晶格常数测试 (Equation of state method)
必要输入文件
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5run_a0.sh POTCAR INCAR 和 KPOINTS可在run_a0.sh中直接设置，也可以单独给出。 EOS.in
三维立方晶格脚本示例：
Si
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108#!/bin/sh cat > INCAR.relax <<! Global Parameters ISTART = 0 (Read existing wavefunction; if there) ICHARG = 2 (Non-self-consistent: GGA/LDA band structures) LREAL = F (Projection operators: automatic) ENCUT = 500 (Cut-off energy for plane wave basis set, in eV) PREC = Accurate (Precision level) LWAVE = .FALSE. (Write WAVECAR or not) LCHARG = .FALSE. (Write CHGCAR or not) ADDGRID= .TRUE. (Increase grid; helps GGA convergence) # LVTOT = .TRUE. (Write total electrostatic potential into LOCPOT or not) # LVHAR = .TRUE. (Write ionic + Hartree electrostatic potential into LOCPOT or not) # NELECT = (No. of electrons: charged cells; be careful) # LPLANE = .TRUE. (Real space distribution; supercells) # NPAR = 4 (Max is no. nodes; don't set for hybrids) Electronic Relaxation ISMEAR = 0 (Gaussian smearing; metals:1) SIGMA = 0.05 (Smearing value in eV; metals:0.2) NELM = 60 (Max electronic SCF steps) NELMIN = 4 (Min electronic SCF steps) EDIFF = 1E-08 (SCF energy convergence; in eV) GGA = PE (PBEsol exchange-correlation) Ionic Relaxation NELMIN = 6 (Min electronic SCF steps) NSW = 60 (Max electronic SCF steps) IBRION = 2 (Algorithm: 0-MD; 1-Quasi-New; 2-CG) ISIF = 4 (Stress/relaxation: 2-Ions, 3-Shape/Ions/V, 4-Shape/Ions) EDIFFG = -0.001 (Ionic convergence; eV/AA) # ISYM = 2 (Symmetry: 0=none; 2=GGA; 3=hybrids) ! cat > INCAR.static <<! Global Parameters ISTART = 0 (Read existing wavefunction; if there) ICHARG = 2 (Non-self-consistent: GGA/LDA band structures) LREAL = F (Projection operators: automatic) ENCUT = 500 (Cut-off energy for plane wave basis set, in eV) PREC = Accurate (Precision level) LWAVE = .FALSE. (Write WAVECAR or not) LCHARG = .FALSE. (Write CHGCAR or not) ADDGRID= .TRUE. (Increase grid; helps GGA convergence) # LVTOT = .TRUE. (Write total electrostatic potential into LOCPOT or not) # LVHAR = .TRUE. (Write ionic + Hartree electrostatic potential into LOCPOT or not) # NELECT = (No. of electrons: charged cells; be careful) # LPLANE = .TRUE. (Real space distribution; supercells) # NPAR = 4 (Max is no. nodes; don't set for hybrids) GGA = PE Static Calculation ISMEAR = -5 (tetrahedron method for DOS) #LORBIT = 11 (PAW radii for projected DOS) #NEDOS = 2001 (DOSCAR points) NELM = 60 (Max electronic SCF steps) EDIFF = 1E-08 (SCF energy convergence; in eV) EDIFFG = -0.001 ! cat > KPOINTS <<! A 0 M 9 9 9 0 0 0 ! echo 'a0' 'volume' 'free_energy(eV)' >ev.out for i in $(seq 5.00 0.05 5.90) do cat > POSCAR <<! Si8 1.0000000000 $i 0.0000000000 0.0000000000 0.0000000000 $i 0.0000000000 0.0000000000 0.0000000000 $i Si 8 Direct 0.0000000000 0.0000000000 0.0000000000 0.2500000000 0.7500000000 0.7500000000 0.5000000000 0.0000000000 0.5000000000 0.0000000000 0.5000000000 0.5000000000 0.5000000000 0.5000000000 0.0000000000 0.7500000000 0.2500000000 0.7500000000 0.7500000000 0.7500000000 0.2500000000 0.2500000000 0.2500000000 0.2500000000 ! #优化计算 cp INCAR.relax INCAR echo "a=$i"; time mpirun -n 16 vasp_std cp CONTCAR POSCAR rm INCAR #静态计算 cp INCAR.static INCAR echo "a=$i"; time mpirun -n 16 vasp_std V=$(grep "volume" OUTCAR | tail -1 | awk '{printf "%12.9f n", $5 }') E=$(grep "TOTEN" OUTCAR | tail -1 | awk '{printf "%12.9f n", $5 }') echo $i $V $E >> ev.out rm INCAR done
