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ABACUS+LibRI 做杂化泛函计算教程
shimengchao@dp.tech
推荐镜像 :ABACUS:3.2.0
推荐机型 :c8_m16_cpu
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ABACUS+LibRI 做杂化泛函计算教程
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推荐镜像：abacus:3.2.0
推荐计算资源：CPU
内容：ABACUS+LibRI 做杂化泛函计算教程
使用方式：您可在 Bohrium Notebook上直接运行。您可以点击界面上方蓝色按钮 开始连接，选择 abacus:3.2.0 镜像及c8_m16_cpu款节点配置，稍等片刻即可运行。如您遇到任何问题，请联系 bohrium@dp.tech 。
共享协议：本作品采用知识共享署名-非商业性使用-相同方式共享 4.0 国际许可协议进行许可。
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本notebook改编自abacus使用指南，更多信息详见这里。
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一、介绍
杂化泛函（Hybrid Functional）是指在密度泛函理论框架中的交换关联项里面加入一部分的 Hartree Fock (简称 HF)的精确交换能。开源密度泛函理论软件 ABACUS 可以结合另一款国产开源软件 LibRI 软件进行杂化密度泛函计算，目前仅支持在数值原子轨道基组下使用该功能。可以通过 dft_functional 参数指定所使用的杂化泛函类型，如可以选择 hf (Hartree-Fock), pbe0(PBE0), hse(HSE06)以及 scan0 杂化泛函。本教程以 HSE 杂化泛函为例，介绍如何在 ABACUS 里调用 LibRI 做杂化泛函自洽迭代、求力和应力以及结构优化。
注 1：使用 ABACUS+LibRI 做杂化泛函计算时，最大并行核数是，其中是原子个数，是 k 点个数。计算资源超出时可以运行，但会造成浪费。
注 2：使用 ABACUS+LibRI 做杂化泛函计算时，因为内存消耗比较大，推荐给定计算资源的前提下，先尽量使用 OpenMP 多线程并行，再考虑使用 MPI 多进程并行。
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二、杂化泛函的使用
1. ABACUS 编译准备
如果要在 ABACUS 中使用杂化泛函进行计算，需要在编译 ABACUS 的时候也编译 Libxc、LibRI 和 LibComm 三个软件包，具体请见线上文档 Advanced Installation Options ‒ ABACUS documentation。
注意在链接 LibRI、LibComm 时如果报错未定义的引用等，可以先注意检查 ABACUS 源代码下 deps 文件夹下是否包含 LibRI、LibComm 两个文件夹。如果未包含这两个文件夹，或文件夹中无内容，在本地Github仓库中可以尝试如下两条语句，以获取这两个子仓库内容：
git submodule init 和 git submodule update --remote --recursive
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2. 采用杂化泛函进行电子自洽迭代计算
本教程在 Gitee 上准备了一个硅晶体使用杂化泛函做自洽计算（SCF）的例子（Gitee 的下载链接），以下是 INPUT 文件及相关的参数。
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[4]
!cd ~ && git clone https://gitee.com/mcresearch/abacus-user-guide.git
Cloning into 'abacus-user-guide'... remote: Enumerating objects: 11168, done. remote: Counting objects: 100% (326/326), done. remote: Compressing objects: 100% (112/112), done. remote: Total 11168 (delta 222), reused 290 (delta 197), pack-reused 10842 Receiving objects: 100% (11168/11168), 48.31 MiB | 8.27 MiB/s, done. Resolving deltas: 100% (3285/3285), done. Updating files: 100% (9398/9398), done.
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[1]
!cd ~/abacus-user-guide/examples/hybrid_functional/1_scf_Si && cat INPUT
INPUT_PARAMETERS calculation scf basis_type lcao ntype 1 nbands 8 ecutwfc 60.000000 scf_nmax 100 dft_functional hse scf_thr 1e-7
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由 dft_functional 设置为hse可知，该例子使用的杂化泛函为HSE泛函。KPT 文件取的是 4*4*4 的布里渊区 k 点。
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[2]
!cd ~/abacus-user-guide/examples/hybrid_functional/1_scf_Si && cat KPT
K_POINTS 0 Gamma 4 4 4 0 0 0
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杂化泛函相关的完整参数列表及解释见 Full List of INPUT Keywords / exact-exchange ‒ ABACUS documentation。这里再进行简单概述：
- 泛函相关参数：
- exx_hybrid_alpha：杂化泛函中加入的 HF 精确交换能（Fock 交换能）的比例，即有。如果 dft_functional 设置为 hf，则默认值为1。目前其他杂化泛函的默认值是0.25。但是，如果是 SCAN0 泛函，有的文献取的是 0.1，所以需要根据你想取的值进行设定[1]。
- exx_hse_omega：为 HSE 泛函中的区间分割参数（range-separation parameter），即有。默认值为0.11（），此时为 HSE06 泛函[2]。
- exx_lambda：在 basis_type 设置为 lcao_in_pw 的情况下，用于补偿使用 lcao_in_pw 方法评估精确交换能时 G=0 处的发散点。默认值为0.3。
- exx_real_number：该参数设定为 True 时，强制 LibRI 使用 double 数据类型，当设定为 False 时，强制 LibRI 使用 complex 数据类型。当gamma_only=1 时，默认为 True，gamma_only=0 时默认为 False。
- 循环相关参数：
- exx_separate_loop：ABACUS 提供了两种迭代方法来评估精确交换能。当 exx_separate_loop 设置为False时：采用单层循环，即先进行 GGA 循环，然后进行 Hybrid 循环，在该过程中，使用电子迭代来更新对应的哈密顿量。当 exx_separate_loop 设置为True时：采用双层循环，在内层循环中，进行自洽迭代并更新密度矩阵，在外层循环中，根据在内层循环中收敛的密度矩阵来计算。默认值为 True，即采用双层循环计算。单层循环有利于难以自洽收敛的体系达到收敛，但会显著增加内存消耗。
- exx_hybrid_step：在 exx_separate_loop 设置为 True 的情况下，外层循环的最大迭代步数。默认值为100。
- exx_mixing_beta：在 exx_separate_loop 设置为 True 的情况下，内层循环每次迭代时，密度矩阵混合的 mixing_beta 取值，默认为1.0。
- exx_pca_threshold：为了加速四中心积分的计算，ABACUS 采用 LRI 方法，将原子轨道的乘积在辅助基函数(ABF)的基础上展开，即，并利用 PCA 减小辅助基函数(ABF)的大小(即个数)。阈值越大，ABF 的数目越少，计算速度越快，计算精度越低。一个相对安全的值是1e-4，也是默认值。
- exx_ccp_rmesh_times：此参数决定计算 Columb 势所需的截断半径比原子轨道的截断半径大多少倍。对于 HSE 泛函，设置为 1 就足够了。但是对于 PBE0，必须使用一个大得多的数字。当使用 HSE 泛函时，默认值为1.5，其他情况下默认值为5。
- 张量筛选相关参数：
针对杂化泛函计算过程中的物理量进行筛选可以加速计算。具体来说，exx_c_threshold、exx_v_threshold、exx_dm_threshold、exx_c_grad_threshold、exx_v_grad_threshold 分别是针对、、密度矩阵、、。阈值越大，筛掉的张量越多，计算速度越快，计算精度越低。具体请查看完整
INPUT参数文档。 - Cauchy-Schwartz 不等式相关参数：
- exx_cauchy_threshold：在实际中，Fock 交换矩阵是稀疏的，利用 Cauchy-Schwartz 不等式，我们可以在进行显式求值之前找到每个矩阵元素的上界。小于 exx_cauchy_threshold 的值将被截断。阈值越大，筛掉的张量越多，计算速度越快，精度越低。一个相对安全的值是1e-7，也是默认值。不等式算法参见参考文献[3]。
- exx_cauchy_force_threshold、exx_cauchy_stress_threshold与exx_cauchy_threshold类似，区别在于它们分别针对的是求力、应力计算中的 Fock 交换矩阵元。
- opt_orb 相关参数：当dft_functional设置为 opt_orb 时使用，opt_orb 参考文献[4]。本功能仅用于生成 opt 辅助基组，不进行杂化泛函计算。
- exx_opt_orb_lmax：球贝塞尔函数的最大角动量 L 值，opt-ABF 的径向部分用球贝塞尔函数的线性组合生成。
- exx_opt_orb_ecut：球贝塞尔函数展开的截断，在优化 opt-ABF 的时候采用的是球贝塞尔函数基组。
- exx_opt_orb_tolerence：解球贝塞尔函数零点时的阈值。
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[7]
!cd ~/abacus-user-guide/examples/hybrid_functional/1_scf_Si && mpirun -n 8 abacus
ABACUS v3.2
Atomic-orbital Based Ab-initio Computation at UStc
Website: http://abacus.ustc.edu.cn/
Documentation: https://abacus.deepmodeling.com/
Repository: https://github.com/abacusmodeling/abacus-develop
https://github.com/deepmodeling/abacus-develop
Wed Aug 23 18:34:54 2023
MAKE THE DIR : OUT.ABACUS/
dft_functional readin is: hse
dft_functional in pseudopot file is: PBE
In Pseudopot_upf::read_pseudo_header : dft_functional from INPUT does not match that in pseudopot file
