{ "cells": [ { "cell_type": "markdown", "id": "afa978ee", "metadata": {}, "source": [ "# L-OPLS, and refitting OPLS torsions by gradient descent\n", "\n", "OPLS-AA was parameterized on *short* alkanes, and it overestimates the\n", "hydrocarbon gauche-trans energy gap — enough that long alkanes and lipid\n", "tails freeze into a gel far above their experimental melting points. L-OPLS\n", "(Siu, Pluhackova & Böckmann, *J. Chem. Theory Comput.* **8**, 1459, 2012)\n", "fixed this by refitting the hydrocarbon torsions to MP2/aug-cc-pVTZ dihedral\n", "scans of hexane (their Fig. 3), plus small nonbonded adjustments.\n", "\n", "Because the `xnn` OPLS implementation is an ordinary differentiable PyTorch\n", "module, that kind of reparameterization is a gradient-descent problem, in\n", "exactly the same workflow used for ReaxFF refits. This notebook\n", "\n", "1. compares the hexane central-torsion profile of **OPLS-AA** and the\n", " **L-OPLS** library shipped with `xnn` (`lopls.frc`, layered over the\n", " OPLS-AA distribution; the paper's headline figure). Both type the\n", " molecule from the SMARTS templates in their parameter files;\n", "2. *re-derives* the L-OPLS `C-C-C-C` torsion (the `opls_18` alkane-carbon\n", " quadruple) from data: starting from OPLS-AA with\n", " `trainable=(\"dihedral_v\",)`, the torsion Fourier coefficients are fit to\n", " reference conformer energies (here generated with the L-OPLS torsion\n", " standing in for the paper's MP2 scans);\n", "3. exports the trained parameters back to a `.frc` force-field file and runs\n", " a short NVE trajectory as a sanity check." ] }, { "cell_type": "markdown", "id": "fa1e1499", "metadata": {}, "source": [ "## 0. Setup" ] }, { "cell_type": "code", "execution_count": 1, "id": "eac69cf0", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:10.881696Z", "iopub.status.busy": "2026-09-15T19:21:10.881583Z", "iopub.status.idle": "2026-09-15T19:21:13.792522Z", "shell.execute_reply": "2026-09-15T19:21:13.791307Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "xnn: 0.1.0 | torch: 2.5.1+cu121\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import math\n", "import os\n", "import numpy as np\n", "import torch\n", "import matplotlib.pyplot as plt\n", "\n", "torch.set_default_dtype(torch.float64)\n", "torch.manual_seed(0)\n", "rng = np.random.default_rng(0)\n", "\n", "from ase import Atoms, units\n", "from ase.constraints import FixInternals\n", "from ase.md.velocitydistribution import MaxwellBoltzmannDistribution\n", "from ase.md.verlet import VelocityVerlet\n", "from ase.optimize import BFGS\n", "\n", "import xnn\n", "from xnn.common.data import collate, structure_to_graph\n", "from xnn.common.deploy import XNNCalculator\n", "from xnn.common.models import ForceStressOutput\n", "from xnn.ffnn.models import OPLS, builtin_library\n", "from xnn.ffnn.models.oplslib import KCAL_TO_EV\n", "\n", "EV_TO_KJ = 96.48533212331\n", "print(\"xnn:\", xnn.__version__, \"| torch:\", torch.__version__)" ] }, { "cell_type": "markdown", "id": "4d3f474b", "metadata": {}, "source": [ "## 1. Hexane with the two parameter sets\n", "\n", "L-OPLS introduced per-connectivity nonbonded types (`lopls_CT_CH3`,\n", "`lopls_HC_CH2`, ...) with adjusted charges and a softer methylene-hydrogen\n", "epsilon, and refit torsions given in the paper's Table 2 — all of which the\n", "built-in `\"lopls\"` library carries. Bonds and angles are the unchanged\n", "OPLS-AA values.