Introductory ASA Tutorial
The aim of this tutorial is to give a light introduction to the operation of the Questaal package using ASA code, lm, as propaedeutic for other tutorials. The presentation is minimal, and the input file is supplied without explanation. See other tutorials such as this tutorial on PbTe for more in depth description. Also see an analogous introductory tutorial for Si, using the full-potential code lmf.
The Command Summary gives the commands, inputs and outputs for each section in this tutorial, without further explanation. It is useful for those who may want to remind themselves of the command usage or check their output against a reference.
Running Band Calculations
Command
~/lmbuild/lmstr si > out.lmstr
Expected Output
-------------- START LMSTR - ref: 87376a95 --------------
HEADER Si in diamond lattice with empty spheres.
LMSTR: nbas = 4 nspec = 2 verb 31,35
Plat Qlat
0.000000 0.500000 0.500000 -1.000000 1.000000 1.000000
0.500000 0.000000 0.500000 1.000000 -1.000000 1.000000
0.500000 0.500000 0.000000 1.000000 1.000000 -1.000000
alat = 10.262661 Cell vol = 270.221506
LATTC: as= 2.000 tol=1.00e-8 alat=10.26266 awald= 0.309 lmax=6
r1= 1.853 nkd= 87 q1= 5.557 nkg= 169
SGROUP: 48 symmetry operations from 2 generators
MKSYM: found 48 space group operations ... includes inversion
ASASTR: strux for 2nd gen LMTOs, and Sdot
avw = 2.526526
pairc, ib= 1: 59 neighbors in range 0.886*alat = 9.10
pairc, ib= 2: 59 neighbors in range 0.886*alat = 9.10
pairc, ib= 3: 59 neighbors in range 0.886*alat = 9.10
pairc, ib= 4: 59 neighbors in range 0.886*alat = 9.10
pairc: 236 pairs total 59 is max cluster size
strscr: generated 236 inequivalent strux from 236 total
Exit 0 LMSTR
CPU time: 0.070s Wall clock 0.140s at 14:11:23 28.04.2021 on ellery
Command
~/lmbuild/lm si > out.lm
Expected Output
--------------- START LM - ref: 87376a95 ----------------
HEADER Si in diamond lattice with empty spheres.
LM: nbas = 4 nspec = 2 verb 31,35
pot XC:BH
bz: metal, tetra, invit
Plat Qlat
0.000000 0.500000 0.500000 -1.000000 1.000000 1.000000
0.500000 0.000000 0.500000 1.000000 -1.000000 1.000000
0.500000 0.500000 0.000000 1.000000 1.000000 -1.000000
alat = 10.262661 Cell vol = 270.221506
LATTC: as= 2.000 tol=1.00e-8 alat=10.26266 awald= 0.309 lmax=6
r1= 1.853 nkd= 87 q1= 5.557 nkg= 169
SGROUP: 48 symmetry operations from 2 generators
MKSYM: found 48 space group operations ... includes inversion
BZMESH: 8 irreducible QP from 64 ( 4 4 4 ) shift= F F F
GETZV: 8 valence electrons
ATOM=SI Z=14 Qc=10 R=2.526526 Qv=0 a=0.025 nr=345
Pl= 3.5 3.5 3.5
Ql= 2.0 2.0 0.0
iter qint drho vh0 rho0 vsum beta
1 14.000000 1.307E+03 70.0159 0.6965E+02 -28.0339 0.30
10 14.000000 1.663E-05 99.1713 0.1936E+04 -79.1078 1.00
v_rmax= -0.898068 etot= -580.086711
thrpv= 0.000000 by l: 0.000000 0.000000 0.000000
PPAR: SI nl=3 nsp=1 ves= 0.00000000