Please make sure this is what you need
UNIFORM GRID DIM : 36 * 36 * 36
UNIFORM GRID DIM(BIG): 12 * 12 * 12
DONE(0.0451407 SEC) : SETUP UNITCELL
DONE(0.0464201 SEC) : INIT K-POINTS
---------------------------------------------------------
Self-consistent calculations for electrons
---------------------------------------------------------
SPIN KPOINTS PROCESSORS NBASE
1 64 8 26
---------------------------------------------------------
Use Systematically Improvable Atomic bases
---------------------------------------------------------
ELEMENT ORBITALS NBASE NATOM XC
Si 2s2p1d-8au 13 2
---------------------------------------------------------
Initial plane wave basis and FFT box
---------------------------------------------------------
-------------------------------------------
SELF-CONSISTENT :
-------------------------------------------
START CHARGE : atomic
DONE(61.0246 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -2.139899e+02 0.000000e+00 1.643e-01 7.520e-01
GE2 -2.140154e+02 -2.550400e-02 3.719e-02 5.216e-01
GE3 -2.140161e+02 -7.010991e-04 3.180e-03 5.237e-01
GE4 -2.140161e+02 -4.635095e-06 1.023e-04 6.171e-01
GE5 -2.140161e+02 -6.808981e-08 2.194e-05 5.134e-01
GE6 -2.140161e+02 7.492814e-09 1.878e-06 5.152e-01
GE7 -2.140161e+02 6.874026e-10 2.007e-07 5.117e-01
GE8 -2.140161e+02 8.057803e-11 2.321e-09 5.241e-01
Updating EXX and rerun SCF
GE1 -2.139728e+02 0.000000e+00 3.330e-02 5.728e-01
GE2 -2.140799e+02 -1.070412e-01 2.546e-02 5.682e-01
GE3 -2.140770e+02 2.869703e-03 1.229e-02 5.634e-01
GE4 -2.140777e+02 -6.881612e-04 8.108e-04 5.693e-01
GE5 -2.140777e+02 -2.591209e-06 2.649e-05 5.702e-01
GE6 -2.140777e+02 -1.278873e-08 1.260e-06 5.650e-01
GE7 -2.140777e+02 -5.094977e-10 3.353e-09 5.711e-01
Updating EXX and rerun SCF
GE1 -2.140792e+02 0.000000e+00 1.046e-03 5.646e-01
GE2 -2.140792e+02 -1.730298e-06 1.973e-04 5.640e-01
GE3 -2.140792e+02 -2.042245e-10 2.303e-05 5.695e-01
GE4 -2.140792e+02 -4.364845e-09 1.059e-07 5.623e-01
GE5 -2.140792e+02 -9.401576e-12 1.026e-09 5.730e-01
Updating EXX and rerun SCF
GE1 -2.140793e+02 0.000000e+00 1.457e-04 5.732e-01
GE2 -2.140793e+02 1.432133e-09 2.517e-05 6.586e-01
GE3 -2.140793e+02 4.711519e-09 3.105e-06 5.778e-01
GE4 -2.140793e+02 -4.886644e-10 1.443e-08 5.896e-01
Updating EXX and rerun SCF
GE1 -2.140793e+02 0.000000e+00 2.016e-05 5.779e-01
GE2 -2.140793e+02 5.174564e-09 3.324e-06 5.692e-01
GE3 -2.140793e+02 7.786631e-10 4.049e-07 5.729e-01
GE4 -2.140793e+02 -6.013141e-11 1.917e-09 5.736e-01
Updating EXX and rerun SCF
GE1 -2.140793e+02 0.000000e+00 2.702e-06 5.693e-01
GE2 -2.140793e+02 8.077138e-10 4.330e-07 5.744e-01
GE3 -2.140793e+02 1.080335e-10 5.285e-08 6.633e-01
Updating EXX and rerun SCF
GE1 -2.140793e+02 0.000000e+00 3.529e-07 5.715e-01
GE2 -2.140793e+02 1.077193e-10 5.634e-08 5.759e-01
Updating EXX and rerun SCF
GE1 -2.140793e+02 0.000000e+00 3.978e-08 5.737e-01
|CLASS_NAME---------|NAME---------------|TIME(Sec)-----|CALLS----|AVG------|PER%-------
total 988.02 7 1.4e+02 1e+02 %
Driver driver_line 988.01 1 9.9e+02 1e+02 %
NOrbital_Lm extra_uniform 1.7662 1828 0.00097 0.18 %
Mathzone_Add1 Cubic_Spline_Interpolation0.90183 1828 0.00049 0.091 %
ORB_control set_orb_tables 0.74524 1 0.75 0.075 %
ORB_gen_tables gen_tables 0.74524 1 0.75 0.075 %
ORB_table_phi init_Table 0.43146 1 0.43 0.044 %
ORB_table_phi cal_ST_Phi12_R 44.679 3359 0.013 4.5 %
ORB_table_beta init_Table_Beta 0.1479 1 0.15 0.015 %
ORB_table_beta VNL_PhiBeta_R 0.14692 26 0.0057 0.015 %
ORB_gaunt_table init_Gaunt_CH 0.21121 4 0.053 0.021 %
ORB_gaunt_table Calc_Gaunt_CH 0.10542 82476 1.3e-06 0.011 %
ORB_gaunt_table init_Gaunt 2.5707 4 0.64 0.26 %
ORB_gaunt_table Get_Gaunt_SH 8.6535 3636325 2.4e-06 0.88 %
Exx_LRI init 56.651 1 57 5.7 %
LRI_CV set_orbitals 48.213 1 48 4.9 %
Matrix_Orbs11 init 0.19949 1 0.2 0.02 %
Matrix_Orbs11 init_radial_table 16.264 1 16 1.6 %
Matrix_Orbs21 init 1.3893 1 1.4 0.14 %
Matrix_Orbs21 init_radial_table 30.357 1 30 3.1 %
ESolver_KS_LCAO Run 930.5 1 9.3e+02 94 %
ESolver_KS_LCAO beforescf 3.5019 1 3.5 0.35 %
ESolver_KS_LCAO beforesolver 0.45503 1 0.46 0.046 %
ESolver_KS_LCAO set_matrix_grid 0.45478 1 0.45 0.046 %
Grid_Technique init 0.45133 1 0.45 0.046 %
Grid_Driver Find_atom 0.1525 8858 1.7e-05 0.015 %
Potential update_from_charge 0.66019 35 0.019 0.067 %
Potential cal_v_eff 0.65933 35 0.019 0.067 %
PotXC cal_v_eff 0.63344 35 0.018 0.064 %
XC_Functional v_xc 396.25 22 18 40 %
Exx_LRI cal_exx_ions 3.0192 1 3 0.31 %
LRI_CV cal_datas 2.1711 2 1.1 0.22 %
HSolverLCAO solve 18.778 34 0.55 1.9 %
HamiltLCAO updateHk 9.3444 2176 0.0043 0.95 %
OperatorLCAO init 8.4823 6016 0.0014 0.86 %
Veff contributeHk 5.0239 2176 0.0023 0.51 %
Gint_interface cal_gint 7.5456 68 0.11 0.76 %
Gint_interface cal_gint_vlocal 4.3993 34 0.13 0.45 %
Gint_Tools cal_psir_ylm 1.3221 19584 6.8e-05 0.13 %
Gint_k folding_vl_k 0.62132 2176 0.00029 0.063 %
Gint_k Distri 0.23973 2176 0.00011 0.024 %
OperatorLCAO folding_fixed 3.2977 2176 0.0015 0.33 %
LCAO_nnr folding_fixedH 3.2864 2176 0.0015 0.33 %
HSolverLCAO hamiltSolvePsiK 4.8101 2176 0.0022 0.49 %
OperatorLCAO get_hs_pointers 4.923 1344 0.0037 0.5 %
DiagoElpa elpa_solve 3.7538 2176 0.0017 0.38 %
ElecStateLCAO psiToRho 4.6185 34 0.14 0.47 %
elecstate cal_dm 0.26965 34 0.0079 0.027 %
psiMulPsiMpi pdgemm 0.26471 2176 0.00012 0.027 %
LCAO_Charge cal_dk_k 1.0112 34 0.03 0.1 %
Gint_interface cal_gint_rho 3.1463 34 0.093 0.32 %
Exx_LRI cal_exx_elec 907.45 7 1.3e+02 92 %
RI_2D_Comm add_Hexx 0.95278 1664 0.00057 0.096 %
XC_Functional v_xc_libxc 0.5896 26 0.023 0.06 %
