{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "26ef5465",
   "metadata": {},
   "source": [
    "# DFT-D3 in xnn vs the reference `simple-dftd3`: accuracy, speed, and deployment with an MLIP\n",
    "\n",
    "A benchmark of xnn's `D3Dispersion` (Grimme *et al.*, *JCP* **132**, 154104, 2010; BJ damping\n",
    "Grimme, Ehrlich & Goerigk, *JCC* **32**, 1456, 2011) against the reference Fortran\n",
    "implementation [`simple-dftd3`](https://github.com/dftd3/simple-dftd3) 1.6.0 (used\n",
    "through its Python package `dftd3` purely as an external reference). PBE0-D3(BJ)-ATM\n",
    "parameters throughout (`s8 = 1.2177, a1 = 0.4145, a2 = 4.8593, s9 = 1`):\n",
    "\n",
    "1. **accuracy** on the S22 complexes and on molecular crystals -- dispersion energies,\n",
    "   interaction-energy contributions, gradients and virials;\n",
    "2. **speed** vs system size on CPU and GPU, with the upstream real-space cutoffs (60 /\n",
    "   40 / 40 bohr) and with the shorter cutoffs an MLIP would use in MD -- the three-body\n",
    "   term is the part to watch: it is enumerated from the neighbor list within\n",
    "   `cutoff_triple`, so its cost grows with $N \\cdot n_{\\rm nb}^2$ rather than $N^3$, but at\n",
    "   40 bohr $n_{\\rm nb}$ is in the thousands for a liquid;\n",
    "3. **deployment** of a D3-corrected MACE through every xnn channel (eager, ASE,\n",
    "   TorchScript whole-system and pair-style ABIs), including forces and stress.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d7a49d51",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-23T20:07:57.845485Z",
     "iopub.status.busy": "2026-09-23T20:07:57.845314Z",
     "iopub.status.idle": "2026-09-23T20:08:00.242811Z",
     "shell.execute_reply": "2026-09-23T20:08:00.241678Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xnn 0.2.1 | simple-dftd3 1.6.0 | torch 2.5.1+cu121 | device for the GPU timings: cuda\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from dftd3.interface import DispersionModel, RationalDampingParam\n",
    "\n",
    "import logging, warnings, time\n",
    "logging.disable(logging.WARNING)\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "from ase import Atoms\n",
    "from ase.build import molecule\n",
    "from ase.data.s22 import create_s22_system, get_number_of_dimer_atoms, get_interaction_energy_cc, s22\n",
    "\n",
    "torch.set_default_dtype(torch.float64)\n",
    "\n",
    "import xnn\n",
    "from xnn.common.config import from_dict\n",
    "from xnn.common.data import structure_to_graph, build_neighbor_list\n",
    "from xnn.common.deploy import TorchScriptPotential, XNNCalculator\n",
    "from xnn.common.models import D3Dispersion, ForceStressOutput, build_model\n",
    "from xnn.common.models.dispersion import BOHR, HARTREE\n",
    "\n",
    "PARAM = dict(s6=1.0, s8=1.2177, a1=0.4145, a2=4.8593, s9=1.0, alp=14.0)     # PBE0-D3(BJ)-ATM\n",
    "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
    "print(\"xnn\", xnn.__version__, \"| simple-dftd3 1.6.0 | torch\", torch.__version__, \"| device for the GPU timings:\", device)\n",
    "\n",
    "def reference(atoms, cutoffs=None, grad=True):\n",
    "    periodic = bool(atoms.pbc.any())\n",
    "    m = DispersionModel(atoms.numbers, atoms.positions / BOHR,\n",
    "                        lattice=atoms.cell[:] / BOHR if periodic else None,\n",
    "                        periodic=np.array(atoms.pbc) if periodic else None)\n",
    "    if cutoffs:\n",
    "        m.set_realspace_cutoff(**cutoffs)\n",
    "    return m.get_dispersion(RationalDampingParam(**PARAM), grad=grad)\n",
    "\n",
    "def xnn_energy(atoms, model=None, device=\"cpu\", stress=False, **options):\n",