l e_nu C +/-del 1/sqrt(p) gam alp
0 -1.13028707 -0.73731517 0.16637532 4.3499527 0.42337892 0.42337892
1 -0.53734316 0.23227394 0.14386818 4.9250003 0.10360085 0.10360085
2 0.40295477 1.50574200 0.12262053 5.0193643 0.04452316 0.04452316
ATOM=ES Z=0 Qc=0 R=2.526526 Qv=0 a=0.025 nr=101
Pl= 1.5 2.5 3.5
Ql= 0.0 0.0 0.0
iter qint drho vh0 rho0 vsum beta
1 0.000000 0.000E+00 0.0000 0.0000E+00 -0.0000 0.30
v_rmax= 0.000000 etot= 0.000000
thrpv= 0.000000 by l: 0.000000 0.000000 0.000000
PPAR: ES nl=3 nsp=1 ves= 0.00000000
l e_nu C +/-del 1/sqrt(p) gam alp
0 -0.00000000 0.39164524 0.16318543 3.5893107 0.41666679 0.41666679
1 0.67878663 1.56971612 0.17050910 5.8127443 0.10804853 0.10804853
2 1.74976676 3.21776590 0.17686576 8.1196305 0.05381162 0.05381162
Class Qtot Qbak Vmad Vh(Rmax) V(Rmax)
SI 0.000000 0.000000 0.000000 0.000000 -0.898068
ES 0.000000 0.000000 0.000000 0.000000 0.000000
Sum Q=0.000000 Emad=0.000000(0.000000) Vmtz=-0.449034
LM: it 0 of 10 ehk0=-1160.173422 pv=0 mmom=0 seref=0
cpudel ... Time this iter: time(s): 0.0401 total: 0.0401s
Makidx: hamiltonian dimensions Low, Int, High, Negl: 36 0 0 0
--- BNDASA : iteration 1 ---
subzi: tetrahedron integration of bands; tetrahedron integration of density
SECMAT: kpt 1 of 8, k= 0.00000 0.00000 0.00000
-0.7597 0.0747 0.0747 0.0747 0.3490 0.3490 0.3490 0.3607 0.7058
BZWTS : --- Tetrahedron Integration ---
... only filled or empty bands encountered: ev=0.074734 ec=0.227756
VBmax = 0.074734 CBmin = 0.227756 gap = 0.153021 Ry = 2.08109 eV
BZINTS: Fermi energy: 0.074734; 8.000000 electrons; D(Ef): 0.000
Sum occ. bands: -2.1054872 incl. Bloechl correction: 0.000000
Saved qp weights ...
LM: ehf=-1155.6083879 ehk=-1156.0328682 sumev=-2.1054872 delsev=4.5650338
mixing: mode=B nmix=2 wc=3 beta=1
PQMIX: read 0 iter from file mixm. RMS DQ=2.30e-1
AMIX: nmix=0 mmix=8 nelts=24 beta=1 tm=10 rmsdel=2.3e-1
GETZV: 8 valence electrons
ATOM=SI Z=14 Qc=10 R=2.526526 Qv=-0.628572 a=0.025 nr=345
l pl q0 q1 q2 id dl
0 3.8394164 1.2099052 0.0000000 0.0503617 0 -1.8111193
1 3.7280551 1.9580060 0.0000000 0.0559823 0 -0.8708176
2 3.2697013 0.2035173 -0.0000000 0.0065939 0 0.8832876
iter qint drho vh0 rho0 vsum beta
1 13.371428 1.986E+00 99.1998 0.1935E+04 -81.3859 0.30
8 13.371428 1.948E-06 99.1952 0.1935E+04 -81.0837 1.00
v_rmax= -0.770037 etot= -577.714953
thrpv= 1.002858 by l: 0.596073 0.607216 -0.200431
PPAR: SI nl=3 nsp=1 ves= -0.06943559
l e_nu C +/-del 1/sqrt(p) gam alp
0 -0.57712189 -0.80153201 0.16020747 3.3590499 0.40253305 0.40253305
1 -0.20357205 0.15202344 0.13214885 4.1743553 0.09549092 0.09549092
2 -0.19646482 1.54368211 0.13914170 6.1624488 0.05120300 0.05120300
ATOM=ES Z=0 Qc=0 R=2.526526 Qv=0.628572 a=0.025 nr=101
l pl q0 q1 q2 id dl
0 1.3178804 0.2175356 -0.0000000 0.0095154 0 0.6440000
1 2.2139024 0.2790947 -0.0000000 0.0181331 0 1.2570628
2 3.1505230 0.1319412 0.0000000 0.0280573 0 1.9546650