----------------------------------------------------------------------------------------
START Time : Wed Aug 23 18:34:54 2023
FINISH Time : Wed Aug 23 18:51:22 2023
TOTAL Time : 988
SEE INFORMATION IN : OUT.ABACUS/
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3. 杂化泛函计算代价
杂化泛函的计算精度高，与此同时它的计算代价也比较高。在 ABACUS 的输入参数文件 INPUT 中，若 exx_separate_loop 参数设为 True（默认），仅在 SCF 步骤中就涉及两层循环。每次内层循环完成，外层循环往前推进一步时，屏幕输出 Updating EXX and rerun SCF。
一次 SCF 需要的时间至少是以上两个循环涉及的单次电子迭代时间之和。对于单次电子迭代所需时间，在此提出一些已有的经验。以一步电子迭代的时间为衡量尺标，使用 DZP 基组，CPU 型号为 Intel(R) Xeon(R) Gold 6132 CPU @ 2.60GHz，使用 4 核计算一个水分子为 0.6s 左右，使用 14 个核计算 32 个水分子为 0.8s 左右，使用 14 个核计算 64 个水需要 1.9s 左右。
若将 exx_separate_loop 参数设为 False，即使用单层循环时，首先会进行 GGA 迭代直到自洽收敛，然后屏幕输出 Entering 2nd SCF, where EXX is updated，进行 Hybrid 迭代，此时每进行一次电子步得到新的密度后，都会更新一次精确交换能。以一步电子迭代 + 更新精确交换能的时间为衡量尺标，使用 DZP 基组，CPU 型号为 Intel(R) Xeon(R) Gold 6132 CPU @ 2.60GHz，使用 4 核计算一个水分子为 0.7s 左右，使用 14 个核计算 32 个水分子为 115s 左右，使用 14 个核计算 64 个水需要 330s 左右。对于更大的体系，如 2048 个 Si 原子的晶体，使用 DZP 基组，CPU 型号为 Intel(R) Xeon(R) Silver 4310 CPU @ 2.10GHz，用一个节点（56 核）算时，PBE 下一步电子迭代大概需要 380s，而 HSE 一步电子迭代 + 更新精确交换能大概需要 1680s。
在进行杂化泛函计算时推荐尽量使用多线程计算（OpenMP），此时内存开销相对较小，计算速度相对较快。
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三、使用杂化泛函做结构优化
1. 数据准备
在 Gitee 上我们准备了一个简单的使用杂化泛函做结构优化的例子。该例子是在 LCAO 基组下，使用 HSE 泛函，优化单个水分子的结构。文件夹中 log.ref 是使用 3.2.1 版本的 ABACUS 软件包，v0.1.0 版本的 LibRI 和 LibComm 计算所得的屏幕输出。
2. 输入文件
准备计算所需的 INPUT 文件、STRU 文件、KPT 文件，以及 H、O 原子对应的数值原子轨道文件。其中 INPUT 文件如下。注意该文件中指明了计算类型为 relax，即不对晶胞做优化（cell relax），只对原子位置做优化（relax）。更多结构优化类型请看文档 Geometry Optimization ‒ ABACUS documentation。
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[4]
! cd ~/abacus-user-guide/examples/hybrid_functional/2_relax_water && cat INPUT
INPUT_PARAMETERS calculation relax basis_type lcao ntype 2 ecutwfc 60.000000 scf_nmax 100 gamma_only 1 dft_functional hse relax_nmax 100 scf_thr 1e-6 force_thr_ev 1e-2
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在该例子中，结构优化包括多个离子步，每个离子步中都要做一次 SCF。由 INPUT 文件可知，SCF 收敛的标准由 scf_thr=1e-6 指定，或达到 SCF 的最大步数 scf_nmax=100，并计算受力。根据上一个离子步计算得到的受力，计算下一个离子步的原子位置，计算收敛的标准此时为 force_thr_ev=1e-2，或达到离子步的最大步数 relax_nmax=100。STRU 文件如下，可见在结构弛豫步骤中，三个原子都可以移动。
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[5]
! cd ~/abacus-user-guide/examples/hybrid_functional/2_relax_water && cat STRU
ATOMIC_SPECIES O 16.00 O_ONCV_PBE-1.0.upf H 1.00 H_ONCV_PBE-1.0.upf LATTICE_CONSTANT 1 LATTICE_VECTORS 28 0 0 0 28 0 0 0 28 ATOMIC_POSITIONS Direct O #label 0 #magnetism 1 #number of atoms 0.677639488918 0.5227809096584 0.232500040128 m 1 1 1 H #label 0 #magnetism 2 #number of atoms 0.641808457616 0.5785821615863 0.228644198512 m 1 1 1 0.708889637644 0.5204300746076 0.175087721492 m 1 1 1 NUMERICAL_ORBITAL O_gga_6au_60Ry_2s2p1d.orb H_gga_6au_60Ry_2s1p.orb
代码
文本
[6]
! cd ~/abacus-user-guide/examples/hybrid_functional/2_relax_water && mpirun -n 4 abacus
ABACUS v3.2
Atomic-orbital Based Ab-initio Computation at UStc
Website: http://abacus.ustc.edu.cn/
Documentation: https://abacus.deepmodeling.com/
Repository: https://github.com/abacusmodeling/abacus-develop
https://github.com/deepmodeling/abacus-develop
Wed Aug 23 18:54:32 2023
MAKE THE DIR : OUT.ABACUS/
dft_functional readin is: hse
dft_functional in pseudopot file is: PBE
In Pseudopot_upf::read_pseudo_header : dft_functional from INPUT does not match that in pseudopot file
Please make sure this is what you need
dft_functional readin is: hse
dft_functional in pseudopot file is: PBE
In Pseudopot_upf::read_pseudo_header : dft_functional from INPUT does not match that in pseudopot file
Please make sure this is what you need
UNIFORM GRID DIM : 144 * 144 * 144
UNIFORM GRID DIM(BIG): 36 * 36 * 36
DONE(0.107146 SEC) : SETUP UNITCELL
DONE(0.107404 SEC) : INIT K-POINTS
---------------------------------------------------------
Ion relaxation calculations
---------------------------------------------------------
SPIN KPOINTS PROCESSORS NBASE
1 Gamma 4 23
---------------------------------------------------------
Use Systematically Improvable Atomic bases
---------------------------------------------------------
ELEMENT ORBITALS NBASE NATOM XC
O 2s2p1d-6au 13 1
H 2s1p-6au 5 2
---------------------------------------------------------
Initial plane wave basis and FFT box
---------------------------------------------------------
-------------------------------------------
STEP OF RELAXATION : 1
-------------------------------------------
START CHARGE : atomic
DONE(44.5786 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.638736e+02 0.000000e+00 2.255e-01 5.869e-01
GE2 -4.654190e+02 -1.545389e+00 1.780e-01 5.501e-01
GE3 -4.661220e+02 -7.030349e-01 3.766e-02 7.735e-01
GE4 -4.661219e+02 6.343602e-05 6.305e-03 6.989e-01
GE5 -4.661226e+02 -6.739980e-04 6.261e-04 6.931e-01
GE6 -4.661226e+02 -9.721355e-06 9.718e-05 6.654e-01
GE7 -4.661226e+02 -1.296570e-07 2.473e-05 6.609e-01
GE8 -4.661226e+02 -2.909568e-08 1.072e-06 5.554e-01
GE9 -4.661226e+02 5.367357e-10 2.144e-07 6.706e-01
Updating EXX and rerun SCF
GE1 -4.643119e+02 0.000000e+00 9.405e-02 7.492e-01
GE2 -4.658078e+02 -1.495868e+00 1.733e-01 7.850e-01
GE3 -4.660945e+02 -2.867386e-01 5.649e-02 7.724e-01
GE4 -4.660576e+02 3.697590e-02 3.201e-02 7.853e-01
GE5 -4.660619e+02 -4.320485e-03 1.206e-02 7.833e-01
GE6 -4.660618e+02 9.444471e-05 4.710e-03 7.776e-01
GE7 -4.660624e+02 -6.422839e-04 9.401e-05 8.174e-01
GE8 -4.660624e+02 -3.548837e-07 4.197e-06 9.664e-01
GE9 -4.660624e+02 1.010150e-09 4.356e-06 8.124e-01
GE10 -4.660624e+02 2.413764e-09 3.041e-08 7.397e-01
Updating EXX and rerun SCF
