{ "cells": [ { "cell_type": "markdown", "id": "6d49f3eb", "metadata": {}, "source": [ "# DFT-D3 in xnn: reproducing examples of the two Grimme papers\n", "\n", "[Grimme, Antony, Ehrlich & Krieg, *J. Chem. Phys.* **132**, 154104 (2010)](https://doi.org/10.1063/1.3382344)\n", "introduced DFT-D3: *ab initio* (TD-DFT) reference $C_6$ coefficients for all elements\n", "H–Pu, interpolated in a **fractional coordination number** (eqs 15–16), recursively\n", "derived $C_8$ (eqs 6–9), a zero-damping pair sum (eqs 3–4) and an optional three-body\n", "Axilrod–Teller–Muto term (eqs 11–14). [Grimme, Ehrlich & Goerigk, *J. Comput. Chem.*\n", "**32**, 1456 (2011)](https://doi.org/10.1002/jcc.21759) replaced the zero damping by\n", "the rational Becke–Johnson damping (eqs 5–7), which damps to a finite value at short\n", "range and became the default. This notebook uses xnn's independent implementation\n", "(`xnn.common.models.D3Dispersion`, verified against the reference `simple-dftd3` in\n", "`examples/fidelity_checks/d3_verification.ipynb`) to reproduce, without external\n", "quantum-chemistry data:\n", "\n", "1. **table II (2010)**: the free-atom rare-gas $C_6$ and the sp³/sp²/sp carbon $C_6$;\n", "2. **table III (2010)**: rare-gas trimer $C_9$ from the geometric-mean approximation of eq 13;\n", "3. **fig 5 (2010)**: the CN dependence of $C_6^{CC}$, $C_6^{NN}$, $C_6^{OO}$;\n", "4. **fig 1 (2010)**: the dispersion energy of two carbon atoms with the BLYP and TPSS parameters and the size of the $C_8$ term;\n", "5. **fig 1 (2011)**: the argon dimer with zero vs BJ damping (TPSS) against the undamped $-C_6/R^6$;\n", "6. **table VII (2010)**: the three-body share of the graphene bilayer binding;\n", "7. **fig 6 (2010)**: molecular $C_6$ coefficients against DOSD reference data.\n", "\n", "Parameters: PBE0-D3(BJ) `s8 = 1.2177, a1 = 0.4145, a2 = 4.8593` (2011 table 2) and\n", "PBE0-D3(0) `sr6 = 1.287, s8 = 0.928` (2010 table IV) are xnn's defaults; the figures\n", "use the BLYP / TPSS sets of the papers where the papers do.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "23fffb50", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:10.137902Z", "iopub.status.busy": "2026-09-23T20:07:10.137661Z", "iopub.status.idle": "2026-09-23T20:07:12.484779Z", "shell.execute_reply": "2026-09-23T20:07:12.484211Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "xnn 0.2.1 | PBE0-D3(BJ): {'s6': 1.0, 's8': 1.2177, 'a1': 0.4145, 'a2': 4.8593, 's9': 0.0, 'alp': 14.0} | PBE0-D3(0): {'s6': 1.0, 's8': 0.928, 'rs6': 1.287, 'rs8': 1.0, 's9': 0.0, 'alp': 14.0}\n" ] } ], "source": [ "import logging, warnings\n", "logging.disable(logging.WARNING)\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "import numpy as np\n", "import torch\n", "import matplotlib.pyplot as plt\n", "from ase import Atoms\n", "from ase.build import molecule\n", "\n", "torch.set_default_dtype(torch.float64)\n", "\n", "import xnn\n", "from xnn.common.data import structure_to_graph\n", "from xnn.common.models import D3Dispersion, DFTD3\n", "from xnn.common.models.d3 import PBE0_D3BJ, PBE0_D3ZERO\n", "from xnn.common.models.dispersion import BOHR, HARTREE\n", "\n", "KCAL = HARTREE / 0.0433641153087705 # hartree -> kcal/mol via eV\n", "print(\"xnn\", xnn.