本教程我们进行介电矩阵能量截断的收敛测试。
阅读输入文件
ndtset 12
udtset 6 2# Calculation of the screening (epsilon^-1 matrix)
optdriver?1 3
nband?1 100# Convergence with respect to the dimension of epsilon^-1 matrix
ecuteps:? 3.0
ecuteps+? 1.0# Calculation of the Self-Energy matrix elements (GW corrections)
optdriver?2 4
getscr?2 -1
ecutsigx 8.0
nband?2 100
nkptgw 1
kptgw 0.000 0.000 0.000
bdgw 4 5
文件中，一共创建了12个数据集，大小为6行2列，第一列表示进行屏蔽计算，第二列表示进行GW计算。每一行代表一个不同的介电矩阵截断精度，分别为3.0、4.0、5.0、6.0、7.0、8.0。
现在我们来看看输出文件，由于GW计算结果是第二列，所以我们只看DATASET?2的数据
== DATASET 12 ==================================================================
...EPSILON^-1 parameters (SCR file):dimension of the eps^-1 matrix on file 59dimension of the eps^-1 matrix used 59number of plane-waves for wavefunctions 283number of bands 100number of q-points in IBZ 3number of frequencies 2number of real frequencies 1number of imag frequencies 1matrix elements of self-energy operator (all in [eV])Perturbative Calculation--- !SelfEnergy_ee
iteration_state: {dtset: 12, }
kpoint : [ 0.000, 0.000, 0.000, ]
spin : 1
KS_gap : 2.443
QP_gap : 3.052
Delta_QP_KS: 0.609
data: !SigmaeeData |Band E0 <VxcDFT> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E2 4.665 -11.412 -13.527 1.899 0.786 -0.272 -11.582 -0.169 4.4963 4.665 -11.412 -13.527 1.899 0.786 -0.272 -11.582 -0.169 4.4964 4.665 -11.412 -13.527 1.899 0.786 -0.272 -11.582 -0.169 4.4965 7.108 -9.962 -4.945 -4.462 0.791 -0.264 -9.523 0.440 7.5486 7.108 -9.962 -4.945 -4.462 0.791 -0.264 -9.523 0.440 7.5487 7.108 -9.962 -4.945 -4.462 0.791 -0.264 -9.523 0.440 7.548
...================================================================================
== DATASET 22 ==================================================================
...EPSILON^-1 parameters (SCR file):dimension of the eps^-1 matrix on file 113dimension of the eps^-1 matrix used 113number of plane-waves for wavefunctions 283number of bands 100number of q-points in IBZ 3number of frequencies 2number of real frequencies 1number of imag frequencies 1matrix elements of self-energy operator (all in [eV])Perturbative Calculation--- !SelfEnergy_ee
iteration_state: {dtset: 22, }
kpoint : [ 0.000, 0.000, 0.000, ]
spin : 1
KS_gap : 2.443
QP_gap : 3.124
Delta_QP_KS: 0.681
data: !SigmaeeData |Band E0 <VxcDFT> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E2 4.665 -11.412 -13.527 1.755 0.784 -0.275 -11.694 -0.282 4.3833 4.665 -11.412 -13.527 1.755 0.784 -0.275 -11.694 -0.282 4.3834 4.665 -11.412 -13.527 1.755 0.784 -0.275 -11.694 -0.282 4.3835 7.108 -9.962 -4.945 -4.513 0.791 -0.264 -9.563 0.400 7.5086 7.108 -9.962 -4.945 -4.513 0.791 -0.264 -9.563 0.400 7.5087 7.108 -9.962 -4.945 -4.513 0.791 -0.264 -9.563 0.400 7.508
...================================================================================
== DATASET 32 ==================================================================
...EPSILON^-1 parameters (SCR file):dimension of the eps^-1 matrix on file 137dimension of the eps^-1 matrix used 137number of plane-waves for wavefunctions 283number of bands 100number of q-points in IBZ 3number of frequencies 2number of real frequencies 1number of imag frequencies 1matrix elements of self-energy operator (all in [eV])Perturbative Calculation--- !SelfEnergy_ee
iteration_state: {dtset: 32, }
kpoint : [ 0.000, 0.000, 0.000, ]
spin : 1
KS_gap : 2.443
QP_gap : 3.141
Delta_QP_KS: 0.698
data: !SigmaeeData |Band E0 <VxcDFT> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E2 4.665 -11.412 -13.527 1.728 0.784 -0.276 -11.715 -0.303 4.3623 4.665 -11.412 -13.527 1.728 0.784 -0.276 -11.715 -0.303 4.3624 4.665 -11.412 -13.527 1.728 0.784 -0.276 -11.715 -0.303 4.3625 7.108 -9.962 -4.945 -4.518 0.791 -0.264 -9.567 0.395 7.5046 7.108 -9.962 -4.945 -4.518 0.791 -0.264 -9.567 0.395 7.5047 7.108 -9.962 -4.945 -4.518 0.791 -0.264 -9.567 0.395 7.504
...================================================================================
== DATASET 42 ==================================================================
...EPSILON^-1 parameters (SCR file):dimension of the eps^-1 matrix on file 169dimension of the eps^-1 matrix used 169number of plane-waves for wavefunctions 283number of bands 100number of q-points in IBZ 3number of frequencies 2number of real frequencies 1number of imag frequencies 1matrix elements of self-energy operator (all in [eV])Perturbative Calculation--- !SelfEnergy_ee