    "    options.setdefault(\"s9\", 1.0)\n",
    "    model = (model or D3Dispersion(**options)).to(device)\n",
    "    s = {\"pos\": atoms.positions, \"atomic_numbers\": atoms.numbers}\n",
    "    if atoms.pbc.any():\n",
    "        s[\"cell\"], s[\"pbc\"] = atoms.cell[:], atoms.pbc\n",
    "    graph = structure_to_graph(s, model.cutoff, device=device)\n",
    "    out = ForceStressOutput(model, compute_stress=stress)(graph)\n",
    "    return {k: v.detach().cpu() for k, v in out.items()}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe493ad7",
   "metadata": {},
   "source": [
    "## 1. Accuracy: S22 dispersion energies and interaction contributions\n",
    "\n",
    "For each S22 complex the dispersion energy of the dimer and of both monomers is computed\n",
    "with both codes, along with the dispersion **contribution to the interaction energy**\n",
    "$E_{\\rm disp}(AB) - E_{\\rm disp}(A) - E_{\\rm disp}(B)$, which is the quantity that enters a\n",
    "DFT-D3 binding energy. Gradients are compared for the dimers.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bea4a453",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-23T20:08:00.245432Z",
     "iopub.status.busy": "2026-09-23T20:08:00.245337Z",
     "iopub.status.idle": "2026-09-23T20:08:01.784390Z",
     "shell.execute_reply": "2026-09-23T20:08:01.783438Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S22 complex                        N   E_disp(AB)     |dE|  |dgrad|  dEint d3  dEint xnn  CCSD(T)\n",
      "Ammonia_dimer                      8  -0.00200998  8.7e-19  6.1e-20    -0.523     -0.523    -3.17\n",
      "Water_dimer                        6  -0.00112367  1.1e-19  5.4e-20    -0.358     -0.358    -5.02\n",
      "Formic_acid_dimer                 10  -0.00514519  1.7e-18  1.1e-19    -1.379     -1.379   -18.80\n",
      "Formamide_dimer                   12  -0.00656213  4.3e-19  1.5e-19    -1.508     -1.508   -16.12\n",
      "Uracil_dimer_h-bonded             24  -0.02310849  1.0e-17  8.7e-19    -2.188     -2.188   -20.69\n",
      "2-pyridoxine_2-aminopyridine_complex  25  -0.02414502  3.5e-18  1.1e-18    -2.597     -2.597   -17.00\n",
      "Adenine-thymine_Watson-Crick_complex  30  -0.03114211  3.5e-18  3.4e-18    -2.816     -2.816   -16.74\n",
      "Methane_dimer                     10  -0.00275785  4.3e-19  8.1e-20    -0.574     -0.574    -0.53\n",
      "Ethene_dimer                      12  -0.00577244  1.7e-18  2.4e-19    -1.236     -1.236    -1.50\n",
      "Benzene-methane_complex           17  -0.01253285  1.7e-18  4.6e-19    -1.412     -1.412    -1.45\n",
      "Benzene_dimer_parallel_displaced  24  -0.02564345  1.4e-17  2.7e-19    -4.343     -4.343    -2.62\n",
      "Pyrazine_dimer                    20  -0.02196277  1.7e-18  3.2e-18    -4.298     -4.298    -4.20\n",
      "Uracil_dimer_stack                24  -0.02879565  3.5e-18  6.0e-19    -5.752     -5.752    -9.74\n",
      "Indole-benzene_complex_stack      28  -0.03407941  6.9e-18  3.7e-18    -6.050     -6.050    -4.59\n",
      "Adenine-thymine_complex_stack     30  -0.03943915  1.7e-18  5.4e-18    -8.014     -8.014   -11.66\n",
      "Ethene-ethyne_complex             10  -0.00403760  1.7e-18  2.2e-19    -0.664     -0.664    -1.51\n",
      "Benzene-water_complex             15  -0.01172569  3.5e-18  7.5e-19    -1.311     -1.311    -3.29\n",
      "Benzene-ammonia_complex           16  -0.01218824  1.1e-19  8.1e-19    -1.405     -1.405    -2.32\n",
      "Benzene-HCN_complex               15  -0.01277941  1.7e-18  6.0e-19    -1.716     -1.716    -4.55\n",
      "Benzene_dimer_T-shaped            24  -0.02265958  1.4e-17  8.4e-19    -2.472     -2.472    -2.71\n",
