{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "8441ebf6", "metadata": { "execution": { "iopub.execute_input": "2025-12-15T08:10:16.542527Z", "iopub.status.busy": "2025-12-15T08:10:16.542446Z", "iopub.status.idle": "2025-12-15T08:10:16.546248Z", "shell.execute_reply": "2025-12-15T08:10:16.545794Z" } }, "outputs": [], "source": [ "# Colab 环境检测与依赖安装\n", "try:\n", " import google.colab # type: ignore\n", " IN_COLAB = True\n", "except ImportError:\n", " IN_COLAB = False\n", "\n", "if IN_COLAB:\n", " !pip install -q git+https://github.com/bud-primordium/AtomSCF.git@main\n", " !pip install -q git+https://github.com/bud-primordium/AtomPPGen.git@main\n" ] }, { "cell_type": "markdown", "id": "7ea733f8", "metadata": {}, "source": [ "# AtomPPGen 教程 03:半局域势反演\n", "\n", "本教程聚焦如何从 TM 伪轨道恢复半局域势 $V_l(r)$,以及如何通过诊断信息评估势的平滑性与节点行为。\n", "\n", "## 教程目标\n", "- 理解径向 Schrödinger 方程与半局域势的关系,掌握 $V_l = \\varepsilon + \\tfrac{1}{2}\\tfrac{u''}{u} - \\tfrac{l(l+1)}{2r^2}$ 的推导过程\n", "- 比较内区(解析导数)与外区(样条导数)两种数值策略\n", "- 学会检测节点、构建诊断表、绘制 $V_s/V_p/V_d$ 与核势 $-Z/r$ 的对比图\n", "\n", "## 阅读建议\n", "建议先完成 00-overview 和 02-tm-pseudization 教程,确保理解 TM 伪化的基本流程。\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "a77ee147", "metadata": { "execution": { "iopub.execute_input": "2025-12-15T08:10:16.547848Z", "iopub.status.busy": "2025-12-15T08:10:16.547765Z", "iopub.status.idle": "2025-12-15T08:10:17.182863Z", "shell.execute_reply": "2025-12-15T08:10:17.182433Z" } }, "outputs": [], "source": [ "# 常用依赖与作图设置\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import platform\n", "\n", "from atomppgen import (\n", " solve_ae_atom,\n", " tm_pseudize,\n", " invert_semilocal_potential,\n", ")\n", "\n", "# 中文字体配置(兼容多平台)\n", "if platform.system() == 'Darwin': # macOS\n", " plt.rcParams['font.sans-serif'] = ['Arial Unicode MS', 'Heiti TC', 'STHeiti']\n", "elif platform.system() == 'Windows':\n", " plt.rcParams['font.sans-serif'] = ['Microsoft YaHei', 'SimHei']\n", "else: # Linux / Colab\n", " plt.rcParams['font.sans-serif'] = ['DejaVu Sans', 'WenQuanYi Micro Hei']\n", "plt.rcParams['axes.unicode_minus'] = False\n", "plt.rcParams['figure.dpi'] = 100\n", "np.set_printoptions(precision=6, suppress=True)\n" ] }, { "cell_type": "markdown", "id": "58432dd9", "metadata": {}, "source": [ "## 反演公式推导\n", "\n", "径向 Schrödinger 方程写成 TM 使用的 $u_l(r)$ 形式:\n", "$$\n", "-\\frac{1}{2}\\frac{d^2 u_l}{dr^2} + \\left[\\frac{l(l+1)}{2r^2} + V_l(r)\\right] u_l(r) = \\varepsilon_l\\, u_l(r)\n", "$$\n", "\n", "把含势项移到等式右侧可以直接得到半局域势表达式:\n", "$$\n", "V_l(r) = \\varepsilon_l + \\frac{1}{2}\\frac{u_l''(r)}{u_l(r)} - \\frac{l(l+1)}{2r^2}\n", "$$\n", "\n", "内区($r \\le r_c$)的 TM 伪轨道可写成 $u_l(r) = r^{l+1} \\exp p(r)$,其中 $p(r)=\\sum_i a_{2i} r^{2i}$。代入有\n", "$$\n", "\\frac{u_l''}{u_l} = \\frac{l(l+1)}{r^2} + 2\\frac{(l+1)p'(r)}{r} + p'(r)^2 + p''(r)\n", "$$\n", "因此\n", "$$\n", "V_l(r) = \\varepsilon_l + (l+1)\\frac{p'(r)}{r} + \\tfrac{1}{2}\\left[p'(r)^2 + p''(r)\\right], \\quad (r \\le r_c)\n", "$$\n", "这条公式避开了 $u$ 与 $u''$ 的直接相除,在 TM 内区实现中可以利用多项式的解析导数计算。外区仍采用一般形式,只要能稳定评估 $u$ 与二阶导数即可。