如何优化TiO2_anatase晶格常数（a, c）？

去离子水

对一系列固定体积的结构进行弛豫，然后根据birch-murnaghan拟合E-V曲线，得到基态的平衡体积V0。知道平衡体积之后何获得a和c的值呢？用到的脚本如下，采用PBE泛函。

INCAR.relax

1. ENCUT = 520 eV # energy cut-off for the calculation
   
2. PREC = High
   
3. LREAL = .FALSE # real space projection .FALSE. or Auto
   
4. NSW = 999
   
5. IBRION = 2 # CG algorithm
   
6. ISIF = 4 # forces and stress are optimized

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INCAR.static

1. PREC = High
   
2. 
   
3. ISTART = 0
   
4. ICHARG = 2
   
5. ISMEAR = -5
   
6. 
   
7. ENCUT = 520 eV
   

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KPOINTS

1. Automatic mesh
   
2.   0
   
3. Gamma
   
4.   5  5  5
   
5.   0  0  0
   

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vasp.pbs

1. #!/bin/bash
   
2. #$ -S /bin/bash
   
3. #$ -cwd
   
4. #$ -j y
   
5. #$ -N test_opt
   
6. #$ -pe make 12
   
7. 
   
8. source /share/apps/intel/Compiler/11.1/073/bin/iccvars.sh intel64
   
9. source /share/apps/intel/Compiler/11.1/073/bin/ifortvars.sh intel64
   
10. source /share/apps/intel/impi/3.2.0.011/bin64/mpivars.sh
    
11. 
    
12. for a in 3.74 3.75 3.76 3.78 3.79 3.80 3.81 3.82 3.83 3.84
    
13. do
    
14. cat > POSCAR <<!
    
15. Anatase
    
16. 1.0
    
17.         $a         0.0000000000         0.0000000000
    
18.         0.0000000000         $a         0.0000000000
    
19.         0.0000000000         0.0000000000         9.737
    
20.    Ti    O
    
21.     4    8
    
22. Direct
    
23.      0.000000000         0.000000000         0.000000000
    
24.      0.500000000         0.500000000         0.500000000
    
25.      0.000000000         0.500000000         0.250000000
    
26.      0.500000000         0.000000000         0.750000000
    
27.      0.000000000         0.000000000         0.208059996
    
28.      0.500000000         0.500000000         0.708060026
    
29.      0.000000000         0.500000000         0.458059996
    
30.      0.500000000         0.000000000         0.958060026
    
31.      0.500000000         0.000000000         0.541939974
    
32.      0.000000000         0.500000000         0.041940004
    
33.      0.500000000         0.500000000         0.291940004
    
34.      0.000000000         0.000000000         0.791939974
    
35. !
    
36. cp INCAR.relax INCAR
    
37. echo "a = $a"; mpirun -r ssh -np 12 ~/bin/vasp5.3.3
    
38. 
    
39. cp CONTCAR POSCAR
    
40. cp INCAR.static INCAR
    
41. echo "a = $a"; mpirun -r ssh -np 12 ~/bin/vasp5.3.3
    
42. 
    
43. E=`grep "TOTEN" OUTCAR | tail -1 | awk '{printf "%12.6f \n", $5 }'`
    
44. V=`grep "volume" OUTCAR | tail -1 | awk '{printf "%12.4f \n" , $5}'`
    
45. echo $a $V $E >> SUMMARY.dat
    
46. 
    
47. done

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得到的结果
SUMMARY.dat

1. 3.74 136.2000 -105.833996
   
2. 3.75 136.9300 -105.865334
   
3. 3.76 137.6600 -105.892136
   
4. 3.78 139.1300 -105.928546
   
5. 3.79 139.8600 -105.944722
   
6. 3.80 140.6000 -105.955402
   
7. 3.81 141.3400 -105.960574
   
8. 3.82 142.0900 -105.960563
   
9. 3.83 142.8300 -105.954437
   
10. 3.84 143.5800 -105.949877
    

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根据birch-murnaghan状态方程拟合的曲线

V0=141.863A^3

1. Select one volume and relax from starting structure keeping the volume fixed (ISIF=4 see sec. 6.24; ISMEAR=0 or 1, see section 6.38).
2. Start a second relaxation from previous CONTCAR file (if the initial cell shape was reasonable this step can be skipped, if the cell shape is kept fixed, you never have run VASP twice).
3. As a final step perform one more energy calculation with the tetrahedron method switched on (ISMEAR=-5), to get very accurate unambiguous energies (no relaxation for the final run).

计算流程参考：http://cms.mpi.univie.ac.at/vasp/vasp/Accurate_bulk_relaxations_with_internal_parameters_two.html
脚本文件参考：http://cms.mpi.univie.ac.at/vasp/vasp/Bulk_calculations_with_internal_parameters.html & 侯老师VASP入门教程



