{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cell-0",
   "metadata": {},
   "source": [
    "# 端到端完整计算示例\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/bud-primordium/AtomSCF/blob/main/docs/source/tutorials/07-complete-example.ipynb)\n",
    "\n",
    "## 学习目标\n",
    "\n",
    "- 完整演示从零开始的原子计算流程\n",
    "- 对比 HF 与 DFT-LDA 方法的结果\n",
    "- 与 NIST 参考数据进行验证\n",
    "\n",
    "## 计算目标\n",
    "\n",
    "对 **Al 原子**（Z=13）进行完整的电子结构计算：\n",
    "- 电子组态：1s² 2s² 2p⁶ 3s² 3p¹（13 个电子）\n",
    "- 方法：LSDA-PZ81、LSDA-VWN、UHF"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02a886d5",
   "metadata": {},
   "source": [
    "## 理论基础：完整计算流程\n",
    "\n",
    "端到端原子自洽场计算整合了所有模块：\n",
    "\n",
    "### 完整算法\n",
    "\n",
    "```\n",
    "输入：原子序数 Z\n",
    "  ↓\n",
    "1. 网格生成：radial_grid_linear(n, rmin, rmax)\n",
    "  ↓\n",
    "2. 配置初始化：SCFConfig(Z, r, w, spin_mode)\n",
    "  ↓\n",
    "3. SCF 迭代：\n",
    "   │  a. 构造有效势：V_eff = V_ext + V_H + V_xc\n",
    "   │  b. 求解 KS 方程：(-∇²/2 + V_eff)ψᵢ = εᵢψᵢ\n",
    "   │  c. 更新密度：n = Σfᵢ|ψᵢ|²\n",
    "   │  d. 混合与收敛检查\n",
    "   └→ 循环直到收敛\n",
    "  ↓\n",
    "4. 提取结果：\n",
    "   - 总能量：E_total\n",
    "   - 轨道能量：eps_by_l_sigma\n",
    "   - 电子密度：n_up, n_dn\n",
    "  ↓\n",
    "输出：SCFResult 对象\n",
    "```\n",
    "\n",
    "### 关键公式\n",
    "\n",
    "总能量分解：\n",
    "\n",
    "$$E_{\\text{total}} = T + E_{\\text{ext}} + E_H + E_{xc}$$\n",
    "\n",
    "其中：\n",
    "- $T = \\sum_i f_i \\langle\\psi_i|-\\nabla^2/2|\\psi_i\\rangle$\n",
    "- $E_{\\text{ext}} = \\int V_{\\text{ext}}(r)n(r)d^3r$\n",
    "- $E_H = \\frac{1}{2}\\int\\int\\frac{n(r)n(r')}{|r-r'|}d^3rd^3r'$\n",
    "- $E_{xc} = \\int\\varepsilon_{xc}(n(r))n(r)d^3r$\n",
    "\n",
    "**验证方法**：与 NIST 原子数据库对比相对误差\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cell-1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:01.193404Z",
     "iopub.status.busy": "2025-12-04T04:17:01.193258Z",
     "iopub.status.idle": "2025-12-04T04:17:01.198068Z",
     "shell.execute_reply": "2025-12-04T04:17:01.197983Z"
    }
   },
   "outputs": [],
   "source": [
    "# 环境配置\n",
    "import sys\n",
    "\n",
    "if \"google.colab\" in sys.modules:\n",
    "    !pip install -q git+https://github.com/bud-primordium/AtomSCF.git"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "74abbc8b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:01.203128Z",
     "iopub.status.busy": "2025-12-04T04:17:01.203040Z",
     "iopub.status.idle": "2025-12-04T04:17:19.272155Z",
     "shell.execute_reply": "2025-12-04T04:17:19.271988Z"
    }
   },
   "outputs": [],
   "source": [
    "# 配置中文字体（避免乱码）\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "\n",
    "# 跨平台中文字体配置\n",
    "matplotlib.rcParams['font.sans-serif'] = [\n",
    "    'Arial Unicode MS',      # macOS\n",
    "    'WenQuanYi Micro Hei',  # Linux\n",
    "    'SimHei',                # Windows\n",
    "    'DejaVu Sans'            # Fallback\n",
    "]\n",
    "matplotlib.rcParams['axes.unicode_minus'] = False\n",
    "\n",
    "# 清除字体缓存（重要！）\n",
    "try:\n",
    "    import matplotlib.font_manager as fm\n",
    "    fm._load_fontmanager(try_read_cache=False)\n",
    "except Exception:\n",