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "f598e081", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:13.794833Z", "iopub.status.busy": "2026-09-15T19:21:13.794506Z", "iopub.status.idle": "2026-09-15T19:21:14.119398Z", "shell.execute_reply": "2026-09-15T19:21:14.118564Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OPLS-AA types: ['opls_80', 'opls_81', 'opls_85']\n", "L-OPLS types: ['lopls_CT_CH2', 'lopls_CT_CH3', 'lopls_HC_CH2', 'lopls_HC_CH3']\n", "hexane: 45 dihedrals, 45 1,4 pairs\n" ] } ], "source": [ "def ideal_alkane(n, seed=42):\n", " \"\"\"A rough all-anti alkane C_nH_{2n+2}: zig-zag backbone + jittered H.\"\"\"\n", " r, ang = 1.529, math.radians(112.7)\n", " pos = [np.zeros(3)]\n", " up = True\n", " for _ in range(1, n):\n", " v = np.array([math.cos(ang / 2), (1 if up else -1) * math.sin(ang / 2), 0.0])\n", " pos.append(pos[-1] + r * v)\n", " up = not up\n", " jit = np.random.default_rng(seed)\n", " H, hb = [], []\n", " for i, p in enumerate(pos):\n", " for k in range(3 if i in (0, n - 1) else 2):\n", " phi = 2 * math.pi * k / 3 + 0.5 * i\n", " H.append(p + 1.09 * np.array([0.3 * (-1 if i == 0 else 1 if i == n - 1 else 0),\n", " 0.7 * math.cos(phi), 0.9 * math.sin(phi)])\n", " + 0.05 * jit.standard_normal(3))\n", " hb.append(i)\n", " z = [6] * n + [1] * len(H)\n", " bonds = [(i, i + 1) for i in range(n - 1)] + [(hb[k], n + k) for k in range(len(H))]\n", " return np.array(list(pos) + H), z, bonds, hb\n", "\n", "\n", "pos0, z, bonds, hb = ideal_alkane(6)\n", "# atom types come from each library's SMARTS templates; the topology is the\n", "# same (derived from the bonds), only the type names differ\n", "top = OPLS.from_atoms((pos0, z), \"oplsaa\", bonds=bonds).topology\n", "top_lo = OPLS.from_atoms((pos0, z), \"lopls\", bonds=bonds).topology\n", "print(\"OPLS-AA types:\", sorted(set(top.types)))\n", "print(\"L-OPLS types: \", sorted(set(top_lo.types)))\n", "KEY = \"opls_18-opls_18-opls_18-opls_18\" # the alkane C-C-C-C torsion\n", "# the fragment rotated by the dihedral driver: everything past the C2-C3 bond\n", "frag = [4, 5] + [6 + k for k in range(len(hb)) if hb[k] >= 3]\n", "print(f\"hexane: {len(top.dihedrals)} dihedrals, {len(top.pairs14)} 1,4 pairs\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "3d51bad8", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:14.121187Z", "iopub.status.busy": "2026-09-15T19:21:14.121060Z", "iopub.status.idle": "2026-09-15T19:21:42.997506Z", "shell.execute_reply": "2026-09-15T19:21:42.996852Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gauche-trans energy gap: OPLS-AA 5.10 kJ/mol, L-OPLS 1.88 kJ/mol\n", "(Siu et al.: OPLS-AA ~4.5 kJ/mol, MP2 target / L-OPLS ~2.1 kJ/mol)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def relaxed_scan(topology, library, angles_deg, fmax=1e-5):\n", " \"\"\"Relaxed scan of the central C-C-C-C dihedral (kJ/mol, relative).\"\"\"\n", " model = OPLS(library, topology, cutoff=50.0)\n", " calc = lambda: XNNCalculator(ForceStressOutput(model), cutoff=model.cutoff)\n", " ref = Atoms(numbers=z, positions=pos0 + 0.03 * rng.standard_normal((len(z), 3)))\n", " ref.calc = calc()\n", " BFGS(ref, logfile=None).run(fmax=fmax, steps=5000)\n", " energies = {}\n", " for a in angles_deg:\n", " w = ref.copy(); w.calc = calc()\n", " w.set_dihedral(1, 2, 3, 4, a, indices=frag)\n", " w.rattle(0.004, seed=2) # break eclipsed-methyl saddle symmetry\n", " w.set_constraint(FixInternals(dihedrals_deg=[[a, [1, 2, 3, 4]]]))\n", " BFGS(w, logfile=None).run(fmax=fmax, steps=5000)\n", " energies[a] = w.get_potential_energy() * EV_TO_KJ\n", " e0 = min(energies.values())\n", " return {a: e - e0 for a, e in energies.items()}\n", "\n", "\n", "angles = list(range(0, 181, 15))\n", "prof_aa = relaxed_scan(top, builtin_library(\"oplsaa\"), angles)\n", "prof_lo = relaxed_scan(top_lo, builtin_library(\"lopls\"), angles)\n", "\n", "print(f\"gauche-trans energy gap: OPLS-AA {prof_aa[60]:.2f} kJ/mol, \"\n", " f\"L-OPLS {prof_lo[60]:.2f} kJ/mol\")\n", "print(\"(Siu et al.: OPLS-AA ~4.5 kJ/mol, MP2 target / L-OPLS ~2.1 kJ/mol)\")\n", "assert 1.5 < prof_lo[60] < 2.6 and prof_aa[60] > 4.0\n", "\n", "fig, ax = plt.subplots(figsize=(6.4, 4.2))\n", "ax.plot(angles, [prof_aa[a] for a in angles], \"o-\", label=\"OPLS-AA\")\n", "ax.plot(angles, [prof_lo[a] for a in angles], \"s-\", label=\"L-OPLS\")\n", "ax.set_xlabel(\"hexane central C-C-C-C dihedral (deg)\")\n", "ax.set_ylabel(\"relative energy (kJ/mol)\")\n", "ax.set_title(\"Relaxed hexane torsion profile (cf. Siu et al. 2012, Fig. 3)\")\n", "ax.legend()\n", "fig.tight_layout()\n", "fig.savefig(\"opls_lopls_hexane_profiles.png\", dpi=150)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "76b99c8c", "metadata": {}, "source": [ "The halved gauche-trans gap is the entire L-OPLS story: OPLS-AA's ~4.5\n", "kJ/mol overpopulates *trans*, packing long chains into a gel; L-OPLS's ~2\n", "kJ/mol matches the MP2 reference and keeps liquid alkanes liquid.\n", "\n", "## 2. Reference data for the refit\n", "\n", "The paper fit the torsion to MP2/aug-cc-pVTZ energies of hexane\n", "conformations. To make this notebook self-contained *and* give the fit a\n", "known right answer, the reference energies are generated with a \"reference\n", "potential\": OPLS-AA with only its `CT-CT-CT-CT` torsion replaced by the\n", "L-OPLS one. The training set is 48 hexane conformations — rigid rotations\n", "of the central dihedral every 15° plus Gaussian jitter, the same kind of\n", "coverage an *ab initio* scan provides.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "f8abea41", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:42.999135Z", "iopub.status.busy": "2026-09-15T19:21:42.999019Z", "iopub.status.idle": "2026-09-15T19:21:44.397373Z", "shell.execute_reply": "2026-09-15T19:21:44.396821Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "48 training conformations, energy spread 87.6 kJ/mol\n" ] } ], "source": [ "ref_lib = builtin_library(\"oplsaa\")\n", "ref_lib.dihedral_types[KEY] = dict(builtin_library(\"lopls\").dihedral_types[KEY])\n", "reference = OPLS(ref_lib, top, cutoff=30.0)\n", "\n", "# relaxed OPLS-AA hexane as the base geometry\n", "base_model = OPLS(\"oplsaa\", top, cutoff=30.0)\n", "base = Atoms(numbers=z, positions=pos0 + 0.03 * rng.standard_normal((len(z), 3)))\n", "base.calc = XNNCalculator(ForceStressOutput(base_model), cutoff=30.0)\n", "BFGS(base, logfile=None).run(fmax=1e-4, steps=3000)\n", "\n", "graphs = []\n", "for a in range(0, 360, 15):\n", " w = base.copy()\n", " w.set_dihedral(1, 2, 3, 4, a, indices=frag)\n", " for _ in range(2):\n", " p = w.get_positions() + 0.03 * rng.standard_normal((len(z), 3))\n", " graphs.append(structure_to_graph(\n", " {\"pos\": torch.tensor(p), \"atomic_numbers\": torch.tensor(z)},\n", " cutoff=30.0))\n", "batch = collate(graphs)\n", "target = reference(batch)[\"energy\"].detach()\n", "print(f\"{batch.num_graphs} training conformations, \"\n", " f\"energy spread {float(target.max() - target.min()) * EV_TO_KJ:.1f} kJ/mol\")" ] }, { "cell_type": "markdown", "id": "a8eb92bf", "metadata": {}, "source": [ "## 3. Gradient-descent refit of `CT-CT-CT-CT`\n", "\n", "`trainable=(\"dihedral_v\",)` exposes the dihedral Fourier table to the\n", "optimizer. Like the paper — which refit only the backbone torsion and kept\n", "the hydrogen ones — a gradient mask restricts the update to the\n", "`CT-CT-CT-CT` row. Everything else is a plain PyTorch loop on the energy\n", "mean-squared error.