__version__, \"| PBE0-D3(BJ):\", PBE0_D3BJ, \"| PBE0-D3(0):\", PBE0_D3ZERO)\n", "\n", "def run(atoms, model):\n", " s = {\"pos\": atoms.positions, \"atomic_numbers\": atoms.numbers}\n", " if atoms.pbc.any():\n", " s[\"cell\"], s[\"pbc\"] = atoms.cell[:], atoms.pbc\n", " return {k: v.detach() for k, v in model(structure_to_graph(s, model.cutoff)).items()}\n", "\n", "core = DFTD3()\n", "\n", "def c6_at_cn(Z, cn):\n", " z = torch.full((len(cn),), Z, dtype=torch.long); cn_t = torch.as_tensor(np.asarray(cn, dtype=float))\n", " w = core.reference_weights(z, cn_t)\n", " return core.c6_matrix(z, w, core._species_vectors(z, w)).diagonal().numpy()\n" ] }, { "cell_type": "markdown", "id": "63c542d6", "metadata": {}, "source": [ "## 1. Reference $C_6$ coefficients · table II (2010)\n", "\n", "Table II compares the TD-DFT (PBE38/daug-def2-QZVP) $C_6$ of the free rare-gas atoms\n", "with reference values, and gives the carbon $C_6$ in ethane, ethene and ethyne obtained\n", "with the partitioning of eq 10. Both sets are reference systems of the D3 table: the\n", "free atoms are the CN = 0 references, the three carbons are the CN ≈ 4, 3, 2 references.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "b4934656", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:12.486433Z", "iopub.status.busy": "2026-09-23T20:07:12.486344Z", "iopub.status.idle": "2026-09-23T20:07:12.490487Z", "shell.execute_reply": "2026-09-23T20:07:12.490091Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pair ref. value paper TDDFT xnn D3 table CN of ref.\n", "He-He 1.46 1.54 1.56 0.0000\n", "Ne-Ne 6.35 6.14 6.29 0.0000\n", "Ar-Ar 64.40 64.20 64.65 0.0000\n", "Kr-Kr 130.10 129.70 130.40 0.0000\n", "Xe-Xe 287.50 288.60 290.22 0.0000\n", "Rn-Rn 420.60 410.50 412.83 0.0000\n", "C-C (sp3) 22.40 18.10 18.21 3.9844\n", "C-C (sp2) 27.40 25.70 25.78 2.9987\n", "C-C (sp) 29.70 29.30 29.36 1.9985\n" ] } ], "source": [ "rows = [(\"He-He\", 2, 0, 1.46, 1.54), (\"Ne-Ne\", 10, 0, 6.35, 6.14), (\"Ar-Ar\", 18, 0, 64.4, 64.2), (\"Kr-Kr\", 36, 0, 130.1, 129.7),\n", " (\"Xe-Xe\", 54, 0, 287.5, 288.6), (\"Rn-Rn\", 86, 0, 420.6, 410.5),\n", " (\"C-C (sp3)\", 6, 4, 22.4, 18.1), (\"C-C (sp2)\", 6, 3, 27.4, 25.7), (\"C-C (sp)\", 6, 2, 29.7, 29.3)]\n", "print(f\"{'pair':10s} {'ref. value':>11s} {'paper TDDFT':>12s} {'xnn D3 table':>13s} {'CN of ref.':>11s}\")\n", "for name, Z, ref, exp, paper in rows:\n", " print(f\"{name:10s} {exp:11.2f} {paper:12.2f} {float(core.c6ref[ref, ref, Z, Z]):13.2f} {float(core.refcn[ref, Z]):11.4f}\")\n" ] }, { "cell_type": "markdown", "id": "7b0eabf4", "metadata": {}, "source": [ "## 2. Rare-gas trimer $C_9$ · table III (2010), eq 13\n", "\n", "The three-body coefficient is approximated by the geometric mean\n", "$C_9^{ABC} \\approx \\sqrt{C_6^{AB} C_6^{BC} C_6^{CA}}$ (eq 13, \"DFT-D3\" column of table\n", "III, given as $-C_9$), which the paper compares with the TD-DFT integration (eq 12) and\n", "with experiment. The column follows from the free-atom $C_6$ of the D3 table.