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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
