在OpenMX当中，可以将晶胞的多条近似重叠的能带打开成原胞仿真结果。构建大一些的晶胞可以方便我们对体系进行赝原子轨道分解，还可以仿真缺陷和掺杂的情况。
先上一个石墨烯的原胞版的能带打开范例。在这个范例当中，由于使用的是原胞，所以仿真结果和晶胞一致，即使不设置参考晶格矢量。
文件名为Graphen_C_Primitive.dat
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 |
# # File Name # System.CurrrentDirectory ./ System.Name graphene_c_primitive level.of.stdout 1 # default=1 (1-3) level.of.fileout 1 # default=1 (1-3) # # Definition of Atomic Species # Species.Number 1 <Definition.of.Atomic.Species C C6.0-s2p2d1 C_PBE13 Definition.of.Atomic.Species> # # Atoms # Atoms.Number 2 Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU <Atoms.SpeciesAndCoordinates 1 C 0.000000000 0.710000000 0.000000000 2.0 2.0 2 C 0.000000000 -0.71000000 0.000000000 2.0 2.0 Atoms.SpeciesAndCoordinates> Atoms.UnitVectors.Unit Ang # Ang|AU <Atoms.UnitVectors 1.22980000000000 2.13000000000000 0.00000000000000 1.22980000000000 -2.13000000000000 0.00000000000000 0.00000000000000 0.00000000000000 20.00000000000000 Atoms.UnitVectors> # # SCF or Electronic System # scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE scf.SpinPolarization off # On|Off scf.SpinOrbit.Coupling off scf.ElectronicTemperature 300.0 # default=300 (K) scf.energycutoff 200.0 # default=150 (Ry) scf.maxIter 300 # default=40 scf.EigenvalueSolver Band # Recursion|Cluster|Band scf.Kgrid 10 10 1 # means n1 x n2 x n3 scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay scf.Init.Mixing.Weight 0.07 # default=0.30 scf.Min.Mixing.Weight 0.003 # default=0.001 scf.Max.Mixing.Weight 0.15 # default=0.40 scf.Mixing.History 39 # default=5 scf.Mixing.StartPulay 10 # default=6 scf.Mixing.EveryPulay 1 scf.criterion 1.0e-7 # default=1.0e-6 (Hartree) # # MD or Geometry Optimization # MD.Type Nomd # Nomd|Opt|DIIS|NVE|NVT_VS|NVT_NH # # Band dispersion # Band.dispersion on # on|off, default=off # # Unfolding of bands # Band.Nkpath 3 <Band.kpath 25 0.5 0.0 0.0 0.333 0.333 0.0 M K 25 0.333 0.333 0.0 0.0 0.0 0.0 K G 25 0.0 0.0 0.0 0.5 0.0 0.0 G M Band.kpath> Unfolding.Electronic.Band on # on|off, default=off Unfolding.LowerBound -15.0 # default=-10 eV Unfolding.UpperBound 15.0 # default= 10 eV Unfolding.desired_totalnkpt 30 Unfolding.Nkpoint 4 <Unfolding.kpoint M 0.5 0.0 0.0 K 0.333 0.333 0.0 G 0.0 0.0 0.0 M 0.5 0.0 0.0 Unfolding.kpoint> |
仿真结果文件有unfold_orbup，这里面第一列是k点，第二列是对应的能量，可以用gnuplot来画1:2出（打开版的）能带。可以验证这样算出的能带和普通方式算出的能带是一样的。
接着说上面代码的结果，上面的代码是最简单的石墨烯的能带打开仿真。出现的文件中有一个.unfold_plotexample文件。文件名为Graphene_C_Primitive_Te.dat，部分内容如下：
|
1 2 3 4 5 6 7 8 9 |
set yrange [-15.000000:15.000000] set ylabel 'Energy (eV)' set xtics('M' 0.000000,'K' 0.450166,'G' 1.350474,'M' 2.130950) set xrange [0:2.130950] set arrow nohead from 0,0 to 2.130950,0 set arrow nohead from 0.450166,-15.000000 to 0.450166,15.000000 set arrow nohead from 1.350474,-15.000000 to 1.350474,15.000000 set style circle radius 0 plot 'graphene_c_primitive.unfold_totup' using 1:2:($3)*0.05 notitle with circles lc rgb 'red' |