\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "82fcc697", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:44.398728Z", "iopub.status.busy": "2026-09-15T19:21:44.398512Z", "iopub.status.idle": "2026-09-15T19:21:51.430496Z", "shell.execute_reply": "2026-09-15T19:21:51.429691Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final RMSE: 2.65e-14 kJ/mol\n" ] } ], "source": [ "model = OPLS(\"oplsaa\", top, cutoff=30.0, trainable=(\"dihedral_v\",))\n", "row = model.ff.dihedral_keys.index(KEY)\n", "mask = torch.zeros_like(model.ff.params[\"dihedral_v\"])\n", "mask[row] = 1.0\n", "model.ff.params[\"dihedral_v\"].register_hook(lambda g: g * mask)\n", "\n", "opt = torch.optim.Adam([model.ff.params[\"dihedral_v\"]], lr=2e-3)\n", "losses = []\n", "for epoch in range(600):\n", " opt.zero_grad()\n", " loss = (model(batch)[\"energy\"] - target).pow(2).mean()\n", " loss.backward()\n", " opt.step()\n", " losses.append(float(loss))\n", "\n", "fig, ax = plt.subplots(figsize=(5.6, 3.6))\n", "ax.semilogy(np.array(losses) * EV_TO_KJ ** 2)\n", "ax.set_xlabel(\"epoch\")\n", "ax.set_ylabel(\"energy MSE ((kJ/mol)$^2$)\")\n", "ax.set_title(\"Torsion refit convergence\")\n", "fig.tight_layout()\n", "fig.savefig(\"opls_refit_loss.png\", dpi=150)\n", "plt.show()\n", "print(f\"final RMSE: {math.sqrt(losses[-1]) * EV_TO_KJ:.2e} kJ/mol\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "5c18e6ba", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:51.432328Z", "iopub.status.busy": "2026-09-15T19:21:51.432209Z", "iopub.status.idle": "2026-09-15T19:21:51.516091Z", "shell.execute_reply": "2026-09-15T19:21:51.515364Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "coefficient OPLS-AA start refit L-OPLS\n", "V0 0.0000 0.0000 0.0000\n", "V1 1.3000 0.6447 0.6447\n", "V2 -0.0500 -0.2143 -0.2143\n", "V3 0.2000 0.1782 0.1782\n", "V4 0.0000 0.0000 0.0000\n", "\n", "the refit recovers the published L-OPLS torsion (kcal/mol)\n" ] } ], "source": [ "learned = (model.ff.params[\"dihedral_v\"][row] / KCAL_TO_EV).detach()\n", "lopls_v = builtin_library(\"lopls\").dihedral_types[KEY][\"v\"]\n", "start_v = builtin_library(\"oplsaa\").dihedral_types[KEY][\"v\"]\n", "print(f\"{'coefficient':<12} {'OPLS-AA start':>14} {'refit':>10} {'L-OPLS':>10}\")\n", "for k in range(5):\n", " print(f\"V{k:<11} {start_v[k]:>14.4f} {float(learned[k]):>10.4f} \"\n", " f\"{lopls_v[k]:>10.4f}\")\n", "# V1..V4 are the physical coefficients; the constant V0 of the published RB\n", "# form has no column in the .frc torsion form and is not in the reference\n", "assert max(abs(float(learned[k]) - lopls_v[k]) for k in range(1, 5)) < 1e-3\n", "print(\"\\nthe refit recovers the published L-OPLS torsion (kcal/mol)\")" ] }, { "cell_type": "markdown", "id": "cb5af4cc", "metadata": {}, "source": [ "The optimizer lands on the published L-OPLS Fourier coefficients to\n", "essentially machine precision — including the constant `V0`, which L-OPLS\n", "carries to make its Fourier and Ryckaert-Bellemans forms match exactly.\n", "Against real *ab initio* data the loop is identical; only `target` changes\n", "(and `xnn.common.train.Trainer` runs the same fit with batching,\n", "validation and checkpoints).\n", "\n", "## 4. Export, and an NVE sanity check\n", "\n", "`export_library()` writes the trained tensors back to an `OPLSLibrary`\n", "(kcal/mol, Angstrom, degrees), which round-trips through JSON. A short\n", "microcanonical trajectory with the trained force field checks that the\n", "refit potential is smooth and its autograd forces conserve energy.