\n" ] }, { "cell_type": "markdown", "id": "855706de", "metadata": {}, "source": [ "## 内区(解析导数)与外区(样条)策略\n", "\n", "| 区域 | 输入数据 | 数值策略 | 推荐场景 |\n", "|------|----------|----------|----------|\n", "| 内区 $r \\le r_c$ | TM 系数 $a_{2i}$、角动量 $l$、能量 $\\varepsilon$ | 利用 $p'(r), p''(r)$ 的解析表达直接带入公式 | 精确匹配 TM 多项式、避免 $u \\to 0$ 导致除零 |\n", "| 外区 $r > r_c$ | 全电子网格与拼接后的伪轨道 $u_{ps}(r)$ | 构建局域三次样条求 $u,u',u''$ | AE 区域本征方程成立,与核势保持一致 |\n", "\n", "注意事项:\n", "- 若外区跳变较大,可设置 `smooth_rc=True` 与 `smooth_width` 来平滑内外区接缝\n", "- `V_max_clip` 限制 $u \\to 0$ 时 $u''/u$ 的发散\n" ] }, { "cell_type": "markdown", "id": "f6b69201", "metadata": {}, "source": [ "## 节点区域与数值保护\n", "\n", "- **节点检测**:`node_tol` 默认 $10^{-10}$,当 $|u(r)| < \\text{node\\_tol}$ 视作节点。`invert_semilocal_potential` 会把这些点的势暂存为占位值,待样条完成后再通过线性插值回填。\n", "- **除零控制**:在节点附近 $u''/u$ 容易爆炸,因此需要先裁剪极端值(`V_max_clip`)。\n", "- **诊断指标**:`diagnostics['n_nodes']` 会统计符号变化次数,可与全电子轨道节点数对比。\n" ] }, { "cell_type": "markdown", "id": "2a1d252f", "metadata": {}, "source": [ "## 实战:Al (Z=13) 的 s/p/d 三通道反演\n", "\n", "沿用前面教程的 Al 原子示例,对三个角动量通道进行势反演。\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "02cbabe7", "metadata": { "execution": { "iopub.execute_input": "2025-12-15T08:10:17.184291Z", "iopub.status.busy": "2025-12-15T08:10:17.184189Z", "iopub.status.idle": "2025-12-15T08:10:37.901224Z", "shell.execute_reply": "2025-12-15T08:10:37.900374Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "AE 求解完成:网格点数 = 1200, SCF 收敛 = True\n", "l=0 (s) rc=2.10 Bohr | norm_err=1.59e-16 | V(rc)=-0.6049 Ha | n_nodes=0\n", "l=1 (p) rc=2.20 Bohr | norm_err=4.65e-15 | V(rc)=-0.5551 Ha | n_nodes=1\n", "l=2 (d) rc=2.40 Bohr | norm_err=2.10e-13 | V(rc)=-0.4696 Ha | n_nodes=2\n" ] } ], "source": [ "# 求解 AE 原子、构造 TM 伪轨道并反演 V_l(r)\n", "Z = 13 # Al\n", "rc_map = {0: 2.1, 1: 2.2, 2: 2.4} # s/p/d 截断半径\n", "channel_labels = {0: 's', 1: 'p', 2: 'd'}\n", "colors = {0: '#1f77b4', 1: '#ff7f0e', 2: '#2ca02c'}\n", "\n", "# 1) 全电子参考解\n", "ae = solve_ae_atom(\n", " Z=Z,\n", " lmax=2,\n", " spin_mode=\"LDA\",\n", " grid_type=\"exp_transformed\",\n", " grid_params={\"n\": 1200, \"total_span\": 6.5},\n", ")\n", "print(f\"AE 求解完成:网格点数 = {ae.r.size}, SCF 收敛 = {ae.converged}\")\n", "\n", "# 2) TM 伪化 + 势反演\n", "tm_results = {}\n", "inv_results = {}\n", "\n", "for l, rc in rc_map.items():\n", " # 选取该通道能量最高的参考态(列表末尾;p/d 通道通常为近零散射态)\n", " u_ae = ae.u_by_l[l][-1]\n", " eps = ae.eps_by_l[l][-1]\n", " \n", " tm_res = tm_pseudize(\n", " r=ae.r,\n", " w=ae.w,\n", " u_ae=u_ae,\n", " eps=eps,\n", " l=l,\n", " rc=rc,\n", " continuity_orders=2,\n", " )\n", " tm_results[l] = tm_res\n", "\n", " inv_res = invert_semilocal_potential(\n", " tm_result=tm_res,\n", " r=ae.r,\n", " node_tol=1e-10,\n", " V_max_clip=1000.0,\n", " )\n", " inv_results[l] = inv_res\n", "\n", " diag = inv_res.diagnostics\n", " print(\n", " f\"l={l} ({channel_labels[l]}) rc={rc:.2f} Bohr | \"\n", " f\"norm_err={tm_res.norm_error:.2e} | V(rc)={diag['V_at_rc']:.4f} Ha | n_nodes={diag['n_nodes']}\"\n", " )\n" ] }, { "cell_type": "markdown", "id": "e49b3a61", "metadata": {}, "source": [ "## `invert_semilocal_potential` 参数说明\n", "\n", "- `tm_result` / `r`:必须复用与 TM 相同的网格\n", "- `node_tol`:越小越敏感,建议从 $10^{-10}$ 起调\n", "- `V_max_clip`:裁剪 $u''/u$ 畸大值\n", "- `smooth_rc` / `smooth_width`:可选的内外区平滑\n", "- `diagnostics`:返回方法名、极值、rc 