只要仿真没错，都会有这个文件。
可以用gnuplot 的load命令直接load这个文件
就可以画出图
貌似为了仿真倒带性质，OpenMX用户手册在SiC的例子里添加了一个Te空原子。我们也在石墨烯的仿真文件中照猫画虎，添加一个Te空原子，修改后的部分文件内容和仿真结果如下：
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 |
Species.Number 2 <Definition.of.Atomic.Species C C6.0-s2p2d1 C_PBE13 Te Te11.0-s2p2d2f1 E Definition.of.Atomic.Species> # # Atoms # Atoms.Number 3 Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU <Atoms.SpeciesAndCoordinates 1 C 0.000000000 0.710000000 0.000000000 2.0 2.0 2 C 0.000000000 -0.71000000 0.000000000 2.0 2.0 3 Te 1.229800000 0.00000000 0.000000000 0 0 Atoms.SpeciesAndCoordinates> Atoms.UnitVectors.Unit Ang # Ang|AU <Atoms.UnitVectors 1.22980000000000 2.13000000000000 0.00000000000000 1.22980000000000 -2.13000000000000 0.00000000000000 0.00000000000000 0.00000000000000 20.00000000000000 Atoms.UnitVectors> |
将晶胞扩充为原胞
我们继续将晶胞扩充为原胞，诸多细节不再列举。代码如下：
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 |
# # File Name # System.CurrrentDirectory ./ System.Name graphene_c_nsp_p level.of.stdout 1 # default=1 (1-3) level.of.fileout 1 # default=1 (1-3) # # Definition of Atomic Species # Species.Number 1 <Definition.of.Atomic.Species C C7.0-s2p2d1 C_PBE13 Definition.of.Atomic.Species> # # Atoms # Atoms.Number 8 Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU <Atoms.SpeciesAndCoordinates 1 C 0.000000000 0.710000000 0.000000000 2.0 2.0 2 C 0.000000000 -0.71000000 0.000000000 2.0 2.0 3 C 1.2298 2.8400 0.00000 2.0 2.0 4 C 1.2298 1.4200 0.00000000 2.0 2.0 5 C 1.2298 -1.4200 0.00000000 2.0 2.0 6 C 1.2298 -2.8400 0.000000000 2.0 2.0 7 C 2.4596 0.7100 0.00000000 2.0 2.0 8 C 2.4596 -0.7100 0.000000000 2.0 2.0 Atoms.SpeciesAndCoordinates> Atoms.UnitVectors.Unit Ang # Ang|AU <Atoms.UnitVectors 2.45960000000000 4.26000000000000 0 2.45960000000000 -4.26000000000000 0 0 0 40 Atoms.UnitVectors> # # SCF or Electronic System # scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE scf.SpinPolarization off # On|Off scf.ElectronicTemperature 300.0 # default=300 (K) scf.energycutoff 200.0 # default=150 (Ry) scf.maxIter 300 # default=40 scf.EigenvalueSolver Band # Recursion|Cluster|Band scf.Kgrid 5 5 1 # means n1 x n2 x n3 scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay scf.Init.Mixing.Weight 0.07 # default=0.30 scf.Min.Mixing.Weight 0.003 # default=0.001 scf.Max.Mixing.Weight 0.15 # default=0.40 scf.Mixing.History 39 # default=5 scf.Mixing.StartPulay 10 # default=6 scf.Mixing.EveryPulay 1 scf.criterion 1.0e-7 # default=1.0e-6 (Hartree) # # MD or