提交脚本运算后得到ev.out。
利用vaspkit软件进行状态方程拟合。
vaspkit需要准EOS.in文件，文件格式及说明如下：
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20cname : name of crystal up to 256 characters natoms : number of atoms in unit cell etype : equation of state type (see below) vplt1, vplt2, nvplt : volume interval over which to plot energy, pressure etc. as well as the number of points in the plot nevpt : number of energy-volume points to be inputted vpt(i) ept(i) : energy-volume points (VASP units) Note that the input units are VASP default untis (i.e., A^3 and eV). The equations of state currently implemented are: 1. Universal EOS (Vinet P et al., J. Phys.: Condens. Matter 1, p1941 (1989)) 2. Murnaghan EOS (Murnaghan F D, Am. J. Math. 49, p235 (1937)) 3. Birch-Murnaghan 3rd-order EOS (Birch F, Phys. Rev. 71, p809 (1947)) 4. Birch-Murnaghan 4th-order EOS 5. Natural strain 3rd-order EOS (Poirier J-P and Tarantola A, Phys. Earth Planet Int. 109, p1 (1998)) 6. Natural strain 4th-order EOS 7. Cubic polynomial in (V-V0)
参考例子
Si
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26Si 8 3 124.00 206 500 19 125.000000000 -39.404864520 128.790000000 -40.307996560 132.650000000 -41.074573950 136.590000000 -41.714702140 140.610000000 -42.237893500 144.700000000 -42.653098650 148.880000000 -42.968706720 153.130000000 -43.192650580 157.460000000 -43.332358630 161.880000000 -43.394826990 166.380000000 -43.386635660 170.950000000 -43.313964240 175.620000000 -43.182635890 180.360000000 -42.998104870 185.190000000 -42.765493980 190.110000000 -42.489611560 195.110000000 -42.174957610 200.200000000 -41.825750520 205.380000000 -41.445910010
运行 vaspkit -task 205
得到主要的输出文件 PARAM.out 如下：
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14Si Birch-Murnaghan 3rd-order EOS Birch F, Phys. Rev. 71, p809 (1947) (Default VASP units: eV, Angstrom etc.) V0 (A^3) = 163.6206779 E0 (eV) = -43.39626828 B0 = 0.2982734905E-02 B0' = 4.260966253 B0 (GPa) = 87.75507591
通过平衡体积可以得到晶格常数 a 0 = 5.4694803016 a_0=5.4694803016 a0=5.4694803016
如果不想状态方程拟合，在较高精度下直接使用
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3
ISIF = 3
ISIF=3 的参数直接弛豫优化晶胞。
INCAR示例如下：
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31Global Parameters ISTART = 0 (Read existing wavefunction; if there) ICHARG = 2 (Non-self-consistent: GGA/LDA band structures) LREAL = F (Projection operators: automatic) ENCUT = 500 (Cut-off energy for plane wave basis set, in eV) PREC = Accurate (Precision level) LWAVE = .FALSE. (Write WAVECAR or not) LCHARG = .FALSE. (Write CHGCAR or not) ADDGRID= .TRUE. (Increase grid; helps GGA convergence) # LVTOT = .TRUE. (Write total electrostatic potential into LOCPOT or not) # LVHAR = .TRUE. (Write ionic + Hartree electrostatic potential into LOCPOT or not) # NELECT = (No. of electrons: charged cells; be careful) # LPLANE = .TRUE. (Real space distribution; supercells) # NPAR = 4 (Max is no. nodes; don't set for hybrids) Electronic Relaxation ISMEAR = 0 (Gaussian smearing; metals:1) SIGMA = 0.05 (Smearing value in eV; metals:0.2) NELM = 60 (Max electronic SCF steps) NELMIN = 4 (Min electronic SCF steps) EDIFF = 1E-08 (SCF energy convergence; in eV) GGA = PE (PBEsol exchange-correlation) Ionic Relaxation NELMIN = 6 (Min electronic SCF steps) NSW = 60 (Max electronic SCF steps) IBRION = 2 (Algorithm: 0-MD; 1-Quasi-New; 2-CG) ISIF = 3 (Stress/relaxation: 2-Ions, 3-Shape/Ions/V, 4-Shape/Ions) EDIFFG = -0.001 (Ionic convergence; eV/AA) # ISYM = 2 (Symmetry: 0=none; 2=GGA; 3=hybrids)