iter qint drho vh0 rho0 vsum beta
1 0.628572 3.589E-01 0.1398 0.2116E-02 4.9045 0.30
4 0.628572 3.279E-05 0.1322 0.1696E-02 4.7721 1.00
v_rmax= -0.603191 etot= -0.365335
thrpv= -0.305671 by l: -0.141959 -0.142956 -0.020756
PPAR: ES nl=3 nsp=1 ves= 0.06943559
l e_nu C +/-del 1/sqrt(p) gam alp
0 -0.72253120 0.08140449 0.18877499 4.7233464 0.43067968 0.43067968
1 -0.61987854 1.32720389 0.20747596 8.2568133 0.11971356 0.11971356
2 -0.38284617 3.14656911 0.23079359 12.6105508 0.06447875 0.06447875
Class Qtot Qbak Vmad Vh(Rmax) V(Rmax)
SI -0.628572 0.000000 0.428142 -0.069436 -0.839473
ES 0.628572 0.000000 -0.428142 0.069436 -0.533755
Sum Q=0.000000 Emad=0.087290(-0.538236) Vmtz=-0.686614
SV: 1 2.304e-1 1.0000 3.600e-1 -1156.03286823 0.000000 L
it 1 of 10 ehf= -1155.608388 ehk= -1156.032868
i ehf=-1155.6083879 ehk=-1156.0328682
cpudel ... Time this iter: time(s): 0.0192 total: 0.0593s
Makidx: hamiltonian dimensions Low, Int, High, Negl: 36 0 0 0
--- BNDASA : iteration 2 ---
subzi: tetrahedron integration of bands; tetrahedron integration of density
SECMAT: kpt 1 of 8, k= 0.00000 0.00000 0.00000
-0.8926 -0.0011 -0.0011 -0.0011 0.1878 0.1878 0.1878 0.2337 0.5473
BZWTS : --- Tetrahedron Integration ---
... only filled or empty bands encountered: ev=-0.001116 ec=0.027324
VBmax = -0.001116 CBmin = 0.027324 gap = 0.028440 Ry = 0.38678 eV
BZINTS: Fermi energy: -0.001116; 8.000000 electrons; D(Ef): 0.000
Sum occ. bands: -3.0519550 incl. Bloechl correction: 0.000000
Saved qp weights ...
LM: ehf=-1156.0901666 ehk=-1156.0807798 sumev=-3.0519550 delsev=-0.0168823
mixing: mode=B nmix=2 wc=3 beta=1
PQMIX: read 1 iter from file mixm. RMS DQ=4.23e-2 last it=2.30e-1
broyj: start beta=1 w0=0.01 isw=0 gmax=0.11
Class Qtot Qbak Vmad Vh(Rmax) V(Rmax)
SI -0.806915 0.000000 0.549618 -0.089136 -0.851194
ES 0.806915 0.000000 -0.549618 0.089136 -0.541898
Sum Q=0.000000 Emad=0.143851(-0.886990) Vmtz=-0.696546
SV: 2 4.232e-2 1.0000 6.576e-2 -1156.08077981 0.000000 B 0.0100
it 2 of 10 ehf= -1156.090167 ehk= -1156.080780
From last iter ehf= -1155.608388 ehk= -1156.032868
diffe(q)= -0.481779 (0.042318) tol= 0.000010 (0.000010) more=T
i ehf=-1156.0901666 ehk=-1156.0807798
cpudel ... Time this iter: time(s): 0.0182 total: 0.0776s
Makidx: hamiltonian dimensions Low, Int, High, Negl: 36 0 0 0
--- BNDASA : iteration 3 ---
subzi: tetrahedron integration of bands; tetrahedron integration of density
SECMAT: kpt 1 of 8, k= 0.00000 0.00000 0.00000
-0.9241 -0.0399 -0.0399 -0.0399 0.1580 0.1580 0.1580 0.1842 0.5220
BZWTS : --- Tetrahedron Integration ---
... only filled or empty bands encountered: ev=-0.039925 ec=0.006901
VBmax = -0.039925 CBmin = 0.006901 gap = 0.046826 Ry = 0.63683 eV
BZINTS: Fermi energy: -0.039925; 8.000000 electrons; D(Ef): 0.000
Sum occ. bands: -3.3208430 incl. Bloechl correction: 0.000000
Saved qp weights ...
