{ "cells": [ { "cell_type": "markdown", "id": "cell-0", "metadata": {}, "source": [ "# 自旋处理:RHF vs UHF\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/06-spin.ipynb)\n", "\n", "## 学习目标\n", "\n", "- 理解限制性(RHF)与非限制性(UHF)Hartree-Fock 的区别\n", "- 掌握 LSDA 自旋极化计算方法\n", "- 分析开壳层体系的自旋密度分布\n", "\n", "## RHF vs UHF 核心区别\n", "\n", "| 方法 | 适用体系 | α/β 轨道 | 自旋极化 |\n", "|------|----------|----------|----------|\n", "| **RHF** | 闭壳层(He, Be, Ne) | 相同 | 无 |\n", "| **UHF** | 开壳层(H, Li, C) | 独立 | 有 |" ] }, { "cell_type": "markdown", "id": "8c7437cc", "metadata": {}, "source": [ "## 理论基础:自旋极化 DFT\n", "\n", "自旋密度泛函理论(SDFT)区分自旋向上和向下通道。\n", "\n", "### LSDA vs LDA\n", "\n", "**LDA(自旋非极化)**:\n", "- 强制 $n_\\uparrow = n_\\downarrow = n/2$\n", "- 对称交换关联势:$v_{xc}^\\uparrow = v_{xc}^\\downarrow$\n", "\n", "**LSDA(自旋极化)**:\n", "- 独立密度:$n_\\uparrow(r) \\neq n_\\downarrow(r)$\n", "- 自旋极化度:$\\zeta = (n_\\uparrow - n_\\downarrow)/n$\n", "- 不对称势:$v_{xc}^\\uparrow \\neq v_{xc}^\\downarrow$\n", "\n", "### 自旋分裂\n", "\n", "交换关联势的自旋依赖性导致轨道能级分裂:\n", "\n", "$$\\Delta \\varepsilon = \\varepsilon_\\uparrow - \\varepsilon_\\downarrow \\approx \\frac{\\partial^2 \\varepsilon_{xc}}{\\partial \\zeta^2}\\Delta\\zeta$$\n", "\n", "**Hund 规则**:最大自旋多重度配置能量最低(如 C: $2p^2 \\rightarrow \\uparrow\\uparrow$ 而非 $\\uparrow\\downarrow$)\n", "\n", "**代码实现**:\n", "- `spin_mode=\"LSDA\"` → 自旋极化计算\n", "- `result.n_up`, `result.n_dn` → 自旋分辨密度\n", "- `eps_by_l_sigma[(l, \"up\")]` → 自旋分辨能量\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "cell-1", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:27.775160Z", "iopub.status.busy": "2025-12-04T04:16:27.775036Z", "iopub.status.idle": "2025-12-04T04:16:27.778904Z", "shell.execute_reply": "2025-12-04T04:16:27.778831Z" } }, "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": "0607fb92", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:27.783827Z", "iopub.status.busy": "2025-12-04T04:16:27.783751Z", "iopub.status.idle": "2025-12-04T04:16:44.632526Z", "shell.execute_reply": "2025-12-04T04:16:44.632412Z" } }, "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": "2025-12-04T04:16:44.637497Z", "iopub.status.busy": "2025-12-04T04:16:44.637357Z", "iopub.status.idle": "2025-12-04T04:16:45.296404Z", "shell.execute_reply": "2025-12-04T04:16:45.296276Z" } }, "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\n", "from atomscf.scf_hf import HFSCFGeneralConfig, HFSCFGeneralResult, run_hf_scf\n", "\n", "plt.style.use('seaborn-v0_8-darkgrid')\n", "plt.rcParams['figure.figsize'] = (12, 5)\n", "\n", "# 便捷函数:安全提取轨道能量\n", "\n", "def get_orbital_energy(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": [ "## 1. 