From 0ea657322bce81c7516fbbc789e4ac97a18ff3a9 Mon Sep 17 00:00:00 2001
From: Marvin Friede <51965259+marvinfriede@users.noreply.github.com>
Date: Sun, 3 Aug 2025 19:13:27 +0200
Subject: [PATCH 1/2] Batched functorch Hessian (#89)

---
 .github/workflows/release.yaml         |   4 +-
 .pre-commit-config.yaml                |  10 +--
 docs/source/modules/data/index.rst     |   1 -
 docs/source/modules/data/radii.rst     |   2 -
 docs/source/modules/typing/builtin.rst |   2 -
 docs/source/modules/typing/index.rst   |   1 -
 examples/batch.py                      |  24 ++----
 examples/hessian.py                    | 105 +++++++++++++++++++++++++
 examples/single.py                     |   4 +-
 setup.cfg                              |   2 +-
 src/tad_dftd3/damping/atm.py           |   7 +-
 src/tad_dftd3/damping/rational.py      |   6 +-
 src/tad_dftd3/data/__init__.py         |   3 +-
 src/tad_dftd3/data/r4r2.py             |  89 +++++++++++++--------
 src/tad_dftd3/data/radii.py            |  63 ---------------
 src/tad_dftd3/data/vdw-d3.pt           | Bin 87275 -> 0 bytes
 src/tad_dftd3/disp.py                  |  43 ++++++----
 src/tad_dftd3/model/c6.py              | 102 ++++++++++++++++++++----
 src/tad_dftd3/model/weights.py         |  11 ++-
 src/tad_dftd3/reference.py             |   5 +-
 src/tad_dftd3/typing/__init__.py       |   1 -
 src/tad_dftd3/typing/builtin.py        |  24 ------
 test/conftest.py                       |   7 +-
 test/test_disp/test_dftd3.py           |   9 ++-
 test/test_disp/test_disp.py            |  19 +++--
 test/test_disp/test_special.py         |   9 ++-
 test/test_grad/test_hessian.py         |  70 ++++++++++++++++-
 test/test_grad/test_param.py           |   6 +-
 test/test_grad/test_pos.py             |   6 +-
 test/test_model/samples.py             |   3 +-
 test/test_model/test_c6.py             |  52 +++++++++++-
 test/test_model/test_load.py           |   7 +-
 test/test_model/test_reference.py      |   5 +-
 test/test_model/test_weights.py        |   2 +-
 34 files changed, 471 insertions(+), 233 deletions(-)
 delete mode 100644 docs/source/modules/data/radii.rst
 delete mode 100644 docs/source/modules/typing/builtin.rst
 create mode 100644 examples/hessian.py
 delete mode 100644 src/tad_dftd3/data/radii.py
 delete mode 100644 src/tad_dftd3/data/vdw-d3.pt
 delete mode 100644 src/tad_dftd3/typing/builtin.py

diff --git a/.github/workflows/release.yaml b/.github/workflows/release.yaml
index 9028cd2..813bb58 100644
--- a/.github/workflows/release.yaml
+++ b/.github/workflows/release.yaml
@@ -140,7 +140,7 @@ jobs:
           merge-multiple: true
 
       - name: Publish to Test PyPI
-        uses: pypa/gh-action-pypi-publish@release/v1
+        uses: pypa/gh-action-pypi-publish@76f52bc884231f62b9a034ebfe128415bbaabdfc  # v1.12
         with:
           repository-url: https://test.pypi.org/legacy/
 
@@ -164,4 +164,4 @@ jobs:
           merge-multiple: true
 
       - name: Publish to PyPI
-        uses: pypa/gh-action-pypi-publish@release/v1
+        uses: pypa/gh-action-pypi-publish@76f52bc884231f62b9a034ebfe128415bbaabdfc  # v1.12
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 81965b1..667bdbb 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -42,7 +42,7 @@ repos:
           ]
 
   - repo: https://github.com/asottile/pyupgrade
-    rev: v3.19.1
+    rev: v3.20.0
     hooks:
       - id: pyupgrade
         args: [--py37-plus, --keep-runtime-typing]
@@ -52,21 +52,21 @@ repos:
     hooks:
       - id: isort
         name: isort (python)
-        args: ["--profile", "black", "--filter-files"]
+        args: ["--profile", "black", "--line-length", "80", "--filter-files"]
 
   - repo: https://github.com/psf/black
     rev: 25.1.0
     hooks:
       - id: black
-        stages: [pre-commit]
+        args: ["--line-length", "80"]
 
   - repo: https://github.com/woodruffw/zizmor-pre-commit
-    rev: v1.5.2
+    rev: v1.11.0
     hooks:
       - id: zizmor
 
   - repo: https://github.com/pre-commit/mirrors-mypy
-    rev: v1.15.0
+    rev: v1.17.1
     hooks:
       - id: mypy
         pass_filenames: false
diff --git a/docs/source/modules/data/index.rst b/docs/source/modules/data/index.rst
index 0593c57..d25a5b6 100644
--- a/docs/source/modules/data/index.rst
+++ b/docs/source/modules/data/index.rst
@@ -5,4 +5,3 @@
 .. toctree::
 
    r4r2
-   radii
diff --git a/docs/source/modules/data/radii.rst b/docs/source/modules/data/radii.rst
deleted file mode 100644
index e0e9ded..0000000
--- a/docs/source/modules/data/radii.rst
+++ /dev/null
@@ -1,2 +0,0 @@
-.. automodule:: tad_dftd3.data.radii
-   :members:
diff --git a/docs/source/modules/typing/builtin.rst b/docs/source/modules/typing/builtin.rst
deleted file mode 100644
index 8f79631..0000000
--- a/docs/source/modules/typing/builtin.rst
+++ /dev/null
@@ -1,2 +0,0 @@
-.. automodule:: tad_dftd3.typing.builtin
-   :members:
diff --git a/docs/source/modules/typing/index.rst b/docs/source/modules/typing/index.rst
index 6c66f2e..b9a2dff 100644
--- a/docs/source/modules/typing/index.rst
+++ b/docs/source/modules/typing/index.rst
@@ -4,6 +4,5 @@
 
 .. toctree::
 
-   builtin
    d3
    pytorch
diff --git a/examples/batch.py b/examples/batch.py
index 935ba27..e87d8a2 100644
--- a/examples/batch.py
+++ b/examples/batch.py
@@ -60,30 +60,18 @@
     )
 )
 ref = d3.reference.Reference()
-rcov = d3.data.COV_D3[numbers]
-rvdw = d3.data.VDW_D3[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
-r4r2 = d3.data.R4R2[numbers]
+rcov = mctc.data.COV_D3()[numbers]
+rvdw = mctc.data.VDW_PAIRWISE()[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
+r4r2 = d3.data.R4R2()[numbers]
 param = {
     "a1": torch.tensor(0.49484001),
     "s8": torch.tensor(0.78981345),
     "a2": torch.tensor(5.73083694),
 }
 