Geometry Optimization # MD.Type Nomd # Nomd|Opt|DIIS|NVE|NVT_VS|NVT_NH # # Band dispersion # Band.dispersion on # on|off, default=off Band.Nkpath 3 <Band.kpath 25 0.5 0.0 0.0 0.333 0.333 0.0 M K 25 0.333 0.333 0.0 0.0 0.0 0.0 K G 25 0.0 0.0 0.0 0.5 0.0 0.0 G M Band.kpath> # # Unfolding of bands # Unfolding.Electronic.Band on # on|off, default=off Unfolding.LowerBound -10.0 # default=-10 eV Unfolding.UpperBound 6.0 # default= 10 eV Unfolding.desired_totalnkpt 30 Unfolding.Nkpoint 4 <Unfolding.kpoint M 0.5 0.0 0.0 K 0.333 0.333 0.0 G 0.0 0.0 0.0 M 0.5 0.0 0.0 Unfolding.kpoint> <Unfolding.ReferenceVectors 1.22980000000000 2.13000000000000 0.00000000000000 1.22980000000000 -2.13000000000000 0.00000000000000 0.00000000000000 0.00000000000000 20.00000000000000 Unfolding.ReferenceVectors> <Unfolding.Map 1 1 2 2 3 1 4 2 5 1 6 2 7 1 8 2 Unfolding.Map> |
用上面介绍的gnuplot方法画出结果：
带隙还在，可以接受。再进一步，填入空隙，结果如下。可以发现，圆圈多了很多。代码放在附录里面。Graphene_C_NSP_P_Te.dat
上面的是总的totup文件的数据。要获得赝原子轨道分解的数据需要将unfold_plotexample文件的代码写成如下这样：
|
1 2 3 4 5 6 7 8 9 |
set yrange [-15.000000:15.000000] set ylabel 'Energy (eV)' set xtics('M' 0.000000,'K' 0.450166,'G' 1.350474,'M' 2.130950) set xrange [0:2.130950] set arrow nohead from 0,0 to 2.130950,0 set arrow nohead from 0.450166,-15.000000 to 0.450166,15.000000 set arrow nohead from 1.350474,-15.000000 to 1.350474,15.000000 set style circle radius 0 plot 'graphene_c_nsp_p_te.unfold_orbup' using 1:2:(($3+$4+$5+$6)*0.5) notitle with circles lc rgb 'green','graphene_c_nsp_p_te.unfold_orbup' using 1:2:($7*0.5) notitle with circles lc rgb 'red' |
得到的图形如下：
仿真掺杂
在石墨烯表面掺入一个磷原子，能带的移动可以用上面的理论与方法直观地看到了。对应的仿真文件为名为Graphene_C_NSP_V.dat。该文件也放在附录当中。
而画出它这个图的plotexample文件为：
|
1 2 3 4 5 6 7 8 9 |
set yrange [-15.000000:15.000000] set ylabel 'Energy (eV)' set xtics('M' 0.000000,'K' 0.450166,'G' 1.350474,'M' 2.130950) set xrange [0:2.130950] set arrow nohead from 0,0 to 2.130950,0 set arrow nohead from 0.450166,-15.000000 to 0.450166,15.000000 set arrow nohead from 1.350474,-15.000000 to 1.350474,15.000000 set style circle radius 0 plot 'graphene_c_nsp_v.unfold_orbup' using 1:2:($4+$5+$6)*0.2 notitle with circles lc rgb 'red','graphene_c_nsp_v.unfold_orbup' using 1:2:($7)*0.2 notitle with circles lc rgb 'green','graphene_c_nsp_v.unfold_totup' using 1:2:($3)*0.05 notitle with circles lc rgb 'black' |
使用Band.kpath和Band.Nkpath命令来控制产生能带数据。如果不要能带，这个就可以不写。产生的.Band文件要用gnuband13处理。
|
1 2 3 4 5 6 |
Band.Nkpath 3 <Band.kpath 25 0.5 0.0 0.0 0.333 0.333 0.0 M K 25 0.333 0.333 0.0 0.0 0.0 0.0 K G 25 0.0 0.0 0.0 0.5 0.0 0.0 G M Band.kpath> |
处理之后，把BANDDAT1的数据和unfold_orbup文件画在一个图中
|
1 |