      "Indole-benzene_T-shape_complex    28  -0.02967281  3.5e-18  4.2e-18    -3.289     -3.289    -5.62\n",
      "Phenol_dimer                      26  -0.02506281  3.5e-18  8.7e-19    -2.625     -2.625    -7.09\n",
      "\n",
      "max |dE| = 1.4e-17 Eh,  max |dgrad| = 5.4e-18 Eh/bohr,  max |d dE_int| = 1.1e-14 kcal/mol\n"
     ]
    }
   ],
   "source": [
    "rows = []\n",
    "for name in s22:\n",
    "    dimer = create_s22_system(name); n_a, n_b = get_number_of_dimer_atoms(name)\n",
    "    parts = [dimer, dimer[:n_a], dimer[n_a:n_a + n_b]]\n",
    "    ref = [reference(a) for a in parts]\n",
    "    mine = [xnn_energy(a) for a in parts]\n",
    "    e_ref = [float(r[\"energy\"]) for r in ref]; e_xnn = [float(m[\"energy\"]) / HARTREE for m in mine]\n",
    "    grad_xnn = -mine[0][\"forces\"].numpy() / HARTREE * BOHR\n",
    "    rows.append({\"name\": name, \"N\": len(dimer), \"E_disp(AB) [Eh]\": e_ref[0],\n",
    "                 \"|dE| [Eh]\": max(abs(a - b) for a, b in zip(e_ref, e_xnn)),\n",
    "                 \"|dgrad| [Eh/bohr]\": np.abs(grad_xnn - ref[0][\"gradient\"]).max(),\n",
    "                 \"dE_int(s-dftd3) [kcal/mol]\": (e_ref[0] - e_ref[1] - e_ref[2]) * 627.5095,\n",
    "                 \"dE_int(xnn) [kcal/mol]\": (e_xnn[0] - e_xnn[1] - e_xnn[2]) * 627.5095,\n",
    "                 \"CCSD(T) [kcal/mol]\": get_interaction_energy_cc(name) * 23.0605})\n",
    "print(f\"{'S22 complex':32s} {'N':>3s} {'E_disp(AB)':>12s} {'|dE|':>8s} {'|dgrad|':>8s} {'dEint d3':>9s} {'dEint xnn':>10s} {'CCSD(T)':>8s}\")\n",
    "for r in rows:\n",
    "    print(f\"{r['name']:32s} {r['N']:3d} {r['E_disp(AB) [Eh]']:12.8f} {r['|dE| [Eh]']:8.1e} {r['|dgrad| [Eh/bohr]']:8.1e} \"\n",
    "          f\"{r['dE_int(s-dftd3) [kcal/mol]']:9.3f} {r['dE_int(xnn) [kcal/mol]']:10.3f} {r['CCSD(T) [kcal/mol]']:8.2f}\")\n",
    "print(f\"\\nmax |dE| = {max(r['|dE| [Eh]'] for r in rows):.1e} Eh,  max |dgrad| = {max(r['|dgrad| [Eh/bohr]'] for r in rows):.1e} Eh/bohr,  \"\n",
    "      f\"max |d dE_int| = {max(abs(r['dE_int(s-dftd3) [kcal/mol]'] - r['dE_int(xnn) [kcal/mol]']) for r in rows):.1e} kcal/mol\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aafe68a",
   "metadata": {},
   "source": [
    "### Crystals: energies, gradients and virials\n",
    "\n",
    "Periodic systems exercise the lattice sums of the coordination numbers and of the two-\n",
    "and three-body terms. Rocksalt NaCl, diamond silicon, a sheared silicon cell, a\n",
    "graphite-like layered cell and a small periodic water box.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c56b02a2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-23T20:08:01.786052Z",
     "iopub.status.busy": "2026-09-23T20:08:01.785965Z",
     "iopub.status.idle": "2026-09-23T20:08:16.937624Z",
     "shell.execute_reply": "2026-09-23T20:08:16.936445Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "crystal                          N    E_disp [Eh]     |dE|  |dgrad| |dvirial|\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NaCl rocksalt (conventional)     8  -0.0641137907  6.9e-16  1.7e-18   1.4e-14\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Si diamond (primitive)           2  -0.0237065254  1.6e-16  1.9e-18   6.6e-16\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Si sheared cell                  2  -0.0237627852  2.8e-16  1.4e-16   6.9e-16\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "graphite                         4  -0.0210407655  1.5e-16  2.1e-18   2.0e-15\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "water box (18 atoms)            18  -0.0105301904  1.7e-18  8.4e-19   1.2e-16\n"
     ]
    }
