Crystalline aluminum

This tutorial explains how to perform the convergence study with respect to the number of k-points and smearing width, and how to analyze the electronic structure, i.e., band structure and density of states.

Convergence study

Metallic systems have the Fermi surface, and to handle it, STATE uses the smearing technique with various smearing functions and the tetrahedron method. Furthermore, the number of k-points to sample the Brillouin zone can be critical for the accurate calculation of the metallic systems.

Convergence with respect to the number of k-points

Here we present the convergence of the total energy with respect to the number of k-points with the Methefeesel-Paxton smearing (default) and tetrahedron methods. Use negative WIDTH (e.g. -0.02) to activate the Methefessel-Paxton smearing (with positive value, a parabolic function is used to treat the Fermi level and the entropic term is not taken into account).

  • Input file for the smearing method
     0  0  0  0  0  0                      : I_CTRL(1:6) (DUMMY)
     4.00  8.00  1  1  1                   : GMAX GMAXP NTYP NATM NATM2
     221   2                               : NUM_SPACE_GROUP TYPE 
     7.5967 7.5967 7.5967 90.0 90.0 90.0   : A B C ALPHA BETA GAMMA
     06    06    06    1    1    1         : N1 N2 N3 M1 M2 M3
     0     0                               : NCORD, NINV
     0.00  0.00  0.00  1    0    1         : CPS(1,1:3) IWEI IMDTYP ITYP
     13    0.50  26.98 6    1    0.2       : IATOMN ALFA AMION ILOC IVAN
     0  0  0  0  0                         : ICOND INIPOS INIVEL ININOS INIACC
     0  1                                  : IPRE IPRI 
     30 30 0  84200.00  0                  : NMD1 NMD2 LAST_ITER CPUMAX IFSTOP
     6  1                                  : WAY_MIX MIX_WHAT
     0  20 0.60                            : ITER_START KBXMIX  MIX_ALPHA
     0.20  0.30  0.20  0.20  0.20          : DTIM1 DTIM2 DTIM3 DTIM4 DTIM
     300.00      4     1     0.50D-09      : DTIO IMDALG IEXPL EDELTA   
    -0.002 0     0.50D+03    0             : WIDTH FORCCR ISTRESS
    ggapbe     1                           : XCTYPE KSPIN
     2.00                                  : DESTM
     101                                   : NBZTYPE
     4  4  4                               : NKX NKY NKZ (DUMMY)
     4  4  4                               : NKX2 NKY2 NKZ2 (DUMMY)
     6                                     : KEG
     1                                     : NEXTST    
     0                                     : (DUMMY)
     2                                     : IMSD 
     0                                     : EVALUATE_EKO_DIFF
     0                                     : NPDOSAO
     0  0.000                              : SM_N DOPPING (DUMMY)
  • Input file for the tetrahedron method
     0  0  0  0  0  0                      : I_CTRL(1:6) (DUMMY)
     4.00  8.00  1  1  1                   : GMAX GMAXP NTYP NATM NATM2
     221   2                               : NUM_SPACE_GROUP TYPE 
     7.5967 7.5967 7.5967 90.0 90.0 90.0   : A B C ALPHA BETA GAMMA
     06    06    06    1    1    1         : N1 N2 N3 M1 M2 M3
     0     0                               : NCORD, NINV
     0.00  0.00  0.00  1    0    1         : CPS(1,1:3) IWEI IMDTYP ITYP
     13    0.50  26.98 6    1    0.2       : IATOMN ALFA AMION ILOC IVAN
     0  0  0  0  0                         : ICOND INIPOS INIVEL ININOS INIACC
     0  1                                  : IPRE IPRI 
     30 30 0  84200.00  0                  : NMD1 NMD2 LAST_ITER CPUMAX IFSTOP
     6  1                                  : WAY_MIX MIX_WHAT
     0  20 0.60                            : ITER_START KBXMIX  MIX_ALPHA
     0.20  0.30  0.20  0.20  0.20          : DTIM1 DTIM2 DTIM3 DTIM4 DTIM
     300.00      4     1     0.50D-09      : DTIO IMDALG IEXPL EDELTA   
    -10.02 0     0.50D+03    0             : WIDTH FORCCR ISTRESS
    ggapbe     1                           : XCTYPE KSPIN
     2.00                                  : DESTM
     101                                   : NBZTYPE
     4  4  4                               : NKX NKY NKZ (DUMMY)
     4  4  4                               : NKX2 NKY2 NKZ2 (DUMMY)
     6                                     : KEG
     1                                     : NEXTST    
     0                                     : (DUMMY)
     2                                     : IMSD 
     0                                     : EVALUATE_EKO_DIFF
     0                                     : NPDOSAO
     0  0.000                              : SM_N DOPPING (DUMMY)
    See the difference in WIDTH.

Convergence with respect to the smearing width

Total (free) energy of the metallic system is sensitive to the smearing width, in particular, with the Gaussian and Fermi-Dirac function. Here we demonstrate the smearing width dependence of the total energy, following the seminal work by de Gironcoli [Phys. Rev. B51, 6773(R) (1995)]. Smearing function can be chosen by adding the section &OTHERS ... &END at the end of the input file. To use the Fermi-Dirac distribution function set

&OTHERS
  FERMI_DIRAC
&END

For the Gaussian smearing

&OTHERS
  GAUSSIAN
&END
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