处势值、节点数等\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "63ceef6a", "metadata": { "execution": { "iopub.execute_input": "2025-12-15T08:10:37.907623Z", "iopub.status.busy": "2025-12-15T08:10:37.907322Z", "iopub.status.idle": "2025-12-15T08:10:37.914246Z", "shell.execute_reply": "2025-12-15T08:10:37.913172Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "l ch rc (Bohr) n_nodes V_min (Ha) V_max (Ha) V(rc) (Ha) \n", "---------------------------------------------------------------------------\n", "0 s 2.10 0 -0.874 1.040 -0.605 \n", "1 p 2.20 1 -0.754 -0.000 -0.555 \n", "2 d 2.40 2 -3.469 0.000 -0.470 \n" ] } ], "source": [ "# 汇总诊断信息\n", "print(f\"{'l':<3}{'ch':<5}{'rc (Bohr)':<12}{'n_nodes':<10}{'V_min (Ha)':<14}{'V_max (Ha)':<14}{'V(rc) (Ha)':<14}\")\n", "print('-' * 75)\n", "for l in sorted(rc_map.keys()):\n", " diag = inv_results[l].diagnostics\n", " print(\n", " f\"{l:<3}{channel_labels[l]:<5}{rc_map[l]:<12.2f}{diag['n_nodes']:<10d}\"\n", " f\"{diag['V_min']:<14.3f}{diag['V_max']:<14.3f}{diag['V_at_rc']:<14.3f}\"\n", " )\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "0405d8bf", "metadata": { "execution": { "iopub.execute_input": "2025-12-15T08:10:37.915990Z", "iopub.status.busy": "2025-12-15T08:10:37.915861Z", "iopub.status.idle": "2025-12-15T08:10:38.071422Z", "shell.execute_reply": "2025-12-15T08:10:38.070837Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 可视化 V_s / V_p / V_d 以及核势 -Z/r\n", "r_mask = ae.r <= 8.0\n", "r_vis = ae.r[r_mask]\n", "r_safe = np.where(r_vis < 1e-3, 1e-3, r_vis)\n", "V_nuc = -Z / r_safe\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4.5))\n", "\n", "# Left: semilocal potentials vs nuclear\n", "for l in sorted(rc_map.keys()):\n", " axes[0].plot(r_vis, inv_results[l].V_l[r_mask], \n", " label=f\"V_{channel_labels[l]}(r)\", color=colors[l])\n", " axes[0].axvline(rc_map[l], color=colors[l], linestyle='--', alpha=0.3)\n", "axes[0].plot(r_vis, V_nuc, label='-Z/r', color='black', linestyle='--')\n", "axes[0].set_xlabel('r (Bohr)')\n", "axes[0].set_ylabel('V(r) (Ha)')\n", "axes[0].set_title('Semilocal potentials vs nuclear potential')\n", "axes[0].set_xlim(0, 8)\n", "axes[0].set_ylim(-80, 20)\n", "axes[0].legend(loc='best')\n", "axes[0].grid(alpha=0.3)\n", "\n", "# Right: difference from nuclear potential\n", "for l in sorted(rc_map.keys()):\n", " axes[1].plot(r_vis, inv_results[l].V_l[r_mask] - V_nuc, \n", " label=f\"V_{channel_labels[l]} - (-Z/r)\", color=colors[l])\n", "axes[1].set_xlabel('r (Bohr)')\n", "axes[1].set_ylabel('Potential difference (Ha)')\n", "axes[1].set_title('Difference from nuclear potential')\n", "axes[1].set_xlim(0, 8)\n", "axes[1].axhline(0.0, color='black', linewidth=0.8, linestyle=':')\n", "axes[1].legend(loc='best')\n", "axes[1].grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "29e7c394", "metadata": {}, "source": [ "## 小结与下一步\n", "\n", "- 通过径向方程反演得到的 $V_l(r)$ 取决于 TM 内区解析导数与外区样条精度\n", "- `diagnostics` 中的节点数、极值、rc 处势值可以快速暴露问题\n", "- 与核势 $-Z/r$ 对比能直观判断局域道候选:通常选择最\"排斥\"的通道(如 d 道)作为 `V_loc`\n", "\n", "**下一步**:进入 04-kb-transform 教程,将半局域势转换为 KB 可分离形式。\n" ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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 }, "nbformat": 4, "nbformat_minor": 5 }