注：在新版本的vaspkit中，给出了更多状态方程及其整个新的拟合流程，具体可参考程序实例。
二维材料的六方晶格示例：
Tl2O
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107#!/bin/sh cat > INCAR.relax <<! Global Parameters ISTART = 0 (Read existing wavefunction; if there) ICHARG = 2 (Non-self-consistent: GGA/LDA band structures) LREAL = F (Projection operators: automatic) ENCUT = 600 (Cut-off energy for plane wave basis set, in eV) PREC = Accurate (Precision level) LWAVE = .FALSE. (Write WAVECAR or not) LCHARG = .FALSE. (Write CHGCAR or not) ADDGRID= .TRUE. (Increase grid; helps GGA convergence) # LVTOT = .TRUE. (Write total electrostatic potential into LOCPOT or not) # LVHAR = .TRUE. (Write ionic + Hartree electrostatic potential into LOCPOT or not) # NELECT = (No. of electrons: charged cells; be careful) # LPLANE = .TRUE. (Real space distribution; supercells) # NPAR = 4 (Max is no. nodes; don't set for hybrids) Electronic Relaxation ISMEAR = 0 (Gaussian smearing; metals:1) SIGMA = 0.05 (Smearing value in eV; metals:0.2) NELM = 60 (Max electronic SCF steps) NELMIN = 4 (Min electronic SCF steps) EDIFF = 1E-08 (SCF energy convergence; in eV) GGA = PE (PBEsol exchange-correlation) Ionic Relaxation NELMIN = 6 (Min electronic SCF steps) NSW = 100 (Max electronic SCF steps) IBRION = 2 (Algorithm: 0-MD; 1-Quasi-New; 2-CG) ISIF = 2 (Stress/relaxation: 2-Ions, 3-Shape/Ions/V, 4-Shape/Ions) EDIFFG = -0.001 (Ionic convergence; eV/AA) # ISYM = 2 (Symmetry: 0=none; 2=GGA; 3=hybrids) ! cat > INCAR.static <<! Global Parameters ISTART = 0 (Read existing wavefunction; if there) ICHARG = 2 (Non-self-consistent: GGA/LDA band structures) LREAL = F (Projection operators: automatic) ENCUT = 600 (Cut-off energy for plane wave basis set, in eV) PREC = Accurate (Precision level) LWAVE = .FALSE. (Write WAVECAR or not) LCHARG = .FALSE. (Write CHGCAR or not) ADDGRID= .TRUE. (Increase grid; helps GGA convergence) # LVTOT = .TRUE. (Write total electrostatic potential into LOCPOT or not) # LVHAR = .TRUE. (Write ionic + Hartree electrostatic potential into LOCPOT or not) # NELECT = (No. of electrons: charged cells; be careful) # LPLANE = .TRUE. (Real space distribution; supercells) # NPAR = 4 (Max is no. nodes; don't set for hybrids) GGA = PE Static Calculation ISMEAR = -5 (tetrahedron method for DOS) #SIGMA = 0.05 #LORBIT = 11 (PAW radii for projected DOS) #NEDOS = 2001 (DOSCAR points) NELM = 60 (Max electronic SCF steps) EDIFF = 1E-08 (SCF energy convergence; in eV) EDIFFG = -0.001 ! cat > KPOINTS <<! A 0 G 12 12 1 0 0 0 ! for i in $(seq 3.10 0.05 4.10) do j=`echo "$i * 0.5000000000"|bc` k=`echo "$i * 0.8660254038"|bc` cat > POSCAR <<! Tl2O 1.0 $i 0.00000000000 0.00000000000 -$j $k 0.00000000000 0.00000000000 0.00000000000 25.00000000000 Tl O 2 1 Direct 0.3333330099999969 0.6666670059999973 0.5606771909028483 0.6666669459999994 0.3333329709999973 0.4393227710971557 0.0000000000000000 0.0000000000000000 0.5000000000000000 ! cp INCAR.relax INCAR echo "a=$j"; time mpirun -np 16 vasp_std cp CONTCAR POSCAR rm INCAR cp INCAR.static INCAR echo "a=$j"; time mpirun -np 16 vasp_std V=$(grep "volume" OUTCAR | tail -1 | awk '{printf "%12.9f n", $5 }') E=$(grep "TOTEN" OUTCAR | tail -1 | awk '{printf "%12.9f n", $5 }') echo $i $V $E >> ev.dat rm POSCAR done
注：对于平面为矩形的二维材料，可以通过修改VASP源代码，直接使用ISIF=3对x、y方向优化。
最后
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