-cn = mctc.ncoord.cn_d3(
-    numbers, positions, counting_function=mctc.ncoord.exp_count, rcov=rcov
-)
-weights = d3.model.weight_references(numbers, cn, ref, d3.model.gaussian_weight)
-c6 = d3.model.atomic_c6(numbers, weights, ref)
-energy = d3.disp.dispersion(
-    numbers,
-    positions,
-    param,
-    c6,
-    rvdw,
-    r4r2,
-    d3.disp.rational_damping,
-)
+energy = d3.dftd3(numbers, positions, param)
 
 torch.set_printoptions(precision=10)
-print(torch.sum(energy, dim=-1))
+print("Expected:", torch.tensor([-0.0014092578, -0.0057840119]))
+print("Actual  :", torch.sum(energy, dim=-1))
 # tensor([-0.0014092578, -0.0057840119])
diff --git a/examples/hessian.py b/examples/hessian.py
new file mode 100644
index 0000000..f77b68f
--- /dev/null
+++ b/examples/hessian.py
@@ -0,0 +1,105 @@
+# SPDX-Identifier: CC0-1.0
+from __future__ import annotations
+
+from typing import Callable
+
+import tad_mctc as mctc
+import torch
+
+import tad_dftd3 as d3
+
+sample1 = dict(
+    numbers=mctc.convert.symbol_to_number("Pb H H H H Bi H H H".split()),
+    positions=torch.tensor(
+        [
+            [-0.00000020988889, -4.98043478877778, +0.00000000000000],
+            [+3.06964045311111, -6.06324400177778, +0.00000000000000],
+            [-1.53482054188889, -6.06324400177778, -2.65838526500000],
+            [-1.53482054188889, -6.06324400177778, +2.65838526500000],
+            [-0.00000020988889, -1.72196703577778, +0.00000000000000],
+            [-0.00000020988889, +4.77334244722222, +0.00000000000000],
+            [+1.35700257511111, +6.70626379422222, -2.35039772300000],
+            [-2.71400388988889, +6.70626379422222, +0.00000000000000],
+            [+1.35700257511111, +6.70626379422222, +2.35039772300000],
+        ]
+    ),
+)
+sample2 = dict(
+    numbers=mctc.convert.symbol_to_number(
+        "C C C C C C I H H H H H S H C H H H".split(" ")
+    ),
+    positions=torch.tensor(
+        [
+            [-1.42754169820131, -1.50508961850828, -1.93430551124333],
+            [+1.19860572924150, -1.66299114873979, -2.03189643761298],
+            [+2.65876001301880, +0.37736955363609, -1.23426391650599],
+            [+1.50963368042358, +2.57230374419743, -0.34128058818180],
+            [-1.12092277855371, +2.71045691257517, -0.25246348639234],
+            [-2.60071517756218, +0.67879949508239, -1.04550707592673],
+            [-2.86169588073340, +5.99660765711210, +1.08394899986031],
+            [+2.09930989272956, -3.36144811062374, -2.72237695164263],
+            [+2.64405246349916, +4.15317840474646, +0.27856972788526],
+            [+4.69864865613751, +0.26922271535391, -1.30274048619151],
+            [-4.63786461351839, +0.79856258572808, -0.96906659938432],
+            [-2.57447518692275, -3.08132039046931, -2.54875517521577],
+            [-5.88211879210329, 11.88491819358157, +2.31866455902233],
+            [-8.18022701418703, 10.95619984550779, +1.83940856333092],
+            [-5.08172874482867, 12.66714386256482, -0.92419491629867],
+            [-3.18311711399702, 13.44626574330220, -0.86977613647871],
+            [-5.07177399637298, 10.99164969235585, -2.10739192258756],
+            [-6.35955320518616, 14.08073002965080, -1.68204314084441],
+        ]
+    ),
+)
+numbers = mctc.batch.pack(
+    (
+        sample1["numbers"],
+        sample2["numbers"],
+    )
+)
+positions = mctc.batch.pack(
+    (
+        sample1["positions"],
+        sample2["positions"],
+    )
+)
+
+param = {
+    "a1": torch.tensor(0.49484001),
+    "s8": torch.tensor(0.78981345),
+    "a2": torch.tensor(5.73083694),
+}
+
+
+def _energy(numbers: torch.Tensor, positions: torch.Tensor) -> torch.Tensor:
+    """
+    Closure over non-tensor argument `param` for `dftd3` function.
+
+    Returns the energy as a scalar, which is required for Hessian computation
+    to obtain the correct shape of ``(..., nat, 3, nat, 3)``.
+    """
+    return d3.dftd3(numbers, positions, param).sum(-1)
+
+
+def hessian(
+    fn: Callable[..., torch.Tensor], argnums: tuple[int] | int = 0
+) -> Callable:
+    """
+    Compute the Hessian using reverse-mode autodiff twice.
+    (Functorch's `hessian` uses forward and backward mode, but forward is
+    not implemented for the custom autograd functions in DFT-D3.)
+    """
+    return torch.func.jacrev(
+        torch.func.jacrev(fn, argnums=argnums), argnums=argnums
+    )
+
+
+hess_fn_single = hessian(_energy, argnums=1)
+hess_fn_batch = torch.func.vmap(hess_fn_single, in_dims=(0, 0))
+
+pos = positions.clone().requires_grad_(True)
+hess = hess_fn_batch(numbers, pos)
+
+print(f"Shape of numbers  : {numbers.shape}")
+print(f"Shape of positions: {positions.shape}")
+print(f"Shape of Hessian  : {hess.shape}")
diff --git a/examples/single.py b/examples/single.py
index 24c2c3f..f0f14c3 100644
--- a/examples/single.py
+++ b/examples/single.py
@@ -4,7 +4,9 @@
 
 import tad_dftd3 as d3
 
-numbers = mctc.convert.symbol_to_number(symbols="C C C C N C S H H H H H".split())
+numbers = mctc.convert.symbol_to_number(
+    symbols="C C C C N C S H H H H H".split()
+)
 positions = torch.tensor(
     [
         [-2.56745685564671, -0.02509985979910, 0.00000000000000],
diff --git a/setup.cfg b/setup.cfg
index 952b8da..1cdd4a3 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -34,7 +34,7 @@ project_urls =
 packages = find:
 install_requires =
     numpy<2
-    tad-mctc
+    tad-mctc==0.5.3
     torch>=1.11,<3
 python_requires = >=3.8, <3.13
 include_package_data = True
diff --git a/src/tad_dftd3/damping/atm.py b/src/tad_dftd3/damping/atm.py
index 52647a6..cd4d38a 100644
--- a/src/tad_dftd3/damping/atm.py
+++ b/src/tad_dftd3/damping/atm.py
@@ -33,9 +33,9 @@
 import torch
 from tad_mctc import storch
 from tad_mctc.batch import real_pairs, real_triples
+from tad_mctc.typing import DD, Tensor
 
 from .. import defaults
-from ..typing import DD, Tensor
 
 __all__ = ["dispersion_atm"]
 
@@ -143,7 +143,10 @@ def dispersion_atm(
     )
 
     ang = torch.where(
-        mask_triples * (r2ij <= cutoff2) * (r2jk <= cutoff2) * (r2jk <= cutoff2),
+        mask_triples
+        * (r2ij <= cutoff2)
+        * (r2jk <= cutoff2)
+        * (r2jk <= cutoff2),
         0.375 * s / r5 + 1.0 / r3,
         torch.tensor(0.0, **dd),
     )
diff --git a/src/tad_dftd3/damping/rational.py b/src/tad_dftd3/damping/rational.py
index 5d08877..739e7ef 100644
--- a/src/tad_dftd3/damping/rational.py
+++ b/src/tad_dftd3/damping/rational.py
@@ -25,12 +25,12 @@
     \dfrac{R^n_{\text{AB}}}{R^n_{\text{AB}} +
     \left( a_1 R_0^{\text{AB}} + a_2 \right)^n}
 """
-from typing import Dict
+from __future__ import annotations
 
 import torch
+from tad_mctc.typing import DD, Tensor
 
 from .. import defaults
-from ..typing import DD, Tensor
 
 __all__ = ["rational_damping"]
 
@@ -39,7 +39,7 @@ def rational_damping(
     order: int,
     distances: Tensor,
     qq: Tensor,
-    param: Dict[str, Tensor],
+    param: dict[str, Tensor],
 ) -> Tensor:
     """
     Rational damped dispersion interaction between pairs.
diff --git a/src/tad_dftd3/data/__init__.py b/src/tad_dftd3/data/__init__.py
index f5645e9..f9ce090 100644
--- a/src/tad_dftd3/data/__init__.py
+++ b/src/tad_dftd3/data/__init__.py
@@ -16,7 +16,6 @@
 Atomic data
 ===========
 