LM: ehf=-1156.0861213 ehk=-1156.0856308 sumev=-3.3208430 delsev=0.0231661
mixing: mode=B nmix=2 wc=3 beta=1
PQMIX: read 2 iter from file mixm. RMS DQ=8.26e-3 last it=4.23e-2
broyj: ir=2 dxmax=0.015 gmax=0.018 wc=3
Class Qtot Qbak Vmad Vh(Rmax) V(Rmax)
SI -0.775618 0.000000 0.528301 -0.085679 -0.848621
ES 0.775618 0.000000 -0.528301 0.085679 -0.540375
Sum Q=0.000000 Emad=0.132909(-0.819519) Vmtz=-0.694498
SV: 3 8.257e-3 1.0000 1.187e-2 -1156.08563079 0.000000 B 3.00
it 3 of 10 ehf= -1156.086121 ehk= -1156.085631
From last iter ehf= -1156.090167 ehk= -1156.080780
diffe(q)= 0.004045 (0.008257) tol= 0.000010 (0.000010) more=T
i ehf=-1156.0861213 ehk=-1156.0856308
cpudel ... Time this iter: time(s): 0.0176 total: 0.0952s
Makidx: hamiltonian dimensions Low, Int, High, Negl: 36 0 0 0
--- BNDASA : iteration 4 ---
subzi: tetrahedron integration of bands; tetrahedron integration of density
SECMAT: kpt 1 of 8, k= 0.00000 0.00000 0.00000
-0.9183 -0.0327 -0.0327 -0.0327 0.1635 0.1635 0.1635 0.1933 0.5267
BZWTS : --- Tetrahedron Integration ---
... only filled or empty bands encountered: ev=-0.032694 ec=0.010334
VBmax = -0.032694 CBmin = 0.010334 gap = 0.043028 Ry = 0.58518 eV
BZINTS: Fermi energy: -0.032694; 8.000000 electrons; D(Ef): 0.000
Sum occ. bands: -3.2711438 incl. Bloechl correction: 0.000000
Saved qp weights ...
LM: ehf=-1156.0853279 ehk=-1156.0853273 sumev=-3.2711438 delsev=0.0257416
mixing: mode=B nmix=2 wc=3 beta=1
PQMIX: read 3 iter from file mixm. RMS DQ=2.79e-4 last it=8.26e-3
broyj: ir=2 dxmax=6.2e-4 gmax=7.3e-4 wc=3
...
Class Qtot Qbak Vmad Vh(Rmax) V(Rmax)
SI -0.776779 0.000000 0.529091 -0.085807 -0.848686
ES 0.776779 0.000000 -0.529091 0.085807 -0.540455
Sum Q=0.000000 Emad=0.133307(-0.821974) Vmtz=-0.694571
SV: 4 2.793e-4 1.0000 4.355e-4 -1156.08532729 0.000000 B 3.00
it 4 of 10 ehf= -1156.085328 ehk= -1156.085327
From last iter ehf= -1156.086121 ehk= -1156.085631
diffe(q)= 0.000793 (0.000279) tol= 0.000010 (0.000010) more=T
i ehf=-1156.0853279 ehk=-1156.0853273
cpudel ... Time this iter: time(s): 0.0165 total: 0.112s
Makidx: hamiltonian dimensions Low, Int, High, Negl: 36 0 0 0
--- BNDASA : iteration 5 ---
subzi: tetrahedron integration of bands; tetrahedron integration of density
SECMAT: kpt 1 of 8, k= 0.00000 0.00000 0.00000
-0.9185 -0.0329 -0.0329 -0.0329 0.1633 0.1633 0.1633 0.1930 0.5266
BZWTS : --- Tetrahedron Integration ---
... only filled or empty bands encountered: ev=-0.032939 ec=0.010219
VBmax = -0.032939 CBmin = 0.010219 gap = 0.043157 Ry = 0.58694 eV
BZINTS: Fermi energy: -0.032939; 8.000000 electrons; D(Ef): 0.000
Sum occ. bands: -3.2728366 incl. Bloechl correction: 0.000000
Saved qp weights ...
