = 1 ntyp = 1 ecutwfc = 30.0 ecutrho = 120.0 occupations = 'smearing' smearing = 'mp' degauss = 0.01 nbnd = 12 / &electrons diagonalization = 'cg' conv_thr = 1.0e12 mixing_beta = 0.5 / &ions ion_dynamics='bfgs' / &cell cell_dynamics='bfgs' / ATOMIC_SPECIES Al 0.0000 Al.pzvbc.UPF ATOMIC_POSITIONS (crystal) Al 0.000000000000 0.000000000000 0.00000000000 K_POINTS (automatic) 16 16 16 0 0 0 The results for the FermiDirac and MethfesselPaxton are shown below. (FermiDirac) #smearing width (Ry) total energy (Ry) 0.005 4.19003452 0.010 4.19061414 0.015 4.19165619 0.020 4.19317708 0.030 4.19764208 0.040 4.20395723 0.050 4.21209681 0.060 4.22205685 0.070 4.23383710 0.080 4.24743412 0.090 4.26283926 0.100 4.28003855 (MethfesselPaxton) #smearing width (Ry) total energy (Ry) 0.005 4.18988203 0.010 4.18986582 0.015 4.18984568 0.020 4.18982833 0.030 4.18978271 0.040 4.18971203 0.050 4.18962976 0.060 4.18956040 0.070 4.18951623 0.080 4.18949432 0.090 4.18948574 0.100 4.18948238 We can see that with the FermiDirac function, total energy descrease significantly as the smearing width increases, while with the MethfesselPaxton scheme, the change is insignificant, and therefore it is possible to use relatively large smearing width with the MP scheme. Note that the smearing width is to treat the Fermi surface efficiently and it is desirable to use small smearing width. Alternatively, one can use the tetrahedron method for the Brillouin zone integration without smearing. In this case the number of kpoints tends to be large. Exercise †