-Data arrays for atomic constants like covalent radii or van-der-Waals radii.
+Data arrays for atomic constants.
 """
 from .r4r2 import *
-from .radii import *
diff --git a/src/tad_dftd3/data/r4r2.py b/src/tad_dftd3/data/r4r2.py
index 559567c..ec6f86a 100644
--- a/src/tad_dftd3/data/r4r2.py
+++ b/src/tad_dftd3/data/r4r2.py
@@ -21,40 +21,65 @@
 Also new super heavies Cn, Nh, Fl, Lv, Og and Am-Rg calculated at
 4c-PBE/Dyall-AE4Z (Dirac 2022).
 """
+from __future__ import annotations
+
 import torch
 
 __all__ = ["R4R2"]
 
 
-# fmt: off
-r4_over_r2 = torch.tensor([
-    0.0000,  # None
-    8.0589, 3.4698,  # H,He
-    29.0974,14.8517,11.8799, 7.8715, 5.5588, 4.7566, 3.8025, 3.1036,  # Li-Ne
-    26.1552,17.2304,17.7210,12.7442, 9.5361, 8.1652, 6.7463, 5.6004,  # Na-Ar
-    29.2012,22.3934,  # K,Ca
-    19.0598,16.8590,15.4023,12.5589,13.4788,  # Sc-
-    12.2309,11.2809,10.5569,10.1428, 9.4907,  # -Zn
-    13.4606,10.8544, 8.9386, 8.1350, 7.1251, 6.1971,  # Ga-Kr
-    30.0162,24.4103,  # Rb,Sr
-    20.3537,17.4780,13.5528,11.8451,11.0355,  # Y-
-    10.1997, 9.5414, 9.0061, 8.6417, 8.9975,  # -Cd
-    14.0834,11.8333,10.0179, 9.3844, 8.4110, 7.5152,  # In-Xe
-    32.7622,27.5708,  # Cs,Ba
-    23.1671,21.6003,20.9615,20.4562,20.1010,19.7475,19.4828,  # La-Eu
-    15.6013,19.2362,17.4717,17.8321,17.4237,17.1954,17.1631,  # Gd-Yb
-    14.5716,15.8758,13.8989,12.4834,11.4421,  # Lu-
-    10.2671, 8.3549, 7.8496, 7.3278, 7.4820,  # -Hg
-    13.5124,11.6554,10.0959, 9.7340, 8.8584, 8.0125,  # Tl-Rn
-    29.8135,26.3157,  # Fr,Ra
-    19.1885,15.8542,16.1305,15.6161,15.1226,16.1576,14.6510,  # Ac-Am
-    14.7178,13.9108,13.5623,13.2326,12.9189,12.6133,12.3142,  # Cm-No
-    14.8326,12.3771,10.6378, 9.3638, 8.2297,  # Lr-
-    7.5667, 6.9456, 6.3946, 5.9159, 5.4929,  # -Cn
-    6.7286, 6.5144,10.9169,10.3600, 9.4723, 8.6641,  # Nh-Og
-])  # fmt: on
-"""Actually calculated r⁴ over r² expectation values."""
-# fmt: on
-
-R4R2 = torch.sqrt(0.5 * (r4_over_r2 * torch.sqrt(torch.arange(r4_over_r2.shape[0]))))
-"""r⁴ over r² expectation values."""
+def R4R2(
+    dtype: torch.dtype | None = None, device: torch.device | None = None
+) -> torch.Tensor:
+    """
+    Returns the r⁴ over r² expectation values as a tensor.
+
+    Parameters
+    ----------
+    dtype : torch.dtype | None, optional
+        The desired data type of the returned tensor. Defaults to None.
+    device : torch.device | None, optional
+        The desired device of the returned tensor. Defaults to None.
+
+    Returns
+    -------
+    Tensor
+        A tensor containing the r⁴ over r² expectation values.
+    """
+
+    # Actually calculated r⁴ over r² expectation values
+    # fmt: off
+    _r4_over_r2 = [
+        0.0000,  # None
+        8.0589, 3.4698,  # H,He
+        29.0974,14.8517,11.8799, 7.8715, 5.5588, 4.7566, 3.8025, 3.1036,  # Li-Ne
+        26.1552,17.2304,17.7210,12.7442, 9.5361, 8.1652, 6.7463, 5.6004,  # Na-Ar
+        29.2012,22.3934,  # K,Ca
+        19.0598,16.8590,15.4023,12.5589,13.4788,  # Sc-
+        12.2309,11.2809,10.5569,10.1428, 9.4907,  # -Zn
+        13.4606,10.8544, 8.9386, 8.1350, 7.1251, 6.1971,  # Ga-Kr
+        30.0162,24.4103,  # Rb,Sr
+        20.3537,17.4780,13.5528,11.8451,11.0355,  # Y-
+        10.1997, 9.5414, 9.0061, 8.6417, 8.9975,  # -Cd
+        14.0834,11.8333,10.0179, 9.3844, 8.4110, 7.5152,  # In-Xe
+        32.7622,27.5708,  # Cs,Ba
+        23.1671,21.6003,20.9615,20.4562,20.1010,19.7475,19.4828,  # La-Eu
+        15.6013,19.2362,17.4717,17.8321,17.4237,17.1954,17.1631,  # Gd-Yb
+        14.5716,15.8758,13.8989,12.4834,11.4421,  # Lu-
+        10.2671, 8.3549, 7.8496, 7.3278, 7.4820,  # -Hg
+        13.5124,11.6554,10.0959, 9.7340, 8.8584, 8.0125,  # Tl-Rn
+        29.8135,26.3157,  # Fr,Ra
+        19.1885,15.8542,16.1305,15.6161,15.1226,16.1576,14.6510,  # Ac-Am
+        14.7178,13.9108,13.5623,13.2326,12.9189,12.6133,12.3142,  # Cm-No
+        14.8326,12.3771,10.6378, 9.3638, 8.2297,  # Lr-
+        7.5667, 6.9456, 6.3946, 5.9159, 5.4929,  # -Cn
+        6.7286, 6.5144,10.9169,10.3600, 9.4723, 8.6641,  # Nh-Og
+    ]
+    # fmt: on
+
+    sqrtz = torch.sqrt(
+        torch.arange(len(_r4_over_r2), device=device, dtype=dtype)
+    )
+    return torch.sqrt(
+        0.5 * (torch.tensor(_r4_over_r2, device=device, dtype=dtype) * sqrtz)
+    )
diff --git a/src/tad_dftd3/data/radii.py b/src/tad_dftd3/data/radii.py
deleted file mode 100644
index ac729c3..0000000
--- a/src/tad_dftd3/data/radii.py
+++ /dev/null
@@ -1,63 +0,0 @@
-# This file is part of tad-dftd3.
-# SPDX-Identifier: Apache-2.0
-#
-# Licensed under the Apache License, Version 2.0 (the "License");
-# you may not use this file except in compliance with the License.
-# You may obtain a copy of the License at
-#
-#     http://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing, software
-# distributed under the License is distributed on an "AS IS" BASIS,
-# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-# See the License for the specific language governing permissions and
-# limitations under the License.
-"""
-Data: Radii
-===========
-
-Data arrays for atomic constants like covalent radii or van-der-Waals radii.
-
-The `vdw_rad_d3` were previously stored explicitly in one list and then
-reshaped to the required `(MAX_ELEMENT, MAX_ELEMENT)` tensor. For the old
-version, see older commits (e.g. https://github.com/dftd3/tad-dftd3/blob/ecc50f19adb8aa8baa38a188d04228c4f26975d6/src/tad_dftd3/data/radii.py)
-"""
-import os.path as op
-from typing import Optional
-
-import torch
-from tad_mctc._version import __tversion__
-from tad_mctc.data.radii import COV_D3
-
-from ..typing import Any, Tensor
-
-__all__ = ["COV_D3", "VDW_D3"]
-
-
-def _load_vdw_rad_d3(
-    dtype: torch.dtype = torch.double, device: Optional[torch.device] = None
-) -> Tensor:
-    """
-    Load reference VDW radii from file.
-
-    Parameters
-    ----------
-    dtype : torch.dtype, optional
-        Floating point precision for tensor. Defaults to `torch.double`.
-    device : Optional[torch.device], optional
-        Device of tensor. Defaults to None.
-
-    Returns
-    -------
-    Tensor
-        VDW radii.
-    """
-    kwargs: dict[str, Any] = {"map_location": device}
-    if __tversion__ > (1, 12, 1):  # pragma: no cover
-        kwargs["weights_only"] = True
-
-    path = op.join(op.dirname(__file__), "vdw-d3.pt")
-    return torch.load(path, **kwargs).type(dtype=dtype)
-
-
-VDW_D3 = _load_vdw_rad_d3()
diff --git a/src/tad_dftd3/data/vdw-d3.pt b/src/tad_dftd3/data/vdw-d3.pt
deleted file mode 100644
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diff --git a/src/tad_dftd3/disp.py b/src/tad_dftd3/disp.py
index e686267..1beca60 100644
--- a/src/tad_dftd3/disp.py
+++ b/src/tad_dftd3/disp.py
@@ -54,17 +54,19 @@
 """
 from __future__ import annotations
 