闭壳层体系:He 原子\n", "\n", "氦原子(Z=2)电子组态 1s²,两个电子自旋配对,适合 RHF。" ] }, { "cell_type": "code", "execution_count": 4, "id": "cell-4", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:45.302052Z", "iopub.status.busy": "2025-12-04T04:16:45.301966Z", "iopub.status.idle": "2025-12-04T04:16:46.769493Z", "shell.execute_reply": "2025-12-04T04:16:46.769366Z" } }, "outputs": [], "source": [ "\n", "# 生成网格\n", "r, w = radial_grid_linear(n=600, rmin=1e-5, rmax=20.0)\n", "\n", "# He: LSDA 计算(自旋非极化)\n", "cfg_he = SCFConfig(\n", " Z=2,\n", " r=r,\n", " w=w,\n", " spin_mode='LDA', # 强制自旋配对\n", ")\n", "result_he_lda = run_lsda_pz81(cfg_he)\n", "\n", "E_total_he = result_he_lda.energies.get('E_total', 0.0) if result_he_lda.energies else 0.0\n", "eps_1s_he = get_orbital_energy(result_he_lda, l=0, spin='up', idx=0)\n", "\n", "print('He 原子 LDA(自旋非极化):')\n", "print(f' 总能量: {E_total_he:.6f} Hartree')\n", "print(f' 1s 能级: {eps_1s_he:.6f} Hartree')\n", "\n" ] }, { "cell_type": "markdown", "id": "cell-5", "metadata": {}, "source": [ "## 2. 开壳层体系:H 原子\n", "\n", "氢原子(Z=1)只有 1 个电子,必须使用自旋极化方法。" ] }, { "cell_type": "code", "execution_count": 5, "id": "cell-6", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:46.774920Z", "iopub.status.busy": "2025-12-04T04:16:46.774820Z", "iopub.status.idle": "2025-12-04T04:16:47.461507Z", "shell.execute_reply": "2025-12-04T04:16:47.461405Z" } }, "outputs": [], "source": [ "\n", "# H: LSDA 自旋极化计算\n", "cfg_h_lsda = SCFConfig(\n", " Z=1,\n", " r=r,\n", " w=w,\n", " spin_mode='LSDA', # 自旋极化\n", ")\n", "result_h_lsda = run_lsda_pz81(cfg_h_lsda)\n", "\n", "E_total_h = result_h_lsda.energies.get('E_total', 0.0) if result_h_lsda.energies else 0.0\n", "eps_1s_up = get_orbital_energy(result_h_lsda, l=0, spin='up', idx=0)\n", "\n", "print('H 原子 LSDA(自旋极化):')\n", "print(f' 总能量: {E_total_h:.6f} Hartree')\n", "print(f' 1s↑ 能级: {eps_1s_up:.6f} Hartree')\n", "print(' 理论值: -0.5 Hartree')\n", "print('\\n自旋密度:')\n", "print(f\" n↑ 积分: {np.sum(result_h_lsda.n_up * w * 4 * np.pi * r**2):.4f}\")\n", "print(f\" n↓ 积分: {np.sum(result_h_lsda.n_dn * w * 4 * np.pi * r**2):.4f}\")\n", "\n" ] }, { "cell_type": "markdown", "id": "cell-7", "metadata": {}, "source": [ "## 3. 自旋密度可视化\n", "\n", "对比 H 原子的 α 和 β 自旋密度分布:" ] }, { "cell_type": "code", "execution_count": 6, "id": "cell-8", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:47.467578Z", "iopub.status.busy": "2025-12-04T04:16:47.467476Z", "iopub.status.idle": "2025-12-04T04:16:47.807952Z", "shell.execute_reply": "2025-12-04T04:16:47.807580Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "# 左图:自旋密度\n", "ax1.plot(r, result_h_lsda.n_up, 'b-', linewidth=2, label='n↑ (α 自旋)')\n", "ax1.plot(r, result_h_lsda.n_dn, 'r--', linewidth=2, label='n↓ (β 自旋)')\n", "ax1.fill_between(r, result_h_lsda.n_up, alpha=0.2, color='blue')\n", "ax1.set_xlabel('r (Bohr)', fontsize=12)\n", "ax1.set_ylabel('n(r) (1/Bohr³)', fontsize=12)\n", "ax1.set_title('H 原子自旋密度分布', fontsize=14)\n", "ax1.set_xlim(0, 