GE1 -4.660627e+02 0.000000e+00 3.512e-04 7.608e-01
GE2 -4.660627e+02 -4.852798e-06 2.770e-04 7.753e-01
GE3 -4.660627e+02 -2.368134e-06 3.070e-05 7.722e-01
GE4 -4.660627e+02 1.561580e-09 1.174e-06 7.754e-01
GE5 -4.660627e+02 -1.609627e-10 2.038e-07 7.265e-01
Updating EXX and rerun SCF
GE1 -4.660627e+02 0.000000e+00 3.071e-05 7.498e-01
GE2 -4.660627e+02 -1.212682e-08 2.523e-05 8.879e-01
GE3 -4.660627e+02 -3.528177e-08 2.411e-06 7.757e-01
GE4 -4.660627e+02 5.733753e-10 1.301e-07 7.281e-01
Updating EXX and rerun SCF
GE1 -4.660627e+02 0.000000e+00 3.211e-06 9.141e-01
GE2 -4.660627e+02 3.006861e-09 2.473e-06 8.071e-01
GE3 -4.660627e+02 -1.946730e-09 3.449e-07 7.281e-01
Updating EXX and rerun SCF
GE1 -4.660627e+02 0.000000e+00 4.138e-07 7.362e-01
LARGEST GRAD (eV/A) : 8.030e-01
-------------------------------------------
STEP OF RELAXATION : 2
-------------------------------------------
DONE(7.066e+01 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.633180e+02 0.000000e+00 1.626e-01 5.023e-01
GE2 -4.652950e+02 -1.977011e+00 1.840e-01 5.247e-01
GE3 -4.658734e+02 -5.783967e-01 3.570e-02 5.259e-01
GE4 -4.658995e+02 -2.609741e-02 4.429e-03 5.262e-01
GE5 -4.659000e+02 -5.509783e-04 1.733e-03 5.209e-01
GE6 -4.659001e+02 -8.955775e-05 9.775e-05 5.250e-01
GE7 -4.659001e+02 1.228547e-08 5.498e-05 5.417e-01
GE8 -4.659001e+02 -1.356979e-07 5.121e-06 5.644e-01
GE9 -4.659001e+02 2.890175e-09 1.843e-07 5.021e-01
Updating EXX and rerun SCF
GE1 -4.642528e+02 0.000000e+00 9.045e-02 8.579e-01
GE2 -4.656984e+02 -1.445554e+00 1.605e-01 7.717e-01
GE3 -4.659219e+02 -2.235052e-01 5.381e-02 7.761e-01
GE4 -4.658952e+02 2.665972e-02 2.913e-02 7.789e-01
GE5 -4.658967e+02 -1.524735e-03 1.166e-02 7.811e-01
GE6 -4.658972e+02 -4.197930e-04 4.110e-03 7.725e-01
GE7 -4.658976e+02 -4.649808e-04 1.918e-04 7.731e-01
GE8 -4.658976e+02 -1.307474e-06 4.986e-06 7.781e-01
GE9 -4.658976e+02 1.399844e-09 4.849e-06 7.827e-01
GE10 -4.658976e+02 2.627704e-09 9.261e-08 7.235e-01
Updating EXX and rerun SCF
GE1 -4.658979e+02 0.000000e+00 3.285e-04 7.679e-01
GE2 -4.658979e+02 -4.808811e-06 2.335e-04 7.868e-01
GE3 -4.658979e+02 -1.780886e-06 2.419e-05 7.693e-01
GE4 -4.658979e+02 -3.312448e-09 1.590e-06 9.441e-01
GE5 -4.658979e+02 -3.168984e-10 1.982e-07 8.444e-01
Updating EXX and rerun SCF
GE1 -4.658979e+02 0.000000e+00 2.691e-05 7.661e-01
GE2 -4.658979e+02 1.272427e-09 1.983e-05 7.796e-01
GE3 -4.658979e+02 -2.490591e-08 1.680e-06 8.151e-01
GE4 -4.658979e+02 4.278804e-10 1.409e-07 7.222e-01
Updating EXX and rerun SCF
GE1 -4.658979e+02 0.000000e+00 2.305e-06 7.686e-01
GE2 -4.658979e+02 2.550365e-09 1.729e-06 7.774e-01
GE3 -4.658979e+02 -1.288958e-09 1.763e-07 7.244e-01
Updating EXX and rerun SCF
GE1 -4.658979e+02 0.000000e+00 1.834e-07 7.569e-01
LARGEST GRAD (eV/A) : 4.375e+00
-------------------------------------------
STEP OF RELAXATION : 3
-------------------------------------------
DONE(9.545e+01 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.620023e+02 0.000000e+00 1.974e-01 6.231e-01
GE2 -4.653713e+02 -3.369088e+00 2.427e-01 6.673e-01
GE3 -4.660288e+02 -6.574756e-01 6.451e-02 6.599e-01
GE4 -4.661188e+02 -9.002318e-02 6.972e-03 6.719e-01
GE5 -4.661197e+02 -8.618186e-04 3.131e-03 6.609e-01
GE6 -4.661200e+02 -3.125826e-04 2.925e-04 6.567e-01
GE7 -4.661200e+02 -2.119623e-06 1.841e-05 6.645e-01
GE8 -4.661200e+02 -1.523916e-08 3.070e-06 5.491e-01
GE9 -4.661200e+02 -2.565059e-09 1.665e-06 5.318e-01
GE10 -4.661200e+02 1.158641e-09 4.466e-08 4.793e-01
Updating EXX and rerun SCF
GE1 -4.643463e+02 0.000000e+00 9.324e-02 7.540e-01
GE2 -4.658312e+02 -1.484960e+00 1.704e-01 7.651e-01
GE3 -4.661022e+02 -2.709996e-01 5.590e-02 7.818e-01
GE4 -4.660678e+02 3.447431e-02 3.130e-02 7.900e-01
GE5 -4.660715e+02 -3.770644e-03 1.187e-02 7.875e-01
GE6 -4.660716e+02 -9.944771e-05 4.460e-03 8.644e-01
GE7 -4.660722e+02 -5.839917e-04 6.424e-05 7.750e-01
GE8 -4.660722e+02 -2.038689e-07 8.242e-06 7.775e-01
GE9 -4.660722e+02 3.267011e-09 3.702e-06 8.880e-01
GE10 -4.660722e+02 2.169468e-09 2.223e-08 7.243e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 3.436e-04 7.603e-01
GE2 -4.660725e+02 -4.629825e-06 2.649e-04 7.704e-01
GE3 -4.660725e+02 -2.186167e-06 2.921e-05 7.824e-01
GE4 -4.660725e+02 1.869488e-09 1.125e-06 7.718e-01
GE5 -4.660725e+02 -1.745938e-10 1.661e-07 7.239e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 2.940e-05 7.675e-01
GE2 -4.660725e+02 -9.945368e-09 2.365e-05 7.871e-01
GE3 -4.660725e+02 -3.188463e-08 2.234e-06 8.721e-01
GE4 -4.660725e+02 5.023197e-10 1.087e-07 9.290e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 2.846e-06 7.498e-01
GE2 -4.660725e+02 2.842804e-09 2.237e-06 7.760e-01
GE3 -4.660725e+02 -1.730180e-09 2.906e-07 8.279e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 3.345e-07 7.290e-01
LARGEST GRAD (eV/A) : 1.126e-01
-------------------------------------------
STEP OF RELAXATION : 4
-------------------------------------------
DONE(1.218e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.631683e+02 0.000000e+00 1.297e-01 5.106e-01
GE2 -4.658947e+02 -2.726347e+00 2.272e-01 5.328e-01
GE3 -4.661691e+02 -2.744342e-01 8.671e-02 5.224e-01
GE4 -4.661514e+02 1.768122e-02 4.590e-02 5.415e-01
GE5 -4.660814e+02 7.006372e-02 2.937e-02 5.401e-01
GE6 -4.661206e+02 -3.923042e-02 1.034e-02 5.405e-01
GE7 -4.661192e+02 1.420415e-03 5.351e-03 5.301e-01
GE8 -4.661200e+02 -8.334082e-04 1.488e-04 6.307e-01
GE9 -4.661200e+02 -4.745423e-07 5.245e-06 5.140e-01
GE10 -4.661200e+02 -4.060997e-09 2.129e-06 5.193e-01
GE11 -4.661200e+02 1.671209e-09 2.776e-08 4.742e-01