+from typing import Any
+
 import torch
 from tad_mctc import storch
+from tad_mctc.autograd import is_functorch_tensor
 from tad_mctc.batch import real_pairs
-from tad_mctc.data import pse
+from tad_mctc.data import pse, radii
 
 from . import data, defaults, model, ncoord
 from .damping import dispersion_atm, rational_damping
 from .reference import Reference
 from .typing import (
     DD,
-    Any,
     CountingFunction,
     DampingFunction,
     Tensor,
@@ -125,22 +127,25 @@ def dftd3(
     """
     dd: DD = {"device": positions.device, "dtype": positions.dtype}
 
-    if torch.max(numbers) >= defaults.MAX_ELEMENT:
-        raise ValueError(
-            f"No D3 parameters available for Z > {defaults.MAX_ELEMENT-1} "
-            f"({pse.Z2S[defaults.MAX_ELEMENT]})."
-        )
+    if not is_functorch_tensor(numbers):
+        if torch.max(numbers) >= defaults.MAX_ELEMENT:
+            raise ValueError(
+                f"No D3 parameters available for Z > {defaults.MAX_ELEMENT-1} "
+                f"({pse.Z2S[defaults.MAX_ELEMENT]})."
+            )
 
     if cutoff is None:
         cutoff = torch.tensor(defaults.D3_DISP_CUTOFF, **dd)
     if ref is None:
         ref = Reference(**dd)
     if rcov is None:
-        rcov = data.COV_D3.to(**dd)[numbers]
+        rcov = radii.COV_D3(**dd)[numbers]
     if rvdw is None:
-        rvdw = data.VDW_D3.to(**dd)[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
+        rvdw = radii.VDW_PAIRWISE(**dd)[
+            numbers.unsqueeze(-1), numbers.unsqueeze(-2)
+        ]
     if r4r2 is None:
-        r4r2 = data.R4R2.to(**dd)[numbers]
+        r4r2 = data.R4R2(**dd)[numbers]
 
     cn = ncoord.cn_d3(
         numbers, positions, counting_function=counting_function, rcov=rcov
@@ -202,7 +207,7 @@ def dispersion(
     if cutoff is None:
         cutoff = torch.tensor(defaults.D3_DISP_CUTOFF, **dd)
     if r4r2 is None:
-        r4r2 = data.R4R2.to(**dd)[numbers]
+        r4r2 = data.R4R2(**dd)[numbers]
 
     if numbers.shape != positions.shape[:-1]:
         raise ValueError(
@@ -212,11 +217,13 @@ def dispersion(
         raise ValueError(
             "Shape of expectation values is not consistent with atomic numbers.",
         )
-    if torch.max(numbers) >= defaults.MAX_ELEMENT:
-        raise ValueError(
-            f"No D3 parameters available for Z > {defaults.MAX_ELEMENT - 1} "
-            f"({pse.Z2S[defaults.MAX_ELEMENT]})."
-        )
+
+    if not is_functorch_tensor(numbers):
+        if torch.max(numbers) >= defaults.MAX_ELEMENT:
+            raise ValueError(
+                f"No D3 parameters available for Z > {defaults.MAX_ELEMENT-1} "
+                f"({pse.Z2S[defaults.MAX_ELEMENT]})."
+            )
 
     # two-body dispersion
     energy = dispersion2(
@@ -226,7 +233,9 @@ def dispersion(
     # three-body dispersion
     if "s9" in param and param["s9"] != 0.0:
         if rvdw is None:
-            rvdw = data.VDW_D3.to(**dd)[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
+            rvdw = radii.VDW_PAIRWISE(**dd)[
+                numbers.unsqueeze(-1), numbers.unsqueeze(-2)
+            ]
 
         energy += dispersion3(numbers, positions, param, c6, rvdw, cutoff)
 
diff --git a/src/tad_dftd3/model/c6.py b/src/tad_dftd3/model/c6.py
index a146202..78805a6 100644
--- a/src/tad_dftd3/model/c6.py
+++ b/src/tad_dftd3/model/c6.py
@@ -23,13 +23,15 @@
 """
 from __future__ import annotations
 
+from typing import NamedTuple, Protocol
+
 import torch
 from tad_mctc._version import __tversion__
 from tad_mctc.math import einsum
 from tad_mctc.tools import memory
+from tad_mctc.typing import Callable, Tensor
 
 from ..reference import Reference
-from ..typing import Callable, Protocol, Tensor
 
 __all__ = ["atomic_c6"]
 
@@ -260,13 +262,18 @@ def _atomic_c6_chunked(
         # (..., n1, n2, r1, r2) * (..., n1, r1) * (..., n2, r2) -> (..., n1, n2)
         contribution = _einsum(rc6_chunk, weights_chunk, weights)
 
