* Bader電荷解析 [#va4ae2b5]
[[Henkelman Group:http://theory.cm.utexas.edu/henkelman/code/bader/]]が配布しているプログラムを利用してBader電荷の計算を行う。
** グラフェン 1x1[#ed3f7d01]
#ref(http://www-cp.prec.eng.osaka-u.ac.jp/puki_state/my_image/gra1x1.png,nolink)
以下ではノルム保存擬ポテンシャルC_pbe6TMを用いる。
*** SCF計算 [#be50a39b]
入力ファイル
0 0 0 0 0 0
8.0000 20.0000 1 2 2 : GMAX, GMAXP, NTYP, NATM, NATM2
191 0 : number of space group, type of bravis lattice
4.655538364 4.655538364 20.000 90.0 90.0 120.0 : a,b,c,alpha,beta,gamma
24 24 1 1 1 1 : knx,kny,knz, k-point shift
0 0 : NCORD, NINV, : IWEI, IMDTYP, ITYP
0.6666666666 0.3333333333 0.0000000000 1 1 1
0.3333333333 0.6666666666 0.0000000000 1 1 1
6 0.1500 12.0107 1 1 0.d0 : TYPE 1IATOMN,ALFA,AMION,ILOC,IVAN
0 0 0 0 0 : ICOND 0-MD, 1-CONT.MD, 2-WAVE FN,, 3-WAVE FN CONT., iconstpw
0 1 : IPRE, IPRI
200 200 0 3600.00 0 : NMD1, NMD2, iter_last, CPUMAX,ifstop
3 1 : Simple=1,Broyd2=3,Blugel=6, 1:charge, 2:potential mix.
0 20 0.8 : starting mixing, kbxmix,alpha
0.60 0.50 0.60 0.70 1.00 : DTIM1, DTIM2, DTIM3, DTIM4, dtim_last
30.00 2 1 0.10D-08 1.d-06 : DTIO ,IMDALG, IEXPL, EDELTA
-0.0010 0.10D+02 0 : WIDTH,FORCCR,ISTRESS
ggapbe 1 : XCTYPE, nspin
1.00 3 : destm, n_stm
101 : NBZTYP 0-SF, 1-BK, 2-SC, 3-BCC, 4-FCC, 5-DIA, 6-HEX
0 0 0 : NKX, NKY, NKZ
0 0 0 : NKX2,NKY2,NKZ2
8 : NEG
1 : NEXTST(MB)
0 : 0; random numbers, 1; matrix diagon
2 0 0 0(MB) : imsd, i_2lm, i_sd2another, wksz for phase
0 : evaluation of eko difference.0 = no ,1 = yes
0 : npdosao
0 0.0 : SM_N, DOPPING
計算結果
$ grep ETOT your_output_file_name|grep "[0-9]"
ETOT: 1 15.49339609 0.1549E+02 0.4996E-01
ETOT: 2 0.34620940 0.1515E+02 0.1209E-01
ETOT: 3 -5.83837125 0.6185E+01 0.1717E-01
ETOT: 4 -8.60080202 0.2762E+01 0.1845E-01
ETOT: 5 -10.11782100 0.1517E+01 0.2536E-01
ETOT: 6 -11.03537609 0.9176E+00 0.2397E-01
ETOT: 7 -11.40509046 0.3697E+00 0.2251E-01
ETOT: 8 -11.45549051 0.5040E-01 0.2050E-01
ETOT: 9 -11.48179862 0.2631E-01 0.1827E-01
ETOT: 10 -11.47035224 0.1145E-01 0.1958E-01
ETOT: 11 -11.53852896 0.6818E-01 0.1092E-01
ETOT: 12 -11.57400237 0.3547E-01 0.4760E-02
ETOT: 13 -11.58514681 0.1114E-01 0.1420E-02
ETOT: 14 -11.58579130 0.6445E-03 0.5748E-03
ETOT: 15 -11.58587175 0.8045E-04 0.1339E-03
ETOT: 16 -11.58587362 0.1875E-05 0.4189E-04
ETOT: 17 -11.58587413 0.5126E-06 0.1486E-04
ETOT: 18 -11.58587420 0.6892E-07 0.3361E-05
ETOT: 19 -11.58587421 0.4461E-08 0.1102E-05
ETOT: 20 -11.58587421 0.1802E-08 0.3413E-06
ETOT: 21 -11.58587421 0.2176E-09 0.1103E-06
ETOT: 22 -11.58587421 0.3718E-10 0.4886E-07
ETOT(Q) + SM_energy = -11.5858742100388 8.35680549919333
*** 実空間の電荷密度 [#u873fbb8]
icond=9として再計算して実空間の電荷密度nfchgt_r.dataを作成する。
*** Gaussian cube fileの作成 [#a3d3331c]
/home/hamada/STATE/tools/ChargeUtil/chg2cubeを用いて電荷密度をGaussian cube形式に変換する。
$ chg2cube
Enter the name of the STATE input file> your_input_file_name
Enter the name of the charge density file> nfchgt_r.data
Enter the prefix for output file(s)> charge
reading nfchgt_r.data...done.