plot "graphene_c_nsp_v.BANDDAT1" using ($1*2):2 w l lc rgb 'green','graphene_c_nsp_v.unfold_orbup' using 1:2:($4+$5+$6)*0.2 notitle with circles lc rgb 'red','graphene_c_nsp_v.unfold_orbup' using 1:2:($7)*0.2 notitle with circles lc rgb 'blue' |
附注
Graphene_C_NSP_P_Te.dat
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 |
# # File Name # System.CurrrentDirectory ./ System.Name graphene_c_nsp_p_te level.of.stdout 1 # default=1 (1-3) level.of.fileout 1 # default=1 (1-3) # # Definition of Atomic Species # Species.Number 2 <Definition.of.Atomic.Species C C7.0-s2p2d1 C_PBE13 Te Te11.0-s2p2d2f1 E Definition.of.Atomic.Species> # # Atoms # Atoms.Number 12 Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU <Atoms.SpeciesAndCoordinates 1 C 0.000000000 0.710000000 0.000000000 2.0 2.0 2 C 0.000000000 -0.71000000 0.000000000 2.0 2.0 3 Te 1.2298000000 0.00000000 0.000000000 0 0 4 C 1.2298 2.8400 0.00000 2.0 2.0 5 C 1.2298 1.4200 0.00000000 2.0 2.0 6 Te 2.4596 2.1300 0.0 0 0 7 C 1.2298 -1.4200 0.00000000 2.0 2.0 8 C 1.2298 -2.8400 0.000000000 2.0 2.0 9 Te 2.4596 -2.1300 0 0 0 10 C 2.4596 0.7100 0.00000000 2.0 2.0 11 C 2.4596 -0.7100 0.000000000 2.0 2.0 12 Te 3.6894 0 0 0 0 Atoms.SpeciesAndCoordinates> Atoms.UnitVectors.Unit Ang # Ang|AU <Atoms.UnitVectors 2.45960000000000 4.26000000000000 0 2.45960000000000 -4.26000000000000 0 0 0 40 Atoms.UnitVectors> # # SCF or Electronic System # scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE scf.SpinPolarization off # On|Off scf.ElectronicTemperature 300.0 # default=300 (K) scf.energycutoff 200.0 # default=150 (Ry) scf.maxIter 300 # default=40 scf.EigenvalueSolver Band # Recursion|Cluster|Band scf.Kgrid 10 10 1 # means n1 x n2 x n3 scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay scf.Init.Mixing.Weight 0.07 # default=0.30 scf.Min.Mixing.Weight 0.003 # default=0.001 scf.Max.Mixing.Weight 0.15 # default=0.40 scf.Mixing.History 39 # default=5 scf.Mixing.StartPulay 10 # default=6 scf.Mixing.EveryPulay 1 scf.criterion 1.0e-7 # default=1.0e-6 (Hartree) # # MD or Geometry Optimization # MD.Type Nomd # Nomd|Opt|DIIS|NVE|NVT_VS|NVT_NH # # Band dispersion # Band.dispersion on # on|off, default=off Band.Nkpath 3 <Band.kpath 25 0.5 0.0 0.0 0.333 0.333 0.0 M K 25 0.333 0.333 0.0 0.0 0.0 0.0 K G 25 0.0 0.0 0.0 0.5 0.0 0.0 G M Band.kpath> # # Unfolding of bands # Unfolding.Electronic.Band on # on|off, default=off Unfolding.LowerBound -15.0 # default=-10 eV Unfolding.UpperBound 15.0 # default= 10 eV Unfolding.desired_totalnkpt 30 Unfolding.Nkpoint 4 <Unfolding.kpoint M 0.5 0.0 0.0 K 0.333 0.333 0.0 G 0.0 0.0 0.0 M 0.5 0.0 0.0 Unfolding.kpoint> <Unfolding.ReferenceVectors 1.22980000000000 2.13000000000000 0.00000000000000 1.22980000000000 -2.13000000000000 0.00000000000000 0.00000000000000 0.00000000000000 20.00000000000000 Unfolding.ReferenceVectors> <Unfolding.Map 1 1 2 2 3 3 4 1 5 2 6 3 7 1 8 2 9 3 10 1 11 2 12 3 Unfolding.Map> |
Graphene_C_NSP_V.dat
