前两篇文章中我们通过对nband和ecuteps两个参数的收敛进行测试，得到了比较令人满意的参数值。本篇文章中我们尝试对一个实际的问题进行计算：计算块状硅中\(\Gamma\)点直接带隙的GW修正。
打开 tgw1_6.abi 文件，并且注释掉
ngkpt 2 2 2 # Density of k points used for the automatic tests of the tutorial
并取消注释
#ngkpt 4 4 4 # Density of k points needed for a converged calculation
运行程序
abinit tgw1_6.abi >& log1_6
这步运行可能会花费一两分钟。
我们先来看一下输入文件做了哪些改动
# Crystalline silicon
# Calculation of the GW correction to the direct band gap in Gamma
# Dataset 1: ground state calculation
# Dataset 2: calculation of the WFK file
# Dataset 3: calculation of the screening (epsilon^-1 matrix for W)
# Dataset 4: calculation of the Self-Energy matrix elements (GW corrections)ndtset 4
# 四组计算#ngkpt 2 2 2 # Density of k points used for the automatic tests of the tutorial
ngkpt 4 4 4 # Density of k points needed for a converged calculationnshiftk 4
shiftk 0.0 0.0 0.0 # This grid contains the Gamma point, which is the point at which0.0 0.5 0.5 # we will compute the (direct) band gap. There are 19 k points0.5 0.0 0.5 # in the irreducible Brillouin zone, if ngkpt 4 4 4 is used.0.5 0.5 0.0
istwfk *1 # For the GW computations, do not take advantage of the# specificities of k points to reduce the number of components of the# wavefunction.# Dataset1: usual self-consistent ground-state calculation
# Definition of the k-point grid
# 自洽基态计算，定义k点网格
nband1 6
tolvrs1 1e-10# Dataset2: calculation of WFK file
# Definition of k-points
# 定义k点，计算WFK文件
iscf2 -2 # Non self-consistent calculation
getden2 -1 # Read previous density file
nband2 120
nbdbuf2 20
tolwfr2 1.0d-12# Dataset3: Calculation of the screening (epsilon^-1 matrix)
# 计算屏蔽效应
optdriver3 3 # Screening calculation
getwfk3 -1 # Obtain WFK file from previous dataset
nband3 50 # Bands to be used in the screening calculation
ecuteps3 6.0 # Dimension of the screening matrix
# 之前进行收敛测试得到的截断误差
ppmfrq3 16.7 eV # Imaginary frequency where to calculate the screening# It is easier (and safer) to let ABINIT compute and use the Drude plasma frequency,# instead of selecting a value by hand. This would be done thanks to the default value ppmfrq 0.0 .# Dataset4: Calculation of the Self-Energy matrix elements (GW corrections)
# 计算自能矩阵元（GW关联）
optdriver4 4 # Self-Energy calculation
getwfk4 -2 # Obtain WFK file from dataset 1
getscr4 -1 # Obtain SCR file from previous dataset
nband4 100 # Bands to be used in the Self-Energy calculation
# 之前收敛测试得到的能带数量
ecutsigx4 8.0 # Dimension of the G sum in Sigma_xnkptgw4 1 # number of k-point where to calculate the GW correction
kptgw4 # k-points0.000 0.000 0.000 # (Gamma)
bdgw4 4 5 # calculate GW corrections for bands from 4 to 5
# 计算能带4到5的GW修正# Definition of the unit cell: fcc
acell 3*10.26 # Experimental lattice constants
rprim 0.0 0.5 0.5 # FCC primitive vectors (to be scaled by acell)0.5 0.0 0.50.5 0.5 0.0# Definition of the atom types
ntypat 1 # There is only one type of atom
znucl 14 # The keyword "znucl" refers to the atomic number of the# possible type(s) of atom. The pseudopotential(s)# mentioned in the "files" file must correspond# to the type(s) of atom. Here, the only type is Silicon.# Definition of the atoms
natom 2 # There are two atoms
typat 1 1 # They both are of type 1, that is, Silicon.
xred # Reduced coordinate of atoms0.0 0.0 0.00.25 0.25 0.25# Definition of the planewave basis set (at convergence 16 Rydberg 8 Hartree)
ecut 8.0 # Maximal kinetic energy cut-off, in Hartree
# 平面波最大动能截断# Definition of the SCF procedure
# 自洽循环
nstep 10 # Maximal number of SCF cycles
diemac 12.0 # Although this is not mandatory, it is worth to# precondition the SCF cycle. The model dielectric# function used as the standard preconditioner# is described in the "dielng" input variable section.# Here, we follow the prescription for bulk silicon.pp_dirpath "$ABI_PSPDIR"pseudos "Psdj_nc_sr_04_pbe_std_psp8/Si.psp8"
# 找到Si的文件
有了之前的基础，阅读上述输入文件还是比较中规中矩的。得到运行结果之后，我们来看一下输出结果
--- !SelfEnergy_ee
iteration_state: {dtset: 4, }
kpoint : [ 0.000, 0.000, 0.000, ]
spin : 1
KS_gap : 2.564
QP_gap : 3.205
Delta_QP_KS: 0.641
data: !SigmaeeData |Band E0 <VxcDFT> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E2 4.369 -11.316 -12.769 0.721 0.764 -0.308 -11.876 -0.560 3.8093 4.369 -11.316 -12.769 0.721 0.764 -0.308 -11.876 -0.560 3.8094 4.369 -11.316 -12.769 0.721 0.764 -0.308 -11.876 -0.560 3.8095 6.933 -10.039 -5.840 -4.093 0.765 -0.307 -9.958 0.081 7.0156 6.933 -10.039 -5.840 -4.093 0.765 -0.307 -9.958 0.081 7.0157 6.933 -10.039 -5.840 -4.093 0.765 -0.307 -9.958 0.081 7.015
...
可以看到ks能带宽度为 2.564，QP能带宽度为 3.205，相差 0.641。现在我们就可以把GW修正后的带隙宽度与文献数据进行对比了，官方给出了几个参考
EXP 3.40 eV Landolt-Boernstein
# 实验值DFT (LDA)LDA 2.57 eV L. Hedin, Phys. Rev. 139, A796 (1965)LDA 2.57 eV M.S. Hybertsen and S. Louie, PRL 55, 1418 (1985)LDA (FLAPW) 2.55 eV N. Hamada, M. Hwang and A.J. Freeman, PRB 41, 3620 (1990)LDA (PAW) 2.53 eV B. Arnaud and M. Alouani, PRB 62, 4464 (2000)LDA 2.53 eV present work
# 局部密度近似得到的结果GW 3.27 eV M.S. Hybertsen and S. Louie, PRL 55, 1418 (1985)GW 3.35 eV M.S. Hybertsen and S. Louie, PRB 34, 5390 (1986)GW 3.30 eV R.W. Godby, M. Schlueter, L.J. Sham, PRB 37, 10159 (1988)GW (FLAPW) 3.30 eV N. Hamada, M. Hwang and A.J. Freeman, PRB 41, 3620 (1990)GW (FLAPW) 3.12 eV W. Ku and A.G. Eguiluz, PRL 89, 126401 (2002)GW 3.20 eV present work
# GW修正后得到的结果
可以发现我们现在得到的数据与实验值相差还是比较小的，还算是圆满完成任务。