    "    pass\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cell-2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:19.277822Z",
     "iopub.status.busy": "2025-12-04T04:17:19.277723Z",
     "iopub.status.idle": "2025-12-04T04:17:19.457564Z",
     "shell.execute_reply": "2025-12-04T04:17:19.457408Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from atomscf.grid import radial_grid_linear\n",
    "from atomscf.scf import SCFConfig, run_lsda_pz81, run_lsda_vwn\n",
    "\n",
    "plt.style.use('seaborn-v0_8-darkgrid')\n",
    "plt.rcParams['figure.figsize'] = (12, 5)\n",
    "\n",
    "\n",
    "def safe_energy(result, key):\n",
    "    return result.energies.get(key, 0.0) if result.energies else 0.0\n",
    "\n",
    "\n",
    "def get_eps(result, l, spin='up', idx=0):\n",
    "    eps_list = result.eps_by_l_sigma.get((l, spin), [])\n",
    "    return eps_list[idx] if idx < len(eps_list) else 0.0\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-3",
   "metadata": {},
   "source": [
    "## Step 1: 网格生成\n",
    "\n",
    "选择合适的径向网格参数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cell-4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:19.463187Z",
     "iopub.status.busy": "2025-12-04T04:17:19.463070Z",
     "iopub.status.idle": "2025-12-04T04:17:19.469336Z",
     "shell.execute_reply": "2025-12-04T04:17:19.469251Z"
    }
   },
   "outputs": [],
   "source": [
    "# 网格参数\n",
    "N_POINTS = 1000     # 网格点数（平衡精度与速度）\n",
    "R_MIN = 1e-5        # 最小半径（避免奇点）\n",
    "R_MAX = 30.0        # 最大半径（确保波函数衰减）\n",
    "\n",
    "r, w = radial_grid_linear(n=N_POINTS, rmin=R_MIN, rmax=R_MAX)\n",
    "\n",
    "print(f\"网格参数:\")\n",
    "print(f\"  点数: {len(r)}\")\n",
    "print(f\"  范围: [{r[0]:.2e}, {r[-1]:.1f}] Bohr\")\n",
    "print(f\"  步长: {(r[1]-r[0]):.4f} Bohr\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-5",
   "metadata": {},
   "source": [
    "## Step 2: 原子配置\n",
    "\n",
    "设置 Al 原子的电子占据数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cell-6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:19.474101Z",
     "iopub.status.busy": "2025-12-04T04:17:19.474014Z",
     "iopub.status.idle": "2025-12-04T04:17:19.479993Z",
     "shell.execute_reply": "2025-12-04T04:17:19.479771Z"
    }
   },
   "outputs": [],
   "source": [
    "# Al 原子配置\n",
    "Z = 13  # 核电荷数\n",
    "\n",
    "# 占据数配置: {l: [(n, 占据数), ...]}\n",
    "occ_al = {\n",
    "    0: [(1, 2.0), (2, 2.0), (3, 2.0)],  # s 轨道: 1s² 2s² 3s²\n",
    "    1: [(2, 6.0), (3, 1.0)],            # p 轨道: 2p⁶ 3p¹\n",
    "}\n",
    "\n",
    "# 验证总电子数\n",
    "total_electrons = sum(occ for l_occ in occ_al.values() for _, occ in l_occ)\n",
    "print(f\"原子: Al (Z={Z})\")\n",
    "print(f\"电子组态: 1s² 2s² 2p⁶ 3s² 3p¹\")\n",
    "print(f\"总电子数: {total_electrons:.0f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-7",
   "metadata": {},
   "source": [
    "## Step 3: LSDA-PZ81 计算\n",
    "\n",
    "使用 Perdew-Zunger 1981 交换关联泛函："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cell-8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:19.485262Z",
     "iopub.status.busy": "2025-12-04T04:17:19.485166Z",
     "iopub.status.idle": "2025-12-04T04:17:30.138264Z",
     "shell.execute_reply": "2025-12-04T04:17:30.138086Z"
    }
   },
   "outputs": [],