# of data in nfchgt_r.data : 1
data #1 : ispin : 1 : ilevel: 1
Creating charge.cube...done.
Program successfully ended
chg2cubeの実行後、対話的に
- STATEの入力ファイルの名前
- 電荷密度ファイルの名前（nfchgt_r.data）
- cubeファイルの名前（上ではcharge）
を入力するとcharge.cubeが生成される。
Gaussian cube形式に関しては例えば[[ここ>http://paulbourke.net/dataformats/cube/]]を参照。
*** Bader電荷の計算 [#i8ab8f23]
上で得られたGaussian cube形式の電荷密度ファイルcharge.cubeを用いてBader電荷を計算する。
$ bader charge.cube
GRID BASED BADER ANALYSIS (Version 0.95a 02/26/16)
OPEN ... charge.cube
GAUSSIAN-STYLE INPUT FILE
FFT-grid: 30 x 30 x 128
CLOSE ... charge.cube
RUN TIME: 0.03 SECONDS
CALCULATING BADER CHARGE DISTRIBUTION
0 10 25 50 75 100
PERCENT DONE: **********************
REFINING AUTOMATICALLY
ITERATION: 1
EDGE POINTS: 23177
REASSIGNED POINTS: 969
ITERATION: 2
CHECKED POINTS: 9850
REASSIGNED POINTS: 0
RUN TIME: 0.15 SECONDS
CALCULATING MINIMUM DISTANCES TO ATOMS
0 10 25 50 75 100
PERCENT DONE: **********************
RUN TIME: 0.01 SECONDS
WRITING BADER ATOMIC CHARGES TO ACF.dat
WRITING BADER VOLUME CHARGES TO BCF.dat
NUMBER OF BADER MAXIMA FOUND: 6
SIGNIFICANT MAXIMA FOUND: 6
VACUUM CHARGE: 0.0205
NUMBER OF ELECTRONS: 8.00003
*** オプション [#g4d7e835]
プログラムbaderのオプションはbader -hで確認できる:
$ bader -h
GRID BASED BADER ANALYSIS (Version 0.95a 02/26/16)
Description of flags
-c | -n < bader | voronoi >
Turn on [-c] or off [-n] the following calculations
bader: Bader atoms in molecules (default)
voronoi: population analysis based on distance
-b < neargrid | ongrid | weight >
Use the default near-grid bader partitioning, the
original on-grid based algorithm, or the weight method
of Yu and Trinkle
-r < refine_edge_method >
By default (-r -1) , only the points around reassigned
points are checked during refinements. The old method,
which checks every edge point during each refinement, can
be enabled using the -r -2 switch:
bader -r -2 CHGCAR
-ref < reference_charge >
Use a reference charge file to do the Bader partitioning.
This is the recommended way to analyze vasp output files:
bader CHGCAR -ref CHGCAR_total
where CHGCAR_total is the sum of AECCAR0 and AECCAR2.
-vac < off | auto | vacuum_density >
Assign low density points to vacuum.
auto: vacuum density cutoff is 1E-3 e/Ang^3 by default
off: do not assign low density points to a vacuum volume
vacuum_density: maximum density assigned to a vacuum volume
-m < known | max >
Determines how trajectories terminate
known: stop when a point is surrounded by known points
max: stop only when a charge density maximum is reached
-p < all_atom | all_bader >
Print calculated Bader volumes
all_atom: all atomic volumes
all_bader: all Bader volumes
-p < sel_atom | sel_bader > <volume list or range>
Print calculated Bader volumes
sel_atom: atomic volume(s) around the selected atom(s)
sel_bader: selected Bader volumes
-p < sum_atom | sum_bader > <volume list or range>
Print calculated Bader volumes
sum_atom: sum of atomic volume(s) around the selected atom(s)
sum_bader: sum of selected Bader volumes
-p < atom_index | bader_index >
Print index of atomic or Bader volumes
atom_index: print atomic volume indicies
bader_index: print Bader volume indicies
-i < cube | chgcar >
Input charge density file type. If not specified, the
program will try to determine the charge density file type
automatically.