Updating EXX and rerun SCF
GE1 -4.643463e+02 0.000000e+00 9.324e-02 7.651e-01
GE2 -4.658312e+02 -1.484960e+00 1.704e-01 7.811e-01
GE3 -4.661022e+02 -2.709996e-01 5.590e-02 8.792e-01
GE4 -4.660678e+02 3.447430e-02 3.130e-02 7.726e-01
GE5 -4.660715e+02 -3.770646e-03 1.187e-02 7.846e-01
GE6 -4.660716e+02 -9.944816e-05 4.460e-03 7.758e-01
GE7 -4.660722e+02 -5.839913e-04 6.424e-05 7.810e-01
GE8 -4.660722e+02 -2.038663e-07 8.242e-06 7.783e-01
GE9 -4.660722e+02 3.277452e-09 3.702e-06 8.027e-01
GE10 -4.660722e+02 2.160381e-09 2.223e-08 7.575e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 3.436e-04 8.225e-01
GE2 -4.660725e+02 -4.629827e-06 2.649e-04 7.739e-01
GE3 -4.660725e+02 -2.186168e-06 2.921e-05 7.800e-01
GE4 -4.660725e+02 1.871228e-09 1.125e-06 7.772e-01
GE5 -4.660725e+02 -1.837778e-10 1.661e-07 7.292e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 2.940e-05 7.668e-01
GE2 -4.660725e+02 -9.942855e-09 2.365e-05 7.819e-01
GE3 -4.660725e+02 -3.189227e-08 2.234e-06 7.753e-01
GE4 -4.660725e+02 4.967125e-10 1.087e-07 7.232e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 2.846e-06 7.743e-01
GE2 -4.660725e+02 2.846285e-09 2.237e-06 7.930e-01
GE3 -4.660725e+02 -1.732113e-09 2.906e-07 7.339e-01
Updating EXX and rerun SCF
GE1 -4.660725e+02 0.000000e+00 3.345e-07 8.174e-01
LARGEST GRAD (eV/A) : 1.126e-01
-------------------------------------------
STEP OF RELAXATION : 5
-------------------------------------------
DONE(1.477e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.632712e+02 0.000000e+00 1.259e-01 5.213e-01
GE2 -4.659058e+02 -2.634612e+00 2.227e-01 5.300e-01
GE3 -4.661109e+02 -2.050866e-01 8.559e-02 5.287e-01
GE4 -4.660833e+02 2.764428e-02 3.743e-02 5.301e-01
GE5 -4.661114e+02 -2.817011e-02 4.581e-03 6.699e-01
GE6 -4.661121e+02 -6.621111e-04 3.328e-04 5.988e-01
GE7 -4.661121e+02 4.016026e-07 1.270e-04 5.204e-01
GE8 -4.661121e+02 -6.626214e-07 2.308e-05 5.229e-01
GE9 -4.661121e+02 -5.442570e-09 2.852e-06 5.315e-01
GE10 -4.661121e+02 -2.310129e-09 3.144e-08 4.987e-01
Updating EXX and rerun SCF
GE1 -4.643557e+02 0.000000e+00 9.285e-02 7.512e-01
GE2 -4.658353e+02 -1.479632e+00 1.690e-01 7.800e-01
GE3 -4.660994e+02 -2.640743e-01 5.562e-02 7.859e-01
GE4 -4.660661e+02 3.334119e-02 3.099e-02 1.000e+00
GE5 -4.660695e+02 -3.472221e-03 1.181e-02 7.815e-01
GE6 -4.660697e+02 -1.727251e-04 4.371e-03 7.805e-01
GE7 -4.660703e+02 -5.627436e-04 6.185e-05 7.889e-01
GE8 -4.660703e+02 2.158977e-07 7.668e-06 7.712e-01
GE9 -4.660703e+02 3.004637e-09 4.040e-06 7.859e-01
GE10 -4.660703e+02 2.312256e-09 2.307e-08 7.284e-01
Updating EXX and rerun SCF
GE1 -4.660705e+02 0.000000e+00 3.409e-04 7.526e-01
GE2 -4.660705e+02 -4.544104e-06 2.600e-04 7.798e-01
GE3 -4.660705e+02 -2.088187e-06 2.854e-05 7.726e-01
GE4 -4.660705e+02 2.051235e-09 1.142e-06 7.692e-01
GE5 -4.660705e+02 -2.058196e-10 1.556e-07 7.265e-01
Updating EXX and rerun SCF
GE1 -4.660705e+02 0.000000e+00 2.891e-05 8.175e-01
GE2 -4.660705e+02 -2.147252e-08 2.302e-05 9.681e-01
GE3 -4.660705e+02 -3.062371e-08 2.158e-06 7.711e-01
GE4 -4.660705e+02 4.784411e-10 1.044e-07 8.046e-01
Updating EXX and rerun SCF
GE1 -4.660705e+02 0.000000e+00 2.713e-06 7.894e-01
GE2 -4.660705e+02 -3.075983e-09 2.145e-06 7.796e-01
GE3 -4.660705e+02 -1.663861e-09 2.701e-07 7.290e-01
Updating EXX and rerun SCF
GE1 -4.660705e+02 0.000000e+00 3.036e-07 7.239e-01
LARGEST GRAD (eV/A) : 4.290e-01
-------------------------------------------
STEP OF RELAXATION : 6
-------------------------------------------
DONE(1.734e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.630834e+02 0.000000e+00 1.337e-01 5.077e-01
GE2 -4.658715e+02 -2.788178e+00 2.289e-01 5.260e-01
GE3 -4.661350e+02 -2.634656e-01 8.618e-02 5.424e-01
GE4 -4.660628e+02 7.225765e-02 4.048e-02 5.286e-01
GE5 -4.661182e+02 -5.539918e-02 5.236e-03 6.710e-01
GE6 -4.661189e+02 -7.164874e-04 1.236e-04 6.651e-01
GE7 -4.661189e+02 2.767427e-06 2.082e-04 6.590e-01
GE8 -4.661189e+02 -1.550398e-06 2.001e-05 5.940e-01
GE9 -4.661189e+02 5.110300e-09 1.750e-06 6.334e-01
GE10 -4.661189e+02 1.255122e-09 4.487e-08 4.827e-01
Updating EXX and rerun SCF
GE1 -4.643489e+02 0.000000e+00 9.315e-02 9.126e-01
GE2 -4.658327e+02 -1.483793e+00 1.701e-01 9.612e-01
GE3 -4.661022e+02 -2.694525e-01 5.584e-02 7.789e-01
GE4 -4.660680e+02 3.422259e-02 3.123e-02 7.764e-01
GE5 -4.660717e+02 -3.707985e-03 1.186e-02 7.719e-01
GE6 -4.660718e+02 -1.168871e-04 4.438e-03 7.787e-01
GE7 -4.660724e+02 -5.785702e-04 6.256e-05 7.818e-01
GE8 -4.660724e+02 -2.022048e-07 8.561e-06 8.586e-01
GE9 -4.660724e+02 3.037216e-09 1.884e-06 7.694e-01
GE10 -4.660724e+02 1.395687e-09 5.307e-08 7.263e-01
Updating EXX and rerun SCF
GE1 -4.660726e+02 0.000000e+00 3.430e-04 7.537e-01
GE2 -4.660726e+02 -4.547779e-06 2.638e-04 7.793e-01
GE3 -4.660726e+02 -2.196825e-06 2.906e-05 7.786e-01
GE4 -4.660726e+02 -4.787698e-09 1.128e-06 7.854e-01
GE5 -4.660726e+02 -6.717027e-09 1.628e-07 7.420e-01
Updating EXX and rerun SCF
GE1 -4.660726e+02 0.000000e+00 2.929e-05 7.695e-01
GE2 -4.660726e+02 -9.803547e-09 2.352e-05 7.757e-01
GE3 -4.660726e+02 -3.157102e-08 2.217e-06 7.714e-01
GE4 -4.660726e+02 4.919755e-10 1.073e-07 7.351e-01
Updating EXX and rerun SCF
GE1 -4.660726e+02 0.000000e+00 2.815e-06 7.691e-01
GE2 -4.660726e+02 2.828787e-09 2.216e-06 8.900e-01
GE3 -4.660726e+02 -1.702821e-09 2.858e-07 7.204e-01
Updating EXX and rerun SCF
GE1 -4.660726e+02 0.000000e+00 3.274e-07 7.207e-01
LARGEST GRAD (eV/A) : 2.725e-02
-------------------------------------------
STEP OF RELAXATION : 7
-------------------------------------------