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "5773d874", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:12.491944Z", "iopub.status.busy": "2026-09-23T20:07:12.491881Z", "iopub.status.idle": "2026-09-23T20:07:12.496330Z", "shell.execute_reply": "2026-09-23T20:07:12.495884Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "atoms D3 eq 13 (paper) xnn eq 13 TDDFT eq 12 expt\n", "Ne Ne Ne 15.8 15.8 11.6 11.9\n", "Ne Ar Kr 219.1 219.1 203.5 204.8\n", "Ar Ar Ar 519.8 519.8 523.0 519.0\n", "Ar Kr Kr 1047.0 1046.5 1100.0 1087.0\n", "Kr Kr Kr 1489.0 1489.1 1600.0 1577.0\n", "Ar Kr Xe 1554.0 1554.4 1669.0 1647.0\n", "Kr Xe Xe 3306.0 3306.2 3716.0 3656.0\n", "Xe Xe Xe 4944.0 4944.2 5694.0 5595.0\n" ] } ], "source": [ "trimers = [(\"Ne Ne Ne\", (10, 10, 10), 15.8, 11.6, 11.9), (\"Ne Ar Kr\", (10, 18, 36), 219.1, 203.5, 204.8), (\"Ar Ar Ar\", (18, 18, 18), 519.8, 523.0, 519.0),\n", " (\"Ar Kr Kr\", (18, 36, 36), 1047, 1100, 1087), (\"Kr Kr Kr\", (36, 36, 36), 1489, 1600, 1577), (\"Ar Kr Xe\", (18, 36, 54), 1554, 1669, 1647),\n", " (\"Kr Xe Xe\", (36, 54, 54), 3306, 3716, 3656), (\"Xe Xe Xe\", (54, 54, 54), 4944, 5694, 5595)]\n", "print(f\"{'atoms':10s} {'D3 eq 13 (paper)':>17s} {'xnn eq 13':>10s} {'TDDFT eq 12':>12s} {'expt':>7s}\")\n", "for name, (a, b, c), paper, tddft, expt in trimers:\n", " c9 = float(torch.sqrt(core.c6ref[0, 0, a, b] * core.c6ref[0, 0, b, c] * core.c6ref[0, 0, a, c]))\n", " print(f\"{name:10s} {paper:17.1f} {c9:10.1f} {tddft:12.1f} {expt:7.1f}\")\n" ] }, { "cell_type": "markdown", "id": "d988ee7f", "metadata": {}, "source": [ "## 3. $C_6$ vs coordination number · fig 5 (2010)\n", "\n", "The Gaussian interpolation (eq 16, $k_3 = 4$) between the reference systems gives smooth\n", "$C_6(\\mathrm{CN})$ curves with plateaus at the integer coordination numbers; the paper\n", "notes the ~25% drop of the carbon $C_6$ between sp² and sp³ and the much larger drop from\n", "the free atom.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "3f8f365a", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:12.497465Z", "iopub.status.busy": "2026-09-23T20:07:12.497401Z", "iopub.status.idle": "2026-09-23T20:07:12.761389Z", "shell.execute_reply": "2026-09-23T20:07:12.760731Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cn = np.linspace(0, 5, 401)\n", "fig, ax = plt.subplots(figsize=(6, 3.8))\n", "for Z, name, ls in [(6, \"carbon\", \"-\"), (7, \"nitrogen\", \"--\"), (8, \"oxygen\", \"-.\")]:\n", " ax.plot(cn, c6_at_cn(Z, cn), \"k\", ls=ls, label=name)\n", " nref = int(core.nref[Z]); ax.plot(core.refcn[:nref, Z].numpy(), [float(core.c6ref[r, r, Z, Z]) for r in range(nref)], \"o\", ms=4, color=\"C3\")\n", "ax.set_xlabel(\"CN\"); ax.set_ylabel(r\"$C_6^{AA}$ [au]\"); ax.set_ylim(0, 50); ax.legend(); ax.set_title(\"2010 paper, fig 5 (red: reference systems)\")\n", "plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "91a31626", "metadata": {}, "source": [ "## 4. Dispersion energy of two carbon atoms · fig 1 (2010)\n", "\n", "Fig 1 shows the total dispersion energy (and the $C_8$ part alone) of two three-fold\n", "coordinated carbon atoms with the BLYP-D3 ($s_{r,6} = 1.094$, $s_8 = 1.682$) and\n", "TPSS-D3 ($s_{r,6} = 1.166$, $s_8 = 1.105$) zero-damping parameters of table IV. The\n", "minimum sits at the typical van der Waals distance (3.3–3.4 Å) and the $C_8$ term is a\n", "large part of it at short range. Here the two carbons are taken as sp² references (CN = 3)\n", "by evaluating the pair with fixed reference weights, exactly as the figure intends.