5)\n", "ax1.legend(fontsize=11)\n", "ax1.grid(alpha=0.3)\n", "\n", "# 右图:自旋极化密度\n", "spin_density = result_h_lsda.n_up - result_h_lsda.n_dn\n", "ax2.plot(r, spin_density, 'g-', linewidth=2)\n", "ax2.fill_between(r, 0, spin_density, alpha=0.3, color='green')\n", "ax2.axhline(y=0, color='k', linestyle='--', alpha=0.5)\n", "ax2.set_xlabel('r (Bohr)', fontsize=12)\n", "ax2.set_ylabel('n↑ - n↓ (1/Bohr³)', fontsize=12)\n", "ax2.set_title('自旋极化密度 (磁化密度)', fontsize=14)\n", "ax2.set_xlim(0, 5)\n", "ax2.grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "# 计算磁矩\n", "mag_moment = np.sum(spin_density * w * 4 * np.pi * r**2)\n", "print(f\"磁矩: {mag_moment:.4f} μ_B\")" ] }, { "cell_type": "markdown", "id": "cell-9", "metadata": {}, "source": [ "## 4. C 原子:开壳层多电子体系\n", "\n", "碳原子(Z=6)电子组态 1s² 2s² 2p²,2p 壳层部分填充。\n", "\n", "根据 **Hund 规则**:2 个 2p 电子自旋平行(↑↑),形成三重态。" ] }, { "cell_type": "code", "execution_count": 7, "id": "cell-10", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:47.819775Z", "iopub.status.busy": "2025-12-04T04:16:47.819643Z", "iopub.status.idle": "2025-12-04T04:16:53.524174Z", "shell.execute_reply": "2025-12-04T04:16:53.524067Z" } }, "outputs": [], "source": [ "\n", "# 网格(C 需要更多点)\n", "r_c, w_c = radial_grid_linear(n=800, rmin=1e-5, rmax=25.0)\n", "\n", "# C: LSDA 自旋极化\n", "# 2p² 按 Hund 规则:2 个电子都是 ↑ 自旋\n", "cfg_c = SCFConfig(\n", " Z=6,\n", " r=r_c,\n", " w=w_c,\n", " spin_mode='LSDA',\n", ")\n", "result_c = run_lsda_pz81(cfg_c)\n", "\n", "E_total_c = result_c.energies.get('E_total', 0.0) if result_c.energies else 0.0\n", "print('C 原子 LSDA:')\n", "print(f' 总能量: {E_total_c:.6f} Hartree')\n", "print('\\n轨道能量 (Hartree):')\n", "for l, label in [(0, 's'), (1, 'p')]:\n", " for spin, spin_mark in [('up', '↑'), ('down', '↓')]:\n", " eps_list = result_c.eps_by_l_sigma.get((l, spin), [])\n", " if not len(eps_list):\n", " continue\n", " for i, eps in enumerate(eps_list):\n", " print(f' {i + l + 1}{label}{spin_mark}: {eps:.6f}')\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "cell-11", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:53.530476Z", "iopub.status.busy": "2025-12-04T04:16:53.530371Z", "iopub.status.idle": "2025-12-04T04:16:53.768554Z", "shell.execute_reply": "2025-12-04T04:16:53.768367Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# C 原子自旋密度可视化\n", "fig, axes = plt.subplots(1, 3, figsize=(16, 4))\n", "\n", "# 总密度\n", "n_total_c = result_c.n_up + result_c.n_dn\n", "axes[0].plot(r_c, n_total_c, 'k-', linewidth=2)\n", "axes[0].fill_between(r_c, 0, n_total_c, alpha=0.2)\n", "axes[0].set_xlabel('r (Bohr)')\n", "axes[0].set_ylabel('n(r)')\n", "axes[0].set_title('C: 总电子密度')\n", "axes[0].set_xlim(0, 3)\n", "\n", "# α/β 密度\n", "axes[1].plot(r_c, result_c.n_up, 'b-', linewidth=2, label='n↑')\n", "axes[1].plot(r_c, result_c.n_dn, 