DONE(1.994e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.631672e+02 0.000000e+00 1.300e-01 5.018e-01
GE2 -4.658928e+02 -2.725615e+00 2.270e-01 5.285e-01
GE3 -4.661666e+02 -2.737056e-01 8.651e-02 5.237e-01
GE4 -4.661691e+02 -2.559425e-03 4.549e-02 5.232e-01
GE5 -4.660783e+02 9.081699e-02 3.423e-02 5.311e-01
GE6 -4.661190e+02 -4.075346e-02 5.061e-03 5.211e-01
GE7 -4.661196e+02 -5.386603e-04 5.088e-04 5.241e-01
GE8 -4.661196e+02 -8.639547e-06 4.469e-05 5.227e-01
GE9 -4.661196e+02 -1.187479e-08 2.122e-06 5.362e-01
GE10 -4.661196e+02 1.357114e-09 4.746e-07 4.777e-01
Updating EXX and rerun SCF
GE1 -4.643477e+02 0.000000e+00 9.319e-02 7.841e-01
GE2 -4.658320e+02 -1.484292e+00 1.702e-01 8.778e-01
GE3 -4.661023e+02 -2.703436e-01 5.587e-02 9.007e-01
GE4 -4.660680e+02 3.436803e-02 3.127e-02 9.049e-01
GE5 -4.660717e+02 -3.731162e-03 1.187e-02 7.991e-01
GE6 -4.660718e+02 -1.030482e-04 4.456e-03 8.237e-01
GE7 -4.660724e+02 -5.831343e-04 6.334e-05 8.942e-01
GE8 -4.660724e+02 -2.071868e-07 8.698e-06 7.694e-01
GE9 -4.660724e+02 3.247290e-09 2.775e-06 7.678e-01
GE10 -4.660724e+02 1.772523e-09 1.984e-08 7.224e-01
Updating EXX and rerun SCF
GE1 -4.660726e+02 0.000000e+00 3.433e-04 7.583e-01
GE2 -4.660727e+02 -4.591226e-06 2.644e-04 7.852e-01
GE3 -4.660727e+02 -2.622625e-06 2.915e-05 8.311e-01
GE4 -4.660727e+02 -4.802392e-09 1.129e-06 9.101e-01
GE5 -4.660727e+02 -1.704368e-10 1.645e-07 7.398e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.935e-05 7.552e-01
GE2 -4.660727e+02 -4.928470e-07 2.360e-05 7.697e-01
GE3 -4.660727e+02 -3.176688e-08 2.229e-06 7.805e-01
GE4 -4.660727e+02 5.012562e-10 1.084e-07 7.336e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.833e-06 7.564e-01
GE2 -4.660727e+02 -3.867359e-09 2.228e-06 7.674e-01
GE3 -4.660727e+02 -1.719449e-09 2.891e-07 7.207e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.321e-07 7.220e-01
LARGEST GRAD (eV/A) : 3.913e-02
-------------------------------------------
STEP OF RELAXATION : 8
-------------------------------------------
DONE(2.250e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.631714e+02 0.000000e+00 1.295e-01 5.294e-01
GE2 -4.658957e+02 -2.724281e+00 2.270e-01 6.334e-01
GE3 -4.661681e+02 -2.724586e-01 8.669e-02 5.153e-01
GE4 -4.661355e+02 3.267496e-02 4.584e-02 5.212e-01
GE5 -4.660916e+02 4.382222e-02 2.499e-02 5.230e-01
GE6 -4.661189e+02 -2.722576e-02 8.454e-03 5.280e-01
GE7 -4.661190e+02 -1.560172e-04 2.982e-03 5.225e-01
GE8 -4.661193e+02 -2.633486e-04 9.492e-05 5.183e-01
GE9 -4.661193e+02 -1.692468e-07 4.702e-06 5.118e-01
GE10 -4.661193e+02 -4.159605e-09 1.174e-06 5.263e-01
GE11 -4.661193e+02 9.383207e-10 8.431e-09 4.676e-01
Updating EXX and rerun SCF
GE1 -4.643482e+02 0.000000e+00 9.318e-02 7.474e-01
GE2 -4.658323e+02 -1.484077e+00 1.701e-01 8.627e-01
GE3 -4.661023e+02 -2.699567e-01 5.585e-02 7.815e-01
GE4 -4.660680e+02 3.430563e-02 3.126e-02 7.773e-01
GE5 -4.660717e+02 -3.722389e-03 1.186e-02 7.819e-01
GE6 -4.660718e+02 -1.086096e-04 4.448e-03 7.929e-01
GE7 -4.660724e+02 -5.811246e-04 6.295e-05 8.763e-01
GE8 -4.660724e+02 -1.979283e-07 8.621e-06 7.779e-01
GE9 -4.660724e+02 3.143171e-09 2.282e-06 7.790e-01
GE10 -4.660724e+02 1.554813e-09 2.229e-08 7.305e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.432e-04 7.615e-01
GE2 -4.660727e+02 -4.893942e-06 2.642e-04 8.825e-01
GE3 -4.660727e+02 -2.155744e-06 2.911e-05 9.086e-01
GE4 -4.660727e+02 1.884955e-09 1.127e-06 9.124e-01
GE5 -4.660727e+02 -1.356466e-08 1.638e-07 8.476e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.932e-05 8.466e-01
GE2 -4.660727e+02 -1.652898e-08 2.356e-05 7.819e-01
GE3 -4.660727e+02 -3.168761e-08 2.224e-06 7.983e-01
GE4 -4.660727e+02 4.882052e-10 1.078e-07 9.032e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.825e-06 7.524e-01
GE2 -4.660727e+02 2.841934e-09 2.223e-06 8.860e-01
GE3 -4.660727e+02 -1.719739e-09 2.878e-07 7.329e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.301e-07 7.303e-01
LARGEST GRAD (eV/A) : 1.884e-02
-------------------------------------------
STEP OF RELAXATION : 9
-------------------------------------------
DONE(2.515e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.631797e+02 0.000000e+00 1.294e-01 5.032e-01
GE2 -4.658959e+02 -2.716173e+00 2.266e-01 5.275e-01
GE3 -4.661680e+02 -2.721225e-01 8.652e-02 5.207e-01
GE4 -4.661609e+02 7.079044e-03 4.577e-02 5.226e-01
GE5 -4.660781e+02 8.287025e-02 3.216e-02 5.271e-01
GE6 -4.661190e+02 -4.094006e-02 7.790e-03 5.214e-01
GE7 -4.661190e+02 -1.562559e-05 2.928e-03 5.228e-01
GE8 -4.661193e+02 -2.473847e-04 6.343e-05 5.681e-01
GE9 -4.661193e+02 -3.228274e-08 3.941e-06 6.231e-01
GE10 -4.661193e+02 2.340195e-09 1.115e-06 5.574e-01
GE11 -4.661193e+02 9.405443e-10 6.437e-08 4.746e-01
Updating EXX and rerun SCF
GE1 -4.643485e+02 0.000000e+00 9.317e-02 7.544e-01
GE2 -4.658324e+02 -1.483918e+00 1.701e-01 8.856e-01
GE3 -4.661023e+02 -2.699133e-01 5.585e-02 7.757e-01
GE4 -4.660680e+02 3.429574e-02 3.126e-02 7.880e-01
GE5 -4.660717e+02 -3.707173e-03 1.187e-02 7.803e-01
GE6 -4.660718e+02 -1.071673e-04 4.451e-03 8.453e-01
GE7 -4.660724e+02 -5.823260e-04 6.230e-05 9.659e-01
GE8 -4.660724e+02 -1.941646e-07 8.528e-06 7.778e-01
GE9 -4.660724e+02 3.069022e-09 1.878e-06 7.737e-01
GE10 -4.660724e+02 1.387760e-09 6.131e-08 7.395e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.432e-04 8.422e-01
GE2 -4.660727e+02 -4.552511e-06 2.642e-04 7.758e-01
GE3 -4.660727e+02 -2.163382e-06 2.911e-05 7.783e-01
GE4 -4.660727e+02 -4.766043e-09 1.130e-06 7.840e-01
GE5 -4.660727e+02 -1.845512e-10 1.643e-07 7.934e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.932e-05 7.548e-01