-h
Help.
-v
Verbose output.
-cp
Find critical points of the charge density
Calculate eigenvalues and eigenvectors at those points
Store results in file named CPF.dat
*** 結果 [#z763bf2f]
Bader電荷の計算結果はACF.datに出力される:
$ cat ACF.dat
# X Y Z CHARGE MIN DIST ATOMIC VOL
--------------------------------------------------------------------------------
1 2.3277690 1.3439380 0.0000000 3.9020033 1.0751426 65.2790699
2 0.0000000 2.6878760 0.0000000 4.0774900 1.2120244 69.3785643
--------------------------------------------------------------------------------
VACUUM CHARGE: 0.0205
VACUUM VOLUME: 240.7492
NUMBER OF ELECTRONS: 8.0000
CHARGEに各原子の電荷が表示される。単位胞内の２つの炭素原子は等価なのに電荷に偏りが生じているのは、電荷密度のグリッドが粗いためと考えられる。
*** カットオフ依存性 [#g65fcc10]
エネルギーカットオフを増加させて（電荷密度のグリッドを細かくして）電荷分布の収束性を調べる。
|gmaxp |CENTER: 20|CENTER: 30|CENTER: 40|CENTER: 50|CENTER: 60|CENTER: 70|CENTER: 80|CENTER: 90|CENTER: 100|h
|grid-X|CENTER: 30|CENTER: 48|CENTER: 60|CENTER: 80|CENTER: 90|CENTER: 108|CENTER:120|CENTER:144|CENTER:150|
|grid-Y|CENTER: 30|CENTER: 48|CENTER: 60|CENTER: 80|CENTER: 90|CENTER: 108|CENTER:120|CENTER:144|CENTER:150|
|grid-Y|CENTER:128|CENTER:192|CENTER:256|CENTER:320|CENTER:384|CENTER: 450|CENTER:512|CENTER:576|CENTER:640|
|炭素原子1の電荷|3.902|3.934|3.945|3.956|3.960|3.965|3.967|3.971|3.972|
|炭素原子2の電荷|4.077|4.044|4.034|4.022|4.019|4.014|4.011|4.008|4.007|
|電荷の偏り |0.175|0.110|0.088|0.066|0.059|0.049|0.044|0.037|0.035|
|電荷の偏り(%) |4.375|2.750|2.200|1.650|1.475|1.225|1.100|0.925|0.875|
カットオフの増加とともに電荷の偏りが減少し精度が向上していることが確認できる。
** グラフェン 1x2/√3 [#h127dc9c]
#ref(http://www-cp.prec.eng.osaka-u.ac.jp/puki_state/my_image/gra1x2_r3.png,nolink)
入力ファイル
0 0 0 0 0 0
8.0000 20.0000 1 4 4 : GMAX, GMAXP, NTYP, NATM, NATM2
1 0 : number of space group, type of bravis lattice
8.063628983 4.655538364 20.000 90.0 90.0 90.0 : a,b,c,alpha,beta,gamma
12 24 1 1 1 1 : knx,kny,knz, k-point shift
1 0 : NCORD, NINV, : IWEI, IMDTYP, ITYP
1.3439381638 0.0000000000 0.0000000000 1 1 1
-1.3439381638 0.0000000000 0.0000000000 1 1 1
2.6878763276 2.3277691820 0.0000000000 1 1 1
-2.6878763276 2.3277691820 0.0000000000 1 1 1
6 0.1500 12.0107 1 1 0.d0 : TYPE 1IATOMN,ALFA,AMION,ILOC,IVAN
0 0 0 0 0 : ICOND 0-MD, 1-CONT.MD, 2-WAVE FN,, 3-WAVE FN CONT., iconstpw
0 1 : IPRE, IPRI
200 200 0 3600.00 0 : NMD1, NMD2, iter_last, CPUMAX,ifstop
3 1 : Simple=1,Broyd2=3,Blugel=6, 1:charge, 2:potential mix.