'r--', linewidth=2, label='n↓')\n", "axes[1].set_xlabel('r (Bohr)')\n", "axes[1].set_ylabel('n(r)')\n", "axes[1].set_title('C: α/β 自旋密度')\n", "axes[1].set_xlim(0, 3)\n", "axes[1].legend()\n", "\n", "# 自旋极化\n", "spin_c = result_c.n_up - result_c.n_dn\n", "axes[2].plot(r_c, spin_c, 'g-', linewidth=2)\n", "axes[2].fill_between(r_c, 0, spin_c, alpha=0.3, color='green')\n", "axes[2].axhline(y=0, color='k', linestyle='--', alpha=0.5)\n", "axes[2].set_xlabel('r (Bohr)')\n", "axes[2].set_ylabel('n↑ - n↓')\n", "axes[2].set_title('C: 自旋极化密度')\n", "axes[2].set_xlim(0, 3)\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "# 验证电子数\n", "N_up = np.sum(result_c.n_up * w_c * 4 * np.pi * r_c**2)\n", "N_dn = np.sum(result_c.n_dn * w_c * 4 * np.pi * r_c**2)\n", "print(f\"\\n电子数: N↑={N_up:.2f}, N↓={N_dn:.2f}, 总={N_up+N_dn:.2f}\")\n", "print(f\"磁矩: {N_up - N_dn:.2f} μ_B\")" ] }, { "cell_type": "markdown", "id": "cell-12", "metadata": {}, "source": [ "## 5. LDA vs LSDA 对比\n", "\n", "对于开壳层体系,强制自旋配对(LDA)会导致能量偏高:" ] }, { "cell_type": "code", "execution_count": 9, "id": "cell-13", "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:53.777933Z", "iopub.status.busy": "2025-12-04T04:16:53.777728Z", "iopub.status.idle": "2025-12-04T04:16:57.299010Z", "shell.execute_reply": "2025-12-04T04:16:57.298901Z" } }, "outputs": [], "source": [ "\n", "# Li 原子:LDA vs LSDA\n", "r_li, w_li = radial_grid_linear(n=600, rmin=1e-5, rmax=25.0)\n", "\n", "# LDA(强制自旋配对)\n", "cfg_li_lda = SCFConfig(\n", " Z=3, r=r_li, w=w_li,\n", " spin_mode='LDA',\n", ")\n", "result_li_lda = run_lsda_pz81(cfg_li_lda)\n", "\n", "# LSDA(自旋极化)\n", "cfg_li_lsda = SCFConfig(\n", " Z=3, r=r_li, w=w_li,\n", " spin_mode='LSDA',\n", ")\n", "result_li_lsda = run_lsda_pz81(cfg_li_lsda)\n", "\n", "E_li_lda = result_li_lda.energies.get('E_total', 0.0) if result_li_lda.energies else 0.0\n", "E_li_lsda = result_li_lsda.energies.get('E_total', 0.0) if result_li_lsda.energies else 0.0\n", "delta_mHa = (E_li_lda - E_li_lsda) * 1000\n", "\n", "print('Li 原子能量对比:')\n", "print(f' LDA(自旋配对): {E_li_lda:.6f} Hartree')\n", "print(f' LSDA(自旋极化): {E_li_lsda:.6f} Hartree')\n", "print(f' 能量差: {delta_mHa:.2f} mHartree')\n", "print('\\n结论: LSDA 能量更低,自旋极化稳定开壳层体系')\n", "\n" ] }, { "cell_type": "markdown", "id": "cell-14", "metadata": {}, "source": [ "## 总结\n", "\n", "### 方法选择指南\n", "\n", "| 体系类型 | 电子组态 | 推荐方法 |\n", "|----------|----------|----------|\n", "| 闭壳层 | He(1s²), Be(2s²), Ne | RHF / LDA |\n", "| 开壳层 | H(1s¹), Li(2s¹), C(2p²) | UHF / LSDA |\n", "\n", "### 关键概念\n", "\n", "- **自旋极化**:α 和 β 电子密度不同,产生磁矩\n", "- **Hund 规则**:同一壳层电子优先自旋平行排列\n", "- **能量稳定化**:自旋极化降低开壳层体系能量\n", "\n", "## 下一步\n", "\n", "→ **[07-complete-example.ipynb](07-complete-example.ipynb)**:端到端完整计算示例" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 5 }