-        # Add contributions to the correct slice of the output tensor
-        c6_output[..., start:end, :] += contribution
+        # Add contributions to the correct slice of the output tensor with
+        # out-of-place aggregation along the "i" axis. In-place aggregation:
+        # c6_output[..., start:end, :] += contribution
+        idx = torch.arange(start, end, device=numbers.device)
+        c6_output = torch.index_add(
+            c6_output, dim=-2, index=idx, source=contribution
+        )
 
     return c6_output
 
 
-# custom autograd functions
+# typing
 
 
 class CTX(Protocol):
@@ -276,6 +283,14 @@ class CTX(Protocol):
     reference: Reference
 
 
+class VmapInfo(NamedTuple):
+    batch_size: int
+    randomness: str
+
+
+# custom autograd functions
+
+
 class AtomicC6Base(torch.autograd.Function):
     """
     Base class for the version-specific autograd function for atomic C6.
@@ -283,7 +298,9 @@ class AtomicC6Base(torch.autograd.Function):
     """
 
     @staticmethod
-    def backward(ctx: CTX, grad_out: Tensor) -> tuple[None, Tensor, None, None]:
+    def backward(
+        ctx: CTX, grad_outputs: Tensor
+    ) -> tuple[None, Tensor, None, None]:
         numbers, weights = ctx.saved_tensors
         chunk_size = ctx.chunk_size
         ref = ctx.reference
@@ -304,14 +321,14 @@ def backward(ctx: CTX, grad_out: Tensor) -> tuple[None, Tensor, None, None]:
             g_jb = einsum("...ijab,...ia->...ijb", rc6, weights)
 
             # vjp: (..., n1, n2) * (..., n1, n2, r2) -> (..., n2, r2)
-            _gj = einsum("...ij,...ijb->...jb", grad_out, g_jb)
+            _gj = einsum("...ij,...ijb->...jb", grad_outputs, g_jb)
 
             # ∂c_ij/∂w_ia = ∑b w_jb * c_ijab
             # (..., n1, n2, r1, r2) * (..., n2, r2) -> (..., n1, n2, r1)
             g_ia = einsum("...ijab,...jb->...ija", rc6, weights)
 
             # vjp: (..., n1, n2) * (..., n1, n2, r1) -> (..., n1, r1)
-            _gi = einsum("...ij,...ija->...ia", grad_out, g_ia)
+            _gi = einsum("...ij,...ija->...ia", grad_outputs, g_ia)
 
             weights_bar = _gi + _gj
 
@@ -322,13 +339,14 @@ def backward(ctx: CTX, grad_out: Tensor) -> tuple[None, Tensor, None, None]:
         #######################
 
         nat = weights.shape[-2]
-        weights_bar = torch.zeros_like(weights)
+        gi_accum = torch.zeros_like(weights)
+        gj_accum = torch.zeros_like(weights)
 
         for start in range(0, nat, chunk_size):
             end = min(start + chunk_size, nat)
 
             # Numbers and derivatives for this chunk
-            grad_chunk = grad_out[..., start:end, :]  # (..., chunk_size, nat)
+            grad_chunk = grad_outputs[..., start:end, :]  # (..., c_size, nat)
             num_chunk = numbers[..., start:end]  # (..., chunk_size)
 
             # Chunked indexing into reference.c6: (..., chunk_size, nat, 7, 7)
@@ -346,11 +364,14 @@ def backward(ctx: CTX, grad_out: Tensor) -> tuple[None, Tensor, None, None]:
             g_jb = einsum("...ijab,...ia->...ijb", rc6_chunk, weights_chunk)
             _gj = einsum("...ij,...ijb->...jb", grad_chunk, g_jb)
 
-            # Accumulate gradients for the current chunk
-            weights_bar[..., start:end, :] += _gi
-            weights_bar += _gj
+            # Accumulate gradients for current chunk with using out-of-place ops
+            # to allow vmap. Old version: weights_bar[..., start:end, :] += _gi
+            idx = torch.arange(start, end, device=weights.device)
+            gi_accum = torch.index_add(gi_accum, dim=-2, index=idx, source=_gi)
 
-        return None, weights_bar, None, None
+            gj_accum = gj_accum + _gj
+
+        return None, gi_accum + gj_accum, None, None
 
 
 class AtomicC6_V1(AtomicC6Base):
@@ -383,16 +404,17 @@ class AtomicC6_V2(AtomicC6Base):
     This is supposed to reduce memory usage.
     """
 
-    generate_vmap_rule = True
-    # https://pytorch.org/docs/master/notes/extending.func.html#automatically-generate-a-vmap-rule
-    # should work since we only use PyTorch operations
+    generate_vmap_rule = False
+    # Auto-generation should work since we only use PyTorch operations,
+    # however, it does not: PyTorch throws an internal error when indexing
+    # `reference.c6` with the `numbers` tensor.
 
     @staticmethod
     def forward(
         numbers: Tensor,
         weights: Tensor,
         reference: Reference,
-        chunk_size: None | int = None,
+        chunk_size: int | None = None,
     ) -> Tensor:
         if chunk_size is None:
             return _atomic_c6_full(numbers, weights, reference)
@@ -410,3 +432,49 @@ def setup_context(
         ctx.save_for_backward(numbers, weights)
         ctx.chunk_size = chunk_size
         ctx.reference = reference
+
+    @staticmethod
+    def vmap(
+        info: VmapInfo,
+        in_dims: tuple[int | None, ...],
+        numbers: Tensor,
+        weights: Tensor,
+        reference: Reference,
+        chunk_size: int | None,
+    ) -> tuple[Tensor, int]:
+        bd_n, bd_w, bd_ref, bd_cs = in_dims
+
+        # Only numbers and weights are batched
+        if bd_ref is not None or bd_cs is not None:  # pragma: no cover
+            raise ValueError(
+                "`Reference` and `chunk_size` must be static under vmap."
+            )
+
+        # Move batch dimensions to the front if necessary
+        if info.batch_size != numbers.shape[0]:
+            raise ValueError(
+                f"Batch size mismatch: expected {info.batch_size}, got "
+                f"{numbers.shape[0]} in `numbers`. The first dimension "
+                "should be the batch dimension."
+            )
+
+        if info.batch_size != weights.shape[0]:
+            raise ValueError(
+                f"Batch size mismatch: expected {info.batch_size}, got "
+                f"{weights.shape[0]} in `weights`. The first dimension "
+                "should be the batch dimension."
+            )
+
+        if bd_n not in (0, None):  # pragma: no cover
+            raise ValueError(
+                f"Batch dimension for `numbers` must be 0 (first dimension) "
+                f"or `None`, got {bd_n}."
+            )
+        if bd_w not in (0, None):  # pragma: no cover
+            raise ValueError(
+                f"Batch dimension for `weights` must be 0 (first dimension) "
+                f"or `None`, got {bd_w}."
+            )
+
+        out = AtomicC6_V2.forward(numbers, weights, reference, chunk_size)
+        return out, 0
diff --git a/src/tad_dftd3/model/weights.py b/src/tad_dftd3/model/weights.py
index c6b7b83..d493aa2 100644
--- a/src/tad_dftd3/model/weights.py
+++ b/src/tad_dftd3/model/weights.py
@@ -42,11 +42,15 @@
 """
 from __future__ import annotations
 