0 20 0.8 : starting mixing, kbxmix,alpha
0.60 0.50 0.60 0.70 1.00 : DTIM1, DTIM2, DTIM3, DTIM4, dtim_last
100.00 2 1 0.10D-08 1.d-06 : DTIO ,IMDALG, IEXPL, EDELTA
-0.0010 0.10D-02 0 : WIDTH,FORCCR,ISTRESS
ggapbe 1 : XCTYPE, nspin
1.00 3 : destm, n_stm
101 : NBZTYP 0-SF, 1-BK, 2-SC, 3-BCC, 4-FCC, 5-DIA, 6-HEX
0 0 0 : NKX, NKY, NKZ
0 0 0 : NKX2,NKY2,NKZ2
24 : NEG
1 : NEXTST(MB)
0 : 0; random numbers, 1; matrix diagon
2 0 0 0(MB) : imsd, i_2lm, i_sd2another, wksz for phase
0 : evaluation of eko difference.0 = no ,1 = yes
0 : npdosao
0 0.0 : SM_N, DOPPING
計算結果
$ grep ETOT nfout_1|grep "[0-9]"
ETOT: 1 26.21341351 0.2621E+02 0.3937E-01
ETOT: 2 -5.07267018 0.3129E+02 0.1212E-01
ETOT: 3 -15.33757551 0.1026E+02 0.1318E-01
ETOT: 4 -19.66071003 0.4323E+01 0.1333E-01
ETOT: 5 -22.00674384 0.2346E+01 0.1766E-01
ETOT: 6 -22.88457509 0.8778E+00 0.1587E-01
ETOT: 7 -22.92511351 0.4054E-01 0.1501E-01
ETOT: 8 -22.97540886 0.5030E-01 0.1372E-01
ETOT: 9 -22.95949325 0.1592E-01 0.1391E-01
ETOT: 10 -22.97376104 0.1427E-01 0.1353E-01
ETOT: 11 -23.04325978 0.6950E-01 0.9979E-02
ETOT: 12 -23.15572141 0.1125E+00 0.3768E-02
ETOT: 13 -23.16991809 0.1420E-01 0.1487E-02
ETOT: 14 -23.17160528 0.1687E-02 0.4518E-03
ETOT: 15 -23.17172043 0.1151E-03 0.1618E-03
ETOT: 16 -23.17173717 0.1673E-04 0.7242E-04
ETOT: 17 -23.17174331 0.6144E-05 0.2139E-04
ETOT: 18 -23.17174360 0.2898E-06 0.7831E-05
ETOT: 19 -23.17174357 0.3402E-07 0.3759E-05
ETOT: 20 -23.17174366 0.8909E-07 0.2707E-05
ETOT: 21 -23.17174376 0.1035E-06 0.1720E-05
ETOT: 22 -23.17174377 0.1106E-07 0.1275E-05
ETOT: 23 -23.17174379 0.1527E-07 0.1788E-05
ETOT: 24 -23.17174380 0.1140E-07 0.6630E-06
ETOT: 25 -23.17174380 0.3104E-08 0.3894E-06
ETOT: 26 -23.17174380 0.7199E-09 0.2579E-06
ETOT: 27 -23.17174380 0.6648E-10 0.5746E-07
ETOT(Q) + SM_energy = -23.1717438004519 16.7136110440348
*** カットオフ依存性 [#l684749f]
|gmaxp |CENTER: 20|CENTER: 40|CENTER: 60|CENTER: 80|CENTER:100|h
|grid-X|CENTER: 54|CENTER:108|CENTER:160|CENTER:216|CENTER:270|
|grid-Y|CENTER: 30|CENTER: 60|CENTER: 90|CENTER:120|CENTER:150|
|grid-Y|CENTER:128|CENTER:256|CENTER:384|CENTER:512|CENTER:640|
|炭素原子1の電荷|3.890|3.967|3.956|3.975|3.969|
|炭素原子2の電荷|4.088|4.011|4.023|4.023|4.009|
|炭素原子3の電荷|4.088|4.011|4.023|4.023|4.009|
|炭素原子4の電荷|3.890|3.967|3.956|3.975|3.969|
|電荷の偏り|0.198|0.043|0.066|0.027|0.039|
|電荷の偏り(%)|4.950|1.075|1.650|0.675|0.975|
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