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 |
# # File Name # System.CurrrentDirectory ./ System.Name graphene_c_nsp_v level.of.stdout 1 # default=1 (1-3) level.of.fileout 1 # default=1 (1-3) # # Definition of Atomic Species # Species.Number 2 <Definition.of.Atomic.Species C C7.0-s2p2d1 C_PBE13 P P8.0-s2p2d1 P_CA13 Definition.of.Atomic.Species> # # Atoms # Atoms.Number 9 Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU <Atoms.SpeciesAndCoordinates 1 C 0.000000000 0.710000000 0.000000000 2.0 2.0 2 C 0.000000000 -0.71000000 0.000000000 2.0 2.0 3 C 1.2298 2.8400 0.00000 2.0 2.0 4 C 1.2298 1.4200 0.00000000 2.0 2.0 5 C 1.2298 -1.4200 0.00000000 2.0 2.0 6 C 1.2298 -2.8400 0.000000000 2.0 2.0 7 C 2.4596 0.7100 0.00000000 2.0 2.0 8 C 2.4596 -0.7100 0.000000000 2.0 2.0 9 P 1.229800000 0.00000000 1.520000000 2.5 2.5 Atoms.SpeciesAndCoordinates> Atoms.UnitVectors.Unit Ang # Ang|AU <Atoms.UnitVectors 2.45960000000000 4.26000000000000 0 2.45960000000000 -4.26000000000000 0 0 0 40 Atoms.UnitVectors> # # SCF or Electronic System # scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE scf.SpinPolarization off # On|Off scf.ElectronicTemperature 300.0 # default=300 (K) scf.energycutoff 200.0 # default=150 (Ry) scf.maxIter 300 # default=40 scf.EigenvalueSolver Band # Recursion|Cluster|Band scf.Kgrid 5 5 1 # means n1 x n2 x n3 scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay scf.Init.Mixing.Weight 0.07 # default=0.30 scf.Min.Mixing.Weight 0.003 # default=0.001 scf.Max.Mixing.Weight 0.15 # default=0.40 scf.Mixing.History 39 # default=5 scf.Mixing.StartPulay 10 # default=6 scf.Mixing.EveryPulay 1 scf.criterion 1.0e-7 # default=1.0e-6 (Hartree) # # MD or Geometry Optimization # MD.Type Nomd # Nomd|Opt|DIIS|NVE|NVT_VS|NVT_NH # # Band dispersion # Band.dispersion on # on|off, default=off Band.Nkpath 3 <Band.kpath 25 0.5 0.0 0.0 0.333 0.333 0.0 M K 25 0.333 0.333 0.0 0.0 0.0 0.0 K G 25 0.0 0.0 0.0 0.5 0.0 0.0 G M Band.kpath> # # Unfolding of bands # Unfolding.Electronic.Band on # on|off, default=off Unfolding.LowerBound -15.0 # default=-10 eV Unfolding.UpperBound 15.0 # default= 10 eV Unfolding.desired_totalnkpt 30 Unfolding.Nkpoint 4 <Unfolding.kpoint M 0.5 0.0 0.0 K 0.333 0.333 0.0 G 0.0 0.0 0.0 M 0.5 0.0 0.0 Unfolding.kpoint> <Unfolding.ReferenceVectors 1.22980000000000 2.13000000000000 0.00000000000000 1.22980000000000 -2.13000000000000 0.00000000000000 0.00000000000000 0.00000000000000 20.00000000000000 Unfolding.ReferenceVectors> <Unfolding.Map 1 1 2 2 3 1 4 2 5 1 6 2 7 1 8 2 9 3 Unfolding.Map> |