\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "75f36658", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:12.763267Z", "iopub.status.busy": "2026-09-23T20:07:12.763192Z", "iopub.status.idle": "2026-09-23T20:07:13.020995Z", "shell.execute_reply": "2026-09-23T20:07:13.020190Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BLYP-D3: minimum -0.250 kcal/mol at R(C-C) = 3.33 Å\n", "TPSS-D3: minimum -0.153 kcal/mol at R(C-C) = 3.33 Å\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def two_carbon_curve(rs6, s8, s8_only=False):\n", " # fixed CN = 3 weights -> C6 of the sp2 reference; damped pair energy of eq 3/4 in kcal/mol\n", " model = DFTD3(damping=\"zero\", rs6=rs6, s8=s8, s6=0.0 if s8_only else 1.0)\n", " z = torch.tensor([6, 6]); w = model.reference_weights(z, torch.tensor([3.0, 3.0]))\n", " c6 = float(model.c6_matrix(z, w, model._species_vectors(z, w))[0, 1])\n", " r = np.linspace(1.6, 8.0, 300) / BOHR\n", " rr = 3 * float(model.r4r2[6]) ** 2; r0 = float(model.rvdw[6, 6])\n", " f6 = 1 / (1 + 6 * (rs6 * r0 / r) ** 14); f8 = 1 / (1 + 6 * (r0 / r) ** 16)\n", " e = -c6 * ((0.0 if s8_only else 1.0) * f6 / r ** 6 + s8 * rr * f8 / r ** 8)\n", " return r * BOHR, e * KCAL\n", "\n", "fig, ax = plt.subplots(figsize=(6, 3.8))\n", "for (rs6, s8, name, color) in [(1.094, 1.682, \"BLYP-D3\", \"k\"), (1.166, 1.105, \"TPSS-D3\", \"C3\")]:\n", " R, e = two_carbon_curve(rs6, s8); ax.plot(R, e, color=color, label=f\"total, {name}\")\n", " R, e8 = two_carbon_curve(rs6, s8, s8_only=True); ax.plot(R, e8, color=color, ls=\"--\", label=f\"$E_8$, {name.split('-')[0]}\")\n", " print(f\"{name}: minimum {e.min():.3f} kcal/mol at R(C-C) = {R[e.argmin()]:.2f} Å\")\n", "ax.set_xlim(1.5, 8); ax.set_ylim(-0.3, 0.0); ax.set_xlabel(\"R(C-C) [Å]\"); ax.set_ylabel(r\"$E_{disp}$ [kcal/mol]\"); ax.legend(fontsize=8)\n", "ax.set_title(\"2010 paper, fig 1: two sp$^2$ carbons, zero damping\"); plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "c1c27f14", "metadata": {}, "source": [ "## 5. Zero vs BJ damping on the argon dimer · fig 1 (2011)\n", "\n", "The 2011 paper's fig 1 contrasts the two damping philosophies on Ar₂ with TPSS parameters\n", "(zero: $s_{r,6} = 1.166$, $s_8 = 1.105$; BJ: $a_1 = 0.4535$, $s_8 = 1.9435$,\n", "$a_2 = 4.4752$): zero damping removes the correction below ~3.3 Å and passes through a\n", "minimum of about −0.45 kcal/mol, BJ damping saturates to a finite value (about −0.7\n", "kcal/mol) at $R \\to 0$; both follow the undamped $-C_6/R^6$ at long range.