得到平衡体积V0=141.863A^3，在POSCAR里面如果第二行为负，则代表体积，所以我又这样试了一下：

INCAR

1. ENCUT = 520 eV # energy cut-off for the calculation
   
2. PREC = High
   
3. LREAL = .FALSE # real space projection .FALSE. or Auto
   
4. NSW = 999
   
5. IBRION = 2 # CG algorithm
   
6. ISIF = 4 # forces and stress are optimized

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POSCAR

1. Anatase
   
2. -141.863
   
3.         3.7844998837         0.0000000000         0.0000000000
   
4.         0.0000000000         3.7844998837         0.0000000000
   
5.         0.0000000000         0.0000000000         9.5143003464
   
6.    Ti    O
   
7.     4    8
   
8. Direct
   
9.      0.000000000         0.000000000         0.000000000
   
10.      0.500000000         0.500000000         0.500000000
    
11.      0.000000000         0.500000000         0.250000000
    
12.      0.500000000         0.000000000         0.750000000
    
13.      0.000000000         0.000000000         0.208059996
    
14.      0.500000000         0.500000000         0.708060026
    
15.      0.000000000         0.500000000         0.458059996
    
16.      0.500000000         0.000000000         0.958060026
    
17.      0.500000000         0.000000000         0.541939974
    
18.      0.000000000         0.500000000         0.041940004
    
19.      0.500000000         0.500000000         0.291940004
    
20.      0.000000000         0.000000000         0.791939974
    

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KPOINTS

1. Automatic mesh
   
2.   0
   
3. Gamma
   
4.   5  5  5
   
5.   0  0  0
   

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vasp.pbs

1. #!/bin/bash
   
2. #$ -S /bin/bash
   
3. #$ -cwd
   
4. #$ -j y
   
5. #$ -N isif4
   
6. #$ -pe make 12
   
7. 
   
8. source /share/apps/intel/Compiler/11.1/073/bin/iccvars.sh intel64
   
9. source /share/apps/intel/Compiler/11.1/073/bin/ifortvars.sh intel64
   
10. source /share/apps/intel/impi/3.2.0.011/bin64/mpivars.sh
    
11. 
    
12. 
    
13. mpirun -r ssh -np 12 ~/bin/vasp5.3.3

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最后得到的CONTCAR

1. Anatase                                 
   
2.    1.01350313575973     
   
3.      3.7709606715685475    0.0000000000000000    0.0000000000000000
   
4.      0.0000000000000000    3.7709606715685475    0.0000000000000000
   
5.      0.0000000000000000    0.0000000000000000    9.5827430546962322
   
6.    Ti   O
   
7.      4     8
   
8. Direct
   
9.   0.0000000000000000  0.0000000000000000  0.0000000000000000
   
10.   0.5000000000000000  0.5000000000000000  0.5000000000000000
    
11.   0.0000000000000000  0.5000000000000000  0.2500000000000000
    
12.   0.5000000000000000  0.0000000000000000  0.7500000000000000
    
13.   0.0000000000000000  0.0000000000000000  0.2066888233929389
    
14.   0.5000000000000000  0.5000000000000000  0.7066888533929343
    
15.   0.0000000000000000  0.5000000000000000  0.4566888233929389
    
16.   0.5000000000000000  0.0000000000000000  0.9566888533929343
    
17.   0.5000000000000000  0.0000000000000000  0.5433111466070657
    
18.   0.0000000000000000  0.5000000000000000  0.0433111766070611
    
19.   0.5000000000000000  0.5000000000000000  0.2933111766070611
    
20.   0.0000000000000000  0.0000000000000000  0.7933111466070657
    
21. 
    
22.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
23.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
24.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
25.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
26.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
27.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
28.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
29.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
30.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
31.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
32.   0.00000000E+00  0.00000000E+00  0.00000000E+00
    
33.   0.00000000E+00  0.00000000E+00  0.00000000E+00

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体积是能对上的：V0=141.863=1.01350313575973^3 * 3.7709606715685475 * 3.7709606715685475 * 9.5827430546962322

所以最后a=1.013*3.771=3.820, c=1.013*9.583=9.707
文献计算值a=3.786, c=9.737（Phys. Rev. B 2001, 63 (15), 155409.）
实验值a=3.782, c=9.502（J. Am. Chem. Soc. 1987, 109 (12), 3639–3646.）
这样对吗？






补充：侯老师VASP入门教程里得到平衡体积之和，不知如何得到循环变量$i的值？？

卡开发发

差不多，一般这样的精度也就行了。其实EOS也只是个近似，晶体内部的实际变量应该不止三个晶格常数这样，说白了就是做不同的晶格常数下晶格的能量，然后找能量极小点，fitting EOS相当于对这些点内插得到极值点而已（dE/dΩ=0）。

原则上来说isif当中isif=3涉及到的优化方式可靠的话能够得到准确的结构而不必fitting EOS，前提是stress和force在几个参数的收敛性测试条件下（通常参考能量，但实际远远不够），当然这有可能也只是理论上讲讲，实际可能影响的因素很复杂。如果再考虑这么复杂的收敛性测试，看起来反而fitting EOS更加省力一些。

去离子水

卡开发发 发表于 2015-10-27 23:44
差不多，一般这样的精度也就行了。其实EOS也只是个近似，晶体内部的实际变量应该不止三个晶格常数这样，说 ...

拟合eos得到平衡体积后，在POSCAR的第二行写上-V0，然后做isif=3。最后从CONTCAT里计算a，c的值，这种做法对吗？还有没有其他方法在知道平衡体积后得到a，c的值

卡开发发

去离子水 发表于 2015-10-28 09:54
拟合eos得到平衡体积后，在POSCAR的第二行写上-V0，然后做isif=3。最后从CONTCAT里计算a，c的值，这种做 ...

可以，你也可以改变形状和改变体积交替进行，不过工作量相应大一些。非立方晶格的情形fitting EOS没准不同的c或是a/c的情形对应的v0可能会不一样，这点非常不容易处理。