   ],
   "source": [
    "from ase.build import bulk\n",
    "from ase.lattice.hexagonal import Graphite\n",
    "\n",
    "rng = np.random.default_rng(0)\n",
    "box = Atoms(cell=[7.0, 7.0, 7.0], pbc=True)\n",
    "for _ in range(6):\n",
    "    w = molecule(\"H2O\"); w.rotate(rng.uniform(0, 360), rng.normal(size=3)); w.translate(rng.uniform(0, 7.0, 3)); box += w\n",
    "sheared = bulk(\"Si\", \"diamond\", a=5.43); c = sheared.cell[:].copy(); c[1, 0] += 0.6; sheared.set_cell(c, scale_atoms=False)\n",
    "crystals = {\"NaCl rocksalt (conventional)\": bulk(\"NaCl\", \"rocksalt\", a=5.64, cubic=True),\n",
    "            \"Si diamond (primitive)\": bulk(\"Si\", \"diamond\", a=5.43),\n",
    "            \"Si sheared cell\": sheared,\n",
    "            \"graphite\": Graphite(\"C\", latticeconstant={\"a\": 2.46, \"c\": 6.70}),\n",
    "            \"water box (18 atoms)\": box}\n",
    "print(f\"{'crystal':30s} {'N':>3s} {'E_disp [Eh]':>14s} {'|dE|':>8s} {'|dgrad|':>8s} {'|dvirial|':>9s}\")\n",
    "for name, atoms in crystals.items():\n",
    "    ref = reference(atoms); mine = xnn_energy(atoms, stress=True)\n",
    "    vol = atoms.get_volume() / BOHR**3\n",
    "    virial = mine[\"stress\"][0].numpy() / HARTREE * BOHR**3 * vol\n",
    "    print(f\"{name:30s} {len(atoms):3d} {float(ref['energy']):14.10f} {abs(float(mine['energy']) / HARTREE - float(ref['energy'])):8.1e} \"\n",
    "          f\"{np.abs(-mine['forces'].numpy() / HARTREE * BOHR - ref['gradient']).max():8.1e} {np.abs(virial - ref['virial']).max():9.1e}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "312d1e05",
   "metadata": {},
   "source": [
    "## 2. Speed vs system size\n",
    "\n",
    "Water clusters cut from a liquid-like configuration (1 g/cm³), from 30 to about 1500\n",
    "atoms, evaluated with\n",
    "\n",
    "* `s-dftd3` (Fortran, OpenMP, energy + analytical gradient),\n",
    "* xnn on the CPU and on the GPU (energy + autograd forces),\n",
    "\n",
    "first with the **upstream cutoffs** (60 / 40 / 40 bohr, the exact-fidelity setting) and\n",
    "then with **MD-style cutoffs** (`cutoff_pair` 12 Å, `cutoff_triple` 6 Å, `cutoff_cn` 8 Å,\n",
    "2 Å switching windows), which is how one would attach D3 to an MLIP for condensed-phase\n",
    "dynamics. The time to build the neighbor list is excluded for xnn (an MD engine supplies\n",
    "it). The neighbor-list cost at 32 Å is not negligible on\n",
    "its own, so beyond 300 atoms only the short-cutoff variant is run.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fd7f2e88",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-23T20:08:16.939905Z",
     "iopub.status.busy": "2026-09-23T20:08:16.939691Z",
     "iopub.status.idle": "2026-09-23T20:08:45.302395Z",
     "shell.execute_reply": "2026-09-23T20:08:45.301064Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 30, 's-dftd3 (upstream cutoffs)': '0.000723', 'xnn CPU (upstream cutoffs)': '0.00877', 'edges (upstream)': 870, '|dE| upstream [Eh]': '0', 'xnn GPU (upstream cutoffs)': '0.0657', 's-dftd3 (MD cutoffs)': '0.000689', 'xnn CPU (MD cutoffs)': '0.01', 'edges (MD)': 870, 'xnn GPU (MD cutoffs)': '0.0664'}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 90, 's-dftd3 (upstream cutoffs)': '0.0164', 'xnn CPU (upstream cutoffs)': '0.0541', 'edges (upstream)': 8010, '|dE| upstream [Eh]': '8.33e-17', 'xnn GPU (upstream cutoffs)': '0.071', 's-dftd3 (MD cutoffs)': '0.00706', 'xnn CPU (MD cutoffs)': '0.0408', 'edges (MD)': 8010, 'xnn GPU (MD cutoffs)': '0.0747'}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 300, 's-dftd3 (upstream cutoffs)': '0.581', 'xnn CPU (upstream cutoffs)': '1.34', 'edges (upstream)': 89700, '|dE| upstream [Eh]': '2.78e-16', 'xnn GPU (upstream cutoffs)': '0.305', 's-dftd3 (MD cutoffs)': '0.0346', 'xnn CPU (MD cutoffs)': '0.158', 'edges (MD)': 72610, 'xnn GPU (MD cutoffs)': '0.062'}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 750, 's-dftd3 (MD cutoffs)': '0.196', 'xnn CPU (MD cutoffs)': '0.722', 'edges (MD)': 292410, 'xnn GPU (MD cutoffs)': '0.126'}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 1500, 's-dftd3 (MD cutoffs)': '0.575', 'xnn CPU (MD cutoffs)': '1.88', 'edges (MD)': 600728, 'xnn GPU (MD cutoffs)': '0.162'}\n"