\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "03e059b7", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:13.022710Z", "iopub.status.busy": "2026-09-23T20:07:13.022624Z", "iopub.status.idle": "2026-09-23T20:07:14.223078Z", "shell.execute_reply": "2026-09-23T20:07:14.222526Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "zero damping: minimum -0.452 kcal/mol at 3.32 Å; BJ damping: E(R -> 1 Å) = -0.692 kcal/mol; C6(Ar-Ar) = 64.6 au\n" ] } ], "source": [ "R = np.linspace(1.0, 8.0, 400)\n", "ar2 = [Atoms(\"Ar2\", positions=[[0, 0, 0], [x, 0, 0]]) for x in R]\n", "zero = D3Dispersion(damping=\"zero\", rs6=1.166, s8=1.105)\n", "bj = D3Dispersion(damping=\"bj\", a1=0.4535, s8=1.9435, a2=4.4752)\n", "e_zero = np.array([float(run(a, zero)[\"energy\"]) for a in ar2]) / HARTREE * KCAL\n", "e_bj = np.array([float(run(a, bj)[\"energy\"]) for a in ar2]) / HARTREE * KCAL\n", "out = run(ar2[-1], bj); c6 = float(out[\"c6_matrix\"][0, 1])\n", "plt.figure(figsize=(6, 3.8))\n", "plt.plot(R, -c6 / (R / BOHR) ** 6 * KCAL, \"k:\", label=r\"un-damped $C_6/R^6$\")\n", "plt.plot(R, e_zero, \"k-\", label=\"total TPSS-D3 (zero damping)\")\n", "plt.plot(R, e_bj, \"k--\", label=\"total TPSS-D3(BJ)\")\n", "plt.ylim(-0.8, 0.02); plt.xlim(1, 8); plt.xlabel(\"R(Ar-Ar) [Å]\"); plt.ylabel(r\"$E_{disp}$ [kcal/mol]\"); plt.legend(fontsize=8)\n", "plt.title(\"2011 paper, fig 1: argon dimer\"); plt.tight_layout(); plt.show()\n", "print(f\"zero damping: minimum {e_zero.min():.3f} kcal/mol at {R[e_zero.argmin()]:.2f} Å; BJ damping: E(R -> 1 Å) = {e_bj[0]:.3f} kcal/mol; C6(Ar-Ar) = {c6:.1f} au\")\n" ] }, { "cell_type": "markdown", "id": "318dbe4b", "metadata": {}, "source": [ "## 6. Three-body share of the graphene bilayer binding · table VII (2010)\n", "\n", "Table VII lists the interlayer dissociation energy of two graphene sheets: including\n", "$E^{(3)}$ lowers the DFT-D3 values by about 5 meV/atom (BLYP: 59 → 54, B97-D: 52 → 46,\n", "revPBE: 55 → 49, PBE: 41 → 35, TPSS: 48 → 43 meV/atom), \"about 10%\" of the binding. The\n", "dispersion part of that number is reproduced here with a periodic AB-stacked bilayer at\n", "the experimental spacing (3.35 Å): the two-body D3 binding and the (repulsive) three-body\n", "contribution per atom, for the five functionals of the table (zero damping, table IV\n", "parameters).\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "453872ee", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:14.224378Z", "iopub.status.busy": "2026-09-23T20:07:14.224303Z", "iopub.status.idle": "2026-09-23T20:07:14.982265Z", "shell.execute_reply": "2026-09-23T20:07:14.981733Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DF E2 disp. binding E3 (repulsive) E3 / E2 paper D3 -> D3+E3 (total, meV/atom)\n", "BLYP -48.8 3.4 6.9% 59 -> 54\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "B97-D -45.9 3.4 7.3% 52 -> 46\n", "revPBE -46.8 3.4 7.2% 55 -> 49\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "PBE -28.1 3.4 12.0% 41 -> 35\n", "TPSS -36.3 3.4 9.3% 48 -> 43\n", "\n", "(the DFT part of the binding is not included: the columns give the dispersion contributions only)\n" ] } ], "source": [ "from ase.lattice.hexagonal import Graphite\n", "\n", "def bilayer(sep=3.35, vacuum=25.0):\n", " g = Graphite(\"C\", latticeconstant={\"a\": 2.46, \"c\": 2 * sep}) # AB-stacked, 4 atoms: two layers per cell\n", " cell = g.cell[:].copy(); cell[2, 2] = 2 * sep + vacuum # isolate one bilayer\n", " g.set_cell(cell, scale_atoms=False)\n", " return g\n", "\n", "def sheet(vacuum=25.0):\n", " g = bilayer(); return g[g.positions[:, 2] < 1.0] # one of the two layers\n", "\n", "params = {\"BLYP\": (1.094, 1.682), \"B97-D\": (0.892, 0.909), \"revPBE\": (0.923, 1.010), \"PBE\": (1.217, 0.722), \"TPSS\": (1.166, 1.105)}\n", "table7 = {\"BLYP\": (59, 54), \"B97-D\": (52, 46), \"revPBE\": (55, 49), \"PBE\": (41, 35), \"TPSS\": (48, 43)}\n", "print(f\"{'DF':8s} {'E2 disp. binding':>17s} {'E3 (repulsive)':>15s} {'E3 / E2':>8s} {'paper D3 -> D3+E3 (total, meV/atom)':>36s}\")\n", "for df, (rs6, s8) in params.items():\n", " model = D3Dispersion(damping=\"zero\", rs6=rs6, s8=s8, s9=1.0)\n", " b, s = run(bilayer(), model), run(sheet(), model)\n", " e2 = (float(b[\"energy_2body\"]) - 2 * float(s[\"energy_2body\"])) / 4 * 1e3 # meV per atom of the bilayer\n", " e3 = (float(b[\"energy_3body\"]) - 2 * float(s[\"energy_3body\"])) / 4 * 1e3\n", " print(f\"{df:8s} {e2:17.1f} {e3:15.1f} {e3 / abs(e2) * 100:7.1f}% {table7[df][0]:>12d} -> {table7[df][1]}\")\n", "print(\"\\n(the DFT part of the binding is not included: the columns give the dispersion contributions only)\")\n" ] }, { "cell_type": "markdown", "id": "7691b0f4", "metadata": {}, "source": [ "## 7. Molecular $C_6$ coefficients vs DOSD · fig 6 (2010)\n", "\n", "Fig 6 compares molecular $C_6$ coefficients (sum of all intramolecular pairs, eq 16) with\n", "experimental dipole-oscillator-strength-distribution values for 174 pairs and reports a\n", "mean absolute deviation of 8.4%. The same small-molecule subset as in the D4 example\n", "notebook is used here (reference values transcribed from the literature; **treat them\n", "as approximate orientation**, see the caveat there), evaluated with both D3 and D4.\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "347ce6db", "metadata": { "execution": { "iopub.execute_input": "2026-09-23T20:07:14.983696Z", "iopub.status.busy": "2026-09-23T20:07:14.983612Z", "iopub.status.idle": "2026-09-23T20:07:15.368666Z", "shell.execute_reply": "2026-09-23T20:07:15.368086Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "molecule DOSD D3 D4 dev D3 % dev D4 %\n", "H2 12.1 12.5 12.2 +3.7 +1.2\n", "N2 73.4 88.5 82.4 +20.6 +12.3\n", "O2 62.0 51.3 60.1 -17.3 -3.0\n", "CO 81.4 100.8 96.1 +23.9 +18.1\n", "CO2 158.7 156.4 175.4 -1.4 +10.5\n", "N2O 184.9 161.0 170.8 -12.9 -7.6\n", "NH3 89.1 84.7 84.1 -5.0 -5.6\n", "H2O 45.4 44.5 44.5 -1.9 -2.1\n", "CH4 129.7 127.7 123.8 -1.6 -4.5\n", "C2H2 204.1 206.7 206.1 +1.3 +1.0\n", "C2H4 300.2 294.5 294.2 -1.9 -2.0\n", "C2H6 381.9 364.0 362.1 -4.7 -5.2\n", "C3H8 768.1 721.1 726.7 -6.1 -5.4\n", "C6H6 1723.0 1659.7 1764.8 -3.7 +2.4\n", "HF 19.0 18.9 19.0 -0.5 -0.1\n", "HCl 130.4 126.9 127.1 -2.7 -2.5\n", "Cl2 389.2 361.7 389.1 -7.1 -0.0\n", "SO2 294.0 331.2 379.5 +12.7 +29.1\n", "CS2 871.1 800.5 850.3 -8.1 -2.4\n", "OCS 402.2 413.4 446.3 +2.8 +11.0\n", "NO 69.8 68.3 