GE2 -4.660727e+02 -1.651023e-08 2.356e-05 7.796e-01
GE3 -4.660727e+02 -3.169351e-08 2.224e-06 7.782e-01
GE4 -4.660727e+02 4.895586e-10 1.081e-07 7.270e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.824e-06 7.564e-01
GE2 -4.660727e+02 2.835941e-09 2.223e-06 7.789e-01
GE3 -4.660727e+02 -1.718096e-09 2.882e-07 7.289e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.304e-07 7.585e-01
LARGEST GRAD (eV/A) : 1.268e-02
-------------------------------------------
STEP OF RELAXATION : 10
-------------------------------------------
DONE(2.776e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.631750e+02 0.000000e+00 1.295e-01 5.029e-01
GE2 -4.658954e+02 -2.720400e+00 2.268e-01 5.305e-01
GE3 -4.661683e+02 -2.729429e-01 8.657e-02 5.317e-01
GE4 -4.661564e+02 1.187302e-02 4.583e-02 5.221e-01
GE5 -4.660777e+02 7.874572e-02 3.094e-02 5.170e-01
GE6 -4.661197e+02 -4.206225e-02 9.916e-03 5.257e-01
GE7 -4.661185e+02 1.242227e-03 5.072e-03 5.289e-01
GE8 -4.661192e+02 -7.435930e-04 1.232e-04 5.199e-01
GE9 -4.661192e+02 -2.851055e-07 3.999e-06 5.232e-01
GE10 -4.661192e+02 -5.767589e-10 6.230e-07 4.799e-01
Updating EXX and rerun SCF
GE1 -4.643486e+02 0.000000e+00 9.316e-02 7.559e-01
GE2 -4.658324e+02 -1.483836e+00 1.701e-01 7.727e-01
GE3 -4.661023e+02 -2.698892e-01 5.585e-02 7.855e-01
GE4 -4.660680e+02 3.429324e-02 3.125e-02 8.127e-01
GE5 -4.660717e+02 -3.701174e-03 1.187e-02 7.815e-01
GE6 -4.660718e+02 -1.078011e-04 4.453e-03 7.804e-01
GE7 -4.660724e+02 -5.827899e-04 6.215e-05 7.769e-01
GE8 -4.660724e+02 -1.938699e-07 8.654e-06 7.754e-01
GE9 -4.660724e+02 3.091257e-09 1.858e-06 8.734e-01
GE10 -4.660724e+02 1.383603e-09 5.671e-08 7.283e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.432e-04 7.647e-01
GE2 -4.660727e+02 -5.017075e-06 2.641e-04 7.821e-01
GE3 -4.660727e+02 -2.193883e-06 2.911e-05 7.706e-01
GE4 -4.660727e+02 1.964132e-09 1.133e-06 7.785e-01
GE5 -4.660727e+02 -1.931552e-10 1.641e-07 7.266e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.931e-05 7.688e-01
GE2 -4.660727e+02 -1.585197e-08 2.355e-05 9.007e-01
GE3 -4.660727e+02 -4.480225e-08 2.225e-06 7.731e-01
GE4 -4.660727e+02 4.867551e-10 1.086e-07 7.279e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.823e-06 7.592e-01
GE2 -4.660727e+02 2.825596e-09 2.222e-06 7.832e-01
GE3 -4.660727e+02 -1.716936e-09 2.883e-07 7.530e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.305e-07 7.267e-01
LARGEST GRAD (eV/A) : 1.887e-02
-------------------------------------------
STEP OF RELAXATION : 11
-------------------------------------------
DONE(3.028e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.631825e+02 0.000000e+00 1.292e-01 5.077e-01
GE2 -4.658968e+02 -2.714331e+00 2.265e-01 5.317e-01
GE3 -4.661677e+02 -2.708530e-01 8.654e-02 5.302e-01
GE4 -4.661417e+02 2.597336e-02 4.578e-02 5.405e-01
GE5 -4.660898e+02 5.186451e-02 2.690e-02 5.357e-01
GE6 -4.661183e+02 -2.846221e-02 6.616e-03 6.240e-01
GE7 -4.661187e+02 -4.627834e-04 1.658e-03 5.260e-01
GE8 -4.661188e+02 -8.127959e-05 4.350e-05 5.326e-01
GE9 -4.661188e+02 -2.960167e-09 1.737e-06 5.188e-01
GE10 -4.661188e+02 5.773389e-10 9.818e-07 4.819e-01
Updating EXX and rerun SCF
GE1 -4.643494e+02 0.000000e+00 9.314e-02 7.532e-01
GE2 -4.658329e+02 -1.483405e+00 1.700e-01 7.827e-01
GE3 -4.661023e+02 -2.694036e-01 5.583e-02 7.761e-01
GE4 -4.660680e+02 3.421388e-02 3.123e-02 7.918e-01
GE5 -4.660717e+02 -3.677106e-03 1.187e-02 7.845e-01
GE6 -4.660718e+02 -1.118952e-04 4.448e-03 7.753e-01
GE7 -4.660724e+02 -5.820779e-04 6.180e-05 7.821e-01
GE8 -4.660724e+02 -1.922805e-07 8.613e-06 7.707e-01
GE9 -4.660724e+02 3.117746e-09 2.232e-06 7.781e-01
GE10 -4.660724e+02 1.534898e-09 2.575e-08 8.016e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.429e-04 8.702e-01
GE2 -4.660727e+02 -4.550310e-06 2.637e-04 7.810e-01
GE3 -4.660727e+02 -2.209194e-06 2.906e-05 7.781e-01
GE4 -4.660727e+02 1.976989e-09 1.135e-06 7.913e-01
GE5 -4.660727e+02 -1.952821e-10 1.636e-07 7.189e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.927e-05 8.097e-01
GE2 -4.660727e+02 -3.027066e-09 2.350e-05 9.603e-01
GE3 -4.660727e+02 -3.158059e-08 2.221e-06 7.786e-01
GE4 -4.660727e+02 5.020296e-10 1.079e-07 7.412e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.813e-06 7.649e-01
GE2 -4.660727e+02 2.834394e-09 2.215e-06 7.785e-01
GE3 -4.660727e+02 -1.719739e-09 2.871e-07 8.261e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.286e-07 8.996e-01
LARGEST GRAD (eV/A) : 1.806e-02
-------------------------------------------
STEP OF RELAXATION : 12
-------------------------------------------
DONE(3.286e+02 SEC) : INIT SCF
ITER ETOT(eV) EDIFF(eV) DRHO TIME(s)
GE1 -4.631672e+02 0.000000e+00 1.298e-01 5.050e-01
GE2 -4.658942e+02 -2.726961e+00 2.270e-01 6.713e-01
GE3 -4.661679e+02 -2.737479e-01 8.661e-02 7.016e-01
GE4 -4.661502e+02 1.777292e-02 4.582e-02 7.121e-01
GE5 -4.660816e+02 6.852395e-02 2.927e-02 7.011e-01
GE6 -4.661192e+02 -3.756359e-02 9.500e-03 7.067e-01
GE7 -4.661184e+02 7.895066e-04 4.477e-03 6.988e-01
GE8 -4.661190e+02 -5.881934e-04 1.401e-04 6.999e-01
GE9 -4.661190e+02 -4.076774e-07 3.949e-06 7.009e-01
GE10 -4.661190e+02 6.640364e-09 6.551e-07 6.406e-01
Updating EXX and rerun SCF
GE1 -4.643491e+02 0.000000e+00 9.315e-02 9.873e-01
GE2 -4.658327e+02 -1.483579e+00 1.701e-01 7.720e-01
GE3 -4.661023e+02 -2.695996e-01 5.583e-02 7.749e-01
GE4 -4.660680e+02 3.424615e-02 3.124e-02 7.860e-01
GE5 -4.660717e+02 -3.686922e-03 1.187e-02 7.773e-01
GE6 -4.660718e+02 -1.103270e-04 4.450e-03 7.830e-01