     ]
    }
   ],
   "source": [
    "def water_cluster(n_water, seed=0):\n",
    "    # a cube of water at 1 g/cm3, molecules on a jittered grid with random orientations\n",
    "    rng = np.random.default_rng(seed)\n",
    "    side = (n_water * 29.9)**(1 / 3)            # 29.9 A^3 per molecule\n",
    "    m = int(np.ceil(n_water ** (1 / 3)))\n",
    "    grid = np.array([[i, j, k] for i in range(m) for j in range(m) for k in range(m)])[:n_water] * side / m\n",
    "    atoms = Atoms()\n",
    "    for g in grid:\n",
    "        w = molecule(\"H2O\"); w.rotate(rng.uniform(0, 360), rng.normal(size=3)); w.translate(g + rng.normal(0, 0.15, 3)); atoms += w\n",
    "    return atoms\n",
    "\n",
    "def time_xnn(atoms, model, device, repeats=3):\n",
    "    model = model.to(device)\n",
    "    s = {\"pos\": atoms.positions, \"atomic_numbers\": atoms.numbers}\n",
    "    graph = structure_to_graph(s, model.cutoff, device=device)\n",
    "    wrapped = ForceStressOutput(model)\n",
    "    wrapped(graph)                                           # warm-up (kernels, allocator)\n",
    "    if device == \"cuda\": torch.cuda.synchronize()\n",
    "    t0 = time.perf_counter()\n",
    "    for _ in range(repeats):\n",
    "        out = wrapped(graph)\n",
    "    if device == \"cuda\": torch.cuda.synchronize()\n",
    "    return (time.perf_counter() - t0) / repeats, float(out[\"energy\"]) / HARTREE, graph.num_edges\n",
    "\n",
    "def time_ref(atoms, cutoffs=None, repeats=3):\n",
    "    reference(atoms, cutoffs=cutoffs)                        # warm-up\n",
    "    t0 = time.perf_counter()\n",
    "    for _ in range(repeats):\n",
    "        e = float(reference(atoms, cutoffs=cutoffs)[\"energy\"])\n",
    "    return (time.perf_counter() - t0) / repeats, e\n",
    "\n",
    "upstream = dict(cutoff_pair=60 * BOHR, cutoff_triple=40 * BOHR, cutoff_cn=40 * BOHR)\n",
    "md_style = dict(cutoff_pair=12.0, cutoff_triple=6.0, cutoff_cn=8.0, switch_width_pair=2.0, switch_width_triple=1.0)\n",
    "md_style_ref = dict(disp2=12.0 / BOHR, disp3=6.0 / BOHR, cn=8.0 / BOHR)\n",
    "\n",
    "sizes = [10, 30, 100, 250, 500]\n",
    "timings = []\n",
    "for n_w in sizes:\n",
    "    atoms = water_cluster(n_w)\n",
    "    row = {\"N\": len(atoms)}\n",
    "    if n_w <= 100:\n",
    "        row[\"s-dftd3 (upstream cutoffs)\"], e_ref = time_ref(atoms)\n",
    "        row[\"xnn CPU (upstream cutoffs)\"], e_cpu, row[\"edges (upstream)\"] = time_xnn(atoms, D3Dispersion(s9=1.0, **upstream), \"cpu\")\n",
    "        row[\"|dE| upstream [Eh]\"] = abs(e_cpu - e_ref)\n",
    "        if device == \"cuda\":\n",
    "            row[\"xnn GPU (upstream cutoffs)\"], _, _ = time_xnn(atoms, D3Dispersion(s9=1.0, **upstream), \"cuda\")\n",
    "    row[\"s-dftd3 (MD cutoffs)\"], _ = time_ref(atoms, cutoffs=md_style_ref)\n",
    "    row[\"xnn CPU (MD cutoffs)\"], _, row[\"edges (MD)\"] = time_xnn(atoms, D3Dispersion(s9=1.0, **md_style), \"cpu\")\n",
    "    if device == \"cuda\":\n",
    "        row[\"xnn GPU (MD cutoffs)\"], _, _ = time_xnn(atoms, D3Dispersion(s9=1.0, **md_style), \"cuda\")\n",
