13. チュートリアル

13.1. Tutorial 1: 指定したセルの範囲内でのすべての原子配置においてエネルギー計算を行う

• 岩塩型MgO-ZnO系

• あらかじめ準備されたDFT構造およびエネルギーを用いる．ここでは，mkposcarは用いず，DFT構造の最適化は行わない．

• ユニットセルを2x1x1倍したセル内でのすべての原子配置において，エネルギー計算を行う．（計算量を軽減するためセルの大きさは小さく指定している．）

13.1.1. Step 1. searching for independent clusters on the lattice

1. preparing lattice information (UPOSCAR and UPOTCAR)

   > cd tutorials/1/cluster
   > cat UPOSCAR
   rocksalt-lattice
   1.0
   4.15700000000000      0.00000000000000      0.00000000000000
   0.00000000000000      4.15700000000000      0.00000000000000
   0.00000000000000      0.00000000000000      4.15700000000000
   4 4
   Direct
   0.00000000000000      0.00000000000000      0.00000000000000
   0.50000000000000      0.50000000000000      0.00000000000000
   0.50000000000000      0.00000000000000      0.50000000000000
   0.00000000000000      0.50000000000000      0.50000000000000
   0.00000000000000      0.00000000000000      0.50000000000000
   0.50000000000000      0.00000000000000      0.00000000000000
   0.00000000000000      0.50000000000000      0.00000000000000
   0.50000000000000      0.50000000000000      0.50000000000000
   
   > cat UPOTCAR
   VRHFIN =Mg:
   VRHFIN =O:
   

2. preparing CE.in

   > cat CE.in
   ISUB = 1
   NMAX = 4
   DTRUNC = 6 6 6 0
   

3. executing cluster for generating cluster.out and position.out

   > cluster
   default parameter : SYMPREC = 1e-05
   n_cluster (empty) = 1
   n_cluster (point) = 1
   seaching for 2 body clusters ...
   n_cluster (2 body) = 4
   seaching for 3 body clusters ...
   n_cluster (3 body) = 12
   seaching for 4 body clusters ...
   n_cluster (4 body) = 35
   n_all_cluster = 53
   
   > ls
   CE.in  UPOSCAR  UPOTCAR  cluster.out  position.out
   

13.1.2. Step 2. calculating correlation functions for DFT structures

1. preparing DFT structures (POSCAR and POTCAR)

   > cd tutorials/1/correlation
   > ls
   001/ 002/ 003/ ... 029/ 030/
   > ls 001/
   POSCAR POTCAR
   

2. preparing lattice information (UPOSCAR and UPOTCAR)

   > cd tutorials/1/correlation
   > for i in {001..030};do cp {UPOSCAR,UPOTCAR} $i;done
   

3. preparing CE.in

   > cd tutorials/1/correlation
   > cat CE.in
   ISUB = 1
   NAMEPOT = Mg Zn O
   SPIN = 1 -1
   NUCELLPOSCAR = 2 2 2
   SYMPREC = 1e-5
   > for i in {001..030};do cp CE.in $i;done
   

4. preparing position.out

   > cd tutorials/1/correlation
   > cp ../cluster/position.out .
   > for i in {001..030};do cp position.out $i;done
   > ls 001/
   CE.in  POSCAR  POTCAR  UPOSCAR  UPOTCAR  position.out
   

5. executing correlation for calculating correlation functions and generating of.out and correlation.out

   > cd tutorials/1/001/
   > echo " structure 001" > correlation.001
   > correlation >> correlation.001
   > cat correlation.001
    structure 001
   1
   1
   1
   ...
   

6. executing correlation for calculating correlation functions of all structures and preparing CORRELATION

   > cd tutorials/1/correlation
   > for i in {001..030};do cd tutorials/1/correlation/$i; echo " structure $i" >| correlation.$i; correlation >> correlation.$i;done
   > cd tutorials/1/correlation
   > for i in {001..030};do cat $i/correlation.$i;done > CORRELATION
   

13.1.3. Step 3. optimizing a set of clusters and estimating their ECIs

1. preparing ENERGY and CORRELATION

   > cd tutorials/1/gasa
   > cp ../correlation/CORRELATION .
   

2. preparing GASA.in

   > cat GASA.in
   NLOOP = 0
   BASECLUSTER = 0 1 2 3 4 5
   NPOP        = 50
   NELITE      = 3
   NALLCLUSTER = 53
   MININDEX    = 6
   MAXINDEX    = 52
   NCLUSTER    = 5
   MAXGENE     = 200
   PMATING     = 0.9
   PMUTATION   = 0.03
   
   > ls
   ENERGY CORRELATION GASA.in
   

3. executing gasa for optimizing a set of clusters (A different result may be obtained.)

   > gasa
    initial population
     cv score = 0.00222288 8 14 37 48 52
     cv score = 0.0013192 6 10 31 39 47
   ...
    generation 1
    generation 2
   ...
    generation 199
    generation 200
   
   > tail -n 51 gasa.out | head -n 2
    generation 200
   0.000380998 12 49 14 50 39
   

4. preparing LS.in

   > grep NALLCLUSTER GASA.in | cut -f 4- -d " " > LS.in
   > grep BASECLUSTER GASA.in | cut -f 4- -d " " >> LS.in
   > tail -n 50 gasa.out | head -n 1 | cut -f 3- -d " " >> LS.in
   

5. executing lsf for estimating ECIs

   > lsf
   0   -0.03762950309
   1   -0.006265528600
   2   0.05964064765
   3   -0.008588932374
   4   -0.01597202189
   5   0.001424126588
   12   0.007407443471
   49   -0.0005923858386
   14   -0.001214238460
   50   0.0006339154097
   39   0.001143178365
   sum of square error = 1.748e-06
   cross validation score = 0.0003810
   --- diagonal terms of precision matrix  ---
   1     0.3565
   2     0.9031
   3     0.1426
   4      1.082
   5     0.1536
   12     0.8314
   49     0.1646
   14     0.5158
   50    0.09850
   39     0.9147
   trace of precision matrix = 5.162
   
   > lsf | head -n 11 > ECI
   

13.1.4. Step 4. calculating energies of possible configurations within 2x1x1 supercell

1. preparing lattice information, ECI, of.out

   > cd tutorials/1/gss
   > ls
   nchange1/  nchange2/  nchange3/  nchange4/  nchange5/  nchange6/  nchange7/
   
   > cp ../correlation/001/of.out .
   > cp ../gasa/ECI .
   > for i in {1..7};do cp {of.out,ECI} nchange$i/;done
   

2. preparing GS.in

   > cat nchange1/GS.in
   ISUB = 1
   NCHANGE = 1
   SPIN = 1 -1
   NUCELL = 2 1 1
   
   > ls nchange1
   ECI  GS.in  UPOSCAR  UPOTCAR  of.out
   

3. executing gss

   > cd nchange4
   > gss
    default parameter : SYMPREC = 1e-05
    cell size (ground state search) = 2 1 1
    cell size (calculation of correlation function) = 2 2 2
   ECI and output energies in gs.out have same unit.
   calculating symmetry operations
   calculating combinations of atoms
    number of configurations = 35
    number of elements in an array for atomic configurations = 140
    required memory for configurations = 0.00028 (MB)
   calculating all cluster positions
   calculating energies for all configurations
   elapse (calculation of energies) = 0.4 (sec)
   

4. drawing a figure using gs.out