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+# Torch Autodiff for DFT-D4
+
+<table>
+  <tr>
+    <td>Compatibility:</td>
+    <td>
+      <img src="https://img.shields.io/badge/Python-3.8%20|%203.9%20|%203.10%20|%203.11-blue.svg" alt="Python Versions"/>
+      <img src="https://img.shields.io/badge/PyTorch-%3E=1.11.0-blue.svg" alt="PyTorch Versions"/>
+    </td>
+  </tr>
+  <tr>
+    <td>Availability:</td>
+    <td>
+      <a href="https://github.com/dftd4/tad-dftd4/releases/latest">
+        <img src="https://img.shields.io/github/v/release/dftd4/tad-dftd4?color=orange" alt="Release"/>
+      </a>
+      <a href="https://pypi.org/project/tad-dftd4/">
+        <img src="https://img.shields.io/pypi/v/tad-dftd4?color=orange" alt="PyPI"/>
+      </a>
+      <a href="https://www.gnu.org/licenses/lgpl-3.0">
+        <img src="https://img.shields.io/badge/License-LGPL_v3-orange.svg" alt="LGPL-3.0"/>
+      </a>
+    </td>
+  </tr>
+  <tr>
+    <td>Status:</td>
+    <td>
+      <a href="https://github.com/dftd4/tad-dftd4/actions/workflows/python.yaml">
+        <img src="https://github.com/dftd4/tad-dftd4/actions/workflows/python.yaml/badge.svg" alt="Test Status"/>
+      </a>
+      <a href="https://github.com/dftd4/tad-dftd4/actions/workflows/release.yaml">
+        <img src="https://github.com/dftd4/tad-dftd4/actions/workflows/release.yaml/badge.svg" alt="Build Status"/>
+      </a>
+      <a href="https://tad-dftd4.readthedocs.io">
+        <img src="https://readthedocs.org/projects/tad-dftd4/badge/?version=latest" alt="Documentation Status"/>
+      </a>
+      <a href="https://results.pre-commit.ci/latest/github/dftd4/tad-dftd4/main">
+        <img src="https://results.pre-commit.ci/badge/github/dftd4/tad-dftd4/main.svg" alt="pre-commit.ci Status"/>
+      </a>
+      <a href="https://codecov.io/gh/dftd4/tad-dftd4">
+        <img src="https://codecov.io/gh/dftd4/tad-dftd4/branch/main/graph/badge.svg?token=OGJJnZ6t4G" alt="Coverage"/>
+      </a>
+    </td>
+  </tr>
+</table>
+
+<br>
+
+Implementation of the DFT-D4 dispersion model in PyTorch. This module allows to process a single structure or a batch of structures for the calculation of atom-resolved dispersion energies.
+
+For details on the D4 dispersion model, see:
+
+- E. Caldeweyher, C. Bannwarth and S. Grimme, *J. Chem. Phys.*, 2017, 147, 034112. [DOI: 10.1063/1.4993215](https://dx.doi.org/10.1063/1.4993215)
+- E. Caldeweyher, S. Ehlert, A. Hansen, H. Neugebauer, S. Spicher, C. Bannwarth and S. Grimme, *J. Chem. Phys.*, 2019, 150, 154122. [DOI: 10.1063/1.5090222](https://dx.doi.org/10.1063/1.5090222)
+- E. Caldeweyher, J.-M. Mewes, S. Ehlert and S. Grimme, *Phys. Chem. Chem. Phys.*, 2020, 22, 8499-8512. [DOI: 10.1039/D0CP00502A](https://doi.org/10.1039/D0CP00502A)
+
+For alternative implementations, also check out:
+
+- [dftd4](https://dftd4.readthedocs.io): Implementation of the DFT-D4 dispersion model in Fortran with Python bindings.
+- [cpp-d4](https://github.com/dftd4/cpp-d4): Implementation of the DFT-D4 dispersion model in C++.
+
+## Installation
+
+### pip
+
+*tad-dftd4* can easily be installed with ``pip``.
+
+```bash
+pip install tad-dftd4
+```
+
+### From source
+
+This project is hosted on GitHub at [dftd4/tad-dftd4](https://github.com/dftd4/tad-dftd4).
+Obtain the source by cloning the repository with
+
+```bash
+git clone https://github.com/dftd4/tad-dftd4
+cd tad-dftd4
+```
+
+We recommend using a [conda](https://conda.io/) environment to install the package.
+You can setup the environment manager using a [mambaforge](https://github.com/conda-forge/miniforge>) installer.
+Install the required dependencies from the conda-forge channel.
+
+```bash
+mamba env create -n torch -f environment.yaml
+mamba activate torch
+```
+
+Install this project with ``pip`` in the environment
+
+```bash
+pip install .
+```
+
+The following dependencies are required
+
+- [numpy](https://numpy.org/)
+- [tad_mctc](https://github.com/tad-mctc/tad_mctc/)
+- [tad_multicharge](https://github.com/tad-mctc/tad_multicharge/)
+- [torch](https://pytorch.org/)
+- [pytest](https://docs.pytest.org/) (tests only)
+
+## Development
+
+For development, additionally install the following tools in your environment.
+
+```bash
+mamba install black covdefaults coverage mypy pre-commit pylint tox
+```
+
+With pip, add the option ``-e`` for installing in development mode, and add ``[dev]`` for the development dependencies
+
+```bash
+pip install -e .[dev]
+```
+
+The pre-commit hooks are initialized by running the following command in the root of the repository.
+
+```bash
+pre-commit install
+```
+
+For testing all Python environments, simply run `tox`.