LM: ehf=-1156.0853417 ehk=-1156.0853417 sumev=-3.2728366 delsev=0.0256042
mixing: mode=B nmix=2 wc=3 beta=1
PQMIX: read 4 iter from file mixm. RMS DQ=4.11e-6 last it=2.79e-4
broyj: ir=2 dxmax=8.4e-6 gmax=9.8e-6 wc=3
Class Qtot Qbak Vmad Vh(Rmax) V(Rmax)
SI -0.776765 0.000000 0.529082 -0.085806 -0.848685
ES 0.776765 0.000000 -0.529082 0.085806 -0.540454
Sum Q=0.000000 Emad=0.133302(-0.821945) Vmtz=-0.694570
SV: 5 4.109e-6 1.0000 5.585e-6 -1156.08534174 0.000000 B 3.00
it 5 of 10 ehf= -1156.085342 ehk= -1156.085342
From last iter ehf= -1156.085328 ehk= -1156.085327
diffe(q)= -0.000014 (0.000004) tol= 0.000010 (0.000010) more=T
i ehf=-1156.0853417 ehk=-1156.0853417
cpudel ... Time this iter: time(s): 0.0153 total: 0.127s
Makidx: hamiltonian dimensions Low, Int, High, Negl: 36 0 0 0
--- BNDASA : iteration 6 ---
subzi: tetrahedron integration of bands; tetrahedron integration of density
SECMAT: kpt 1 of 8, k= 0.00000 0.00000 0.00000
-0.9185 -0.0329 -0.0329 -0.0329 0.1633 0.1633 0.1633 0.1930 0.5266
BZWTS : --- Tetrahedron Integration ---
... only filled or empty bands encountered: ev=-0.032936 ec=0.010220
VBmax = -0.032936 CBmin = 0.010220 gap = 0.043156 Ry = 0.58692 eV
BZINTS: Fermi energy: -0.032936; 8.000000 electrons; D(Ef): 0.000
Sum occ. bands: -3.2728157 incl. Bloechl correction: 0.000000
Saved qp weights ...
LM: ehf=-1156.0853416 ehk=-1156.0853416 sumev=-3.2728157 delsev=0.0256041
mixing: mode=B nmix=2 wc=3 beta=1
PQMIX: read 5 iter from file mixm. RMS DQ=5.44e-8 last it=4.11e-6
broyj: ir=2 dxmax=1.2e-7 gmax=1.4e-7 wc=3
...
Class Qtot Qbak Vmad Vh(Rmax) V(Rmax)
SI -0.776765 0.000000 0.529082 -0.085806 -0.848685
ES 0.776765 0.000000 -0.529082 0.085806 -0.540454
Sum Q=0.000000 Emad=0.133302(-0.821945) Vmtz=-0.694570
SV: 6 5.441e-8 1.0000 7.730e-8 -1156.08534156 0.000000 B 3.00
it 6 of 10 ehf= -1156.085342 ehk= -1156.085342
From last iter ehf= -1156.085342 ehk= -1156.085342
diffe(q)= 0.000000 (0.000000) tol= 0.000010 (0.000010) more=F
c ehf=-1156.0853416 ehk=-1156.0853416
cpudel ... Time this iter: time(s): 0.0143 total: 0.141s
Jolly good show ! You converged to rms DQ= 0.000000
Exit 0 LM
CPU time: 0.141s Wall clock 0.207s at 14:18:10 28.04.2021 on ellery
Command
~/lmbuild/lmchk ctrl.si --syml~n=21~mq~lblq:G=0,0,0,L=1/2,1/2,1/2,X=0,1/2,1/2,W=1/4,1/2,3/4,K=3/8,3/8,3/4~lbl=LGXWGK
Expected Output
HEADER Si in diamond lattice with empty spheres.