   "source": [
    "# 配置 SCF 参数\n",
    "cfg_pz81 = SCFConfig(\n",
    "    Z=Z,\n",
    "    r=r,\n",
    "    w=w,\n",
    "    maxiter=50,\n",
    "    tol=1e-6,\n",
    ")\n",
    "result_pz81 = run_lsda_pz81(cfg_pz81)\n",
    "print(f\"迭代次数: {result_pz81.iterations}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-9",
   "metadata": {},
   "source": [
    "## Step 4: LSDA-VWN 计算\n",
    "\n",
    "使用 Vosko-Wilk-Nusair 关联泛函进行对比："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cell-10",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:30.145762Z",
     "iopub.status.busy": "2025-12-04T04:17:30.145640Z",
     "iopub.status.idle": "2025-12-04T04:17:42.883702Z",
     "shell.execute_reply": "2025-12-04T04:17:42.883565Z"
    }
   },
   "outputs": [],
   "source": [
    "# VWN 配置（复用网格和占据数）\n",
    "cfg_vwn = SCFConfig(\n",
    "    Z=Z,\n",
    "    r=r,\n",
    "    w=w,\n",
    "    maxiter=50,\n",
    "    tol=1e-6,\n",
    ")\n",
    "result_vwn = run_lsda_vwn(cfg_vwn)\n",
    "print(f\"迭代次数: {result_vwn.iterations}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-11",
   "metadata": {},
   "source": [
    "## Step 5: 结果汇总与对比"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cell-12",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:42.890789Z",
     "iopub.status.busy": "2025-12-04T04:17:42.890645Z",
     "iopub.status.idle": "2025-12-04T04:17:42.899264Z",
     "shell.execute_reply": "2025-12-04T04:17:42.899178Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "# NIST 参考值（LSDA）\n",
    "NIST_AL = {\n",
    "    'E_total': -241.321,  # Hartree\n",
    "    'eps_1s': -55.154,\n",
    "    'eps_2s': -3.933,\n",
    "    'eps_2p': -2.532,\n",
    "    'eps_3s': -0.287,\n",
    "    'eps_3p': -0.104,\n",
    "}\n",
    "\n",
    "print('='*60)\n",
    "print('Al 原子计算结果汇总')\n",
    "print('='*60)\n",
    "\n",
    "E_total_pz81 = safe_energy(result_pz81, 'E_total')\n",
    "E_total_vwn = safe_energy(result_vwn, 'E_total')\n",
    "\n",
    "print(f\"\\n{'方法':<15} {'总能量 (Ha)':<15} {'与 NIST 差 (%)':<15}\")\n",
    "print('-'*45)\n",
    "print(f\"{'LSDA-PZ81':<15} {E_total_pz81:<15.6f} {abs(E_total_pz81 - NIST_AL['E_total'])/abs(NIST_AL['E_total'])*100:<15.2f}\")\n",
    "print(f\"{'LSDA-VWN':<15} {E_total_vwn:<15.6f} {abs(E_total_vwn - NIST_AL['E_total'])/abs(NIST_AL['E_total'])*100:<15.2f}\")\n",
    "print(f\"{'NIST (参考)':<15} {NIST_AL['E_total']:<15.3f}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cell-13",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:42.905297Z",
     "iopub.status.busy": "2025-12-04T04:17:42.905184Z",
     "iopub.status.idle": "2025-12-04T04:17:42.912433Z",
     "shell.execute_reply": "2025-12-04T04:17:42.912347Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "# 轨道能量对比\n",
    "print('\\n轨道能量 (Hartree):')\n",
    "print(f\"{'轨道':<8} {'PZ81':<12} {'VWN':<12} {'NIST':<12} {'PZ81误差%':<12}\")\n",
    "print('-'*56)\n",
    "\n",
    "orbital_map = [\n",
    "    ('1s', 0, 0, 'eps_1s'),\n",
    "    ('2s', 0, 1, 'eps_2s'),\n",
    "    ('2p', 1, 0, 'eps_2p'),\n",
    "    ('3s', 0, 2, 'eps_3s'),\n",
    "    ('3p', 1, 1, 'eps_3p'),\n",
    "]\n",
    "\n",
    "for label, l, idx, nist_key in orbital_map:\n",