71.3 -2.1 +2.2\n", "CH3OH 222.0 208.7 212.9 -6.0 -4.1\n", "SiH4 343.9 372.3 368.1 +8.3 +7.0\n", "PH3 307.5 309.2 308.2 +0.5 +0.2\n", "\n", "MAD: D3 6.5 % D4 5.8 % (2010 paper, 174 DOSD pairs: D3 8.4 %, Becke-Johnson 12.2 %; 2019 D4 paper: D3 4.7 %, D4 3.8 %)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from xnn.common.models import D4Dispersion, c6_matrix\n", "dosd = {\"H2\": 12.1, \"N2\": 73.4, \"O2\": 62.0, \"CO\": 81.4, \"CO2\": 158.7, \"N2O\": 184.9, \"NH3\": 89.1, \"H2O\": 45.4, \"CH4\": 129.7,\n", " \"C2H2\": 204.1, \"C2H4\": 300.2, \"C2H6\": 381.9, \"C3H8\": 768.1, \"C6H6\": 1723.0, \"HF\": 19.0, \"HCl\": 130.4, \"Cl2\": 389.2,\n", " \"SO2\": 294.0, \"CS2\": 871.1, \"OCS\": 402.2, \"NO\": 69.8, \"CH3OH\": 222.0, \"SiH4\": 343.9, \"PH3\": 307.5}\n", "d3 = D3Dispersion(); d4 = D4Dispersion()\n", "rows = []\n", "for name, ref in dosd.items():\n", " a = molecule(name)\n", " c3 = float(run(a, d3)[\"c6_matrix\"].sum()); c4 = float(c6_matrix(run(a, d4)[\"dynamic_polarizabilities\"]).sum())\n", " rows.append((name, ref, c3, c4))\n", "dev3 = np.array([(r[2] / r[1] - 1) * 100 for r in rows]); dev4 = np.array([(r[3] / r[1] - 1) * 100 for r in rows])\n", "print(f\"{'molecule':9s} {'DOSD':>8s} {'D3':>8s} {'D4':>8s} {'dev D3 %':>9s} {'dev D4 %':>9s}\")\n", "for (name, ref, c3, c4), e3, e4 in zip(rows, dev3, dev4):\n", " print(f\"{name:9s} {ref:8.1f} {c3:8.1f} {c4:8.1f} {e3:+9.1f} {e4:+9.1f}\")\n", "print(f\"\\nMAD: D3 {np.abs(dev3).mean():.1f} % D4 {np.abs(dev4).mean():.1f} % (2010 paper, 174 DOSD pairs: D3 8.4 %, Becke-Johnson 12.2 %; 2019 D4 paper: D3 4.7 %, D4 3.8 %)\")\n", "plt.figure(figsize=(4.6, 4.2))\n", "ref = np.array([r[1] for r in rows])\n", "plt.loglog(ref, [r[2] for r in rows], \"ko\", label=f\"D3, MAD {np.abs(dev3).mean():.1f} %\")\n", "plt.loglog(ref, [r[3] for r in rows], \"C0+\", ms=9, label=f\"D4, MAD {np.abs(dev4).mean():.1f} %\")\n", "lim = [8, 2500]; plt.plot(lim, lim, \"k:\", lw=0.8); plt.xlabel(\"C6 (DOSD, transcribed) [au]\"); plt.ylabel(\"C6 (calc.) [au]\"); plt.legend(); plt.title(\"2010 paper, fig 6 (subset)\"); plt.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "41ddb12b", "metadata": {}, "source": [ "## Summary\n", "\n", "* The D3 reference table reproduces table II and, through eq 13, table III of the 2010 paper.\n", "* The Gaussian CN interpolation gives the $C_6(\\mathrm{CN})$ curves of fig 5, and the\n", " damped pair energies the two-carbon curves of fig 1 (2010) and the argon-dimer contrast of\n", " fig 1 (2011): zero damping vanishes at short range, BJ damping saturates.\n", "* The three-body term repels the graphene layers by the ~10% of the dispersion binding\n", " that table VII reports for the total binding.\n", "* Molecular $C_6$ coefficients deviate from (transcribed) DOSD data by the several percent\n", " the paper quotes, with D4 improving on D3.\n", "\n", "`d3_benchmark.ipynb` compares xnn with the reference `s-dftd3` code on accuracy and speed\n", "and deploys a D3-corrected MLIP.\n" ] } ], "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": "3.13.12" } }, "nbformat": 4, "nbformat_minor": 5 }