LMCHK: nbas = 4 nspec = 2 verb 31,35
pot XC:BH
float: float P LDA-style
autoread: none
Plat Qlat
0.000000 0.500000 0.500000 -1.000000 1.000000 1.000000
0.500000 0.000000 0.500000 1.000000 -1.000000 1.000000
0.500000 0.500000 0.000000 1.000000 1.000000 -1.000000
alat = 10.262661 Cell vol = 270.221506
LATTC: as= 2.000 tol=1.00e-8 alat=10.26266 awald= 0.309 lmax=6
r1= 1.853 nkd= 87 q1= 5.557 nkg= 169
SGROUP: 48 symmetry operations from 2 generators
MKSYM: found 48 space group operations ... includes inversion
MKSYML: generating symmetry line file ...
rotating qp to Cartesian coordinates ...
Exit 0 wrote symmetry lines to syml file
CPU time: 0.027s Wall clock 0.091s at 15:32:24 28.04.2021 on ellery
Command
~/lmbuild/lmdos si -vnk=16 --dos:npts=1001:window=-1,.3
Expected Output
-------------- START LMDOS - ref: 87376a95 --------------
HEADER Si in diamond lattice with empty spheres.
LMDOS: nbas = 4 nspec = 2 verb 31,35
bz: metal, tetra, invit
Plat Qlat
0.000000 0.500000 0.500000 -1.000000 1.000000 1.000000
0.500000 0.000000 0.500000 1.000000 -1.000000 1.000000
0.500000 0.500000 0.000000 1.000000 1.000000 -1.000000
alat = 10.262661 Cell vol = 270.221506
LATTC: as= 2.000 tol=1.00e-8 alat=10.26266 awald= 0.309 lmax=6
r1= 1.853 nkd= 87 q1= 5.557 nkg= 169
SGROUP: 48 symmetry operations from 2 generators
MKSYM: found 48 space group operations ... includes inversion
BZMESH: 145 irreducible QP from 4096 ( 16 16 16 ) shift= F F F
TETIRR: sorting 24576 tetrahedra ... 570 inequivalent ones found
ASADOS: reading weights from file moms
expecting file to be resolved by l
file has 6 channel(s)
Using npts=1001 emin=-1 emax=0.3
IOMOMQ: read 145 qp efermi=-0.032936 vmtz=-0.694570
ASADOS: make dos for 1001 points from 9 bands in window (-1,0.3)
Channels in dos file generated by LMDOS:
site class label spin-1
1 1 SI 1:3
3 2 ES 4:6
Exit 0 LMDOS
CPU time: 0.044s Wall clock 0.105s at 17:34:23 28.04.2021 on ellery
Preliminaries
This tutorial assumes you have downloaded the repository (see here for instructions on getting access to and downloading the Questaal package), and, in a separate directory, built (compiled) the executable codes. For the purpose of demonstration, ~/lm will refer to the location of the downloaded repository and ~/lmbuild will refer to the build directory.
All instances of si in the command lines can be replaced with ctrl.si
1. Building the Input File
Shown below is a basic input file that can be used for this tutorial. First, navigate to a test directory testdir.
mkdir testdir ; cd testdir
Once you have entered testdir, create a new file named ctrl.si with your preferred text editor. Paste into ctrl.si the text shown in the box below; this file is now your input file.
VERS LM:7 ASA:7
HEADER Si in diamond lattice with empty spheres.
SYMGRP i*r3(1,1,-1)::(1/4,1/4,1/4) r4x::(1/4,1/4,1/4)
IO SHOW=F HELP=F VERBOS=31,35 WKP=F
HEADER [ The contents of HEADER reside within the category delimiters,
] so this line isn't part of it.