    "    eps_pz81 = get_eps(result_pz81, l=l, spin='up', idx=idx)\n",
    "    eps_vwn = get_eps(result_vwn, l=l, spin='up', idx=idx)\n",
    "    eps_nist = NIST_AL[nist_key]\n",
    "    err_pz81 = abs(eps_pz81 - eps_nist) / abs(eps_nist) * 100 if eps_nist else 0.0\n",
    "    print(f\"{label:<8} {eps_pz81:<12.6f} {eps_vwn:<12.6f} {eps_nist:<12.3f} {err_pz81:<12.1f}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-14",
   "metadata": {},
   "source": [
    "## Step 6: 波函数可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cell-15",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:42.918243Z",
     "iopub.status.busy": "2025-12-04T04:17:42.918120Z",
     "iopub.status.idle": "2025-12-04T04:17:43.463512Z",
     "shell.execute_reply": "2025-12-04T04:17:43.463405Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(16, 5))\n",
    "\n",
    "# s 轨道\n",
    "ax = axes[0]\n",
    "u_s = result_pz81.u_by_l_sigma.get((0, \"up\"), [])\n",
    "colors = ['#1f77b4', '#ff7f0e', '#2ca02c']\n",
    "for i, (n, _) in enumerate(occ_al[0]):\n",
    "    if i < len(u_s):\n",
    "        ax.plot(r, u_s[i], color=colors[i], linewidth=2, label=f'{n}s')\n",
    "ax.set_xlabel('r (Bohr)', fontsize=12)\n",
    "ax.set_ylabel('u(r)', fontsize=12)\n",
    "ax.set_title('s 轨道波函数', fontsize=14)\n",
    "ax.set_xlim(0, 8)\n",
    "ax.legend(fontsize=11)\n",
    "ax.grid(alpha=0.3)\n",
    "\n",
    "# p 轨道\n",
    "ax = axes[1]\n",
    "u_p = result_pz81.u_by_l_sigma.get((1, \"up\"), [])\n",
    "colors_p = ['#d62728', '#9467bd']\n",
    "for i, (n, _) in enumerate(occ_al[1]):\n",
    "    if i < len(u_p):\n",
    "        ax.plot(r, u_p[i], color=colors_p[i], linewidth=2, label=f'{n}p')\n",
    "ax.set_xlabel('r (Bohr)', fontsize=12)\n",
    "ax.set_ylabel('u(r)', fontsize=12)\n",
    "ax.set_title('p 轨道波函数', fontsize=14)\n",
    "ax.set_xlim(0, 12)\n",
    "ax.legend(fontsize=11)\n",
    "ax.grid(alpha=0.3)\n",
    "\n",
    "# 电子密度\n",
    "ax = axes[2]\n",
    "n_total = result_pz81.n_up + result_pz81.n_dn\n",
    "ax.semilogy(r, n_total + 1e-15, 'k-', linewidth=2)\n",
    "ax.set_xlabel('r (Bohr)', fontsize=12)\n",
    "ax.set_ylabel('n(r) (1/Bohr³)', fontsize=12)\n",
    "ax.set_title('总电子密度（对数刻度）', fontsize=14)\n",
    "ax.set_xlim(0, 10)\n",
    "ax.grid(alpha=0.3, which='both')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-16",
   "metadata": {},
   "source": [
    "## Step 7: 能量分解分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cell-17",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:43.470646Z",
     "iopub.status.busy": "2025-12-04T04:17:43.470445Z",
     "iopub.status.idle": "2025-12-04T04:17:43.479425Z",
     "shell.execute_reply": "2025-12-04T04:17:43.479252Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "# 能量分解\n",
    "print('能量分解 (Hartree):')\n",
    "print(f\"{'分量':<20} {'PZ81':<15} {'VWN':<15}\")\n",
    "print('-'*50)\n",
    "E_kin_pz81 = safe_energy(result_pz81, 'E_kin')\n",
    "E_kin_vwn = safe_energy(result_vwn, 'E_kin')\n",
    "E_ext_pz81 = safe_energy(result_pz81, 'E_ext')\n",
    "E_ext_vwn = safe_energy(result_vwn, 'E_ext')\n",
    "E_H_pz81 = safe_energy(result_pz81, 'E_H')\n",
    "E_H_vwn = safe_energy(result_vwn, 'E_H')\n",