\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "0d41cd55", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:51.517370Z", "iopub.status.busy": "2026-09-15T19:21:51.517259Z", "iopub.status.idle": "2026-09-15T19:21:51.578269Z", "shell.execute_reply": "2026-09-15T19:21:51.577572Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "saved runs/opls_lopls_refit/opls_trained.{frc,json}\n", "refit C-C-C-C: [0.0, 0.6447, -0.2143, 0.1782, 0.0]\n" ] } ], "source": [ "os.makedirs(\"runs/opls_lopls_refit\", exist_ok=True)\n", "trained_lib = model.export_library()\n", "trained_lib.name = \"oplsaa-refit-cccc\"\n", "trained_lib.save_frc(\"runs/opls_lopls_refit/opls_trained.frc\") # standard .frc\n", "trained_lib.save(\"runs/opls_lopls_refit/opls_trained.json\") # native JSON\n", "print(\"saved runs/opls_lopls_refit/opls_trained.{frc,json}\")\n", "print(\"refit C-C-C-C:\", [round(v, 4) for v in trained_lib.dihedral_types[KEY][\"v\"]])" ] }, { "cell_type": "code", "execution_count": 8, "id": "ad0fe281", "metadata": { "execution": { "iopub.execute_input": "2026-09-15T19:21:51.579602Z", "iopub.status.busy": "2026-09-15T19:21:51.579489Z", "iopub.status.idle": "2026-09-15T19:21:58.965225Z", "shell.execute_reply": "2026-09-15T19:21:58.964460Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NVE, 1 ps @ 0.5 fs: total-energy drift +1.227 meV (fluctuation 0.517 meV), = 135 K\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "md_model = OPLS(\"runs/opls_lopls_refit/opls_trained.frc\", top, cutoff=12.0)\n", "atoms = base.copy()\n", "atoms.calc = XNNCalculator(ForceStressOutput(md_model), cutoff=md_model.cutoff)\n", "MaxwellBoltzmannDistribution(atoms, temperature_K=300, rng=np.random.default_rng(7))\n", "\n", "dyn = VelocityVerlet(atoms, timestep=0.5 * units.fs)\n", "etot, temps = [], []\n", "def log():\n", " etot.append(atoms.get_potential_energy() + atoms.get_kinetic_energy())\n", " temps.append(atoms.get_temperature())\n", "dyn.attach(log, interval=5)\n", "dyn.run(2000)\n", "\n", "etot = np.array(etot)\n", "drift = (etot[-1] - etot[0]) * 1000\n", "print(f\"NVE, 1 ps @ 0.5 fs: total-energy drift {drift:+.3f} meV \"\n", " f\"(fluctuation {etot.std() * 1000:.3f} meV), = {np.mean(temps):.0f} K\")\n", "assert abs(drift) < 2.0\n", "\n", "fig, ax = plt.subplots(figsize=(5.6, 3.4))\n", "ax.plot(np.arange(len(etot)) * 5 * 0.5 / 1000, (etot - etot[0]) * 1000)\n", "ax.set_xlabel(\"time (ps)\")\n", "ax.set_ylabel(r\"$E_{tot} - E_{tot}(0)$ (meV)\")\n", "ax.set_title(\"NVE energy conservation, refit hexane\")\n", "fig.tight_layout()\n", "fig.savefig(\"opls_refit_nve.png\", dpi=150)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7b0024a8", "metadata": {}, "source": [ "## Summary\n", "\n", "* The built-in `\"lopls\"` library reproduces the L-OPLS physics: the hexane\n", " gauche-trans gap drops from ~5 kJ/mol (OPLS-AA) to ~2 kJ/mol, the\n", " paper's central result.\n", "* Refitting a torsion is a standard PyTorch loop: mark `dihedral_v`\n", " trainable, mask the rows to refit, minimize the energy MSE. The loop\n", " recovers the published L-OPLS `CT-CT-CT-CT` coefficients to machine\n", " precision from conformer energies alone.\n", "* Trained parameters export back to a portable JSON library, and the refit\n", " force field conserves energy in NVE dynamics through `XNNCalculator`.\n" ] } ], "metadata": { "kernelspec": { "display_name": "xnn (.venv)", "language": "python", "name": "xnn" }, "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 }