STR RMAX=3.6
STR RMAX[3.6] # An equivalent was of writing the previous line
OPTIONS NSPIN=1 ASA[ADNF=F TWOC=F CCOR=T]
% const a0=.5292 nk=4
BZ NKABC={nk}
STRUC NBAS=4 NSPEC=2 NL=3
ALAT=5.431/{a0} PLAT= 0 .5 .5 .5 0 .5 .5 .5 0 # Lattice constant of Si = 5.431 Angstrom
SITE ATOM=SI POS= 0 0 0
ATOM=SI POS= .25 .25 .25
ATOM=ES POS= .5 .5 .5
ATOM=ES POS= .75 .75 .75
SPEC ATOM=SI R/W=1 Z=14
ATOM=ES R/W=1 Z=0
ITER MIX=B2,wc=3,b0 CONVC=1D-5 NIT=10
START
% iffile si.si
CNTROL=F (=T to use following to override disk; =F to ignore following)
% else
BEGMOM=T (=T to begin with moments, =F to begin with band-structure)
CNTROL=T (=T to use following to override disk; =F to ignore following)
ATOM=SI P=3.5 3.5 3.5 Q=2 0 0 2 0 0 0 0 0
ATOM=ES P=1.5 2.5 3.5
% endif
Note: the input file includes a fictitious “atom” ES, with atomic number zero. This is because the ASA is designed for reasonably close-packed systems (for an explanation, see this page). The diamond lattice of Si is quite open, but by adding the fictitious empty spheres it can artifically be made more close-packed and be reasonably accurate.
2. Running Band Calculations
The band calculation can be done with a combination of executables located in your build directory: lmstr, the structure constant utility, and lm, the ASA band program.
You must first run lmstr. To invoke lmstr and to pipe the output to a file, do the following
~/lmbuild/lmstr si > out.lmstr
This will run lmstr using the input file, ctrl.si, created above. lmstr must be run in advance of the band code lm, as it makes structure constants lm requires.
The output will be redirected from the screen to file out.lmstr.
Note: The output file can be named differently, and its extension does not matter. Further, it is not necessary to save the output to a file at all if you do not wish to, simply omit the > out.lmstr.
Next run lm
~/lmbuild/lm si > out.lm
The expected output is listed in full in the Command Summary at the top of this tutorial. To see the progression to self-consistency enter
grep DQ out.lm
The system should have become well converged after 5 iterations. To see the bandgap, enter
grep gap out.lm
It should have converged to about 0.58 eV (the initial values are a bit erratic, as the trial density is initially poor). As is typical, the local-density approximation underestimates the bandgap (it it is actually about 1.17 eV at 0 K).
Note: If you are going to use these codes often, it is recommended that you install theses codes into some directory in your path, e.g. ~/bin. Set the prefix variable as desired in ~/lmbuild/flags.mk, for example, using
prefix = ~
will cause the installer to copy the files into ~/bin. After modifying flags.mk, do the following:
cd ~/lmbuild/
ninja install
3. Generating Energy Bands
To draw energy bands, you must choose what lines in k space to draw them on. For fcc, the most common points are those denoted as the L point (k = (1/2,1/2,1/2) in units of 2π/a, a being the lattice constant, which is 5.431 Å for Si), the Γ point (k = (0,0,0)) and the X point k = (0,0,1).
lm reads this information from a symmetry lines file. With your text editor, you can make one on your own, though here we will use an auto-generator in Questaal’s lmchk utility.
Si crystallizes in the diamond cubic structure, which has an fcc Bravais lattice. For the fcc lattice, lmchk will generate a symmetry line file with the following instruction, adapted from this page:
~/lmbuild/lmchk ctrl.si --syml~n=21~mq~lblq:G=0,0,0,L=1/2,1/2,1/2,X=0,1/2,1/2,W=1/4,1/2,3/4,K=3/8,3/8,3/4~lbl=LGXWGK
Inspect syml.si. It should be Questaal’s standard format for symmetry line mode.
# generated from text ~n=21~mq~lblq:G=0,0,0,L=1/2,1/2,1/2,X=0,1/2,1/2,W=1/4,1/2,3/4,K=3/8,3/8,3/4~lbl=LGXWGK
18 0.5000000 0.5000000 0.5000000 0.0000000 0.0000000 0.0000000 L to G
21 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 G to X
11 1.0000000 0.0000000 0.0000000 1.0000000 0.5000000 0.0000000 X to W
23 1.0000000 0.5000000 0.0000000 0.0000000 0.0000000 0.0000000 W to G
22 0.0000000 0.0000000 0.0000000 0.7500000 0.7500000 0.0000000 G to K
Run lm in band mode to generate bnds.si.
lm si --iactiv --band:fn=syml
bnds.si is written in a format described on this page.