iteration_state: {dtset: 42, }
kpoint : [ 0.000, 0.000, 0.000, ]
spin : 1
KS_gap : 2.443
QP_gap : 3.153
Delta_QP_KS: 0.709
data: !SigmaeeData |Band E0 <VxcDFT> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E2 4.665 -11.412 -13.527 1.708 0.784 -0.276 -11.731 -0.318 4.3473 4.665 -11.412 -13.527 1.708 0.784 -0.276 -11.731 -0.318 4.3474 4.665 -11.412 -13.527 1.708 0.784 -0.276 -11.731 -0.318 4.3475 7.108 -9.962 -4.945 -4.523 0.791 -0.264 -9.571 0.391 7.4996 7.108 -9.962 -4.945 -4.523 0.791 -0.264 -9.571 0.391 7.4997 7.108 -9.962 -4.945 -4.523 0.791 -0.264 -9.571 0.391 7.499
...================================================================================
== DATASET 52 ==================================================================
...EPSILON^-1 parameters (SCR file):dimension of the eps^-1 matrix on file 259dimension of the eps^-1 matrix used 259number of plane-waves for wavefunctions 283number of bands 100number of q-points in IBZ 3number of frequencies 2number of real frequencies 1number of imag frequencies 1matrix elements of self-energy operator (all in [eV])Perturbative Calculation--- !SelfEnergy_ee
iteration_state: {dtset: 52, }
kpoint : [ 0.000, 0.000, 0.000, ]
spin : 1
KS_gap : 2.443
QP_gap : 3.159
Delta_QP_KS: 0.716
data: !SigmaeeData |Band E0 <VxcDFT> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E2 4.665 -11.412 -13.527 1.696 0.784 -0.276 -11.740 -0.328 4.3383 4.665 -11.412 -13.527 1.696 0.784 -0.276 -11.740 -0.328 4.3384 4.665 -11.412 -13.527 1.696 0.784 -0.276 -11.740 -0.328 4.3385 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.574 0.388 7.4966 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.574 0.388 7.4967 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.574 0.388 7.496
...================================================================================
== DATASET 62 ==================================================================
...EPSILON^-1 parameters (SCR file):dimension of the eps^-1 matrix on file 283dimension of the eps^-1 matrix used 283number of plane-waves for wavefunctions 283number of bands 100number of q-points in IBZ 3number of frequencies 2number of real frequencies 1number of imag frequencies 1matrix elements of self-energy operator (all in [eV])Perturbative Calculation--- !SelfEnergy_ee
iteration_state: {dtset: 62, }
kpoint : [ 0.000, 0.000, 0.000, ]
spin : 1
KS_gap : 2.443
QP_gap : 3.159
Delta_QP_KS: 0.716
data: !SigmaeeData |Band E0 <VxcDFT> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E2 4.665 -11.412 -13.527 1.695 0.784 -0.276 -11.741 -0.329 4.3373 4.665 -11.412 -13.527 1.695 0.784 -0.276 -11.741 -0.329 4.3374 4.665 -11.412 -13.527 1.695 0.784 -0.276 -11.741 -0.329 4.3375 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.575 0.388 7.4966 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.575 0.388 7.4967 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.575 0.388 7.496
...== END DATASET(S) ==============================================================
我们把比较重要的信息都择了出来，其中需要注意的是
dimension of the eps^-1 matrix 594 4.665 -11.412 -13.527 1.899 0.786 -0.272 -11.582 -0.169 4.4965 7.108 -9.962 -4.945 -4.462 0.791 -0.264 -9.523 0.440 7.548dimension of the eps^-1 matrix 1134 4.665 -11.412 -13.527 1.755 0.784 -0.275 -11.694 -0.282 4.3835 7.108 -9.962 -4.945 -4.513 0.791 -0.264 -9.563 0.400 7.508dimension of the eps^-1 matrix 1374 4.665 -11.412 -13.527 1.728 0.784 -0.276 -11.715 -0.303 4.3625 7.108 -9.962 -4.945 -4.518 0.791 -0.264 -9.567 0.395 7.504dimension of the eps^-1 matrix 1694 4.665 -11.412 -13.527 1.708 0.784 -0.276 -11.731 -0.318 4.3475 7.108 -9.962 -4.945 -4.523 0.791 -0.264 -9.571 0.391 7.499dimension of the eps^-1 matrix 2594 4.665 -11.412 -13.527 1.696 0.784 -0.276 -11.740 -0.328 4.3385 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.574 0.388 7.496dimension of the eps^-1 matrix 2834 4.665 -11.412 -13.527 1.695 0.784 -0.276 -11.741 -0.329 4.3375 7.108 -9.962 -4.945 -4.527 0.791 -0.264 -9.575 0.388 7.496
可以看到不同的介电矩阵截断能量，会对应于不同的矩阵维度，能量越小，截断越多，矩阵越小，误差对应的也就越大。那么收敛判据是什么呢？官方给出的回答是：小于 10 meV。观察过后，发现第四组数据和第五组数据的能量差小于0.01，因此我们取 ecuteps=6.0。
加上前面的，我们确定 nband=100，ecuteps=6.0 。