+from typing import Any
+
 import torch
 from tad_mctc import storch
+from tad_mctc.autograd import is_functorch_tensor
+from tad_mctc.typing import Tensor
 
 from ..reference import Reference
-from ..typing import Any, Tensor, WeightingFunction
+from ..typing import WeightingFunction
 
 __all__ = ["gaussian_weight", "weight_references"]
 
@@ -141,7 +145,10 @@ def weight_references(
 
     # back to real dtype
     gw_temp = storch.divide(weights, norm, eps=small).type(cn.dtype)
-    assert torch.isnan(gw_temp).sum() == 0
+
+    # If the tensor is not a grad tracking tensor, we can check for NaN's
+    if not is_functorch_tensor(gw_temp):
+        assert torch.isnan(gw_temp).sum() == 0
 
     # The following section handles cases with large CNs that lead to zeros in
     # after the exponential in the weighting function. If this happens all
diff --git a/src/tad_dftd3/reference.py b/src/tad_dftd3/reference.py
index ba277bf..80b556e 100644
--- a/src/tad_dftd3/reference.py
+++ b/src/tad_dftd3/reference.py
@@ -20,12 +20,11 @@
 C6 dispersion coefficients.
 """
 import os.path as op
-from typing import Optional
+from typing import Any, NoReturn, Optional
 
 import torch
 from tad_mctc._version import __tversion__
-
-from .typing import Any, NoReturn, Tensor, get_default_device, get_default_dtype
+from tad_mctc.typing import Tensor, get_default_device, get_default_dtype
 
 __all__ = ["Reference"]
 
diff --git a/src/tad_dftd3/typing/__init__.py b/src/tad_dftd3/typing/__init__.py
index 45c1d5b..51bbf70 100644
--- a/src/tad_dftd3/typing/__init__.py
+++ b/src/tad_dftd3/typing/__init__.py
@@ -18,6 +18,5 @@
 
 All type annotations for this project.
 """
-from .builtin import *
 from .d3 import *
 from .pytorch import *
diff --git a/src/tad_dftd3/typing/builtin.py b/src/tad_dftd3/typing/builtin.py
deleted file mode 100644
index aab741b..0000000
--- a/src/tad_dftd3/typing/builtin.py
+++ /dev/null
@@ -1,24 +0,0 @@
-# This file is part of tad-dftd3.
-# SPDX-Identifier: Apache-2.0
-#
-# Licensed under the Apache License, Version 2.0 (the "License");
-# you may not use this file except in compliance with the License.
-# You may obtain a copy of the License at
-#
-#     http://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing, software
-# distributed under the License is distributed on an "AS IS" BASIS,
-# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-# See the License for the specific language governing permissions and
-# limitations under the License.
-"""
-Type annotations: Built-ins
-===========================
-
-Built-in type annotations are imported from the *tad-mctc* library, which
-handles some version checking.
-"""
-from tad_mctc.typing import Any, Callable, NoReturn, Protocol, TypedDict
-
-__all__ = ["Any", "Callable", "NoReturn", "Protocol", "TypedDict"]
diff --git a/test/conftest.py b/test/conftest.py
index 6f2c6fa..4fd143f 100644
--- a/test/conftest.py
+++ b/test/conftest.py
@@ -96,7 +96,8 @@ def pytest_addoption(parser: pytest.Parser) -> None:
         default=6,
         type=int,
         help=(
-            "Number of digits of precision for floating point output " "(default = 4)."
+            "Number of digits of precision for floating point output "
+            "(default = 4)."
         ),
     )
 
@@ -176,4 +177,6 @@ def pytest_runtest_setup(item: pytest.Function) -> None:
 
     for _ in item.iter_markers(name="cuda"):
         if not torch.cuda.is_available():
-            pytest.skip("Torch not compiled with CUDA or no CUDA device available.")
+            pytest.skip(
+                "Torch not compiled with CUDA or no CUDA device available."
+            )
diff --git a/test/test_disp/test_dftd3.py b/test/test_disp/test_dftd3.py
index 778f9c8..3d0d69d 100644
--- a/test/test_disp/test_dftd3.py
+++ b/test/test_disp/test_dftd3.py
@@ -18,6 +18,7 @@
 import pytest
 import torch
 from tad_mctc.batch import pack
+from tad_mctc.data import radii
 
 from tad_dftd3 import damping, data, dftd3, model, reference
 from tad_dftd3.ncoord import exp_count
@@ -59,9 +60,11 @@ def test_single(dtype: torch.dtype, name: str) -> None:
     positions = sample["positions"].to(**dd)
     ref = (sample["disp2"] + sample["disp3"]).to(**dd)
 
-    rcov = data.COV_D3.to(**dd)[numbers]
-    rvdw = data.VDW_D3.to(**dd)[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
-    r4r2 = data.R4R2.to(**dd)[numbers]
+    rcov = radii.COV_D3(**dd)[numbers]
+    rvdw = radii.VDW_PAIRWISE(**dd)[
+        numbers.unsqueeze(-1), numbers.unsqueeze(-2)
+    ]
+    r4r2 = data.R4R2(**dd)[numbers]
     cutoff = torch.tensor(50, **dd)
 
     param = {
diff --git a/test/test_disp/test_disp.py b/test/test_disp/test_disp.py
index 5820b2c..4e67dc7 100644
--- a/test/test_disp/test_disp.py
+++ b/test/test_disp/test_disp.py
@@ -20,6 +20,7 @@
 import pytest
 import torch
 from tad_mctc.batch import pack
+from tad_mctc.data import radii
 
 from tad_dftd3 import damping, data, disp
 from tad_dftd3.typing import DD
@@ -40,7 +41,9 @@
 }
 
 # TPSS0-D3BJ parameters
-param_noatm = {k: torch.tensor(0.0) if k == "s9" else v for k, v in param.items()}
+param_noatm = {
+    k: torch.tensor(0.0) if k == "s9" else v for k, v in param.items()
+}
 
 
 def test_fail() -> None:
@@ -73,8 +76,10 @@ def test_disp2_single(dtype: torch.dtype, name: str) -> None:
     positions = sample["positions"].to(**dd)
     ref = sample["disp2"].to(**dd)
     c6 = sample["c6"].to(**dd)
-    rvdw = data.VDW_D3.to(**dd)[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
-    r4r2 = data.R4R2.to(**dd)[numbers]
+    rvdw = radii.VDW_PAIRWISE(**dd)[
+        numbers.unsqueeze(-1), numbers.unsqueeze(-2)
+    ]
+    r4r2 = data.R4R2(**dd)[numbers]
     cutoff = torch.tensor(50.0, **dd)
 
     par = {k: v.to(**dd) for k, v in param_noatm.items()}
@@ -147,7 +152,9 @@ def test_atm_single(dtype: torch.dtype, name: str) -> None:
     c6 = sample["c6"].to(**dd)
     ref = sample["disp3"].to(**dd)
 