GE7 -4.660724e+02 -5.821078e-04 6.185e-05 7.832e-01
GE8 -4.660724e+02 -1.988637e-07 8.572e-06 7.851e-01
GE9 -4.660724e+02 3.089614e-09 1.939e-06 7.774e-01
GE10 -4.660724e+02 1.396074e-09 4.616e-08 7.249e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.430e-04 7.619e-01
GE2 -4.660727e+02 -4.600364e-06 2.639e-04 7.773e-01
GE3 -4.660727e+02 -2.158162e-06 2.908e-05 8.367e-01
GE4 -4.660727e+02 1.962295e-09 1.132e-06 7.894e-01
GE5 -4.660727e+02 -1.745938e-10 1.636e-07 7.292e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.929e-05 7.479e-01
GE2 -4.660727e+02 -2.314160e-08 2.352e-05 7.754e-01
GE3 -4.660727e+02 -2.398731e-08 2.222e-06 7.846e-01
GE4 -4.660727e+02 4.969059e-10 1.084e-07 7.316e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 2.817e-06 7.710e-01
GE2 -4.660727e+02 -2.895589e-09 2.217e-06 7.813e-01
GE3 -4.660727e+02 -1.716356e-09 2.876e-07 7.201e-01
Updating EXX and rerun SCF
GE1 -4.660727e+02 0.000000e+00 3.293e-07 7.235e-01
LARGEST GRAD (eV/A) : 7.944e-03
|CLASS_NAME---------|NAME---------------|TIME(Sec)-----|CALLS----|AVG------|PER%-------
total 354.31 29 12 1e+02 %
Driver driver_line 354.3 1 3.5e+02 1e+02 %
PW_Basis setup_struc_factor 0.62915 23 0.027 0.18 %
NOrbital_Lm extra_uniform 7.0586 2492 0.0028 2 %
Mathzone_Add1 Cubic_Spline_Interpolation0.43508 2492 0.00017 0.12 %
Mathzone_Add1 Uni_Deriv_Phi 6.2102 2492 0.0025 1.8 %
ORB_control set_orb_tables 0.65464 1 0.65 0.18 %
ORB_gen_tables gen_tables 0.65464 1 0.65 0.18 %
ORB_table_phi init_Table 0.31469 1 0.31 0.089 %
ORB_table_phi cal_ST_Phi12_R 28.612 4573 0.0063 8.1 %
ORB_table_beta init_Table_Beta 0.17634 1 0.18 0.05 %
ORB_table_beta VNL_PhiBeta_R 0.17508 56 0.0031 0.049 %
ORB_gaunt_table init_Gaunt_CH 0.17554 4 0.044 0.05 %
ORB_gaunt_table init_Gaunt 1.483 4 0.37 0.42 %
ORB_gaunt_table Get_Gaunt_SH 7.8267 3636325 2.2e-06 2.2 %
Exx_LRI init 42.293 1 42 12 %
LRI_CV set_orbitals 34.636 1 35 9.8 %
Matrix_Orbs11 init 0.17237 1 0.17 0.049 %
Matrix_Orbs11 init_radial_table 10.458 1 10 3 %
Matrix_Orbs21 init 0.84311 1 0.84 0.24 %
Matrix_Orbs21 init_radial_table 23.159 1 23 6.5 %
ESolver_KS_LCAO Run 303.78 12 25 86 %
ESolver_KS_LCAO beforescf 12.29 12 1 3.5 %
ESolver_KS_LCAO beforesolver 0.79554 12 0.066 0.22 %
ESolver_KS_LCAO set_matrix_grid 0.79162 12 0.066 0.22 %
Grid_Technique init 0.78961 12 0.066 0.22 %
Charge atomic_rho 1.7091 23 0.074 0.48 %
PW_Basis recip2real 40.785 2080 0.02 12 %
PW_Basis gathers_scatterp 16.455 2080 0.0079 4.6 %
Potential init_pot 6.8381 12 0.57 1.9 %
Potential update_from_charge 207.82 409 0.51 59 %
Potential cal_fixed_v 0.29386 12 0.024 0.083 %
PotLocal cal_fixed_v 0.27842 12 0.023 0.079 %
Potential cal_v_eff 207.52 409 0.51 59 %
H_Hartree_pw v_hartree 23.234 409 0.057 6.6 %
PW_Basis real2recip 54.229 2985 0.018 15 %
PW_Basis gatherp_scatters 21.506 2985 0.0072 6.1 %
PotXC cal_v_eff 183.14 409 0.45 52 %
XC_Functional v_xc 155.47 266 0.58 44 %
Exx_LRI cal_exx_ions 2.1816 12 0.18 0.62 %
LRI_CV cal_datas 0.48732 36 0.014 0.14 %
H_Ewald_pw compute_ewald 0.29237 12 0.024 0.083 %
HSolverLCAO solve 48.375 397 0.12 14 %
HamiltLCAO updateHk 21.875 397 0.055 6.2 %
Veff contributeHk 21.809 397 0.055 6.2 %
Gint_interface cal_gint 49.731 806 0.062 14 %
Gint_interface cal_gint_vlocal 21.624 397 0.054 6.1 %
Gint_Tools cal_psir_ylm 0.66098 151654 4.4e-06 0.19 %
Gint_Gamma distri_vl 0.18178 397 0.00046 0.051 %
Gint_Gamma distri_vl_value 0.18014 397 0.00045 0.051 %
HSolverLCAO hamiltSolvePsiK 0.56902 397 0.0014 0.16 %
OperatorLCAO get_hs_pointers 152.23 199 0.76 43 %
DiagoElpa elpa_solve 0.3538 397 0.00089 0.1 %
ElecStateLCAO psiToRho 25.927 397 0.065 7.3 %
Gint_interface cal_gint_rho 24.643 397 0.062 7 %
Charge_Mixing rhog_dot_product 0.54728 397 0.0014 0.15 %
Charge mix_rho 14.989 325 0.046 4.2 %
Charge Pulay_mixing 14.271 325 0.044 4 %
Exx_LRI cal_exx_elec 5.7744 60 0.096 1.6 %
XC_Functional v_xc_libxc 147.79 287 0.51 42 %
Force_Stress_LCAO getForceStress 6.952 12 0.58 2 %
Forces cal_force_loc 0.5469 12 0.046 0.15 %
Forces cal_force_ew 0.32831 12 0.027 0.093 %
Forces cal_force_scc 1.0304 12 0.086 0.29 %
Force_LCAO_gamma ftable_gamma 3.4823 12 0.29 0.98 %
Force_LCAO_gamma cal_fvl_dphi 3.4644 12 0.29 0.98 %
Gint_interface cal_gint_force 3.4644 12 0.29 0.98 %
Exx_LRI cal_exx_force 1.563 12 0.13 0.44 %
----------------------------------------------------------------------------------------
START Time : Wed Aug 23 18:54:32 2023
FINISH Time : Wed Aug 23 19:00:26 2023
TOTAL Time : 354
SEE INFORMATION IN : OUT.ABACUS/
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3. 结果
结构弛豫（relax）后的原子结构可见 OUT.ABACUS/STRU_ION_D。由输出文件可知，即使该例子中采用了相对稳定的构型，且 scf_thr 仅设为 1e-6，使用 HSE 做结构弛豫的计算代价仍然很高，使用4个核计算需要6分钟左右。
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四、参考文献
[1] Staroverov V N, Scuseria G E, Tao J, et al. Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes[J]. The Journal of chemical physics, 2003, 119(23): 12129-12137.
[2] Aliaksandr V. Krukau, Oleg A. Vydrov, Artur F. Izmaylov, Gustavo E. Scuseria; Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 14 December 2006; 125 (22): 224106.
[3] Lin P, Ren X, He L. Efficient hybrid density functional calculations for large periodic systems using numerical atomic orbitals. Journal of Chemical Theory and Computation, 2021, 17(1): 222–239.
[4] Lin P, Ren X, He L. Accuracy of localized resolution of the identity in periodic hybrid functional calculations with numerical atomic orbitals[J]. The Journal of Physical Chemistry Letters, 2020, 11(8): 3082-3088.
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