    "E_xc_pz81 = safe_energy(result_pz81, 'E_xc')\n",
    "E_xc_vwn = safe_energy(result_vwn, 'E_xc')\n",
    "E_total_pz81 = safe_energy(result_pz81, 'E_total')\n",
    "E_total_vwn = safe_energy(result_vwn, 'E_total')\n",
    "print(f\"{'动能 (E_kin)':<20} {E_kin_pz81:<15.6f} {E_kin_vwn:<15.6f}\")\n",
    "print(f\"{'外势能 (E_ext)':<20} {E_ext_pz81:<15.6f} {E_ext_vwn:<15.6f}\")\n",
    "print(f\"{'Hartree (E_H)':<20} {E_H_pz81:<15.6f} {E_H_vwn:<15.6f}\")\n",
    "print(f\"{'交换关联 (E_xc)':<20} {E_xc_pz81:<15.6f} {E_xc_vwn:<15.6f}\")\n",
    "print('-'*50)\n",
    "print(f\"{'总能量':<20} {E_total_pz81:<15.6f} {E_total_vwn:<15.6f}\")\n",
    "\n",
    "virial_pz81 = (-E_total_pz81 / E_kin_pz81) if E_kin_pz81 else 0.0\n",
    "virial_vwn = (-E_total_vwn / E_kin_vwn) if E_kin_vwn else 0.0\n",
    "print(f\"\\nVirial 比 (-E/T): PZ81={virial_pz81:.4f}, VWN={virial_vwn:.4f} (理论=2)\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-18",
   "metadata": {},
   "source": [
    "## 额外示例：C 原子和 He 原子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cell-19",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-04T04:17:43.485378Z",
     "iopub.status.busy": "2025-12-04T04:17:43.485248Z",
     "iopub.status.idle": "2025-12-04T04:17:57.247456Z",
     "shell.execute_reply": "2025-12-04T04:17:57.247361Z"
    }
   },
   "outputs": [],
   "source": [
    "# 快速计算 He 和 C\n",
    "atoms = [\n",
    "    ('He', 2, {0: [(1, 2.0)]}),\n",
    "    ('C', 6, {0: [(1, 2.0), (2, 2.0)], 1: [(2, 2.0)]}),\n",
    "]\n",
    "\n",
    "# NIST 参考值\n",
    "nist_ref = {'He': -2.8348, 'C': -37.470}\n",
    "\n",
    "print(\"\\n多原子快速计算:\")\n",
    "print(f\"{'原子':<6} {'Z':<4} {'E_total (Ha)':<15} {'NIST (Ha)':<12} {'误差 (%)':<10}\")\n",
    "print(\"-\"*50)\n",
    "\n",
    "for name, Z_atom, occ in atoms:\n",
    "    cfg = SCFConfig(\n",
    "        Z=Z_atom, r=r, w=w, spin_mode=\"LSDA\", maxiter=50, tol=1e-6,\n",
    "    )\n",
    "    result = run_lsda_pz81(cfg)\n",
    "    nist = nist_ref[name]\n",
    "    err = abs((result.energies.get('E_total', 0.0) if result.energies else 0.0) - nist) / abs(nist) * 100\n",
    "    print(f\"{name:<6} {Z_atom:<4} {(result.energies.get('E_total', 0.0) if result.energies else 0.0):<15.6f} {nist:<12.4f} {err:<10.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cell-20",
   "metadata": {},
   "source": [
    "## 总结\n",
    "\n",
    "### 完成的计算流程\n",
    "\n",
    "1. ✅ **网格生成**：线性网格 1000 点\n",
    "2. ✅ **原子配置**：Al (Z=13) 电子占据\n",
    "3. ✅ **LSDA-PZ81**：自洽计算收敛\n",
    "4. ✅ **LSDA-VWN**：对比计算\n",
    "5. ✅ **结果验证**：与 NIST 参考对比\n",
    "6. ✅ **可视化**：波函数与电子密度\n",
    "\n",
    "### 关键结论\n",
    "\n",
    "- **精度**：总能量误差 ~1-2%（相对 NIST）\n",
    "- **泛函差异**：PZ81 与 VWN 结果接近\n",
    "- **收敛性**：典型 20-30 次迭代\n",
    "\n",
    "### AtomSCF 使用要点\n",
    "\n",
    "```python\n",
    "# 标准计算流程\n",
    "from atomscf.grid import radial_grid_linear\n",
    "from atomscf.scf import SCFConfig, run_lsda_pz81\n",
    "\n",
    "r, w = radial_grid_linear(n=1000, rmin=1e-5, rmax=30.0)\n",
    "cfg = SCFConfig(Z=13, r=r, w=w, occ={...})\n",
    "result = run_lsda_pz81(cfg)\n",
    "```\n",
    "\n",
    "---\n",
    "\n",
    "🎉 **教程完成！** 你已掌握 AtomSCF 的完整使用方法。"
   ]
  }
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