    "    timings.append(row)\n",
    "    print({k: (f\"{v:.3g}\" if isinstance(v, float) else v) for k, v in row.items()})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3a68c4c9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-23T20:08:45.304440Z",
     "iopub.status.busy": "2026-09-23T20:08:45.304329Z",
     "iopub.status.idle": "2026-09-23T20:08:46.137326Z",
     "shell.execute_reply": "2026-09-23T20:08:46.136495Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(11, 4), sharey=True)\n",
    "N = [r[\"N\"] for r in timings]\n",
    "for a, tag, keys in [(ax[0], \"upstream cutoffs (60 / 40 / 40 bohr)\", [\"s-dftd3 (upstream cutoffs)\", \"xnn CPU (upstream cutoffs)\", \"xnn GPU (upstream cutoffs)\"]),\n",
    "                     (ax[1], \"MD cutoffs (12 / 6 / 8 Å, switched)\", [\"s-dftd3 (MD cutoffs)\", \"xnn CPU (MD cutoffs)\", \"xnn GPU (MD cutoffs)\"])]:\n",
    "    for key, style in zip(keys, [\"ks-\", \"C0o-\", \"C3^-\"]):\n",
    "        pts = [(r[\"N\"], r[key]) for r in timings if key in r]\n",
    "        if pts:\n",
    "            a.loglog(*zip(*pts), style, label=key)\n",
    "    a.set_title(tag); a.set_xlabel(\"atoms\"); a.grid(alpha=0.3); a.legend(fontsize=8)\n",
    "ax[0].set_ylabel(\"wall time per energy+gradient evaluation [s]\")\n",
    "plt.tight_layout(); plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc24d9b2",
   "metadata": {},
   "source": [
    "**Reading the timings.** With the upstream cutoffs every atom of a liquid has thousands\n",
    "of neighbors inside 40 bohr, so the three-body sum -- $O(N\\,n_{\\rm nb}^2)$ triples -- dominates\n",
    "both codes, and the GPU is what makes it affordable. With MD-style cutoffs the triple count\n",
    "drops by orders of magnitude and the D3 term costs a small fraction of a typical MLIP\n",
    "evaluation. The `|dE|` column confirms that the shorter cutoffs are still evaluated\n",
    "identically by both codes; what they change is the physics one chooses to include, and\n",
    "the switching windows (an xnn extension) keep that choice smooth for dynamics.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11f712df",
   "metadata": {},
   "source": [
    "## 3. D3 on top of a short-range MLIP, through every channel\n",
    "\n",
    "The wrapper adds the dispersion energy to any registered model: here an (untrained, but\n",
    "structurally complete) MACE for water with a 4.5 Å neighborhood. The wrapper's cutoff is\n",
    "the D3 pair cutoff, the core sees only its own edges, and the same object deploys through\n",
    "the eager `AtomicGraph` path, the ASE calculator, and the TorchScript export with its two\n",
    "tensor ABIs (whole-system and LAMMPS pair-style). Forces and stress carry the D3 term.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "509d4192",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-23T20:08:46.139755Z",
     "iopub.status.busy": "2026-09-23T20:08:46.139617Z",
     "iopub.status.idle": "2026-09-23T20:08:48.723089Z",
     "shell.execute_reply": "2026-09-23T20:08:48.722222Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D3Dispersion around MACE | neighbor-list cutoff 12.0 Å | core cutoff 4.5 Å\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eager:       E = -41346.047549 eV = E_sr -41344.128236 + E_disp -1.919312  (2-body -1.9935, ATM +0.0742);  CN range 0.99..2.02\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ASE:         E = -41346.047549 eV, |F| max 5.8047 eV/Å, stress xx -0.156413 eV/ų\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TorchScript: E = -41346.047549 eV, |dF| vs eager 1.5e-14, |dstress| 7.5e-16\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pair-style:  E = -41346.047549 eV (the LAMMPS ABI, neighbor list supplied; 44416 edges at 12.0 Å)\n"