The bands can be plotted with various plotting packages. This is a personal choice, but you can do it efficiently with Questaal’s utilities, which are built with the all the other Questaal executables.
You can immediately make a postscript file with Questaal’s plbnds utility:
echo -13,10,5,10 | ~/lmbuild/plbnds -scl=13.6 -lbl bnds.si
It makes a (primitive) postscript file fplot.ps directly. You can do much better with the following:
echo -13,10,5,10 | ~/lmbuild/plbnds -fplot -ef=0 -scl=13.6 -lbl bnds.si
The -fplot switch tells plbnds to creates a file plot.plbnds. This is a script for Questaal’s graphics utility, fplot utility. Use fplot to create a postscript file based on the contents of plot.plbnds:
~/lmbuild/fplot -f plot.plbnds
This which creates a postscript file fplot.ps, much prettier than the one plbnds makes. You can tailor the script to tune the figure.
The bands you get should look very similar to the LDA band structure generated by the full-potential program lmf.
Click here to see the LDA band structure for Si.
You can see that silicon has an indirect band gap of around 0.60 eV. The valence band maximum falls at the point while the conduction band minimum lies between and X, at about 0.85 of the distance to X. The experimental gap is about 1.2 eV.
The energy bands generator has an optional feature that enables you to highlight a particular orbital character in the energy bands; see for example this page.
4. Generating Densities-of-States
You can generate the total density-of-states (DOS) by setting BZ_SAVDOS=T in ctrl.si before running lm. This will generate the DOS just with lm. To resolve the DOS by orbital, you must do an extra step, using the lmdos utility.
In the steps below we first re-run lm with a finer k mesh. This isn’t necessary but it makes a smoother DOS.
~/lmbuild/lm si -vnk=16 --quit=band
Now generate the orbital resolved DOS
~/lmbuild/lmdos si -vnk=16
During execution, a prompt will appear:
Enter npts (def=501), emin and emax (def=-1,0):
Enter:
1001 -1 0.3 <return>
Or run lmdos non-interactively
lmdos si -vnk=16 --dos:npts=1001:window=-1,.3
This generates an ASCII file dos.si, and its format is described on this page. It contains 6 channels, as shown in the output from lmdos :
Channels in dos file generated by LMDOS:
site class label spin-1
1 1 SI 1:3
3 2 ES 4:6
Channels 1-3 are partial Si DOS for s, p, and d orbitals; channels 4-6 are the corresponding DOS for the empty spheres.
How to draw figures from this file is a personal choice, but you can do it efficiently with Questaal’s pldos utility.
For example,
echo 8 7 / | ~/lmbuild/pldos -fplot '-lst=1,2,3;4,5,6' dos.si
reads dos.si and creates a script plot.pldos the fplot utility can read, along with a data file dosp.dat in the standard Questaal format for 2D arrays. It has two columns containing partial DOS (one column combines DOS 1,2,3 —the Si DOS and the other combines DOS 4,5,6—the ES DOS). Use fplot to make a figure:
~/lmbuild/fplot -pr10 -f plot.dos
This creates postscript file fplot.ps, which you can view with your favorite view, e.g. the ghostscript utility, gs. The DOS should show a gap at the Fermi level of about 0.04 Ry, which is the LDA gap for Si.
You can resolve the DOS in other ways. In the instruction below Example: in file dos.dat the majority DOS are in channels 1,3,5 (atom 1) and 7,9,11 (atom 2), and the minority DOS are in channels 2,4,6 (atom 1) and 8,10,12 (atom 2), invoke, e.g.
echo 8 7 / | ~/lmbuild/pldos -fplot '-lst=1;2;3;4,5,6' dos.si
creates four panels: panels 1-3 are DOS for s, p, and d, and the fourth panel combines all the DOS for the ES channels
Note: there is a facility to draw two DOS in a single panel, one above the ‘zero’ and one below. This is particularly convenient in spin polarized cases when you want to compare the majority and minority DOS. See -lst2 in the pldos manual.
Further Reading
An overview of the Questaal package, and its main programs
Guide to the input file
The ASA suite and its programs explained
Drawing energy bands with colour weights