-    rvdw = data.VDW_D3.to(**dd)[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
+    rvdw = radii.VDW_PAIRWISE(**dd)[
+        numbers.unsqueeze(-1), numbers.unsqueeze(-2)
+    ]
 
     par = {k: v.to(**dd) for k, v in param.items()}
 
@@ -200,7 +207,9 @@ def test_atm_batch(dtype: torch.dtype, name1: str, name2: str) -> None:
 
     par = {k: v.to(**dd) for k, v in param.items()}
 
-    rvdw = data.VDW_D3.to(**dd)[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
+    rvdw = radii.VDW_PAIRWISE(**dd)[
+        numbers.unsqueeze(-1), numbers.unsqueeze(-2)
+    ]
 
     energy = damping.dispersion_atm(
         numbers,
diff --git a/test/test_disp/test_special.py b/test/test_disp/test_special.py
index 7fc697e..31d4f69 100644
--- a/test/test_disp/test_special.py
+++ b/test/test_disp/test_special.py
@@ -19,6 +19,7 @@
 import pytest
 import torch
 from tad_mctc.batch import pack
+from tad_mctc.data import radii
 
 from tad_dftd3 import damping, data, dftd3, model, reference
 from tad_dftd3.ncoord import exp_count
@@ -38,9 +39,11 @@ def test_single(dtype: torch.dtype, name: str) -> None:
     positions = sample["positions"].to(**dd)
     ref = sample["disp2"].to(**dd)
 
-    rcov = data.COV_D3.to(**dd)[numbers]
-    rvdw = data.VDW_D3.to(**dd)[numbers.unsqueeze(-1), numbers.unsqueeze(-2)]
-    r4r2 = data.R4R2.to(**dd)[numbers]
+    rcov = radii.COV_D3(**dd)[numbers]
+    rvdw = radii.VDW_PAIRWISE(**dd)[
+        numbers.unsqueeze(-1), numbers.unsqueeze(-2)
+    ]
+    r4r2 = data.R4R2(**dd)[numbers]
     cutoff = torch.tensor(50, **dd)
 
     # GFN1-xTB parameters
diff --git a/test/test_grad/test_hessian.py b/test/test_grad/test_hessian.py
index abc0c90..829b8dc 100644
--- a/test/test_grad/test_hessian.py
+++ b/test/test_grad/test_hessian.py
@@ -19,7 +19,8 @@
 
 import pytest
 import torch
-from tad_mctc.autograd import hessian
+from tad_mctc._version import __tversion__
+from tad_mctc.autograd import hess_fn_rev, hessian
 from tad_mctc.batch import pack
 from tad_mctc.convert import reshape_fortran
 
@@ -88,11 +89,59 @@ def test_single(dtype: torch.dtype, name: str) -> None:
     positions.detach_()
 
 
-# TODO: Figure out batched Hessian computation
+@pytest.mark.skipif(__tversion__ < (2, 0, 0), reason="Requires PyTorch>=2.0.0")
+@pytest.mark.parametrize("dtype", [torch.double])
+@pytest.mark.parametrize("name", sample_list)
+def test_single_v2(dtype: torch.dtype, name: str) -> None:
+    dd: DD = {"device": DEVICE, "dtype": dtype}
+
+    sample = samples[name]
+    numbers = sample["numbers"].to(DEVICE)
+    positions = sample["positions"].to(**dd)
+
+    # GFN1-xTB parameters
+    param = {
+        "s6": torch.tensor(1.00000000, **dd),
+        "s8": torch.tensor(2.40000000, **dd),
+        "s9": torch.tensor(0.00000000, **dd),
+        "a1": torch.tensor(0.63000000, **dd),
+        "a2": torch.tensor(5.00000000, **dd),
+    }
+
+    ref = reshape_fortran(
+        sample["hessian"].to(**dd),
+        torch.Size(2 * (numbers.shape[-1], 3)),
+    )
+
+    # variable to be differentiated
+    positions.requires_grad_(True)
+
+    def _energy(numbers: torch.Tensor, positions: torch.Tensor) -> torch.Tensor:
+        """
+        Closure over non-tensor argument `param` for `dftd3` function.
+
+        Returns energy as scalar, which is required for Hessian computation
+        to obtain the correct shape of ``(..., nat, 3, nat, 3)``.
+        """
+        return dftd3(numbers, positions, param).sum(-1)
+
+    pos = positions.clone().requires_grad_(True)
+    hess = hess_fn_rev(_energy, argnums=1)(numbers, pos)
+    assert isinstance(hess, Tensor)
+
+    assert pytest.approx(ref.cpu(), abs=tol, rel=tol) == hess.detach().cpu()
+
+    positions.detach_()
+
+
+@pytest.mark.skipif(__tversion__ < (2, 0, 0), reason="Requires PyTorch>=2.0.0")
 @pytest.mark.parametrize("dtype", [torch.double])
 @pytest.mark.parametrize("name1", ["LiH"])
 @pytest.mark.parametrize("name2", sample_list)
-def skip_test_batch(dtype: torch.dtype, name1: str, name2: str) -> None:
+@pytest.mark.parametrize("chunk_size", [None, 2])
+def test_batch(
+    dtype: torch.dtype, name1: str, name2: str, chunk_size: int | None
+) -> None:
     dd: DD = {"device": DEVICE, "dtype": dtype}
 
     sample1, sample2 = samples[name1], samples[name2]
@@ -134,7 +183,20 @@ def skip_test_batch(dtype: torch.dtype, name1: str, name2: str) -> None:
     # variable to be differentiated
     positions.requires_grad_(True)
 
-    hess = hessian(dftd3, (numbers, positions, param), argnums=1)
+    def _energy(numbers: torch.Tensor, positions: torch.Tensor) -> torch.Tensor:
+        """
+        Closure over non-tensor argument `param` for `dftd3` function.
+
+        Returns energy as scalar, which is required for Hessian computation
+        to obtain the correct shape of ``(..., nat, 3, nat, 3)``.
+        """
+        return dftd3(numbers, positions, param, chunk_size=chunk_size).sum(-1)
+
+    hess_fn = hess_fn_rev(_energy, argnums=1)
+    hess_fn_batch = torch.func.vmap(hess_fn, in_dims=(0, 0))
+
+    hess = hess_fn_batch(numbers, positions)
+    assert isinstance(hess, Tensor)
     assert pytest.approx(ref.cpu(), abs=tol, rel=tol) == hess.detach().cpu()
 
     positions.detach_()
diff --git a/test/test_grad/test_param.py b/test/test_grad/test_param.py
index dfc166d..a9d6715 100644
--- a/test/test_grad/test_param.py
+++ b/test/test_grad/test_param.py
@@ -22,9 +22,9 @@
 from tad_mctc.autograd import dgradcheck, dgradgradcheck
 from tad_mctc.batch import pack
 from tad_mctc.data.molecules import mols as samples
+from tad_mctc.typing import DD, Callable, Tensor
 
 from tad_dftd3 import dftd3
-from tad_dftd3.typing import DD, Callable, Tensor
 
 from ..conftest import DEVICE, FAST_MODE
 
@@ -136,7 +136,9 @@ def test_gradcheck_batch(dtype: torch.dtype, name1: str, name2: str) -> None:
 @pytest.mark.parametrize("dtype", [torch.double])
 @pytest.mark.parametrize("name1", ["LiH"])
 @pytest.mark.parametrize("name2", sample_list)
-def test_gradgradcheck_batch(dtype: torch.dtype, name1: str, name2: str) -> None:
+def test_gradgradcheck_batch(
+    dtype: torch.dtype, name1: str, name2: str
+) -> None:
     """
     Check a single analytical gradient of parameters against numerical
     gradient from `torch.autograd.gradgradcheck`.
diff --git a/test/test_grad/test_pos.py b/test/test_grad/test_pos.py
index e1693b4..1be8ccc 100644
--- a/test/test_grad/test_pos.py
+++ b/test/test_grad/test_pos.py
@@ -21,9 +21,9 @@
 import torch
 from tad_mctc.autograd import dgradcheck, dgradgradcheck, jacrev
 from tad_mctc.batch import pack
+from tad_mctc.typing import DD, Callable, Tensor
 