+
+```bash
+tox
+```
+
+Note that this randomizes the order of tests but skips "large" tests. To modify this behavior, `tox` has to skip the optional *posargs*.
+
+```bash
+tox -- test
+```
+
+## Examples
+
+The following example shows how to calculate the DFT-D4 dispersion energy for a single structure.
+
+```python
+import torch
+import tad_dftd4 as d4
+import tad_mctc as mctc
+
+numbers = mctc.convert.symbol_to_number(symbols="C C C C N C S H H H H H".split())
+
+# coordinates in Bohr
+positions = torch.tensor(
+    [
+        [-2.56745685564671, -0.02509985979910, 0.00000000000000],
+        [-1.39177582455797, +2.27696188880014, 0.00000000000000],
+        [+1.27784995624894, +2.45107479759386, 0.00000000000000],
+        [+2.62801937615793, +0.25927727028120, 0.00000000000000],
+        [+1.41097033661123, -1.99890996077412, 0.00000000000000],
+        [-1.17186102298849, -2.34220576284180, 0.00000000000000],
+        [-2.39505990368378, -5.22635838332362, 0.00000000000000],
+        [+2.41961980455457, -3.62158019253045, 0.00000000000000],
+        [-2.51744374846065, +3.98181713686746, 0.00000000000000],
+        [+2.24269048384775, +4.24389473203647, 0.00000000000000],
+        [+4.66488984573956, +0.17907568006409, 0.00000000000000],
+        [-4.60044244782237, -0.17794734637413, 0.00000000000000],
+    ]
+)
+
+# total charge of the system
+charge = torch.tensor(0.0)
+
+# TPSSh-D4-ATM parameters
+param = {
+    "s6": positions.new_tensor(1.0),
+    "s8": positions.new_tensor(1.85897750),
+    "s9": positions.new_tensor(1.0),
+    "a1": positions.new_tensor(0.44286966),
+    "a2": positions.new_tensor(4.60230534),
+}
+
+energy = d4.dftd4(numbers, positions, charge, param)
+torch.set_printoptions(precision=10)
+print(energy)
+# tensor([-0.0020841344, -0.0018971195, -0.0018107513, -0.0018305695,
+#         -0.0021737693, -0.0019484236, -0.0022788253, -0.0004080658,
+#         -0.0004261866, -0.0004199839, -0.0004280768, -0.0005108935])
+```
+
+The next example shows the calculation of dispersion energies for a batch of structures.
+
+```python
+
+import torch
+import tad_dftd4 as d4
+import tad_mctc as mctc
+
+# S22 system 4: formamide dimer
+numbers = mctc.batch.pack((
+    mctc.convert.symbol_to_number("C C N N H H H H H H O O".split()),
+    mctc.convert.symbol_to_number("C O N H H H".split()),
+))
+
+# coordinates in Bohr
+positions = mctc.batch.pack((
+    torch.tensor([
+        [-3.81469488143921, +0.09993441402912, 0.00000000000000],
+        [+3.81469488143921, -0.09993441402912, 0.00000000000000],
+        [-2.66030049324036, -2.15898251533508, 0.00000000000000],
+        [+2.66030049324036, +2.15898251533508, 0.00000000000000],
+        [-0.73178529739380, -2.28237795829773, 0.00000000000000],
+        [-5.89039325714111, -0.02589114569128, 0.00000000000000],
+        [-3.71254944801331, -3.73605775833130, 0.00000000000000],
+        [+3.71254944801331, +3.73605775833130, 0.00000000000000],
+        [+0.73178529739380, +2.28237795829773, 0.00000000000000],
+        [+5.89039325714111, +0.02589114569128, 0.00000000000000],
+        [-2.74426102638245, +2.16115570068359, 0.00000000000000],
+        [+2.74426102638245, -2.16115570068359, 0.00000000000000],
+    ]),
+    torch.tensor([
+        [-0.55569743203406, +1.09030425468557, 0.00000000000000],
+        [+0.51473634678469, +3.15152550263611, 0.00000000000000],
+        [+0.59869690244446, -1.16861263789477, 0.00000000000000],
+        [-0.45355203669134, -2.74568780438064, 0.00000000000000],
+        [+2.52721209544999, -1.29200800956867, 0.00000000000000],
+        [-2.63139587595376, +0.96447869452240, 0.00000000000000],
+    ]),
+))
+
+# total charge of both system
+charge = torch.tensor([0.0, 0.0])
+
+# TPSSh-D4-ATM parameters
+param = {
+    "s6": positions.new_tensor(1.0),
+    "s8": positions.new_tensor(1.85897750),
+    "s9": positions.new_tensor(1.0),
+    "a1": positions.new_tensor(0.44286966),
+    "a2": positions.new_tensor(4.60230534),
+}
+
+# calculate dispersion energy in Hartree
+energy = torch.sum(d4.dftd4(numbers, positions, charge, param), -1)
+torch.set_printoptions(precision=10)
+print(energy)
+# tensor([-0.0088341432, -0.0027013607])
+print(energy[0] - 2*energy[1])
+# tensor(-0.0034314217)
+```
+
+## Contributing
+
+This is a volunteer open source projects and contributions are always welcome.
+Please, take a moment to read the [contributing guidelines](CONTRIBUTING.md).
+
+## License
+
+This project is free software: you can redistribute it and/or modify it under the terms of the Lesser GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
+
+This project is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the Lesser GNU General Public License for more details.
+
+Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in this project by you, as defined in the Lesser GNU General Public license, shall be licensed as above, without any additional terms or conditions.