     ]
    }
   ],
   "source": [
    "cfg = from_dict({\"model\": {\"name\": \"mace\", \"cutoff\": 4.5, \"n_interactions\": 2, \"n_rbf\": 8, \"n_features\": 16,\n",
    "                           \"extra\": {\"species\": [1, 8], \"l_max\": 2, \"atomic_energies\": [-13.6, -2041.0],\n",
    "                                     \"dispersion\": {\"name\": \"d3\", **md_style, \"s9\": 1.0}}}})\n",
    "torch.manual_seed(0)\n",
    "model = build_model(cfg.model).eval()\n",
    "print(type(model).__name__, \"around\", type(model.model).__name__, \"| neighbor-list cutoff\", model.cutoff, \"Å | core cutoff\", model.model.cutoff, \"Å\")\n",
    "\n",
    "box = water_cluster(20); box.set_cell([8.4, 8.4, 8.4]); box.pbc = True\n",
    "graph = structure_to_graph({\"pos\": box.positions, \"atomic_numbers\": box.numbers, \"cell\": box.cell[:], \"pbc\": box.pbc}, model.cutoff)\n",
    "eager = ForceStressOutput(model, compute_stress=True)(graph)\n",
    "print(f\"eager:       E = {float(eager['energy']):.6f} eV = E_sr {float(eager['energy_sr']):.6f} + E_disp {float(eager['energy_disp']):.6f}  \"\n",
    "      f\"(2-body {float(eager['energy_2body']):.4f}, ATM {float(eager['energy_3body']):+.4f});  CN range {float(eager['coordination_numbers'].min()):.2f}..{float(eager['coordination_numbers'].max()):.2f}\")\n",
    "\n",
    "box.calc = XNNCalculator(ForceStressOutput(model, compute_stress=True), cutoff=model.cutoff)\n",
    "print(f\"ASE:         E = {box.get_potential_energy():.6f} eV, |F| max {np.abs(box.get_forces()).max():.4f} eV/Å, stress xx {box.get_stress()[0]:.6f} eV/ų\")\n",
    "\n",
    "scripted = torch.jit.script(TorchScriptPotential(model, model.cutoff).eval())\n",
    "ts = scripted(torch.tensor(box.positions), torch.tensor(box.numbers), torch.tensor(box.cell[:]), torch.tensor(box.pbc))\n",
    "print(f\"TorchScript: E = {float(ts['energy']):.6f} eV, |dF| vs eager {float((ts['forces'] - eager['forces'].detach()).abs().max()):.1e}, \"\n",
    "      f\"|dstress| {float((ts['stress'] - eager['stress'][0].detach()).abs().max()):.1e}\")\n",
    "ei, cs = build_neighbor_list(torch.tensor(box.positions), model.cutoff, torch.tensor(box.cell[:]), torch.tensor(box.pbc))\n",
    "pair = scripted.forward_lammps(torch.tensor(box.positions), ei, cs, torch.tensor(box.numbers), torch.tensor(box.cell[:]))\n",
    "print(f\"pair-style:  E = {float(pair['energy']):.6f} eV (the LAMMPS ABI, neighbor list supplied; {ei.shape[1]} edges at {model.cutoff} Å)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7497e477",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "* **Accuracy.** xnn reproduces `s-dftd3` to ~1e-17 Eh in dispersion energies, gradients and\n",
    "  virials, for the S22 complexes and for crystals; the dispersion contributions to\n",
    "  interaction energies agree to better than 1e-12 kcal/mol.\n",
    "* **Speed.** The Fortran reference is fast for small molecules; xnn's vectorized evaluation\n",
    "  scales to condensed-phase sizes on the GPU, and with MD-style cutoffs the D3 term is cheap\n",
    "  next to the MLIP it supplements. The three-body term with the upstream 40 bohr cutoff is\n",
    "  the one setting that should not be carried into large-scale MD.\n",
    "* **Deployment.** One `DFTD3` module serves training and every deploy channel; a D3-corrected\n",
    "  MACE exports to a self-contained TorchScript artifact with both tensor ABIs.\n"
   ]
  }
 ],
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   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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