 from tad_dftd3 import dftd3
-from tad_dftd3.typing import DD, Callable, Tensor
 
 from ..conftest import DEVICE, FAST_MODE
 from .samples import samples
@@ -137,7 +137,9 @@ def test_gradcheck_batch(dtype: torch.dtype, name1: str, name2: str) -> None:
 @pytest.mark.parametrize("dtype", [torch.double])
 @pytest.mark.parametrize("name1", ["LiH"])
 @pytest.mark.parametrize("name2", sample_list)
-def test_gradgradcheck_batch(dtype: torch.dtype, name1: str, name2: str) -> None:
+def test_gradgradcheck_batch(
+    dtype: torch.dtype, name1: str, name2: str
+) -> None:
     """
     Check a single analytical gradient of parameters against numerical
     gradient from `torch.autograd.gradgradcheck`.
diff --git a/test/test_model/samples.py b/test/test_model/samples.py
index c4bdfff..c8dd9cf 100644
--- a/test/test_model/samples.py
+++ b/test/test_model/samples.py
@@ -19,8 +19,7 @@
 
 import torch
 from tad_mctc.data.molecules import merge_nested_dicts, mols
-
-from tad_dftd3.typing import Molecule, Tensor, TypedDict
+from tad_mctc.typing import Molecule, Tensor, TypedDict
 
 
 class Refs(TypedDict):
diff --git a/test/test_model/test_c6.py b/test/test_model/test_c6.py
index f27092d..a66db6b 100644
--- a/test/test_model/test_c6.py
+++ b/test/test_model/test_c6.py
@@ -17,13 +17,16 @@
 """
 from __future__ import annotations
 
+from typing import Protocol
+
 import pytest
 import torch
+from tad_mctc._version import __tversion__
 from tad_mctc.autograd import dgradcheck, dgradgradcheck
 from tad_mctc.batch import pack
+from tad_mctc.typing import DD, Callable, Tensor
 
 from tad_dftd3 import model, ncoord, reference
-from tad_dftd3.typing import DD, Callable, Protocol, Tensor
 
 from ..conftest import DEVICE, FAST_MODE
 from .samples import samples
@@ -109,6 +112,53 @@ def test_chunked(dtype: torch.dtype, size: int, chunk_size: int) -> None:
     assert pytest.approx(c6.cpu(), abs=tol, rel=tol) == c6_chunked.cpu()
 
 
+@pytest.mark.skipif(__tversion__ < (2, 1, 0), reason="Requires PyTorch>=2.1.0")
+def test_fail() -> None:
+    dd: DD = {"device": DEVICE, "dtype": torch.float64}
+    size = 10
+    nbatch = 2
+
+    ref = reference.Reference(**dd)
+    numbers = torch.randint(1, 86, (nbatch, size), device=DEVICE)
+    positions = torch.rand((nbatch, size, 3), **dd) * 10
+
+    cn = ncoord.cn_d3(numbers, positions)
+    weights = model.weight_references(numbers, cn, ref)
+
+    def _c6(nums: Tensor, ws: Tensor) -> Tensor:
+        return model.atomic_c6(nums, ws, ref)
+
+    jac = torch.func.jacrev(_c6, argnums=1)
+
+    # Correct batch dimensions
+    with pytest.raises(ValueError) as excinfo:
+        vjac = torch.func.vmap(jac, in_dims=(0, None))
+        _ = vjac(numbers, weights.moveaxis(1, 0))
+
+    assert "Batch size mismatch" in str(excinfo.value)
+    assert "weights" in str(excinfo.value)
+
+    # Correct batch dimensions
+    with pytest.raises(ValueError) as excinfo:
+        vjac = torch.func.vmap(jac, in_dims=(None, 0))
+        _ = vjac(numbers.moveaxis(1, 0), weights)
+
+    assert "Batch size mismatch" in str(excinfo.value)
+    assert "numbers" in str(excinfo.value)
+
+    # Internal vmap errors
+
+    # Batch dimensions is always 0 for numbers and weights
+    with pytest.raises(ValueError) as excinfo:
+        vjac = torch.func.vmap(jac, in_dims=(1, 0))
+        _ = vjac(numbers, weights)
+
+    # Batch dimensions is always 0 for numbers and weights
+    with pytest.raises(ValueError):
+        vjac = torch.func.vmap(jac, in_dims=(0, 1))
+        _ = vjac(numbers, weights)
+
+
 ###############################################################################
 
 
diff --git a/test/test_model/test_load.py b/test/test_model/test_load.py
index 14637a2..c7a7dc4 100644
--- a/test/test_model/test_load.py
+++ b/test/test_model/test_load.py
@@ -17,7 +17,7 @@
 """
 import torch
 
-from tad_dftd3 import data, defaults, reference
+from tad_dftd3 import defaults, reference
 
 
 def test_ref() -> None:
@@ -25,8 +25,3 @@ def test_ref() -> None:
     assert c6.shape == torch.Size(
         (defaults.MAX_ELEMENT, defaults.MAX_ELEMENT, 7, 7),
     )
-
-
-def test_vdw() -> None:
-    vdw = data.radii._load_vdw_rad_d3(dtype=torch.double)
-    assert vdw.shape == torch.Size((defaults.MAX_ELEMENT, defaults.MAX_ELEMENT))
diff --git a/test/test_model/test_reference.py b/test/test_model/test_reference.py
index b92c7c6..f498461 100644
--- a/test/test_model/test_reference.py
+++ b/test/test_model/test_reference.py
@@ -15,16 +15,15 @@
 """
 Test the reference.
 """
-from typing import Optional, Union
+from typing import Any, Optional, TypedDict, Union
 from unittest.mock import patch
 
 import pytest
 import torch
 from tad_mctc.convert import str_to_device
-from tad_mctc.typing import MockTensor
+from tad_mctc.typing import DD, MockTensor, Tensor
 
 from tad_dftd3 import reference
-from tad_dftd3.typing import DD, Any, Tensor, TypedDict
 
 from ..conftest import DEVICE
 
diff --git a/test/test_model/test_weights.py b/test/test_model/test_weights.py
index 38fe4ba..72bfa47 100644
--- a/test/test_model/test_weights.py
+++ b/test/test_model/test_weights.py
@@ -18,9 +18,9 @@
 import pytest
 import torch
 from tad_mctc.batch import pack
+from tad_mctc.typing import DD
 
 from tad_dftd3 import model, reference
-from tad_dftd3.typing import DD
 
 from ..conftest import DEVICE
 from .samples import samples

From 1640456ddd1dbc99b8903c7c51367b8bdb46c10f Mon Sep 17 00:00:00 2001
From: Marvin Friede <51965259+marvinfriede@users.noreply.github.com>
Date: Sun, 3 Aug 2025 19:23:10 +0200
Subject: [PATCH 2/2] Bump version to 0.5.0 (#90)

---
 src/tad_dftd3/__version__.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/tad_dftd3/__version__.py b/src/tad_dftd3/__version__.py
index a1c88f7..b6f2a57 100644
--- a/src/tad_dftd3/__version__.py
+++ b/src/tad_dftd3/__version__.py
@@ -15,4 +15,4 @@
 """
 Version module for *tad-dftd3*.
 """
-__version__ = "0.4.1"
+__version__ = "0.5.0"